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https://en.wikipedia.org/wiki/Suspension%20%28topology%29
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In topology, a branch of mathematics, the suspension of a topological space X is intuitively obtained by stretching X into a cylinder and then collapsing both end faces to points. One views X as "suspended" between these end points. The suspension of X is denoted by SX or susp(X).
There is a variation of the suspension for pointed space, which is called the reduced suspension and denoted by ΣX. The "usual" suspension SX is sometimes called the unreduced suspension, unbased suspension, or free suspension of X, to distinguish it from ΣX.
Free suspension
The (free) suspension of a topological space can be defined in several ways.
1. is the quotient space . In other words, it can be constructed as follows:
Construct the cylinder .
Consider the entire set as a single point ("glue" all its points together).
Consider the entire set as a single point ("glue" all its points together).
2. Another way to write this is:
Where are two points, and for each i in {0,1}, is the projection to the point (a function that maps everything to ). That means, the suspension is the result of constructing the cylinder , and then attaching it by its faces, and , to the points along the projections .
3. One can view as two cones on X, glued together at their base.
4. can also be defined as the join where is a discrete space with two points.
Properties
In rough terms, S increases the dimension of a space by one: for example, it takes an n-sphere to an (n + 1)-sphere for n ≥
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https://en.wikipedia.org/wiki/Full%20scale
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In electronics and signal processing, full scale represents the maximum amplitude a system can represent.
In digital systems, a signal is said to be at digital full scale when its magnitude has reached the maximum representable value. Once a signal has reached digital full scale, all headroom has been utilized, and any further increase in amplitude will result in an error known as clipping. The amplitude of a digital signal can be represented in percent; full scale; or decibels, full scale (dBFS).
In analog systems, full scale may be defined by the maximum voltage available, or the maximum deflection (full scale deflection or FSD) or indication of an analog instrument such as a moving coil meter or galvanometer.
Binary representation
Since binary integer representation range is asymmetrical, full scale is defined using the maximum positive value that can be represented. For example, 16-bit PCM audio is centered on the value 0, and can contain values from −32,768 to +32,767. A signal is at full-scale if it reaches from −32,767 to +32,767. (This means that −32,768, the lowest possible value, slightly exceeds full-scale.)
Signal processing in digital audio workstations often uses floating-point arithmetic, which can include values past full-scale, to avoid clipping in intermediate processing stages. In a floating-point representation, a full-scale signal is typically defined to reach from −1.0 to +1.0.
Processing
The signal passes through an anti-aliasing, resampling, o
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https://en.wikipedia.org/wiki/Biological%20Physics
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Biological Physics: Energy, Information, Life: With new art by David Goodsell is a book by Philip Nelson, illustrated by David Goodsell. The fifth printing was published by W. H. Freeman in late 2013. It is a work on biology with an emphasis on the application of physical principles.
References
.
.
.
Science books
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https://en.wikipedia.org/wiki/Raurimu%20Spiral
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The Raurimu Spiral is a single-track railway spiral, starting with a horseshoe curve, overcoming a height difference, in the central North Island of New Zealand, on the North Island Main Trunk railway (NIMT) between Wellington and Auckland. It is a notable feat of civil engineering, having been called an "engineering masterpiece." The Institute of Professional Engineers of New Zealand has designated the spiral as a significant engineering heritage site.
Background
During the construction of the central section of the NIMT, a major obstacle arose: how to cross the steep slopes between the North Island Volcanic Plateau to the east and the valleys and gorges of the Whanganui River to the west?
South of Taumarunui, the terrain is steep but not unmanageable, with the exception of the stretch between Raurimu and National Park, where the land rises too steeply for a direct rail route. A direct line between these two points would rise in a distance of some , a gradient of 1 in 24. The area was thoroughly surveyed during the 1880s in an attempt to find a route with a lesser grade, but the only viable possibility seemed to require a detour and nine massive viaducts. Even then, the gradient would have been over 1 in 50.
Construction
The problem was solved in 1898 by a surveyor in the employ of Robert Holmes, Public Works Department engineer. He proposed a line that looped back upon itself and then spiralled around with the aid of tunnels and bridges, rising at a gradient of 1 i
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https://en.wikipedia.org/wiki/THM
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THM, Thm, thm or ThM may refer to:
Turbo-Hydramatic, GM vehicle transmission
Ton of heavy metal in a nuclear power plant
Ton of hot metal in the steel industry
Trihalomethanes in chemistry
Therm, a unit of heat energy
Technische Hochschule Mittelhessen—University of Applied Sciences
Master of Theology postnominal, ThM
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https://en.wikipedia.org/wiki/Inelastic%20scattering
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In chemistry, nuclear physics, and particle physics, inelastic scattering is a process in which the kinetic energy of a particle or a system of particles changes after a collision. Formally, the kinetic energy of the incident particle is not conserved (in contrast to elastic scattering). In an inelastic scattering process, some of the energy of the incident particle is lost or increased. Although inelastic scattering is historically related to the concept of inelastic collision in dynamics, the two concepts are quite distinct; inelastic collision in dynamics refers to processes in which the total macroscopic kinetic energy is not conserved. In general, scattering due to inelastic collisions will be inelastic, but, since elastic collisions often transfer kinetic energy between particles, scattering due to elastic collisions can also be inelastic, as in Compton scattering meaning the two particles in the collision transfer energy causing a loss of energy in one particle.
Electrons
When an electron is the incident particle, the probability of inelastic scattering, depending on the energy of the incident electron, is usually smaller than that of elastic scattering. Thus in the case of gas electron diffraction (GED), reflection high-energy electron diffraction (RHEED), and transmission electron diffraction, because the energy of the incident electron is high, the contribution of inelastic electron scattering can be ignored. Deep inelastic scattering of electrons from protons pro
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https://en.wikipedia.org/wiki/Nemmers%20Prize%20in%20Mathematics
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The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Erwin Plein Nemmers Prize in Economics, as part of a $14 million donation from the Nemmers brothers. They envisioned creating an award that would be as prestigious as the Nobel Prize. To this end, the majority of the income earned from the endowment is returned to the principal to increase the size of the award.
As of 2023, the award carries a $300,000 stipend and the scholar spends several weeks in residence at Northwestern University.
Recipients
Following recipients received this award:
1994 Yuri I. Manin
1996 Joseph B. Keller
1998 John H. Conway
2000 Edward Witten
2002 Yakov G. Sinai
2004 Mikhail Gromov
2006 Robert Langlands
2008 Simon Donaldson
2010 Terence Tao
2012 Ingrid Daubechies
2014 Michael J. Hopkins
2016 János Kollár
2018 Assaf Naor
2020 Nalini Anantharaman
2022 Bhargav Bhatt
See also
List of mathematics awards
References
External links
Citations page
Nemmers Prize 2012
Mathematics awards
Northwestern University
1994 establishments in Illinois
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https://en.wikipedia.org/wiki/Leroy%20P.%20Steele%20Prize
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The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
The prizes have been given since 1970, from a bequest of Leroy P. Steele, and were set up in honor of George David Birkhoff, William Fogg Osgood and William Caspar Graustein. The way the prizes are awarded was changed in 1976 and 1993, but the initial aim of honoring expository writing as well as research has been retained. The prizes of $5,000 are not given on a strict national basis, but relate to mathematical activity in the USA, and writing in English (originally, or in translation).
Steele Prize for Lifetime Achievement
2023 Nicholas M. Katz
2022 Richard P. Stanley
2021 Spencer Bloch
2020 Karen Uhlenbeck
2019 Jeff Cheeger
2018 Jean Bourgain
2017 James G. Arthur
2016 Barry Simon
2015 Victor Kac
2014 Phillip A. Griffiths
2013 Yakov G. Sinai
2012 Ivo M. Babuška
2011 John W. Milnor
2010 William Fulton
2009 Luis Caffarelli
2008 George Lusztig
2007 Henry P. McKean
2006 Frederick W. Gehring, Dennis P. Sullivan
2005 Israel M. Gelfand
2004 Cathleen Synge Morawetz
2003 Ronald Graham, Victor Guillemin
2002 Michael Artin, Elias Stein
2001 Harry Kesten
2000 Isadore M. Singer
1999 Richard V. Kadison
1998 Nathan Jacobson
1997 Ralph S. Phillips
1996 Goro Shimura
1995 John T. Tate
1994 Louis Nirenberg
1993 Eugene B. Dynkin
Steele Prize for Mathematical Exposit
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https://en.wikipedia.org/wiki/Douglas%20Hartree
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Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the construction of a differential analyser using Meccano.
Early life and education
Douglas Hartree was born in Cambridge, England. His father, William, was a lecturer in engineering at the University of Cambridge and his mother, Eva Rayner, was president of the National Council of Women of Great Britain and first woman to be mayor of the city of Cambridge. One of his great-grandfathers was Samuel Smiles; another was the marine engineer William Hartree, partner of John Penn. Douglas Hartree was the oldest of three sons that survived infancy. A brother and sister died in infancy when he was still a child, but his two brothers would later also die. Hartree's 7-year-old brother John Edwin died when Hartree was 17, and Hartree's 22-year-old brother Colin William died from meningitis in February 1920 when Hartree was 23. His maternal cousin was the geologist Dorothy Helen Rayner.
Hartree attended St John's College, Cambridge but the first World War interrupted his studies. He (and his father and brother) joined a group working on anti-aircraft ballistics under A. V. Hill, where he gained considerable skill and an abiding interest in practical calculation and numerical methods for differential equations, executing most of his own work with pencil and paper
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https://en.wikipedia.org/wiki/Graph%20rewriting
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In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It has numerous applications, ranging from software engineering (software construction and also software verification) to layout algorithms and picture generation.
Graph transformations can be used as a computation abstraction. The basic idea is that if the state of a computation can be represented as a graph, further steps in that computation can then be represented as transformation rules on that graph. Such rules consist of an original graph, which is to be matched to a subgraph in the complete state, and a replacing graph, which will replace the matched subgraph.
Formally, a graph rewriting system usually consists of a set of graph rewrite rules of the form , with being called pattern graph (or left-hand side) and being called replacement graph (or right-hand side of the rule). A graph rewrite rule is applied to the host graph by searching for an occurrence of the pattern graph (pattern matching, thus solving the subgraph isomorphism problem) and by replacing the found occurrence by an instance of the replacement graph. Rewrite rules can be further regulated in the case of labeled graphs, such as in string-regulated graph grammars.
Sometimes graph grammar is used as a synonym for graph rewriting system, especially in the context of formal languages; the different wording is used to emphasize the goal of constructions,
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https://en.wikipedia.org/wiki/Orbital%20hybridisation
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In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory. For example, in a carbon atom which forms four single bonds the valence-shell s orbital combines with three valence-shell p orbitals to form four equivalent sp3 mixtures in a tetrahedral arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.
History and uses
Chemist Linus Pauling first developed the hybridisation theory in 1931 to explain the structure of simple molecules such as methane (CH4) using atomic orbitals. Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals, so that "it might be inferred" that a carbon atom would form three bonds at right angles (using p orbitals) and a fourth weaker bond using the s orbital in some arbitrary direction. In reality, methane has four C-H bonds of equivalent strength. The angle between any two bonds is the tetrahedral bond angle of 109°28' (around 109.5°). Pauling supposed that in the presence of four hydrogen atoms, the s and p orbitals form four equivalent combinations which he called
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https://en.wikipedia.org/wiki/Hartle%E2%80%93Hawking%20state
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The Hartle–Hawking state is a proposal in theoretical physics concerning the state of the universe prior to the Planck epoch. It is named after James Hartle and Stephen Hawking.
According to the Hartle–Hawking proposal, the universe has no origin as we would understand it: before the Big Bang, which happened about 13.8 billion years ago, the universe was a singularity in both space and time. Hartle and Hawking suggest that if we could travel backwards in time towards the beginning of the universe, we would note that quite near what might have been the beginning, time gives way to space so that there is only space and no time.
Technical explanation
More precisely, the Hartle-Hawking state is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the universe.
It is a functional of the metric tensor defined at a (D − 1)-dimensional compact surface, the universe, where D is the spacetime dimension. The precise form of the Hartle–Hawking state is the path integral over all D-dimensional geometries that have the required induced metric on their boundary. According to the theory, time, as it is currently observed, diverged from a three-state dimension after the universe was in the age of the Planck time.
Such a wave function of the universe can be shown to satisfy, approximately, the Wheeler–DeWitt equation.
See also
Imaginary time
Multiple histories
Signature change
Notes
References
Physical cosmology
Stephe
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https://en.wikipedia.org/wiki/Induced%20metric
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In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold that is induced from the metric tensor on a manifold into which the submanifold is embedded, through the pullback. It may be determined using the following formula (using the Einstein summation convention), which is the component form of the pullback operation:
Here , describe the indices of coordinates of the submanifold while the functions encode the embedding into the higher-dimensional manifold whose tangent indices are denoted , .
Example – Curve in 3D
Let
be a map from the domain of the curve with parameter into the Euclidean manifold . Here are constants.
Then there is a metric given on as
.
and we compute
Therefore
See also
First fundamental form
References
Differential geometry
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https://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt%20equation
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The Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity.
In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called 'problem of time'. More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergman–Komar "group" (which is the diffeomorphism group on-shell).
Motivation and background
In canonical gravity, spacetime is foliated into spacelike submanifolds. The three-metric (i.e., metric on the hypersurface) is and given by
In that equation the Latin indices run over the values 1, 2, 3 and the Greek indices run over the values 1, 2, 3, 4. The three-metric is the field, and we denote its conjugate momenta as . The Hamiltonian is a constraint (characteristic of most relativistic systems)
where and is the Wheeler–DeWitt metric. In index-free notation, the Wheeler–DeWitt metric on the space of positive definite quadratic forms g in three dimensions is
Quantization "puts hats" on the momenta and field variables; that is, the functions of numbers in the classical case become operators that modify the state function in the quantum case.
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https://en.wikipedia.org/wiki/RQC
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RQC may refer to:
Relativistic quantum chemistry, a subfield of quantum chemistry.
Remote Access Quarantine Client, a program, rqc.exe, in the Windows Server 2003 operating system.
Review Quality Collector, a service aiming at improving the quality of scientific peer review.
Russian Quantum Center, a non-commercial scientific organization in Russia doing research in quantum mechanics and quantum computing.
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https://en.wikipedia.org/wiki/Relativistic%20quantum%20chemistry
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Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of gold: due to relativistic effects, it is not silvery like most other metals.
The term relativistic effects was developed in light of the history of quantum mechanics. Initially, quantum mechanics was developed without considering the theory of relativity. Relativistic effects are those discrepancies between values calculated by models that consider relativity and those that do not. Relativistic effects are important for heavier elements with high atomic numbers, such as lanthanides and actinides.
Relativistic effects in chemistry can be considered to be perturbations, or small corrections, to the non-relativistic theory of chemistry, which is developed from the solutions of the Schrödinger equation. These corrections affect the electrons differently depending on the electron speed compared with the speed of light. Relativistic effects are more prominent in heavy elements because only in these elements do electrons attain sufficient speeds for the elements to have properties that differ from what non-relativistic chemistry predicts.
History
Beginning in 1935, Bertha Swirles described a relativistic treatment of a many-electron system, despite Paul Dirac's 1929 assertion that the only imperfections remaining in quantum mechanics "
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https://en.wikipedia.org/wiki/Panorama%20Tools
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Panorama Tools (also known as PanoTools) are a suite of programs and libraries for image stitching, i.e., re-projecting and blending multiple source images into immersive panoramas of many types. It was originally written by German physics and mathematics professor Helmut Dersch. Panorama Tools provides a framework An updated version of the Panorama Tools library serves as the underlying core engine for many software panorama graphical user interface front ends.
History
Dersch started development on Panorama Tools in 1998, producing software available for creating panoramas and more, but had to stop development in 2001 due to legal harassment and claims of patent infringement by the company IPIX. Dersch released the core library (pano12) and some of the programs of Panorama Tools under the terms of the GNU General Public License. The rest of the applications were made available as binary executables only and for free without a copyleft license.
The development of the source code of Panorama Tools was continued by some members of the original Panorama Tools mailing list. In December 2003 they initiated a free software project which is currently hosted by SourceForge. SourceForge requires that all hosted software is released under an open source license. For this reason Dersch's unlicensed binaries are not hosted there, although they can still be found on mirror websites.
On 5 August 2007, Dersch announced his intention to relicense the Panorama Tools source code. On 9 Augus
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https://en.wikipedia.org/wiki/Jean-Fran%C3%A7ois%20Paillard
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Jean-François Paillard (12 April 1928 – 15 April 2013) was a French conductor.
He was born in Vitry-le-François and received his musical training at the Conservatoire de Paris, where he won first prize in music history, and the Salzburg Mozarteum.
He also earned a degree in mathematics at the Sorbonne.
In 1953, he founded the Jean-Marie Leclair Instrumental Ensemble, which in 1959 became the Orchestre de Chambre Jean-François Paillard. The ensemble has made recordings of much of the Baroque repertoire for Erato Records and has toured throughout Europe and the United States. It has also recorded with many leading French instrumentalists, including Maurice André, Jean-Pierre Rampal, Pierre Pierlot, Lily Laskine, Jacques Lancelot, Michel Arrignon.
A 1968 recording by the orchestra of the "Canon and Gigue for 3 violins and basso continuo" by Johann Pachelbel, familiarly known as Pachelbel's Canon, nearly single-handedly brought the piece from obscurity to great renown. The recording was done in a more Romantic style, at a significantly slower tempo than it had been played at before, and contained obligato parts, written by Paillard, that are now closely associated with the piece. It was released on an Erato Records album, and was also included on a widely distributed album by mail-order label Musical Heritage Society album in 1968. The recording began to get significant attention in the United States, particularly in San Francisco, during the early 1970s. By the late 1970s va
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https://en.wikipedia.org/wiki/Bloom
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Bloom or blooming may refer to:
Science and technology
Biology
Bloom, one or more flowers on a flowering plant
Algal bloom, a rapid increase or accumulation in the population of algae in an aquatic system
Jellyfish bloom, a collective noun for a large group of jellyfish
Epicuticular wax bloom, a whitish haze due to small crystals of wax, occurring on the surface of many fruits
Bloom syndrome, an autosomal recessive human genetic disorder that predisposes the patient to a wide variety of cancer
Computing
Bloom filter, a probabilistic method to find a subset of a given set
Bloom (shader effect), a graphics effect used in modern 3D computer games
Bloom (software), a generative music application for the iPhone and iPod Touch
BLOOM (language model), an open-source language model
Art conservation
Wax bloom, an efflorescence of wax or stearic acid affecting oil pastels
Saponification in art conservation, a chalky white efflorescence on old oil paintings
Bloom, pigment migration from wetter to drier surfaces of a watercolor painting
Other science and technology
Bloom (bloomery) (sponge iron), a porous mass of iron and slag produced in a bloomery
Bloom (casting), a semi-finished metal casting
Bloom (sulfur), the migration of sulfur to the exterior of a rubber
Bloom (test), a test to measure the strength of a gel or gelatin
Blooming (CCD), an effect that happens when a pixel in a CCD image sensor is overloaded
Blooming (directed-energy weapon), an effect of l
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https://en.wikipedia.org/wiki/Lichen%20%28disambiguation%29
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Lichen is a type of symbiotic organism.
Lichen may also refer to:
Arts, entertainment, and media
Lichens (musician), Robert Lowe's solo musical project
"Lichen", the nickname for an untitled song by Aphex Twin from the album Selected Ambient Works Volume II
Biology
Asphodelus albus, a herbaceous perennial plant sometimes called white lichen
Lichen planus, an inflammatory disease
Lichen sclerosus, a skin disease
Lichen simplex chronicus, a skin disease
Places
Licheń Stary, a village in central Poland
Sanctuary of Our Lady of Licheń, a large church at Licheń Stary
Licheń, Lubusz Voivodeship, a village in western Poland
See also
Li Chen (disambiguation)
Lich, an undead creature
Lichen Lake (disambiguation)
Lycan (disambiguation)
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https://en.wikipedia.org/wiki/Growth%20curve
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Growth curve can refer to:
Growth curve (statistics), an empirical model of the evolution of a quantity over time.
Growth curve (biology), a statistical growth curve used to model a biological quantity.
Curve of growth (astronomy), the relation between the equivalent width and the optical depth.
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https://en.wikipedia.org/wiki/Taut%20foliation
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In mathematics, tautness is a rigidity property of foliations. A taut foliation is a codimension 1 foliation of a closed manifold with the property that every leaf meets a transverse circle. By transverse circle, is meant a closed loop that is always transverse to the tangent field of the foliation.
If the foliated manifold has non-empty tangential boundary, then a codimension 1 foliation is taut if every leaf meets a transverse circle or a transverse arc with endpoints on the tangential boundary. Equivalently, by a result of Dennis Sullivan, a codimension 1 foliation is taut if there exists a Riemannian metric that makes each leaf a minimal surface. Furthermore, for compact manifolds the existence, for every leaf , of a transverse circle meeting , implies the existence of a single transverse circle meeting every leaf.
Taut foliations were brought to prominence by the work of William Thurston and David Gabai.
Relation to Reebless foliations
Taut foliations are closely related to the concept of Reebless foliation. A taut foliation cannot have a Reeb component, since the component would act like a "dead-end" from which a transverse curve could never escape; consequently, the boundary torus of the Reeb component has no transverse circle puncturing it. A Reebless foliation can fail to be taut but the only leaves of the foliation with no puncturing transverse circle must be compact, and in particular, homeomorphic to a torus.
Properties
The existence of a taut foliation imp
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https://en.wikipedia.org/wiki/Pseudogroup
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In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example). The modern theory of pseudogroups was developed by Élie Cartan in the early 1900s.
Definition
A pseudogroup imposes several conditions on a sets of homeomorphisms (respectively, diffeomorphisms) defined on open sets U of a given Euclidean space or more generally of a fixed topological space (respectively, smooth manifold). Since two homeomorphisms and compose to a homeomorphism from U to W, one asks that the pseudogroup is closed under composition and inversion. However, unlike those for a group, the axioms defining a pseudogroup are not purely algebraic; the further requirements are related to the possibility of restricting and of patching homeomorphisms (similar to the gluing axiom for sections of a sheaf).
More precisely, a pseudogroup on a topological space is a collection of homeomorphisms between open subsets of satisfying the following properties:
The domains of the elements in cover ("cover").
The restriction of an element in to any open set contained in its domain is also in ("restriction").
The composition ○ of two elements of , when defined, is in ("composition").
The inverse o
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https://en.wikipedia.org/wiki/Princess%20Alexandra%20Hospital%2C%20Brisbane
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The Princess Alexandra Hospital (PAH) is a major Australian teaching hospital of the University of Queensland, located in Brisbane, Queensland. It is a tertiary level teaching hospital with all major medical and surgical specialities onsite except for obstetrics, gynaecology, paediatrics, and medical genetics. It has a catchment population of 1.6 million people with 1038 beds and 5,800 full-time equivalent staff. In 2005, the hospital received Magnet Recognition.
The hospital is located on Ipswich Road in Woolloongabba, an inner-city suburb of Brisbane.
History
The hospital is built on the site of the 1883 Diamantina Orphanage, named after Diamantina Bowen, wife of the first Governor of Queensland. In 1901, it became Diamantina Hospital for Chronic Diseases. In 1943, it became the South Brisbane Auxiliary Hospital and then the South Brisbane Hospital in 1956.
In 1959, it became the Princess Alexandra Hospital and was opened by and named after HRH Princess Alexandra, to mark the Centennial of Queensland. In 2000, a new building was opened to replace the ageing red-brick hospital complex built in the 1950s. The current emergency department is situated on the site of the former nurses' quarters building, while the demolished pathology wing was located at the front of the campus off Ipswich Road.
Major milestones for the hospital included: opening of its first short-stay medical assessment unit in 1960, dialysis unit in 1963, ICU in 1964 (which was a 12-bed bay in the operat
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https://en.wikipedia.org/wiki/Phasor
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In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (), angular frequency (), and initial phase () are time-invariant. It is related to a more general concept called analytic representation, which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and (in older texts) sinor or even complexor.
A common situation in electrical networks powered by time varying current is the existence of multiple sinusoids all with the same frequency, but different amplitudes and phases. The only difference in their analytic representations is the complex amplitude (phasor). A linear combination of such functions can be represented as a linear combination of phasors (known as phasor arithmetic or phasor algebra) and the time/frequency dependent factor that they all have in common.
The origin of the term phasor rightfully suggests that a (diagrammatic) calculus somewhat similar to that possible for vectors is possible for phasors as well. An important additional feature of the phasor transform is that differentiation and integration of sinusoidal signals (having constant amplitude, period and phase) corresponds to simple algebraic operations on the phasors; the phasor transform thus allows the analysis (calculation) of the AC steady state of RLC cir
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https://en.wikipedia.org/wiki/Direct%20integral
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In mathematics and functional analysis a direct integral or Hilbert integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers in the series On Rings of Operators. One of von Neumann's goals in this paper was to reduce the classification of (what are now called) von Neumann algebras on separable Hilbert spaces to the classification of so-called factors. Factors are analogous to full matrix algebras over a field, and von Neumann wanted to prove a continuous analogue of the Artin–Wedderburn theorem classifying semi-simple rings.
Results on direct integrals can be viewed as generalizations of results about finite-dimensional C*-algebras of matrices; in this case the results are easy to prove directly. The infinite-dimensional case is complicated by measure-theoretic technicalities.
Direct integral theory was also used by George Mackey in his analysis of systems of imprimitivity and his general theory of induced representations of locally compact separable groups.
Direct integrals of Hilbert spaces
The simplest example of a direct integral are the L2 spaces associated to a (σ-finite) countably additive measure μ on a measurable space X. Somewhat more generally one can consider a separable Hilbert space H and the space of square-integrable H-valued functions
Terminological note: The termin
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https://en.wikipedia.org/wiki/Peter%20D.%20Mitchell
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Peter Dennis Mitchell FRS (29 September 1920 – 10 April 1992) was a British biochemist who was awarded the 1978 Nobel Prize for Chemistry for his theory of the chemiosmotic mechanism of ATP synthesis.
Education and early life
Mitchell was born in Mitcham, Surrey on 29 September 1920. His parents were Christopher Gibbs Mitchell, a civil servant, and Kate Beatrice Dorothy (née) Taplin. His uncle was Sir Godfrey Way Mitchell, chairman of George Wimpey. He was educated at Queen's College, Taunton and Jesus College, Cambridge where he studied the Natural Sciences Tripos specialising in Biochemistry.
He was appointed a research post in the Department of Biochemistry, Cambridge, in 1942, and was awarded a Ph.D. in early 1951 for work on the mode of action of penicillin.
Career and research
In 1955 he was invited by Professor Michael Swann to set up a biochemical research unit, called the Chemical Biology Unit, in the Department of Zoology, at the University of Edinburgh, where he was appointed a Senior Lecturer in 1961, then Reader in 1962, although institutional opposition to his work coupled with ill health led to his resignation in 1963.
From 1963 to 1965, he supervised the restoration of a Regency-fronted Mansion, known as Glynn House, at Cardinham near Bodmin, Cornwall - adapting a major part of it for use as a research laboratory. He and his former research colleague, Jennifer Moyle founded a charitable company, known as Glynn Research Ltd., to promote fundamental biologic
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https://en.wikipedia.org/wiki/Roke%20Manor%20Research
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Roke Manor Research Limited is a British company based at Roke Manor near Romsey, Hampshire, which conducts research and development in the fields of communications, networks, electronic sensors, artificial intelligence, machine learning, data science, Military decision support consultancy and operational analysis, information assurance, and human science. In addition to supporting its parent Chemring, Roke undertakes contract research and development, and product development work for both public and private sector customers. Products developed from research at Roke Manor include the Hawk-Eye ball tracker, which is now used widely in sports such as tennis, football, and cricket.
Roke has been part of the Chemring Group since 2010, having been founded as part of the Plessey company to operate as a dedicated research and development centre, with mass production elsewhere, and later owned for almost 20 years by Siemens where it had a similar research role.
History
1956 – Founded as Plessey Research Roke Manor Limited by the Plessey company. The first managing director was Harold J. Finden, an electrical engineer at Plessey.
1990 – Passed to GEC-Siemens AG in a joint takeover.
1991 – Became wholly owned by Siemens AG when GEC sold their 50% shareholding to Siemens Plessey Electronic Systems.
2010 – Acquired by the Chemring Group PLC.
2021 – Roke made its first acquisition since the founding in 1956, acquiring Cubica Technology Ltd. and their holding company Cubica Group.
Sites
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https://en.wikipedia.org/wiki/Robert%20Bruce%20Merrifield
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Robert Bruce Merrifield (July 15, 1921 – May 14, 2006) was an American biochemist who won the Nobel Prize in Chemistry in 1984 for the invention of solid phase peptide synthesis.
Early life
He was born in Fort Worth, Texas, on 15 July 1921, the only son of George E. Merrifield and Lorene née Lucas. In 1923 the family moved to California where he attended nine grade schools and two high schools before graduating from Montebello High School in 1939. It was there that he developed an interest both in chemistry and in astronomy.
After two years at Pasadena Junior College he transferred to the University of California at Los Angeles (UCLA). After graduation in chemistry he worked for a year at the Philip R. Park Research Foundation taking care of an animal colony and assisting with growth experiments on synthetic amino acid diets. One of these was the experiment by Geiger that first demonstrated that the essential amino acids must be present simultaneously for growth to occur.
He returned to graduate school at the UCLA chemistry department with professor of biochemistry M.S. Dunn to develop microbiological methods for the quantitation of the pyrimidines. The day after graduating on 19 June 1949, he married Elizabeth Furlong and the next day left for New York City and the Rockefeller Institute for Medical Research.
Career
At the institute, later Rockefeller University, he worked as an Assistant for Dr. D.W. Woolley on a dinucleotide growth factor he discovered in graduate schoo
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https://en.wikipedia.org/wiki/Carl%20Adolph%20Agardh
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Carl Adolph Agardh (23 January 1785 in Båstad, Sweden – 28 January 1859 in Karlstad) was a Swedish botanist specializing in algae, who was eventually appointed bishop of Karlstad.
Biography
In 1807 he was appointed teacher of mathematics at Lund University, in 1812 appointed professor of botany and natural sciences, and was elected a member of the Royal Swedish Academy of Sciences in 1817, and of the Swedish Academy in 1831.
He was ordained a clergyman in 1816, received two parishes as prebend, and was a representative in the clerical chamber of the Swedish Parliament on several occasions from 1817. He was rector magnificus of Lund University 1819-1820 and was appointed bishop of Karlstad in 1835, where he remained until his death. He was the father of Jacob Georg Agardh, also a botanist.
System of plant classification
The Classes Plantarum has nine primary divisions into which his classes and natural orders are grouped. These are, with class numbers;
Acotyledonae 1–3 (Algae, Lichenes, Fungi)
Pseudocotyledonae 4–7 (Muscoideae, Tetradidymae, Filices, Equisetaceae)
Cryptocotyledonae 8–12 (Macropodae, Spadicinae, Glumiflorae, Liliiflorae, Gynandrae)
Phanerocotyledonae incompletae 13–16 (Micranthae, Oleraceae, Epichlamydeae, Columnantherae)
Phanerocotyledonae completae, hypogynae, monopetalae 17 (Tubiflorae)
Phanerocotyledonae completae, hypogynae, polypetalae 18–22 (Centrisporae, Brevistylae, Polycarpellae, Valvisporae, Columniferae)
Phanerocotyledonae completae,
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https://en.wikipedia.org/wiki/Electrocyclic%20reaction
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In organic chemistry, an electrocyclic reaction is a type of pericyclic rearrangement where the net result is one pi bond being converted into one sigma bond or vice versa. These reactions are usually categorized by the following criteria:
Reactions can be either photochemical or thermal.
Reactions can be either ring-opening or ring-closing (electrocyclization).
Depending on the type of reaction (photochemical or thermal) and the number of pi electrons, the reaction can happen through either a conrotatory or disrotatory mechanism.
The type of rotation determines whether the cis or trans isomer of the product will be formed.
Classical examples
The Nazarov cyclization reaction is a named electrocyclic reaction converting divinylketones to cyclopentenones.
A classic example is the thermal ring-opening reaction of 3,4-dimethylcyclobutene. The cis isomer exclusively yields whereas the trans isomer gives the trans,trans diene:
This reaction course can be explained in a simple analysis through the frontier-orbital method: the sigma bond in the reactant will open in such a way that the resulting p-orbitals will have the same symmetry as the HOMO of the product (a hexadiene). The only way to accomplish this is through a conrotatory ring-opening which results in opposite signs for the terminal lobes.
Stereospecificity of electrocyclic reactions
When performing an electrocyclic reaction, it is often desirable to predict the cis/trans geometry of the reaction's product. The fi
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https://en.wikipedia.org/wiki/Cycloaddition
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In organic chemistry, a cycloaddition is a chemical reaction in which "two or more unsaturated molecules (or parts of the same molecule) combine with the formation of a cyclic adduct in which there is a net reduction of the bond multiplicity". The resulting reaction is a cyclization reaction. Many but not all cycloadditions are concerted and thus pericyclic. Nonconcerted cycloadditions are not pericyclic. As a class of addition reaction, cycloadditions permit carbon–carbon bond formation without the use of a nucleophile or electrophile.
Cycloadditions can be described using two systems of notation. An older but still common notation is based on the size of linear arrangements of atoms in the reactants. It uses parentheses: where the variables are the numbers of linear atoms in each reactant. The product is a cycle of size . In this system, the standard Diels-Alder reaction is a (4 + 2)-cycloaddition, the 1,3-dipolar cycloaddition is a (3 + 2)-cycloaddition and cyclopropanation of a carbene with an alkene a (2 + 1)-cycloaddition.
A more recent, IUPAC-preferred notation, first introduced by Woodward and Hoffmann, uses square brackets to indicate the number of electrons, rather than carbon atoms, involved in the formation of the product. In the [i + j + ...] notation, the standard Diels-Alder reaction is a [4 + 2]-cycloaddition, while the 1,3-dipolar cycloaddition is also a [4 + 2]-cycloaddition.
Thermal cycloadditions and their stereochemistry
Thermal cycloadditions are tho
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https://en.wikipedia.org/wiki/Sigmatropic%20reaction
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A sigmatropic reaction in organic chemistry is a pericyclic reaction wherein the net result is one σ-bond is changed to another σ-bond in an uncatalyzed intramolecular reaction. The name sigmatropic is the result of a compounding of the long-established sigma designation from single carbon–carbon bonds and the Greek word tropos, meaning turn. In this type of rearrangement reaction, a substituent moves from one part of a π-bonded system to another part in an intramolecular reaction with simultaneous rearrangement of the π system. True sigmatropic reactions are usually uncatalyzed, although Lewis acid catalysis is possible. Sigmatropic reactions often have transition-metal catalysts that form intermediates in analogous reactions. The most well-known of the sigmatropic rearrangements are the [3,3] Cope rearrangement, Claisen rearrangement, Carroll rearrangement, and the Fischer indole synthesis.
Overview of sigmatropic shifts
Woodward–Hoffman sigmatropic shift nomenclature
Sigmatropic rearrangements are concisely described by an order term [i,j], which is defined as the migration of a σ-bond adjacent to one or more π systems to a new position (i−1) and (j−1) atoms removed from the original location of the σ-bond. When the sum of i and j is an even number, this is an indication of the involvement of a neutral, all C atom chain. An odd number is an indication of the involvement of a charged C atom or of a heteroatom lone pair replacing a CC double bond. Thus, [1,5] and [3,3] shi
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https://en.wikipedia.org/wiki/Group%20transfer%20reaction
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In organic chemistry, a group transfer reaction is a pericyclic process where one or more groups of atoms is transferred from one molecule to another. They can sometimes be difficult to identify when separate reactant molecules combine into a single product molecule (like in the ene reaction). Unlike other pericyclic reaction classes, group transfer reactions do not have a specific conversion of pi bonds into sigma bonds or vice versa, and tend to be less frequently encountered. Like all pericyclic reactions, they must obey the Woodward–Hoffmann rules.
The best known group transfer reaction is the ene reaction in which an allylic hydrogen is transferred to an alkene.
References
Rearrangement reactions
Pericyclic reactions
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https://en.wikipedia.org/wiki/Zeno%20machine
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In mathematics and computer science, Zeno machines (abbreviated ZM, and also called accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that are capable of carrying out computations involving a countably infinite number of algorithmic steps. These machines are ruled out in most models of computation.
The idea of Zeno machines was first discussed by Hermann Weyl in 1927; the name refers to Zeno's paradoxes, attributed to the ancient Greek philosopher Zeno of Elea. Zeno machines play a crucial role in some theories. The theory of the Omega Point devised by physicist Frank J. Tipler, for instance, can only be valid if Zeno machines are possible.
Definition
A Zeno machine is a Turing machine that can take an infinite number of steps, and then continue take more steps. This can be thought of as a supertask where units of time are taken to perform the -th step; thus, the first step takes 0.5 units of time, the second takes 0.25, the third 0.125 and so on, so that after one unit of time, a countably infinite number of steps will have been performed.
Infinite time Turing machines
A more formal model of the Zeno machine is the infinite time Turing machine. Defined first in unpublished work by Jeffrey Kidder and expanded upon by Joel Hamkins and Andy Lewis, in Infinite Time Turing Machines, the infinite time Turing machine is an extension of the classical Turing machine model, to include transfinite time; that is time beyond all
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https://en.wikipedia.org/wiki/Ene%20reaction
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In organic chemistry, the ene reaction (also known as the Alder-ene reaction by its discoverer Kurt Alder in 1943) is a chemical reaction between an alkene with an allylic hydrogen (the ene) and a compound containing a multiple bond (the enophile), in order to form a new σ-bond with migration of the ene double bond and 1,5 hydrogen shift. The product is a substituted alkene with the double bond shifted to the allylic position.
This transformation is a group transfer pericyclic reaction, and therefore, usually requires highly activated substrates and/or high temperatures. Nonetheless, the reaction is compatible with a wide variety of functional groups that can be appended to the ene and enophile moieties. Many useful Lewis acid-catalyzed ene reactions have been also developed, which can afford high yields and selectivities at significantly lower temperatures, making the ene reaction a useful C–C forming tool for the synthesis of complex molecules and natural products.
Ene component
Enes are π-bonded molecules that contain at least one active hydrogen atom at the allylic, propargylic, or α-position. Possible ene components include olefinic, acetylenic, allenic, aromatic, cyclopropyl, and carbon-hetero bonds. Usually, the allylic hydrogen of allenic components participates in ene reactions, but in the case of allenyl silanes, the allenic hydrogen atom α to the silicon substituent is the one transferred, affording a silylalkyne. Phenol can act as an ene component, for example
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https://en.wikipedia.org/wiki/Homeorhesis
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Homeorhesis, derived from the Greek for "similar flow", is a concept encompassing dynamical systems which return to a trajectory, as opposed to systems which return to a particular state, which is termed homeostasis.
Biology
Homeorhesis is steady flow. Often biological systems are inaccurately described as homeostatic, being in a steady state. Steady state implies equilibrium which is never reached, nor are organisms and ecosystems in a closed environment. During his tenure at the State University of New York at Oneonta, Dr William Butts correctly applied the term homeorhesis to biological organisms. The term was first used in biology by C.H. Waddington around 1940, where he described the tendency of developing or changing organisms to continue development or adapting to their environment and changing towards a given state.
Gaia hypothesis
In ecology the concept is important as an element of the Gaia hypothesis, where the system under consideration is the ecological balance of different forms of life on the planet. It was Lynn Margulis, the coauthor of Gaia hypothesis, who wrote in particular that only homeorhetic, and not homeostatic, balances are involved in the theory. That is, the composition of Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in homeostasis, but those set points change with time.
References
Systems theory
Ecology
Homeostasis
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https://en.wikipedia.org/wiki/Diverticulum
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In medicine or biology, a diverticulum is an outpouching of a hollow (or a fluid-filled) structure in the body. Depending upon which layers of the structure are involved, diverticula are described as being either true or false.
In medicine, the term usually implies the structure is not normally present, but in embryology, the term is used for some normal structures arising from others, as for instance the thyroid diverticulum, which arises from the tongue.
The word comes from Latin dīverticulum, "bypath" or "byway".
Classification
Diverticula are described as being true or false depending upon the layers involved:
False diverticula (also known as "pseudodiverticula") do not involve muscular layers or adventitia. False diverticula, in the gastrointestinal tract for instance, involve only the submucosa and mucosa.
True diverticula involve all layers of the structure, including muscularis propria and adventitia, such as Meckel's diverticulum.
Embryology
The kidneys are originally diverticula in the development of the urinary and reproductive organs.
The lungs are originally diverticula forming off of the ventral foregut.
The thymus appears in the form of two flask-shape diverticula, which arise from the third branchial pouch (pharyngeal pouch) of the endoderm.
The thyroid gland develops as a diverticulum arising from a point on the tongue, demarcated as the foramen cecum.
Human pathology
Gastrointestinal tract diverticula
Esophageal diverticula may occur in one of three
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https://en.wikipedia.org/wiki/Peptide%20synthesis
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In organic chemistry, peptide synthesis is the production of peptides, compounds where multiple amino acids are linked via amide bonds, also known as peptide bonds. Peptides are chemically synthesized by the condensation reaction of the carboxyl group of one amino acid to the amino group of another. Protecting group strategies are usually necessary to prevent undesirable side reactions with the various amino acid side chains. Chemical peptide synthesis most commonly starts at the carboxyl end of the peptide (C-terminus), and proceeds toward the amino-terminus (N-terminus). Protein biosynthesis (long peptides) in living organisms occurs in the opposite direction.
The chemical synthesis of peptides can be carried out using classical solution-phase techniques, although these have been replaced in most research and development settings by solid-phase methods (see below). Solution-phase synthesis retains its usefulness in large-scale production of peptides for industrial purposes moreover.
Chemical synthesis facilitates the production of peptides that are difficult to express in bacteria, the incorporation of unnatural amino acids, peptide/protein backbone modification, and the synthesis of D-proteins, which consist of D-amino acids.
Solid-phase synthesis
The established method for the production of synthetic peptides in the lab is known as solid phase peptide synthesis (SPPS). Pioneered by Robert Bruce Merrifield, SPPS allows the rapid assembly of a peptide chain through succ
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https://en.wikipedia.org/wiki/Scott%20core%20theorem
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In mathematics, the Scott core theorem is a theorem about the finite presentability of fundamental groups of 3-manifolds due to G. Peter Scott, . The precise statement is as follows:
Given a 3-manifold (not necessarily compact) with finitely generated fundamental group, there is a compact three-dimensional submanifold, called the compact core or Scott core, such that its inclusion map induces an isomorphism on fundamental groups. In particular, this means a finitely generated 3-manifold group is finitely presentable.
A simplified proof is given in , and a stronger uniqueness statement is proven in .
References
3-manifolds
Theorems in group theory
Theorems in topology
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https://en.wikipedia.org/wiki/Proof%20assistant
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In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer.
A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
System comparison
ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition.
Coq – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems the logical core is a library of their programming language. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include:
HOL4 – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has
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https://en.wikipedia.org/wiki/James%20Burnell-Nugent
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Admiral Sir James Michael Burnell-Nugent, (born 20 November 1949) is a retired Royal Navy officer who served as Commander-in-Chief Fleet from 2005 to 2007.
Early life and education
Burnell-Nugent was educated at Stowe School, then an all-boys private school in Buckinghamshire. He studied mathematics at Corpus Christi College, Cambridge, graduating with a Bachelor of Arts (BA) degree: as per tradition, his BA was later promoted to a Master of Arts (MA Cantab) degree.
Naval career
Burnell-Nugent joined the Royal Navy in 1971. He was appointed an acting lieutenant on 1 November 1972, and confirmed in this rank in June 1974.
He was given command of the diesel submarine in 1978, and was promoted to lieutenant-commander on 1 November 1980. Appointed in command of the nuclear-powered submarine in 1984, he carried out many Cold War patrols. He was promoted to commander on 30 June 1985. He became Commanding Officer of the frigate as well as Captain of the 2nd Frigate Squadron in 1992, and in that capacity was involved in the early stages of the Bosnia Crisis. He was in command of the aircraft carrier and made two joint operational deployments to the Gulf for air operations over Iraq and then conducted further air operations during the Kosovo War. He became Assistant Chief of the Naval Staff in 1999. As Commander United Kingdom Maritime Forces from 2001 to 2002, he was Maritime Commander of the UK Joint Force and the Deputy Maritime Commander of the Coalition for the first 6 mo
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https://en.wikipedia.org/wiki/Phenylenediamine
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Phenylenediamine may refer to:
o-phenylenediamine or OPD, a chemical compound C6H4(NH2)2
m-phenylenediamine or MPD, a chemical compound C6H4(NH2)2
p-phenylenediamine or PPD, a chemical compound C6H4(NH2)2
N,N-dimethyl-p-phenylenediamine or DMPD
N,N,N′,N′-tetramethyl-p-phenylenediamine or TMPD, used in microbiology
N,N-diethyl-p-phenylenediamine or DPD
Diamines
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https://en.wikipedia.org/wiki/Zeitschrift%20f%C3%BCr%20Angewandte%20Mathematik%20und%20Physik
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The Zeitschrift für Angewandte Mathematik und Physik (English: Journal of Applied Mathematics and Physics) is a bimonthly peer-reviewed scientific journal published by Birkhäuser Verlag. The editor-in-chief is Kaspar Nipp (ETH Zurich). It was established in 1950 and covers the fields of theoretical and applied mechanics, applied mathematics, and related topics. According to the Journal Citation Reports, the journal has a 2017 impact factor of 1.711.
References
External links
Mathematics journals
Physics journals
Academic journals established in 1950
Springer Science+Business Media academic journals
Bimonthly journals
English-language journals
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https://en.wikipedia.org/wiki/Evolutionary%20ecology
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Evolutionary ecology lies at the intersection of ecology and evolutionary biology. It approaches the study of ecology in a way that explicitly considers the evolutionary histories of species and the interactions between them. Conversely, it can be seen as an approach to the study of evolution that incorporates an understanding of the interactions between the species under consideration. The main subfields of evolutionary ecology are life history evolution, sociobiology (the evolution of social behavior), the evolution of interspecific interactions (e.g. cooperation, predator–prey interactions, parasitism, mutualism) and the evolution of biodiversity and of ecological communities.
Evolutionary ecology mostly considers two things: how interactions (both among species and between species and their physical environment) shape species through selection and adaptation, and the consequences of the resulting evolutionary change.
Evolutionary models
A large part of evolutionary ecology is about utilising models and finding empirical data as proof. Examples include the Lack clutch size model devised by David Lack and his study of Darwin's finches on the Galapagos Islands. Lack's study of Darwin's finches was important in analyzing the role of different ecological factors in speciation. Lack suggested that differences in species were adaptive and produced by natural selection, based on the assertion by G.F. Gause that two species cannot occupy the same niche.
Richard Levins introduc
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https://en.wikipedia.org/wiki/Alexander%20McAulay
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Alexander McAulay (9 December 1863 – 6 July 1931) was the first professor of mathematics and physics at the University of Tasmania, Hobart, Tasmania. He was also a proponent of dual quaternions, which he termed "octonions" or "Clifford biquaternions".
McAulay was born on 9 December 1863 and attended Kingswood School in Bath. He proceeded to Caius College, Cambridge, there taking up a study of the quaternion algebra. In 1883 he published an article "Some general theorems in quaternion integration". McAulay took his degree in 1886, and began to reflect on the instruction of students in quaternion theory. In an article "Establishment of the fundamental properties of quaternions" he suggested improvements to the texts then in use. He also wrote a technical article on integration.
Departing for Australia, he lectured at Ormond College, University of Melbourne from 1893 to 1895. As a distant correspondent, he participated in a vigorous debate about the place of quaternions in physics education. In 1893 his book Utility of Quaternions in Physics was published. A. S. Hathaway contributed a positive review and Peter Guthrie Tait praised
it in these terms:
Here, at last, we exclaim, is a man who has caught the full spirit of the quaternion system: the real aestus, the awen of the Welsh Bards, the divinus afflatus that transports the poet beyond the limits of sublunary things! Intuitively recognizing its power, he snatches up the magnificent weapon which Hamilton tenders us all, and
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https://en.wikipedia.org/wiki/Paul%20Davis%20%28programmer%29
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Paul Davis (formerly known as Paul Barton-Davis) is a British-American software developer best known for his work on audio software (JACK) for the Linux operating system, and for his role as one of the first two programmers at Amazon.com.
Davis grew up in the English Midlands and in London. After studying molecular biology and biophysics, he did post-graduate studies in computational biology at the Weizmann Institute of Science in Rehovot and EMBL in Heidelberg.
He immigrated to the U.S. in 1989. He lived in Seattle for seven years, where he worked for the Computer Science and Engineering Department at the University of Washington, and several smaller software companies in Seattle. While in Seattle, he helped to get Amazon.com off the ground during the period 1994–1996, making critical contributions to Amazon's backend systems alongside Shel Kaphan, before subsequently moving to Philadelphia in 1996. In 2019 he moved with his wife to Galisteo, NM
He went on to fund the development of various audio software for Linux, including Ardour and the JACK Audio Connection Kit. He works full-time on free software.
He is also an ultra-marathon runner and touring cyclist.
References
External links
Paul Davis' home page
Computer programmers
Living people
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Dephasing
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In physics, dephasing is a mechanism that recovers classical behaviour from a quantum system. It refers to the ways in which coherence caused by perturbation decays over time, and the system returns to the state before perturbation. It is an important effect in molecular and atomic spectroscopy, and in the condensed matter physics of mesoscopic devices.
The reason can be understood by describing the conduction in metals as a classical phenomenon with quantum effects all embedded into an effective mass that can be computed quantum mechanically, as also happens to resistance that can be seen as a scattering effect of conduction electrons. When the temperature is lowered and the dimensions of the device are meaningfully reduced, this classical behaviour should disappear and the laws of quantum mechanics should govern the behavior of conducting electrons seen as waves that move ballistically inside the conductor without any kind of dissipation. Most of the time this is what one observes. But it appeared as a surprise to uncover that the so-called dephasing time, that is the time it takes for the conducting electrons to lose their quantum behavior, becomes finite rather than infinite when the temperature approaches zero in mesoscopic devices violating the expectations of the theory of Boris Altshuler, Arkady Aronov and David E. Khmelnitskii. This kind of saturation of the dephasing time at low temperatures is an open problem even as several proposals have been put forward.
The c
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https://en.wikipedia.org/wiki/Diazo
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In organic chemistry, the diazo group is an organic moiety consisting of two linked nitrogen atoms at the terminal position. Overall charge-neutral organic compounds containing the diazo group bound to a carbon atom are called diazo compounds or diazoalkanes and are described by the general structural formula . The simplest example of a diazo compound is diazomethane, . Diazo compounds () should not be confused with azo compounds () or with diazonium compounds ().
Structure
The electronic structure of diazo compounds is characterized by π electron density delocalized over the α-carbon and two nitrogen atoms, along with an orthogonal π system with electron density delocalized over only the terminal nitrogen atoms. Because all octet rule-satisfying resonance forms of diazo compounds have formal charges, they are members of a class of compounds known as 1,3-dipoles. Some of the most stable diazo compounds are α-diazo-β-diketones and α-diazo-β-diesters, in which the electron density is further delocalized into an electron-withdrawing carbonyl group. In contrast, most diazoalkanes without electron-withdrawing substituents, including diazomethane itself, are explosive. A commercially relevant diazo compound is ethyl diazoacetate (N2CHCOOEt). A group of isomeric compounds with only few similar properties are the diazirines, where the carbon and two nitrogens are linked as a ring.
Four resonance structures can be drawn:
Compounds with the diazo moiety should be distinguished
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https://en.wikipedia.org/wiki/Oxford%20Internet%20Institute
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The Oxford Internet Institute (OII) serves as a hub for interdisciplinary research, combining social and computer science to explore information, communication, and technology. It is an integral part of the University of Oxford's Social Sciences Division in England.
Overview
The OII is spread across three locations on St Giles in Oxford, with its main hub at 1 St Giles, owned by Balliol College. This department focuses on exploring digital life to influence Internet research, policy, and usage.
Founded in 2001, the OII explores how the Internet affects our lives. It unites experts in fields like politics, sociology, and science to study online behavior. The current director is Professor Victoria Nash.
Research
Research at the OII covers a diverse range of topics, with faculty publishing journal articles and books on issues including privacy and security, e-government and e-democracy, virtual economies, smart cities, digital exclusion, digital humanities, online gaming, big data and Internet geography. The OII currently has the following research clusters reflecting the diverse expertise of faculty:
Digital Politics and Government
Information Governance, and Security
Social Data Science
Connectivity, Inclusion, and Inequality
Internet Economies
Digital Knowledge and Culture
Education, Digital Life, and Wellbeing
Ethics and Philosophy of Information
The research conducted at the OII covers a wide range of topics in Internet studies and the social impact of onli
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https://en.wikipedia.org/wiki/Vector%20algebra
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In mathematics, vector algebra may mean:
Linear algebra, specifically the basic algebraic operations of vector addition and scalar multiplication; see vector space.
The algebraic operations in vector calculus, namely the specific additional structure of vectors in 3-dimensional Euclidean space of dot product and especially cross product. In this sense, vector algebra is contrasted with geometric algebra, which provides an alternative generalization to higher dimensions.
An algebra over a field, a vector space equipped with a bilinear product
Original vector algebras of the nineteenth century like quaternions, tessarines, or coquaternions, each of which has its own product. The vector algebras biquaternions and hyperbolic quaternions enabled the revolution in physics called special relativity by providing mathematical models.
Algebra
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https://en.wikipedia.org/wiki/Herbert%20A.%20Hauptman
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Herbert Aaron Hauptman (February 14, 1917 – October 23, 2011) was an American mathematician and Nobel laureate. He pioneered and developed a mathematical method that has changed the whole field of chemistry and opened a new era in research in determination of molecular structures of crystallized materials. Today, Hauptman's direct methods, which he continued to improve and refine, are routinely used to solve complicated structures. It was the application of this mathematical method to a wide variety of chemical structures that led the Royal Swedish Academy of Sciences to name Hauptman and Jerome Karle recipients of the 1985 Nobel Prize in Chemistry.
Life
He was born in to a Jewish family in New York City, the oldest child of Leah (Rosenfeld) and Israel Hauptman. He was married to Edith Citrynell since November 10, 1940, with two daughters, Barbara (1947) and Carol (1950).
He was interested in science and mathematics from an early age which he pursued at Townsend Harris High School, graduated from the City College of New York (1937) and obtained an M.A. degree in mathematics from Columbia University in 1939.
After the war he started a collaboration with Jerome Karle at the Naval Research Laboratory in Washington, D.C., and at the same time enrolled in the Ph.D. program at the University of Maryland, College Park. He received his Ph.D. from the University of Maryland in 1955 in physics, which is part of the University of Maryland College of Computer, Mathematical, and Natura
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https://en.wikipedia.org/wiki/Mel
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Mel, Mels or MEL may refer to:
Biology
Mouse erythroleukemia cell line (MEL)
National Herbarium of Victoria, a herbarium with the Index Herbariorum code MEL
People
Mel (given name), the abbreviated version of several given names (including a list of people with the name)
Mel (surname)
Manuel Zelaya, former president of Honduras, nicknamed "Mel"
Places
Mel, Veneto, an ex-comune in Italy
Mel Moraine, a moraine in Antarctica
Melbourne Airport (IATA airport code)
Mels, a municipality in Switzerland
Métropole Européenne de Lille (MEL), the intercommunality of Lille in France
Technology and engineering
Maya Embedded Language, a scripting language used in the 3D graphics program Maya
Michigan eLibrary, an online service of the Library of Michigan
Ford MEL engine, a "Mercury-Edsel-Lincoln" engine series
Minimum equipment list, a categorized list of instruments and equipment on an aircraft
Miscellaneous electric load, the electricity use of appliances, electronics and other small electric devices in buildings
Arts and entertainment
Mel (film), a 1998 film with Ernest Borgnine
Mel (album), a 1979 album by Maria Bethânia
Portal Stories: Mel, a mod of the video game Portal 2
Other uses
Mel languages, spoken in western Africa
Mel scale, a scale for measuring auditory pitches as perceived by the human ear
Midland Expressway Ltd, operator of the UK M6 Toll road
Musical Electronics Library, a lending library of homemade electronic musical devices in New Zealand
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https://en.wikipedia.org/wiki/James%20Brown%20%28ecologist%29
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James Hemphill Brown (born 1942) is an American biologist and academic.
He is an ecologist, and a Distinguished Professor of Biology at the University of New Mexico. His work has focused on 3 distinct aspects of ecology: 1) the population and community ecology of rodents and harvester ants in the Chihuahuan Desert, 2) large-scale questions relating to the distribution of body size, abundance and geographic range of animals, leading to the development of the field of macroecology, a term that was coined in a paper Brown co-authored with Brian Maurer of Michigan State University. and 3) the Metabolic Theory of Ecology. In 2005 he was awarded the Robert H. MacArthur Award by the Ecological Society of America for his work, including his work toward a metabolic theory of ecology. Between 1969 and 2011 he was awarded over $18.4 million in grants for his research.
Education and honors
Education
Brown received a bachelors with honors in 1963 before obtaining his PhD in 1967:
Bachelor of Arts, Zoology, 1963, Cornell University
PhD, Zoology, 1967, University of Michigan
Honors
Honors James Brown has received include:
American Association for the Advancement of Science, Fellow, 1988
C. Hart Merriam Award (American Society of Mammalogists) 1989
Fellow of the American Academy of Arts and Sciences, 1995
Eugene P. Odum Award for Education (Ecological Society of America), 2001
Marsh Ward for Career Achievement, (British Ecological Society), 2002
Robert H. MacArthur Award (Ecological So
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https://en.wikipedia.org/wiki/Acetylide
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In organometallic chemistry, acetylide refers to chemical compounds with the chemical formulas and , where M is a metal. The term is used loosely and can refer to substituted acetylides having the general structure (where R is an organic side chain). Acetylides are reagents in organic synthesis. The calcium acetylide commonly called calcium carbide is a major compound of commerce.
Structure and bonding
Alkali metal and alkaline earth metal acetylides of the general formula MC≡CM are salt-like Zintl phase compounds, containing ions. Evidence for this ionic character can be seen in the ready hydrolysis of these compounds to form acetylene and metal oxides, there is also some evidence for the solubility of ions in liquid ammonia. The ion has a closed shell ground state of 1Σ, making it isoelectronic to a neutral molecule N2, which may afford it some stability.
Analogous acetylides prepared from other metals, particularly transition metals, show covalent character and are invariably associated with their metal centers. This can be seen in their general stability to water (such as silver acetylide, copper acetylide) and radically different chemical applications.
Acetylides of the general formula RC≡CM (where R = H or alkyl) generally show similar properties to their doubly substituted analogues. In the absence of additional ligands, metal acetylides adopt polymeric structures wherein the acetylide groups are bridging ligands.
Preparation
Terminal alkynes are weak acids
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https://en.wikipedia.org/wiki/K-line
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K-line may refer to:
Chemistry
K-line (spectrometry), one of two features in spectroscopy:
Calcium K line, a Fraunhofer spectral line from ionised calcium
K-line (x-ray), an x-ray peak in astronomical spectrometry
K line, a term used in Internal conversion electron spectroscopy
Computing
K-line (artificial intelligence) (Knowledge-line), a mental agent in artificial intelligence
K-line (IRC), a server ban in IRC
Finance
Candlestick chart, or K-line, a style of financial chart used to describe price movements of a security, derivative, or currency
Sports
K line, the line marking the calculation point in ski jumping
Transportation
K (Broadway Brooklyn Local), earlier KK, discontinued in 1976
K (Eighth Avenue Local), a defunct train service on the New York City Subway, which was known as the AA until 1985
K Ingleside, a service of the San Francisco Municipal Railway sometimes called the K Line
K Line (Los Angeles Metro), a light rail line in Los Angeles County, California
K (Los Angeles Railway), defunct streetcar line in Los Angeles, California
K Line, a Japanese shipping company
K-Line, a model railway locomotive company
K-Line bus operator in Yorkshire, England since rebranded as Tiger Blue
K-Line, part of the ISO 9141 on-board diagnostics vehicle network interface standard
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https://en.wikipedia.org/wiki/Programme%20for%20International%20Student%20Assessment
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The Programme for International Student Assessment (PISA) is a worldwide study by the Organisation for Economic Co-operation and Development (OECD) in member and non-member nations intended to evaluate educational systems by measuring 15-year-old school pupils' scholastic performance on mathematics, science, and reading. It was first performed in 2000 and then repeated every three years. Its aim is to provide comparable data with a view to enabling countries to improve their education policies and outcomes. It measures problem solving and cognition.
The results of the 2018 data collection were released on 3 December 2019.
Influence and impact
PISA, and similar international standardised assessments of educational attainment are increasingly used in the process of education policymaking at both national and international levels.
PISA was conceived to set in a wider context the information provided by national monitoring of education system performance through regular assessments within a common, internationally agreed framework; by investigating relationships between student learning and other factors they can "offer insights into sources of variation in performances within and between countries".
Until the 1990s, few European countries used national tests. In the 1990s, ten countries / regions introduced standardised assessment, and since the early 2000s, ten more followed suit. By 2009, only five European education systems had no national student assessments.
The impact
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https://en.wikipedia.org/wiki/Interaction%20point
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In particle physics, an interaction point (IP) is the place where particles collide in an accelerator experiment. The nominal interaction point is the design position, which may differ from the real or physics interaction point, where the particles actually collide. A related, but distinct, concept is the primary vertex: the reconstructed location of an individual particle collision.
For fixed target experiments, the interaction point is the point where beam and target interact. For colliders, it is the place where the beams interact.
Experiments (detectors) at particle accelerators are built around the nominal interaction points of the accelerators. The whole region around the interaction point (the experimental hall) is called an interaction region.
Particle colliders such as LEP, HERA, RHIC, Tevatron and LHC can host several interaction regions and therefore several experiments taking advantage of the same beam.
Accelerator physics
Experimental particle physics
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https://en.wikipedia.org/wiki/Reaction%20coordinate
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In chemistry, a reaction coordinate is an abstract one-dimensional coordinate chosen to represent progress along a reaction pathway. Where possible it is usually a geometric parameter that changes during the conversion of one or more molecular entities, such as bond length or bond angle. For example, in the homolytic dissociation of molecular hydrogen, an apt choice would be the coordinate corresponding to the bond length. Non-geometric parameters such as bond order are also used, but such direct representation of the reaction process can be difficult, especially for more complex reactions.
In molecular dynamics simulations, a reaction coordinate is called a collective variable.
A reaction coordinate parametrises reaction process at the level of the molecular entities involved. It differs from extent of reaction, which measures reaction progress in terms of the composition of the reaction system.
(Free) energy is often plotted against reaction coordinate(s) to demonstrate in schematic form the potential energy profile (an intersection of a potential energy surface) associated with the reaction.
In the formalism of transition-state theory the reaction coordinate for each reaction step is one of a set of curvilinear coordinates obtained from the conventional coordinates for the reactants, and leads smoothly among configurations, from reactants to products via the transition state. It is typically chosen to follow the path defined by potential energy gradient – shallowes
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https://en.wikipedia.org/wiki/Hyperbolic%20coordinates
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In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane
.
Hyperbolic coordinates take values in the hyperbolic plane defined as:
.
These coordinates in HP are useful for studying logarithmic comparisons of direct proportion in Q and measuring deviations from direct proportion.
For in take
and
.
The parameter u is the hyperbolic angle to (x, y) and v is the geometric mean of x and y.
The inverse mapping is
.
The function is a continuous mapping, but not an analytic function.
Alternative quadrant metric
Since HP carries the metric space structure of the Poincaré half-plane model of hyperbolic geometry, the bijective correspondence
brings this structure to Q. It can be grasped using the notion of hyperbolic motions. Since geodesics in HP are semicircles with centers on the boundary, the geodesics in Q are obtained from the correspondence and turn out to be rays from the origin or petal-shaped curves leaving and re-entering the origin. And the hyperbolic motion of HP given by a left-right shift corresponds to a squeeze mapping applied to Q.
Since hyperbolas in Q correspond to lines parallel to the boundary of HP, they are horocycles in the metric geometry of Q.
If one only considers the Euclidean topology of the plane and the topology inherited by Q, then the lines bounding Q seem close to Q. Insight from the metric space HP shows that the open set Q has only the origin as boundary when viewed through the corr
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https://en.wikipedia.org/wiki/Microcosm%20%28CERN%29
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Microcosm or CERN Museum was an interactive exhibition presenting the work of the CERN particle physics laboratory and its flagship accelerator the Large Hadron Collider (LHC). It first opened to the public in 1990 and closed permanently in September 2022, to be replaced by the Science Gateway in 2023. The final version of the exhibition opened in January 2016, developed by CERN in collaboration with Spanish design team Indissoluble.
History
The project was approved by the CERN Directorate in February 1988. The initial construction, to a large extent completed in 1989, was financed through contributions from the Canton of Geneva, the Swiss Confederation, neighbouring France, banks, and industrial firms.
Main exhibits
The exhibition displayed many real objects, taking visitors on a journey through CERN's key installations, from the hydrogen bottle, source of the protons that are injected into the LHC, through the first step in the accelerator chain, the linac, on to a model of a section of the Large Hadron Collider including elements from the superconducting magnets. Visitors could interact with the displays to try their hand at the controls of a particle accelerator – simulating the acceleration of protons in the LHC and bringing them into collision inside the experiments.
The exhibition contained a 1:1 scale model of a complete slice through the CMS experiment at the LHC. The computing section displayed some of the Oracle data tapes used to store the 30-40 petabytes of
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https://en.wikipedia.org/wiki/Xenobiology
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Xenobiology (XB) is a subfield of synthetic biology, the study of synthesizing and manipulating biological devices and systems. The name "xenobiology" derives from the Greek word xenos, which means "stranger, alien". Xenobiology is a form of biology that is not (yet) familiar to science and is not found in nature. In practice, it describes novel biological systems and biochemistries that differ from the canonical DNA–RNA-20 amino acid system (see central dogma of molecular biology). For example, instead of DNA or RNA, XB explores nucleic acid analogues, termed xeno nucleic acid (XNA) as information carriers. It also focuses on an expanded genetic code and the incorporation of non-proteinogenic amino acids into proteins.
Difference between xeno-, exo-, and astro-biology
"Astro" means "star" and "exo" means "outside". Both exo- and astrobiology deal with the search for naturally evolved life in the Universe, mostly on other planets in the circumstellar habitable zone. (These are also occasionally referred to as xenobiology.) Whereas astrobiologists are concerned with the detection and analysis of life elsewhere in the Universe, xenobiology attempts to design forms of life with a different biochemistry or different genetic code than on planet Earth.
Aims
Xenobiology has the potential to reveal fundamental knowledge about biology and the origin of life. In order to better understand the origin of life, it is necessary to know why life evolved seemingly via an early RNA world
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https://en.wikipedia.org/wiki/CLS
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CLS may refer to:
Academic fields
Critical legal studies, school of legal philosophy
Constrained least square statistical estimator
CLs method to set bounds on particle physics model parameters
The .cls file extension, used to hold LaTeX manuscripts - see LaTeX § Compatibility and converters
Education
California Labor School, San Francisco, US 1942–57
City of London School, UK
Covington Latin School, Kentucky, US
Crystal Lake South High School, Illinois, US
Chicago Law School at The University of Chicago, US
Columbia Law School at Columbia University, US
Cornell Law School at Cornell University, US
Coalition of Latino and Latina Scholars at Teachers College, Columbia University, US
Critical Language Scholarship Program of the US State Department
Societies and associations
Caribbean Labour Solidarity, based in London, UK
Chicago Linguistic Society
Christian Legal Society
Communist League of Struggle, US, 1931-1937
Software and technology
Cable landing station, where a submarine cable comes ashore
Common Language Specification, Microsoft
CLS (command) to clear computer screen in several environments
CLS (CONFIG.SYS directive), in DR-DOS
Creative Lighting System, in Nikon speedlights
Medical and science
Computational Science, an academical research discipline
Canadian Light Source, a synchrotron light source
Clinical laboratory science, another name for Medical Technology or Medical Laboratory Science
Combat lifesaver, US non-medical military role
Musi
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https://en.wikipedia.org/wiki/Prime%20Obsession
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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications.
The book was awarded the Mathematical Association of America's inaugural Euler Book Prize in 2007.
Overview
The book is written such that even-numbered chapters present historical elements related to the development of the conjecture, and odd-numbered chapters deal with the mathematical and technical aspects. Despite the title, the book provides biographical information on many iconic mathematicians including Euler, Gauss, and Lagrange.
In chapter 1, "Card Trick", Derbyshire introduces the idea of an infinite series and the ideas of convergence and divergence of these series. He imagines that there is a deck of cards stacked neatly together, and that one pulls off the top card so that it overhangs from the deck. Explaining that it can overhang only as far as the center of gravity allows, the card is pulled so that exactly half of it is overhanging. Then, without moving the top card, he slides the second card so that it is overhanging too at equilibrium. As he does this more and more, the fractional amount of overhanging cards as they accumulate becomes less and less. He explores various types of series such as the harmonic series.
In chapter 2, Bernhard Riemann is introduced and a brief historical account of Eastern Europe
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https://en.wikipedia.org/wiki/Smoothed-particle%20hydrodynamics
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Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a meshfree Lagrangian method (where the co-ordinates move with the fluid), and the resolution of the method can easily be adjusted with respect to variables such as density.
Method
Advantages
By construction, SPH is a meshfree method, which makes it ideally suited to simulate problems dominated by complex boundary dynamics, like free surface flows, or large boundary displacement.
The lack of a mesh significantly simplifies the model implementation and its parallelization, even for many-core architectures.
SPH can be easily extended to a wide variety of fields, and hybridized with some other models, as discussed in Modelling Physics.
As discussed in section on weakly compressible SPH, the method has great conservation features.
The computational cost of SPH simulations per number of particles is significantly less than the cost of grid-based simulations per number of cells when the metric of interest is related to fluid density (e.g., the probability density function of density fluctuations). This is the case because in SPH the resolution is put where the matter is.
Limitations
Setting boundary
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https://en.wikipedia.org/wiki/Open%20University%20of%20Catalonia
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The Open University of Catalonia (; ) is a private open university based in Barcelona, Spain.
The UOC offers graduate and postgraduate programs in Catalan, Spanish and English in fields such as Psychology, Computer Science, Education sciences, Information and Knowledge Society, and Economics. Also, an Information and Knowledge Society Doctoral Program is available that explores research fields such as e-law, e-learning, network society, education, and online communities. It has support centers in a number of cities in Spain, Andorra, Mexico and Colombia.
History
The UOC was created in 1994 following a by the Parliament of Catalonia, by which the Government of the Generalitat of Catalonia was urged to adopt the relevant measures to consolidate a teaching distance learning system. It was constituted through a public deed on October 6, 1994, adopting the legal form of a foundation, the Fundació per la Universitat Oberta de Catalunya. At the same time, the UOC was recognized through the Law of the Parliament of Catalonia 3/1995, of April 6, recognizing it as a member of the catalan universities system.
It was born with the mission of offering lifelong learning, of encouraging that every person who wants to improve their abilities and skills can access the university, and in this way to grow the educational level and skills of society in general.
Organization and administration
UOC is governed by a Foundation (Fundació per a la Universitat Oberta de Catalunya, FUOC). The ad
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https://en.wikipedia.org/wiki/Jerome%20Karle
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Jerome Karle (born Jerome Karfunkle; June 18, 1918 – June 6, 2013) was an American physical chemist. Jointly with Herbert A. Hauptman, he was awarded the Nobel Prize in Chemistry in 1985, for the direct analysis of crystal structures using X-ray scattering techniques.
Early life and education
Karle was born in New York City, on June 18, 1918, the son of Sadie Helen (Kun) and Louis Karfunkle. He was born into a Jewish family with a strong interest in the arts. He had played piano as a youth and had participated in a number of competitions, but he was far more interested in science. He attended Abraham Lincoln High School in Brooklyn, and would later join Arthur Kornberg (awarded the Nobel in Medicine in 1959) and Paul Berg (a winner in Chemistry in 1980), as graduates of the school to win Nobel Prizes. As a youth, Karle enjoyed handball, ice skating, touch football and swimming in the nearby Atlantic Ocean.
He started college at the age of 15 and received his bachelor's degree from the City College of New York in 1937, where he took additional courses in biology, chemistry and math in addition to the required curriculum there. He earned a master's degree from Harvard University in 1938, having majored in biology.
As part of a plan to accumulate enough money to pay for further graduate studies, Karle took a position in Albany, New York with the New York State Department of Health, where he developed a method to measure dissolved fluoride levels, a technique that would become
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https://en.wikipedia.org/wiki/Point%20particle
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A point particle, ideal particle or point-like particle (often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space. A point particle is an appropriate representation of any object whenever its size, shape, and structure are irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. Point masses and point charges, discussed below, are two common cases. When a point particle has an additive property, such as mass or charge, it is often represented mathematically by a Dirac delta function.
In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume. For example, the atomic orbit of an electron in the hydrogen atom occupies a volume of ~. There is nevertheless a distinction between elementary particles such as electrons or quarks, which have no known internal structure, versus composite particles such as protons, which do have internal structure: A proton is made of three quarks.
Elementary particles are sometimes called "point particles" in reference to their lack of internal structure, but this is in a different sense than discussed above.
Point mass
Point mass (pointlike mass) is the concept, for example in classical physics, o
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https://en.wikipedia.org/wiki/Cayley%27s%20formula
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In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley. It states that for every positive integer , the number of trees on labeled vertices is .
The formula equivalently counts the number of spanning trees of a complete graph with labeled vertices .
Proof
Many proofs of Cayley's tree formula are known.
One classical proof of the formula uses Kirchhoff's matrix tree theorem, a formula for the number of spanning trees in an arbitrary graph involving the determinant of a matrix. Prüfer sequences yield a bijective proof of Cayley's formula. Another bijective proof, by André Joyal, finds a one-to-one transformation between n-node trees with two distinguished nodes and maximal directed pseudoforests.
A proof by double counting due to Jim Pitman counts in two different ways the number of different sequences of directed edges that can be added to an empty graph on n vertices to form from it a rooted tree; see .
History
The formula was first discovered by Carl Wilhelm Borchardt in 1860, and proved via a determinant. In a short 1889 note, Cayley extended the formula in several directions, by taking into account the degrees of the vertices. Although he referred to Borchardt's original paper, the name "Cayley's formula" became standard in the field.
Other properties
Cayley's formula immediately gives the number of labelled rooted forests on n vertices, namely .
Each labelled rooted forest can be turned into a labelled tree with one extra vertex,
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https://en.wikipedia.org/wiki/David%20C.%20Geary
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David Cyril Geary (born June 7, 1957, in Providence, Rhode Island) is an American cognitive developmental and evolutionary psychologist with interests in mathematical learning and sex differences. He is currently a Curators’ Professor and Thomas Jefferson Fellow in the Department of Psychological Sciences and Interdisciplinary Neuroscience Program at the University of Missouri in Columbia, Missouri.
Education
Geary received a BS degree in psychology from Santa Clara University (California) in 1979, and an MS from the clinical child/school psychology program at California State University at Hayward (now East Bay) in 1981. After completing the MS degree, he worked for the emergency treatment center of the Mental Research Institute in Palo Alto, California, and began the Ph.D. program at the University of California, Riverside, in 1982. His initial interests were in hemispheric laterality and associated sex differences, but focused his dissertation work on mathematical cognition under the direction of Keith Widaman (now at UC, Davis).
Career
After completing his Ph.D. in developmental psychology in 1986, Geary took a one-year position at the University of Texas at El Paso and then moved to the University of Missouri, first at the Rolla campus (1987–1989) and then in Columbia. During this time, he served as chair of the Department of Psychological Sciences (2002–2005) and contributed heavily to the creation of the Ph.D. program in developmental psychology.
Research
Geary's w
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https://en.wikipedia.org/wiki/Radical%20substitution
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In organic chemistry, a radical-substitution reaction is a substitution reaction involving free radicals as a reactive intermediate.
The reaction always involves at least two steps, and possibly a third.
In the first step called initiation (2,3), a free radical is created by homolysis. Homolysis can be brought about by heat or ultraviolet light, but also by radical initiators such as organic peroxides or azo compounds. UV Light is used to create two free radicals from one diatomic species. The final step is called termination (6,7), in which the radical recombines with another radical species. If the reaction is not terminated, but instead the radical group(s) go on to react further, the steps where new radicals are formed and then react are collectively known as propagation (4,5). This is because a new radical is created, able to participate in secondary reactions.
Radical substitution reactions
In free radical halogenation reactions, radical substitution takes place with halogen reagents and alkane substrates. Another important class of radical substitutions involve aryl radicals. One example is the hydroxylation of benzene by Fenton's reagent. Many oxidation and reduction reactions in organic chemistry have free radical intermediates, for example the oxidation of aldehydes to carboxylic acids with chromic acid. Coupling reactions can also be considered radical substitutions. Certain aromatic substitutions takes place by radical-nucleophilic aromatic substitution. Aut
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https://en.wikipedia.org/wiki/Sympatry
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In biology, two related species or populations are considered sympatric when they exist in the same geographic area and thus frequently encounter one another. An initially interbreeding population that splits into two or more distinct species sharing a common range exemplifies sympatric speciation. Such speciation may be a product of reproductive isolation – which prevents hybrid offspring from being viable or able to reproduce, thereby reducing gene flow – that results in genetic divergence. Sympatric speciation may, but need not, arise through secondary contact, which refers to speciation or divergence in allopatry followed by range expansions leading to an area of sympatry. Sympatric species or taxa in secondary contact may or may not interbreed.
Types of populations
Four main types of population pairs exist in nature. Sympatric populations (or species) contrast with parapatric populations, which contact one another in adjacent but not shared ranges and do not interbreed; peripatric species, which are separated only by areas in which neither organism occurs; and allopatric species, which occur in entirely distinct ranges that are neither adjacent nor overlapping. Allopatric populations isolated from one another by geographical factors (e.g., mountain ranges or bodies of water) may experience genetic—and, ultimately, phenotypic—changes in response to their varying environments. These may drive allopatric speciation, which is arguably the dominant mode of speciation.
Evolv
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https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Hopf%20theorem
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In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology. It is named after Henri Poincaré and Heinz Hopf.
The Poincaré–Hopf theorem is often
illustrated by the special case of the hairy ball theorem, which simply states that there is no smooth vector field on an even-dimensional n-sphere having no sources or sinks.
Formal statement
Let be a differentiable manifold, of dimension , and a vector field on . Suppose that is an isolated zero of , and fix some local coordinates near . Pick a closed ball centered at , so that is the only zero of in . Then the index of at , , can be defined as the degree of the map from the boundary of to the -sphere given by .
Theorem. Let be a compact differentiable manifold. Let be a vector field on with isolated zeroes. If has boundary, then we insist that be pointing in the outward normal direction along the boundary. Then we have the formula
where the sum of the indices is over all the isolated zeroes of and is the Euler characteristic of . A particularly useful corollary is when there is a non-vanishing vector field implying Euler characteristic 0.
The theorem was proven for two dimensions by Henri Poincaré and later generalized to higher dimensions by Heinz Hopf.
Significance
The Euler characteristic of a closed surface is a purely topological concept, whereas the index o
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https://en.wikipedia.org/wiki/TU%20Wien
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TU Wien (), also known as the Vienna University of Technology, is a public research university in Vienna, Austria.
The university's teaching and research are focused on engineering, computer science, and natural sciences. It currently has about 28,100 students (29% women), eight faculties, and about 5,000 staff members (3,800 academics).
History
The institution was founded in 1815 by Emperor Francis I of Austria as the k.k. Polytechnische Institut (Imperial-Royal Polytechnic Institute). The first rector was Johann Joseph von Prechtl. It was renamed the Technische Hochschule (College of Technology) in 1872. When it began granting doctoral and higher degrees in 1975, it was renamed the Technische Universität Wien (Vienna University of Technology).
Academic reputation
As a university of technology, TU Wien covers a wide spectrum of scientific concepts from abstract pure research and the fundamental principles of science to applied technological research and partnership with industry.
TU Wien is ranked #192 by the QS World University Ranking, #406 by the Center of World University Rankings, and it is positioned among the best 401-500 higher education institutions globally by the Times Higher Education World University Rankings. The computer science department has been consistently ranked among the top 100 in the world by the QS World University Ranking and The Times Higher Education World University Rankings respectively.
Organization
TU Wien has eight faculties led by de
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https://en.wikipedia.org/wiki/Jacques-Louis%20Soret
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Jacques-Louis Soret (30 June 1827 – 13 May 1890) was a Swiss chemist and spectroscopist. He studied both spectroscopy and electrolysis.
Career
Soret held the chairs of chemistry (1873-1887) and medical physics (1887-1890) at the University of Geneva.
Soret determined the chemical composition and density of ozone and the conditions for its production. He described it correctly as being composed of three oxygen atoms bound together.
Soret also developed optical instruments. He climbed Mont Blanc, where he was the first scientist to make actinometric measurements of solar radiation. These observations were published in the Philosophical Magazine in 1867.
In 1878, he and Marc Delafontaine were the first to spectroscopically observe the element later named holmium, which they identified simply as an "earth X" derived from "erbia". Independently, Per Teodor Cleve separated it chemically from thulium and erbium in 1879. All three researchers are given credit for the element's discovery.
The Soret peak or Soret band, a strong absorption band at approximately 420 nm in the absorption spectra of hemoglobin, is also named after him.
Death
Jacques-Louis Soret died in Geneva on 13 May 1890.
His son was Charles Soret, a recognized physicist and chemist in his own right.
References
Swiss chemists
1827 births
1890 deaths
Discoverers of chemical elements
Rare earth scientists
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https://en.wikipedia.org/wiki/Variable%20speed%20of%20light
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A variable speed of light (VSL) is a feature of a family of hypotheses stating that the speed of light may in some way not be constant, for example, that it varies in space or time, or depending on frequency. Accepted classical theories of physics, and in particular general relativity, predict a constant speed of light in any local frame of reference and in some situations these predict apparent variations of the speed of light depending on frame of reference, but this article does not refer to this as a variable speed of light. Various alternative theories of gravitation and cosmology, many of them non-mainstream, incorporate variations in the local speed of light.
Attempts to incorporate a variable speed of light into physics were made by Robert Dicke in 1957, and by several researchers starting from the late 1980s.
VSL should not be confused with faster than light theories, its dependence on a medium's refractive index or its measurement in a remote observer's frame of reference in a gravitational potential. In this context, the "speed of light" refers to the limiting speed c of the theory rather than to the velocity of propagation of photons.
Historical proposals
Background
Einstein's equivalence principle, on which general relativity is founded, requires that in any local, freely falling reference frame, the speed of light is always the same. This leaves open the possibility, however, that an inertial observer inferring the apparent speed of light in a distant region
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https://en.wikipedia.org/wiki/Paxos%20%28disambiguation%29
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Paxos or Paxi is a Greek island in the Ionian sea.
Paxos may also refer to:
Paxos (computer science), a family of algorithms
Paxos Trust Company, an American financial institution and technology company
See also
Paxo
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https://en.wikipedia.org/wiki/Mercury%28I%29%20chloride
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Mercury(I) chloride is the chemical compound with the formula Hg2Cl2. Also known as the mineral calomel (a rare mineral) or mercurous chloride, this dense white or yellowish-white, odorless solid is the principal example of a mercury(I) compound. It is a component of reference electrodes in electrochemistry.
History
The name calomel is thought to come from the Greek καλός "beautiful", and μέλας "black"; or καλός and μέλι "honey" from its sweet taste. The "black" name (somewhat surprising for a white compound) is probably due to its characteristic disproportionation reaction with ammonia, which gives a spectacular black coloration due to the finely dispersed metallic mercury formed. It is also referred to as the mineral horn quicksilver or horn mercury.
Calomel was taken internally and used as a laxative, for example to treat George III in 1801, and disinfectant, as well as in the treatment of syphilis, until the early 20th century. Until fairly recently, it was also used as a horticultural fungicide, most notably as a root dip to help prevent the occurrence of clubroot amongst crops of the family Brassicaceae.
Mercury became a popular remedy for a variety of physical and mental ailments during the age of "heroic medicine". It was prescribed by doctors in America throughout the 18th century, and during the revolution, to make patients regurgitate and release their body from "impurities". Benjamin Rush was a well-known advocate of mercury in medicine and used calomel to t
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https://en.wikipedia.org/wiki/Neurophenomenology
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Neurophenomenology refers to a scientific research program aimed to address the hard problem of consciousness in a pragmatic way. It combines neuroscience with phenomenology in order to study experience, mind, and consciousness with an emphasis on the embodied condition of the human mind. The field is very much linked to fields such as neuropsychology, neuroanthropology and behavioral neuroscience (also known as biopsychology) and the study of phenomenology in psychology.
Overview
The label was coined by C. Laughlin, J. McManus and E. d'Aquili in 1990. However, the term was appropriated and given a distinctive understanding by the cognitive neuroscientist Francisco Varela in the mid-1990s, whose work has inspired many philosophers and neuroscientists to continue with this new direction of research.
Phenomenology is a philosophical method of inquiry of everyday experience. The focus in phenomenology is on the examination of different phenomena (from Greek, phainomenon, "that which shows itself") as they appear to consciousness, i.e. in a first-person perspective. Thus, phenomenology is a discipline particularly useful for understanding how it is that appearances present themselves to us and how it is that we attribute meaning to them.
Neuroscience is the scientific study of the brain, and deals with the third-person aspects of consciousness. Some scientists studying consciousness believe that the exclusive utilization of either first- or third-person methods will not provid
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https://en.wikipedia.org/wiki/Hankel%20contour
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In mathematics, a Hankel contour is a path in the complex plane which extends from
(+∞,δ), around the origin counter clockwise and back to
(+∞,−δ), where δ is an arbitrarily small positive number. The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values of x. The Hankel contour can also be represented by a path that has mirror images just above and below the real axis, connected to a circle of radius ε, centered at the origin, where ε is an arbitrarily small number. The two linear portions of the contour are said to be a distance of δ from the real axis. Thus, the total distance between the linear portions of the contour is 2δ. The contour is traversed in the positively-oriented sense, meaning that the circle around the origin is traversed counter-clockwise.
Use of Hankel contours is one of the methods of contour integration. This type of path for contour integrals was first used by Hermann Hankel in his investigations of the Gamma function.
The Hankel contour is used to evaluate integrals such as the Gamma function, the Riemann zeta function, and other Hankel functions (which are Bessel functions of the third kind).
Applications
The Hankel contour and the Gamma function
The Hankel contour is helpful in expressing and solving the Gamma function in the complex t-plane. The Gamma function can be defined for any complex value in the plane if we evaluate the integral along the Hankel contour. The Hankel contou
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https://en.wikipedia.org/wiki/Harold%20Pender
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Harold Pender (13 January 1879, Tarboro, North Carolina – 6 Kennebunkport, Maine1959) was an American academic, author, and inventor. He was the first Dean of the University of Pennsylvania's Moore School of Electrical Engineering, a position he held from the founding of the School in 1923 until his retirement in 1949. During his tenure, the Moore School built the ENIAC, the first general-purpose electronic digital computer, and began construction of its successor machine, the EDVAC. Pender also proposed the Moore School Lectures, the first course in computers, which the Moore School offered by invitation in the summer of 1946.
Pender was elected to the American Academy of Arts and Sciences in 1913 and the American Philosophical Society in 1917.
The Harold Pender Award is named after him.
He and his wife Ailsa had one son, bridge player and figure skater Peter Pender.
References
1879 births
1959 deaths
University of Pennsylvania faculty
American electrical engineers
Fellows of the American Physical Society
Members of the American Philosophical Society
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https://en.wikipedia.org/wiki/Function%20of%20a%20real%20variable
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In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval.
The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers.
Nevertheless, the codomain of a function of a real variable may be any set. However, it is often assumed to have a structure of -vector space over the reals. That is, the codomain may be a Euclidean space, a coordinate vector, the set of matrices of real numbers of a given size, or an -algebra, such as the complex numbers or the quaternions. The structure -vector space of the codomain induces a structure of -vector space on the functions. If the codomain has a structure of -algebra, the same is true for the functions.
The image of a function of a real variable is a curve in the codomain. In this context, a function that defines curve is called a parametric equation of the curve.
When the codomain of a function of a real variable is a finite-dimensional vector space, the function may be viewed as a sequence of real functions. This is often used in applications.
Real function
A real function is a function from a subset of to where
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https://en.wikipedia.org/wiki/Graham%20Cairns-Smith
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Alexander Graham Cairns-Smith FRSE (24 November 1931 – 26 August 2016) was an organic chemist and molecular biologist at the University of Glasgow. He studied at the University of Edinburgh, where he gained a Ph.D. in Chemistry (1957). He was most famous for his controversial 1985 book Seven Clues to the Origin of Life.
The book popularized a hypothesis he began to develop in the mid-1960s—that self-replication of clay crystals in solution might provide a simple intermediate step between biologically inert matter and organic life. He inspired other ideas about chemical evolution, including the Miller–Urey experiment and the RNA World, all of which are hypotheses that have played important roles in attempts to understand the origin of life.
Cairns-Smith also published on the evolution of consciousness, in Evolving the Mind (1996), favoring a role for quantum mechanics in human thought. He died on 26 August 2016.
Clay hypothesis
The clay hypothesis suggests how biologically inert matter helped the evolution of early life forms: clay minerals form naturally from silicates in solution. Clay crystals, as other crystals, preserve their external formal arrangement as they grow, snap, and grow further. Clay crystal masses of a particular external form may happen to affect their environment in ways that affect their chances of further replication. For example, a "stickier" clay crystal is more likely to silt a stream bed, creating an environment conducive to further sedimentation.
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https://en.wikipedia.org/wiki/Sharaf%20al-Din%20Ali%20Yazdi
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Sharaf ad-Din Ali Yazdi or Sharif al-Din Ali’ Yazdi (; died 1454, Yazd), also known by his pen name Sharaf, was a 15th-century Persian scholar who authored several works in the arts and sciences, including mathematics, astronomy, enigma, literature such as poetry, and history. The Zafarnama, a life of Timur, is his most famous work.
Sharif al-Din was born in the city of Yazd, Iran in the 1370s. He devoted much of his life to scholarship, furthering his education in Syria and Egypt until Timur's death in 1405.
As a young man, he was a teacher in his native city of Yazd and a close companion of the Timurid ruler Shahrukh (1405–47) and his son Ibrahim Sultan. In 1442/43 he became the close advisor of the governor of Iraq, Mirza Sultan Muhammad, who lived in the city of Qom.
Sharif al-Din rebelled against Shahrukh Timur in 1446/47 when the government was vulnerable, but was later sent to different cities for his acumen. The later years of his life were spent in Taft, where he died in 1454.
Sharif al-Din was directed to write a biography of Timur in 1421 known as the Zafarnama, which he completed four years later in 1425. Timur's grandson Sultan Abu al-Fath Ibrahim Mirza was Sharif al-Din's patron during the completion of his grandfather's biography.
Translated works
The History of Timur-Bec: Known by the Name of Tamerlain the Great, Emperor of the Moguls and Tartars: Being an Historical Journal of His Conquests in Asia and Europe, Volume 2 (1723)
References
External li
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https://en.wikipedia.org/wiki/Legendre%20chi%20function
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In mathematics, the Legendre chi function is a special function whose Taylor series is also a Dirichlet series, given by
As such, it resembles the Dirichlet series for the polylogarithm, and, indeed, is trivially expressible in terms of the polylogarithm as
The Legendre chi function appears as the discrete Fourier transform, with respect to the order ν, of the Hurwitz zeta function, and also of the Euler polynomials, with the explicit relationships given in those articles.
The Legendre chi function is a special case of the Lerch transcendent, and is given by
Identities
Integral relations
References
Special functions
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https://en.wikipedia.org/wiki/Robert%20Gunning
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Robert Gunning may refer to:
Sir Robert Gunning, 1st Baronet (1731–1816), British diplomat
Robert C. Gunning, professor of mathematics at Princeton University
Robert Halliday Gunning (1818–1900), Scottish physician
Robert Gunning, American businessman, creator of the Gunning fog index of readability
Robert Gunning, musician, guitarist for The Infected
Sir Robert Gunning, 3rd Baronet (1795–1862), of the Gunning baronets, MP for Northampton
Sir Robert Charles Gunning, 8th Baronet (1901–1989), of the Gunning baronets
See also
Gunning (disambiguation)
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https://en.wikipedia.org/wiki/Methoxy%20group
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In organic chemistry, a methoxy group is the functional group consisting of a methyl group bound to oxygen. This alkoxy group has the formula .
On a benzene ring, the Hammett equation classifies a methoxy substituent at the para position as an electron-donating group, but as an electron-withdrawing group if at the meta position. At the ortho position, steric effects are likely to cause a significant alteration in the Hammett equation prediction which otherwise follows the same trend as that of the para position.
Occurrence
The simplest of methoxy compounds are methanol and dimethyl ether. Other methoxy ethers include anisole and vanillin. Many metal alkoxides contain methoxy groups, such as tetramethyl orthosilicate and titanium methoxide. Esters with a methoxy group can be referred to as methyl esters, and the —COOCH3 substituent is called a methoxycarbonyl.
Biosynthesis
In nature, methoxy groups are found on nucleosides that have been subjected to 2′-O-methylation, for example in variations of the 5′-cap structure known as cap-1 and cap-2. They are also common substituents in O-methylated flavonoids, whose formation is catalyzed by O-methyltransferases that act on phenols, such as catechol-O-methyl transferase (COMT). Many natural products in plants, such as lignins, are generated via catalysis by caffeoyl-CoA O-methyltransferase.
Methoxylation
Organic methoxides are often produced by methylation of alkoxides. Some aryl methoxides can be synthesized by metal-catalyzed m
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https://en.wikipedia.org/wiki/Random%20minimum%20spanning%20tree
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In mathematics, a random minimum spanning tree may be formed by assigning random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of the graph.
When the given graph is a complete graph on vertices, and the edge weights have a continuous distribution function whose derivative at zero is , then the expected weight of its random minimum spanning trees is bounded by a constant, rather than growing as a function of . More precisely, this constant tends in the limit (as goes to infinity) to , where is the Riemann zeta function and is Apéry's constant. For instance, for edge weights that are uniformly distributed on the unit interval, the derivative is , and the limit is just .
In contrast to uniformly random spanning trees of complete graphs, for which the typical diameter is proportional to the square root of the number of vertices, random minimum spanning trees of complete graphs have typical diameter proportional to the cube root.
Random minimum spanning trees of grid graphs may be used for invasion percolation models of liquid flow through a porous medium, and for maze generation.
References
Spanning tree
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https://en.wikipedia.org/wiki/Sergey%20Katanandov
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Sergey Leonidovich Katanandov () is the former leader of the Republic of Karelia, an autonomous entity of Russia, in 1998–2010, first as Prime Minister, then as Head of the Republic.
Katanandov was born in 1955, in the Karelian capital of Petrozavodsk. Educated in civil engineering and law, Katanandov served as Mayor of Petrozavodsk from 1990 to 1998, and became Chairman of the Government of Karelia in 1998. From May 2002 till June 30, 2010, he was the Head of the Republic of Karelia.
Biography
Katanandov was born to Karelian parents in Petrozavodsk on April 21, 1955. He graduated from the Faculty of industrial and civil construction of Petrozavodsk State University in 1977. After graduation he worked as a foreman at a construction site. This was followed by a foreman, chief of section, chief engineer of SMU-1 Trust "Petrozavodskstroy, chief engineer of the trust, the head of design and construction of large housing associations. Eventually he ended up becoming a popular politician in Russia. In April 2000, was awarded the Order of Honor. Katanandov is married, and has two sons.
External links
Government of Karelia - Sergey Katanandov
1955 births
Living people
People from Petrozavodsk
Mayors of Petrozavodsk
Heads of the Republic of Karelia
United Russia politicians
21st-century Russian politicians
Members of the Federation Council of Russia (after 2000)
Prime Ministers of the Republic of Karelia
Deputies of the Legislative Assembly of the Republic of Karelia
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https://en.wikipedia.org/wiki/QED%3A%20The%20Strange%20Theory%20of%20Light%20and%20Matter
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QED: The Strange Theory of Light and Matter is an adaptation for the general reader of four lectures on quantum electrodynamics (QED) published in 1985 by American physicist and Nobel laureate Richard Feynman.
QED was designed to be a popular science book, written in a witty style, and containing just enough quantum-mechanical mathematics to allow the solving of very basic problems in quantum electrodynamics by an educated lay audience. It is unusual for a popular science book in the level of mathematical detail it goes into, actually allowing the reader to solve simple optics problems, as might be found in an actual textbook. But unlike in a typical textbook, the mathematics is taught in very simple terms, with no attempt to solve problems efficiently, use standard terminology, or facilitate further advancement in the field. The focus instead is on nurturing a basic conceptual understanding of what is really going on in such calculations. Complex numbers are taught, for instance, by asking the reader to imagine that there are tiny clocks attached to subatomic particles. The book was first published in 1985 by the Princeton University Press.
The book
In an acknowledgement Feynman wrote:
This book purports to be a record of the lectures on quantum electrodynamics I gave at UCLA, transcribed and edited by my good friend Ralph Leighton. Actually, the manuscript has undergone considerable modification. Mr. Leighton's experience in teaching and in writing was of considerable va
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https://en.wikipedia.org/wiki/Organochlorine%20chemistry
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Organochlorine chemistry is concerned with the properties of organochlorine compounds, or organochlorides, organic compounds containing at least one covalently bonded atom of chlorine. The chloroalkane class (alkanes with one or more hydrogens substituted by chlorine) includes common examples. The wide structural variety and divergent chemical properties of organochlorides lead to a broad range of names, applications, and properties. Organochlorine compounds have wide use in many applications, though some are of profound environmental concern, with TCDD being one of the most notorious.
Physical and chemical properties
Chlorination modifies the physical properties of hydrocarbons in several ways. These compounds are typically denser than water due to the higher atomic weight of chlorine versus hydrogen. They have higher boiling and melting points compared to related hydrocarbons. Aliphatic organochlorides are often alkylating agents as chlorine can act as a leaving group, which can result in cellular damage.
Natural occurrence
Many organochlorine compounds have been isolated from natural sources ranging from bacteria to humans. Chlorinated organic compounds are found in nearly every class of biomolecules and natural products including alkaloids, terpenes, amino acids, flavonoids, steroids, and fatty acids. Dioxins, which are of particular concern to human and environmental health, are produced in the high temperature environment of forest fires and have been found in the pre
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https://en.wikipedia.org/wiki/Projective%20line%20over%20a%20ring
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In mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A with 1, the projective line P(A) over A consists of points identified by projective coordinates. Let U be the group of units of A; pairs and from are related when there is a u in U such that and . This relation is an equivalence relation. A typical equivalence class is written U[a, b].
that is, U[a, b] is in the projective line if the ideal generated by a and b is all of A.
The projective line P(A) is equipped with a group of homographies. The homographies are expressed through use of the matrix ring over A and its group of units V as follows: If c is in Z(U), the center of U, then the group action of matrix on P(A) is the same as the action of the identity matrix. Such matrices represent a normal subgroup N of V. The homographies of P(A) correspond to elements of the quotient group .
P(A) is considered an extension of the ring A since it contains a copy of A due to the embedding
. The multiplicative inverse mapping , ordinarily restricted to the group of units U of A, is expressed by a homography on P(A):
Furthermore, for , the mapping can be extended to a homography:
Since u is arbitrary, it may be substituted for u−1.
Homographies on P(A) are called linear-fractional transformations since
Instances
Rings that are fields are most familiar: The projective line over GF(2) has three elements: , , and . Its homography group is the
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https://en.wikipedia.org/wiki/Dope
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Dope may refer to:
Chemistry
Biochemistry
Dope, a slang word for a euphoria-producing drug, particularly:
Cocaine
Cannabis (drug)
Heroin
Opium
DOPE, or 1,2-Dioleoyl-sn-glycero-3-phosphoethanolamine, a phospholipid
Discrete optimized protein energy, a method of assessing homology models in protein structure prediction
Dopamine, also colloquially called "dope", a neurotransmitter in the human brain that causes pleasure
Dopant, an impurity added to a substance to alter its properties
Industrial substances
Aircraft dope, a substance painted onto fabric-covered aircraft to tauten the skin
Dope, a technical expression for the solution of polymers from which fibers are spun; see Wet processing engineering
Peg dope, a substance used to coat the bearing surfaces of the tuning pegs of string instruments
Pipe dope, a sealant applied to pipe threads to ensure a leakproof and pressure-tight seal
Arts, entertainment, and media
Films
Dope (1924 film), a 1924 Australian silent film
Dope (2015 film), a 2015 film starring Shameik Moore, Zoë Kravitz and A$AP Rocky
Literature
Dope (novel), a 1919 novel by Sax Rohmer
DOPE (an acronym for Data on Personal Equipment, or Data on Previous Engagement), a book used with sniper equipment
Music
Groups
Dope (band), an industrial metal band from the U.S. city of Villa Park, Illinois
Edsel Dope (born 1974), the lead singer and rhythm guitarist of the band Dope
Dope D.O.D., a Dutch hip hop crew
D.O.P.E., a Southern hip hop grou
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https://en.wikipedia.org/wiki/Institut%20de%20g%C3%A9nie%20informatique%20et%20industriel
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Ingénieur en Génie Informatique et Industriel (IG2I, EC-Lille) is an information engineering school in Lens, France.
Founded in 1992 by "Ecole Centrale de Lille", it offers courses in computer Science, networking, and industrial engineering.
References
IG2I web-site in French
IG2I page on Facebook
Grandes écoles
Educational institutions established in 1992
1992 establishments in France
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https://en.wikipedia.org/wiki/Drop%20tube
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In physics and materials science, a drop tower or drop tube is a structure used to produce a controlled period of weightlessness for an object under study. Air bags, polystyrene pellets, and magnetic or mechanical brakes are sometimes used to arrest the fall of the experimental payload. In other cases, high-speed impact with a substrate at the bottom of the tower is an intentional part of the experimental protocol.
Not all such facilities are towers: NASA Glenn's Zero Gravity Research Facility is based on a vertical shaft, extending to below ground level.
Typical operation
For a typical materials science experiment, a sample of the material under study is loaded into the top of the drop tube, which is filled with inert gas or evacuated to create a low-pressure environment. Following any desired preprocessing (e.g. induction heating to melt a metal alloy), the sample is released to fall to the bottom of the tube. During its flight or upon impact the sample can be characterized with instruments such as cameras and pyrometers.
Drop towers are also commonly used in combustion research. For this work, oxygen must be present and the payload may be enclosed in a drag shield to isolate it from high-speed "wind" as the apparatus accelerates toward the bottom of the tower. See a video of a microgravity combustion experiment in the NASA Glenn Five Second Drop Facility at .
Fluid physics experiments and development and testing of space-based hardware can also be conducted usi
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https://en.wikipedia.org/wiki/Hans-Peter%20D%C3%BCrr
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Hans-Peter Dürr (7 October 1929 – 18 May 2014) was a German physicist. He worked on nuclear and quantum physics, elementary particles and gravitation, epistemology, and philosophy, and he advocated responsible scientific and energy policies. In 1987, he was awarded the Right Livelihood Award for "his profound critique of the Strategic Defense Initiative (SDI) and his work to convert high technology to peaceful uses."
Biography
Born in Stuttgart. Between 1978 and 1992 he was executive Director of the Max Planck Institute for Physics and Astrophysics in Munich several times. He was Vice executive director at the Max Planck Institute for Physics (Werner-Heisenberg-Institute) 1972-1977, 1981–1986 and 1993-1995. Until 1997 he was professor of physics at the Ludwig Maximilian University, both in Munich, Germany.
Dürr completed his Ph.D. in 1956 after studying physics in Stuttgart (Dipl.-Phys. 1953) and at University of California, Berkeley, supervised by Edward Teller. In 1962 he was a guest professor in Berkeley, California and Madras, India.
As "the" follower of Werner Heisenberg, he specialized in nuclear physics, quantum physics, elementary particles and gravitation, epistemology and philosophy. He was Heisenberg's closest ally in their attempts to develop a unified field theory of elementary particles. He also champions various social justice causes, and helped fund the "David against Goliath" organization protesting against a nuclear fuel reprocessing plant in Bavaria.
I
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https://en.wikipedia.org/wiki/Exsecant
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The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, astronomy, and spherical trigonometry and could help improve accuracy, but are rarely used today except to simplify some calculations.
Exsecant
The exsecant, (Latin: secans exterior) also known as exterior, external, outward or outer secant and abbreviated as exsec or exs, is a trigonometric function defined in terms of the secant function sec(θ):
The name exsecant can be understood from a graphical construction of the various trigonometric functions from a unit circle, such as was used historically. sec(θ) is the secant line , and the exsecant is the portion of this secant that lies exterior to the circle (ex is Latin for out of).
Excosecant
A related function is the excosecant or coexsecant, also known as exterior, external, outward or outer cosecant and abbreviated as excosec, coexsec, excsc or exc, the exsecant of the complementary angle:
Usage
Important in fields such as surveying, railway engineering (for example to lay out railroad curves and superelevation), civil engineering, astronomy, and spherical trigonometry up into the 1980s, the exsecant function is now little-used. Mainly, this is because the broad availability of calculators and computers has removed the need for trigonometric tables of specialized functions such a
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https://en.wikipedia.org/wiki/Cognitive%20development
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Cognitive development is a field of study in neuroscience and psychology focusing on a child's development in terms of information processing, conceptual resources, perceptual skill, language learning, and other aspects of the developed adult brain and cognitive psychology. Qualitative differences between how a child processes their waking experience and how an adult processes their waking experience are acknowledged (such as object permanence, the understanding of logical relations, and cause-effect reasoning in school-age children). Cognitive development is defined as the emergence of the ability to consciously cognize, understand, and articulate their understanding in adult terms. Cognitive development is how a person perceives, thinks, and gains understanding of their world through the relations of genetic and learning factors. There are four stages to cognitive information development. They are, reasoning, intelligence, language, and memory. These stages start when the baby is about 18 months old, they play with toys, listen to their parents speak, they watch tv, anything that catches their attention helps build their cognitive development.
Jean Piaget was a major force establishing this field, forming his "theory of cognitive development". Piaget proposed four stages of cognitive development: the sensorimotor, preoperational, concrete operational, and formal operational period. Many of Piaget's theoretical claims have since fallen out of favor. His description of the
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https://en.wikipedia.org/wiki/Signal%20propagation%20delay
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Propagation delay is the time duration taken for a signal to reach its destination. It can relate to networking, electronics or physics.
Networking
In computer networks, propagation delay is the amount of time it takes for the head of the signal to travel from the sender to the receiver. It can be computed as the ratio between the link length and the propagation speed over the specific medium.
Propagation delay is equal to d / s where d is the distance and s is the wave propagation speed. In wireless communication, s=c, i.e. the speed of light. In copper wire, the speed s generally ranges from .59c to .77c. This delay is the major obstacle in the development of high-speed computers and is called the interconnect bottleneck in IC systems.
Electronics
In electronics, digital circuits and digital electronics, the propagation delay, or gate delay, is the length of time which starts when the input to a logic gate becomes stable and valid to change, to the time that the output of that logic gate is stable and valid to change. Often on manufacturers' datasheets this refers to the time required for the output to reach 50% of its final output level from when the input changes to 50% of its final input level. This may depend on the direction of the level change, in which case separate fall and rise delays tPHL and tPLH or tf and tr are given. Reducing gate delays in digital circuits allows them to process data at a faster rate and improve overall performance. The determination of t
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https://en.wikipedia.org/wiki/Disruptive%20selection
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Disruptive selection, also called diversifying selection, describes changes in population genetics in which extreme values for a trait are favored over intermediate values. In this case, the variance of the trait increases and the population is divided into two distinct groups. In this more individuals acquire peripheral character value at both ends of the distribution curve.
Overview
Natural selection is known to be one of the most important biological processes behind evolution. There are many variations of traits, and some cause greater or lesser reproductive success of the individual. The effect of selection is to promote certain alleles, traits, and individuals that have a higher chance to survive and reproduce in their specific environment. Since the environment has a carrying capacity, nature acts on this mode of selection on individuals to let only the most fit offspring survive and reproduce to their full potential. The more advantageous the trait is the more common it will become in the population. Disruptive selection is a specific type of natural selection that actively selects against the intermediate in a population, favoring both extremes of the spectrum.
Disruptive selection is inferred to oftentimes lead to sympatric speciation through a phyletic gradualism mode of evolution. Disruptive selection can be caused or influenced by multiple factors and also have multiple outcomes, in addition to speciation. Individuals within the same environment can develop a
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