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https://en.wikipedia.org/wiki/Thomas%20B.%20Sheridan
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Thomas B. Sheridan (born December 23, 1929) is American professor of mechanical engineering and Applied Psychology Emeritus at the Massachusetts Institute of Technology. He is a pioneer of robotics and remote control technology.
Early life and education
Sheridan was born Cincinnati, Ohio. In 1951, he received his B.S. degree in Mechanical Engineering from Purdue University, a M.S. Eng. degree from University of California, Los Angeles in 1954, and a Sc.D. degree from the Massachusetts Institute of Technology (MIT) in 1959. He has also received an honorary doctorate from Delft University of Technology in the Netherlands.
Career
For most of his professional career he remained at MIT. He was assistant Professor of Mechanical Engineering from 1959 to 1964. Associate Professor of Mechanical Engineering from 1964 to 1970. Professor of Mechanical Engineering from 1970 to 1984. Professor of Engineering and Applied Psychology since 1984, and Professor of Aeronautics and Astronautics since 1993. In 1995-96 he was Ford Professor.
He is currently Professor Emeritus in the Departments of Mechanical Engineering and Department of Aeronautics and Astronautics. He has also served as a visiting professor at University of California, Berkeley, Stanford, Delft University, Kassel University, Germany, and Ben Gurion University, Israel.
He was co-editor of the MIT Press journal Presence: Teleoperators and Virtual Environments and served on several editorial boards; and was editor of IEEE Transa
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https://en.wikipedia.org/wiki/Epistemic%20modal%20logic
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Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Avicenna, Ockham, and Duns Scotus developed many of their observations, it was C. I. Lewis who created the first symbolic and systematic approach to the topic, in 1912. It continued to mature as a field, reaching its modern form in 1963 with the work of Kripke.
Historical development
Many papers were written in the 1950s that spoke of a logic of knowledge in passing, but the Finnish philosopher G. H. von Wright's 1951 paper titled An Essay in Modal Logic is seen as a founding document. It was not until 1962 that another Finn, Hintikka, would write Knowledge and Belief, the first book-length work to suggest using modalities to capture the semantics of knowledge rather than the alethic statements typically discussed in modal logic. This work laid much of the groundwork for the subject, but a great deal of research has taken place since that time. For example, epistemic logic has been combined recently with some ideas from dynamic logic to create dynamic epistemic logic, which can be used to specify and reason
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https://en.wikipedia.org/wiki/Software%20pipelining
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In computer science, software pipelining is a technique used to optimize loops, in a manner that parallels hardware pipelining. Software pipelining is a type of out-of-order execution, except that the reordering is done by a compiler (or in the case of hand written assembly code, by the programmer) instead of the processor. Some computer architectures have explicit support for software pipelining, notably Intel's IA-64 architecture.
It is important to distinguish software pipelining, which is a target code technique for overlapping loop iterations, from modulo scheduling, the currently most effective known compiler technique for generating software pipelined loops.
Software pipelining has been known to assembly language programmers of machines with instruction-level parallelism since such architectures existed. Effective compiler generation of such code dates to the invention of modulo scheduling by Rau and Glaeser.
Lam showed that special hardware is unnecessary for effective modulo scheduling. Her technique, modulo variable expansion is widely used in practice.
Gao et al. formulated optimal software pipelining in integer linear programming, culminating in validation of advanced heuristics in an evaluation paper. This paper has a
good set of references on the topic.
Example
Consider the following loop:
for i = 1 to bignumber
A(i)
B(i)
C(i)
end
In this example, let A(i), B(i), C(i) be instructions, each operating on data i, that are dependent on each other. I
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https://en.wikipedia.org/wiki/EROS
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EROS may refer to:
Science and technology
Center for Earth Resources Observation and Science, the US national archive of remotely sensed images of the Earth's land surface
Encyclopedia of Reagents for Organic Synthesis, containing a description of the use of all reagents in organic chemistry
Extremely Reliable Operating System, an operating system developed by The EROS Group, the University of Pennsylvania and Johns Hopkins University
Earth Resources Observation Satellite, a series of Israeli commercial Earth observation satellites
Event-related optical signal, a brain-scanning signal
Other uses
Eelam Revolutionary Organisation of Students, a militant Tamil separatist group in Sri Lanka
JDT 1650R EROS, a Mini-MAX aircraft
See also
Eros (disambiguation)
ERO (disambiguation)
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https://en.wikipedia.org/wiki/Weka%20%28software%29
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Waikato Environment for Knowledge Analysis (Weka) is a collection of machine learning and data analysis free software licensed under the GNU General Public License. It was developed at the University of Waikato, New Zealand and is the companion software to the book "Data Mining: Practical Machine Learning Tools and Techniques".
Description
Weka contains a collection of visualization tools and algorithms for data analysis and predictive modeling, together with graphical user interfaces for easy access to these functions. The original non-Java version of Weka was a Tcl/Tk front-end to (mostly third-party) modeling algorithms implemented in other programming languages, plus data preprocessing utilities in C, and a makefile-based system for running machine learning experiments. This original version was primarily designed as a tool for analyzing data from agricultural domains, but the more recent fully Java-based version (Weka 3), for which development started in 1997, is now used in many different application areas, in particular for educational purposes and research. Advantages of Weka include:
Free availability under the GNU General Public License.
Portability, since it is fully implemented in the Java programming language and thus runs on almost any modern computing platform.
A comprehensive collection of data preprocessing and modeling techniques.
Ease of use due to its graphical user interfaces.
Weka supports several standard data mining tasks, more specifically, dat
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https://en.wikipedia.org/wiki/LCP
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LCP may refer to:
Science, medicine and technology
Large Combustion Plant, see Large Combustion Plant Directive
Le Chatelier's principle, equilibrium law in chemistry
Left Circular polarization, in radio communications
Legg–Calvé–Perthes syndrome, hip disorder
Licensed Clinical Psychologist, see Clinical psychology
Ligand close packing theory, in chemistry
Light compensation point, in biology
Linear complementarity problem, in mathematical optimisation
Link Control Protocol, in computer networking
Liquid Crystal Polymer, a kind of polymer
Liverpool Care Pathway for the Dying Patient, care guidance for dying hospital patients
Living cationic polymerization, a process in chemistry
Locking Compression Plate, an implant aiding the healing of a bone fracture
Long-chain polyunsaturated fatty acid
Longest Common Prefix array, in computer science
Organisations
Latvijas Centrālās Padomes, Latvian Central Council
Lebanese Communist Party
Liberal and Country Party, the name of the Victorian division of the Liberal Party of Australia from 1949 to 1965
Liberal Country Party, splinter group of the Victorian branch of the Australian Country Party 1938–1943
Library Company of Philadelphia, US library founded by Benjamin Franklin
London College of Communication, formerly the London College of Printing
Other uses
La Chaîne parlementaire, French parliamentary television channel
Lance Corporal, military rank
Least cost planning methodology, in economics modelling
Little Computer People, 1980
|
https://en.wikipedia.org/wiki/Ecology%20and%20Evolutionary%20Biology
|
Ecology and evolutionary biology is an interdisciplinary field of study concerning interactions between organisms and their ever-changing environment, including perspectives from both evolutionary biology and ecology. This field of study includes topics such as the way organisms respond and evolve, as well as the relationships among animals, plants, and micro-organisms, when their habitats change. Ecology and evolutionary biology is a broad field of study that covers various ranges of ages and scales, which can also help us to comprehend human impacts on the global ecosystem and find measures to achieve more sustainable development.
Examples of current research topics
Birdsong
There is a number of acoustic research about birds. Birds learn to sing in specific patterns because birdsong conveys information to select partners, which is a result of evolution. However, this evolution is also affected by ecological factors. Research with recorded birdsong of male white-crowned sparrows from different regions found that the birdsongs from the same location have the same traits, while birdsongs from different locations are more likely to have different song types. Birdsongs from areas with dense vegetation tend to only have slow trilling sounds and low frequencies, while birdsongs from more open areas have fast trilling sounds and higher frequencies. This is probably due to differences in the propagation of sound through vegetation. Low frequencies can be heard from further away w
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https://en.wikipedia.org/wiki/Richard%20Dalitz
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Richard Henry Dalitz, FRS (28 February 1925 – 13 January 2006) was an Australian physicist known for his work in particle physics.
Education and early life
Born in the town of Dimboola, Victoria, Dalitz studied physics and mathematics at Melbourne University before moving to the United Kingdom in 1946, to study at the University of Cambridge. His PhD was awarded in 1950 for research on zero-zero transitions in the atomic nucleus supervised by Nicholas Kemmer.
Research and career
After his PhD, he took up a one-year post at the University of Bristol, and then joined Rudolf Peierls' group at University of Birmingham. Dalitz moved to Cornell University in 1953. He then became a professor at the Enrico Fermi Institute in Chicago from 1956 to 1963. Next, he moved to the University of Oxford as a Royal Society research professor, although keeping a connection with Chicago until 1966. He retired in 1990.
At Birmingham he completed his thesis demonstrating that the electrically neutral pion could decay into a photon and an electron-positron pair, now known as a Dalitz pair. In addition, he is known for other key developments in particle physics: the Dalitz plot and the Castillejo–Dalitz–Dyson (CDD) poles. The Dalitz plots were discovered in 1953, while he was at Cornell.
Dalitz plots play a central role in the discovery of new particles in current high-energy physics experiments, including Higgs boson research, and are tools in exploratory efforts that might open avenues beyond
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https://en.wikipedia.org/wiki/Howard%20Alper
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Howard Alper, (born October 17, 1941) is a Canadian chemist. He is a Professor of Chemistry at the University of Ottawa. He is best known for his research of catalysis in chemistry.
Career and research
Born in Montreal, Quebec, he received a Bachelor of Science from Sir George Williams University in 1963 and a Ph.D. from McGill University in 1967. In 1968, he started teaching at the State University of New York and became an associate professor in 1971. He joined the University of Ottawa in 1975 as an associate professor and was appointed a Professor in 1978, later being made a Distinguished University Professor in 2006.
He has published over 400 papers, has over forty patents, and has edited several books.
He was the vice-president (Research) of the University of Ottawa from 1997 to 2006. From 2001 to 2003, he was the President of the Royal Society of Canada.
Alper served as the Chair of Canada’s Science, Technology and Innovation Council from 2007 to 2015, and as one of the two co-chairs of the InterAcademy Panel on International Issues from 2006 to 2013.
Honours
He was named a Fellow of the Royal Society of Canada in 1984. In 1998, he was made an Officer of the Order of Canada. In 2000, he was awarded the first Gerhard Herzberg Canada Gold Medal for Science and Engineering, Canada's highest research honour in the field. In 2014, he was made a Commander of the Order of Merit of the Italian Republic. He was elevated to a Companion of the Order of Canada in 2020. In 2015
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https://en.wikipedia.org/wiki/David%20Pritchard
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David Pritchard may refer to:
David Pritchard (chess player) (1919–2005), British chess writer
David Pritchard (cricketer) (1893–1983), Australian cricketer
David Pritchard (footballer) (born 1972), English former footballer
David Pritchard (musician) (born 1949), American guitarist
David E. Pritchard (born 1941), physics professor at the Massachusetts Institute of Technology
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https://en.wikipedia.org/wiki/Claudia%20Zaslavsky
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Claudia Zaslavsky (January 12, 1917 – January 13, 2006) was an American mathematics teacher and ethnomathematician.
Life
She was born Claudia Natoma Cohen (later changed to Cogan) on January 12, 1917, in Upper Manhattan in New York City and grew up in Allentown, Pennsylvania. She attributed her first interest in mathematics to her early childhood experiences when she helped her parents in their dry goods store.
She studied mathematics at Hunter College and then earned a master's degree in statistics at the University of Michigan.
In the 1950's while raising her children she was the bookkeeper at Chelsea Publishing Co. and taught pre-instrument classes to small children.
Math teacher
She became a mathematics teacher at Woodlands High School in Hartsdale, New York.
She pursued postgraduate study in mathematics education at Teachers College, Columbia University, in 1974–1978.
During that time she sought to learn about mathematics in Africa to better capture the interest of the African-American students in her classes.
She discovered "that little of what was known about this topic [African cultural mathematics] was available in accessible sources." Thus began a years-long project of assembling, organizing and interpreting a vast amount of little-known material on expressions of mathematics in diverse African cultures, including number words and signs, reckoning of time, games, and architectural and decorative patterns. Her field work on a trip to East Africa in 1970 w
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https://en.wikipedia.org/wiki/Brian%20Cantwell%20Smith
|
Brian Cantwell Smith is a philosopher and cognitive scientist working in the fields of cognitive science, computer science, information studies, and philosophy, especially ontology.
His research has focused on the foundations and philosophy of computing, both in the practice and theory of computer science, and in the use of computational metaphors in other fields, such as philosophy, cognitive science, physics, and art. He is currently professor of information, computer science, and philosophy at University of Toronto.
Career
Smith received his BS, MS and PhD degrees from the Massachusetts Institute of Technology. Smith's 1982 doctoral dissertation introduced the notion of computational reflection in programming languages, an area of active ongoing research in computer science. Past publications have addressed questions in computational reflection, meta-level architecture, programming languages, and knowledge representation. Over the last decade, his work has focused on fundamental issues in the foundations of epistemology, ontology, and metaphysics.
He was a founder of the Center for the Study of Language and Information at Stanford University, and a founder and first president of Computer Professionals for Social Responsibility. Smith served as principal scientist at the Xerox Palo Alto Research Center, in the 1980s.
Smith is the author of more than 35 articles and three books,. One of his books is called On the Origin of Objects, MIT Press, 1996. He had promised for
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https://en.wikipedia.org/wiki/Formal%20derivative
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In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit, which is in general impossible to define for a ring. Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not.
Formal differentiation is used in algebra to test for multiple roots of a polynomial.
Definition
Fix a ring (not necessarily commutative) and let be the ring of polynomials over .
(If is not commutative, this is the Free algebra over a single indeterminate variable.)
Then the formal derivative is an operation on elements of , where if
then its formal derivative is
In the above definition, for any nonnegative integer and , is defined as usual in a Ring: (with if ).
This definition also works even if does not have a multiplicative identity.
Alternative axiomatic definition
One may also define the formal derivative axiomatically as the map satisfying the following properties.
1) for all
2) The normalization axiom,
3) The map commutes with the addition operation in the polynomial ring,
4) The map satisfies Leibniz's law with respect to the polynomial ring's multiplication operation,
One may prove that this axiomatic definition yields a well-defined map respecti
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https://en.wikipedia.org/wiki/Clyst%20Vale%20Community%20College
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Clyst Vale Community College is a school in Broadclyst, East Devon near Exeter in England, UK. Since April 2011 it has been an academy.
The school is a Microsoft partnership school and therefore specialises in ICT as well as Mathematics and Science. The buildings cater for secondary education from ages 11 to 16 as well as being a sixth form college where people can study for A levels, NVQs and GNVQs. It also acts as an extracurricular college for those of the school and of the community offering after-school hours classes such as Carpentry , Music and Art
Notable former pupils
Jim Causley - Musician (born 1980) -
Luke Newberry - Actor (born 1990) -
Abbie Brown (rugby union) (born 1996) -
Secondary schools in Devon
Academies in Devon
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https://en.wikipedia.org/wiki/Vasily%20Mishin
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Vasily Pavlovich Mishin (; 18 January 1917 – 10 October 2001) was a Russian engineer in the former Soviet Union, and a prominent rocket pioneer, best remembered for the failures in the Soviet space program that took place under his management.
Biography
Mishin was born in Byvalino in the Bogorodsky Uyezd, and studied mathematics at the Moscow Aviation Institute.
Mishin was one of the first Soviet specialists to see Nazi Germany's V-2 facilities at the end of World War II, along with others such as Sergei Korolev, who preceded him as the OKB-1 design bureau head, and Valentin Glushko, who succeeded him.
Mishin worked with Korolev as his deputy in the Experimental Design Bureau working on projects such as the development of the first Soviet ICBM as well in the Sputnik and Vostok programs. He became head of Korolev's OKB-1 design bureau and was the Chief Designer after Korolev's death in 1966, during surgery to remove a tumor from Korolev's colon. He inherited the N1 rocket program, intended to land a man on the Moon, but which turned out to be fatally flawed (largely due to lack of adequate funding).
N1 development began on 14 September 1956, a decade before Mishin took control. It was selected for a lunar landing mission, which required a design capable of putting ninety-five tons of cargo into orbit, up from fifty and later seventy-five ton requirements earlier in development. Under Korolev, a precedent of forgoing much of the usual ground testing had been begun. Accordi
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https://en.wikipedia.org/wiki/Comparability
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In mathematics, two elements x and y of a set P are said to be comparable with respect to a binary relation ≤ if at least one of x ≤ y or y ≤ x is true. They are called incomparable if they are not comparable.
Rigorous definition
A binary relation on a set is by definition any subset of Given is written if and only if in which case is said to be to by
An element is said to be , or (), to an element if or
Often, a symbol indicating comparison, such as (or and many others) is used instead of in which case is written in place of which is why the term "comparable" is used.
Comparability with respect to induces a canonical binary relation on ; specifically, the induced by is defined to be the set of all pairs such that is comparable to ; that is, such that at least one of and is true.
Similarly, the on induced by is defined to be the set of all pairs such that is incomparable to that is, such that neither nor is true.
If the symbol is used in place of then comparability with respect to is sometimes denoted by the symbol , and incomparability by the symbol .
Thus, for any two elements and of a partially ordered set, exactly one of and is true.
Example
A totally ordered set is a partially ordered set in which any two elements are comparable. The Szpilrajn extension theorem states that every partial order is contained in a total order. Intuitively, the theorem says that any method of comparing elements that leaves some pairs
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https://en.wikipedia.org/wiki/Carles%20Sol%C3%A0
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Carles Solà was born in Xàtiva, Valencia Province on 1 January 1945.
He awarded a PhD degree in Chemistry at the UV, he has carried out research in Biochemical Engineering with 130 publications, having tutored 22 doctoral theses and directed various research projects. He was Rector of the UAB (1994-2002). He was a lecturer in Chemical Engineering at the UAB.
President of the Conference of Rectors of Spanish Universities (1996–98). Member of the Executive Committee for the International Association of University Presidents (2000-2002). Member of the Board of the European University Association (2001–05). Member of the Executive Committee of the Spanish Society of Biotechnology (2002–06). Doctor Honoris Causa in Science from the University of Southampton (1999). Member of the American Institute of Chemical Engineers. Member of ACPV. Member of the IEC.
References
1945 births
Living people
People from Xàtiva
Spanish biochemists
University of Valencia alumni
Members of the Institute for Catalan Studies
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https://en.wikipedia.org/wiki/Jerre%20Noe
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Jerre Noe (February 1, 1923 – November 12, 2005) was an American computer scientist. In the 1950s, he led the technical team for the ERMA project, the Bank of America's first venture into computerized banking. In 1968 he became the first chair of the University of Washington's Computer Science Group, which later evolved into the Computer Science and Engineering Department.
Early life and education
Noe was born in McCloud, California. He received a Bachelor's degree in electrical engineering from the University of California, Berkeley. Stationed in Europe during World War II, he conducted research and development related to radar, before returning to California to complete a Ph.D. in electrical engineering at Stanford University.
Career
During the 1950s, Noe served as the assistant director of Engineering at Stanford Research Institute (now SRI International), during which time he led the technical team for the Electronic Recording Machine, Accounting (ERMA) project. Noe and the ERMA team were honored by SRI in 2001 with the Weldon B. Gibson Achievement Award for their work.
In 1968 he was recruited by the University of Washington to chair its newly founded Computer Science Group, a role in which he continued until 1976. Initially, this was mainly a graduate department but in 1975 it introduced a baccalaureate program. In the early 1980s, Noe directed the Eden Project, the first recipient of the National Science Foundation's Coordinated Experimental Research Program award,
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https://en.wikipedia.org/wiki/Theodore%20Cooper
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Theodore Cooper (January 13, 1839 – August 24, 1919) was an American civil engineer. He may be best known as consulting engineer on the Quebec Bridge that collapsed in 1907.
Biography
Upon receiving a degree in civil engineering from Resselaer Institute (now Rensselaer Polytechnic Institute) in 1858, Cooper accepted a position as assistant engineer on the Troy and Greenfield Railroad and Hoosac Tunnel. He entered the Navy in 1861; his military career lasted over a decade and included active duty aboard the gunboat Chocorua and the Nyack in the South Pacific, as well as assignments as an instructor and engineer at the Naval Academy. After resigning from the Navy in 1872 with the rank of first assistant engineer, he was appointed inspector at the Midvale Steel Works by James Eads, designer of the noteworthy Mississippi River steel arch bridge (Eads Bridge) at St. Louis; he succeeded Eads as engineer of the Bridge and Tunnel Company from 1872 to 1875. Cooper was also assistant engineer in charge of the construction of the first elevated railroads in New York City. He was one of the five expert engineers selected by the president to determine the Hudson River bridge span. Cooper was also the consulting engineer for the New York Public Library.
Cooper's designs included a broad variety of structures, ranging from the Laredo Shops of the Mexican National Railroad to the furnace plant of the Lackawanna Coal and Iron Company at Scranton, Pennsylvania, but his most memorable contrib
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https://en.wikipedia.org/wiki/Protein%20trimer
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In biochemistry, a protein trimer is a macromolecular complex formed by three, usually non-covalently bound, macromolecules like proteins or nucleic acids. A homotrimer would be formed by three identical molecules. A heterotrimer would be formed by three different macromolecules. Type II Collagen is an example of homotrimeric protein, while Type I collagen is an AAB-type heterotrimeric protein.
Porins usually arrange themselves in membranes as trimers.
Bacteriophage T4 tail fiber
Multiple copies of a polypeptide encoded by a gene often can form an aggregate referred to as a multimer. When a multimer is formed from polypeptides produced by two different mutant alleles of a particular gene, the mixed multimer may exhibit greater functional activity than the unmixed multimers formed by each of the mutants alone. When a mixed multimer displays increased functionality relative to the unmixed multimers, the phenomenon is referred to as intragenic complementation. The distal portion of each of the bacteriophage T4 tail fibers is encoded by gene 37 and mutants defective in this gene undergo intragenic complementation. This finding indicated that the distal tail fibers are a multimer of the gene 37 encoded polypeptide. An analysis of the complementation data further indicated that the polypeptides making up the multimer were folded back on themselves in the form of a hairpin. A further high-resolution crystal structure analysis of the distal tail fiber indicated that the gene
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https://en.wikipedia.org/wiki/Polyphase
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Polyphase may refer to:
Polyphase matrix, in signal processing
Polyphase system, in electrical engineering
Polyphasic sleep
Polyphase quadrature filter
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https://en.wikipedia.org/wiki/John%20Sealy%20Townsend
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Sir John Sealy Edward Townsend, FRS (7 June 1868 – 16 February 1957) was an Irish-British mathematical physicist who conducted various studies concerning the electrical conduction of gases (concerning the kinetics of electrons and ions) and directly measured the electrical charge. He was a Wykeham Professor of physics at Oxford University.
The phenomenon of the electron avalanche was discovered by him, and is known as the Townsend discharge.
Career
John Townsend was born at Galway in County Galway, Ireland, son of Edward Townsend, a Professor of Civil Engineering at Queen's College Galway and Judith Townsend. In 1885, he entered Trinity College Dublin, was elected a Scholar of the College in 1888, and came top of the class in mathematics with a BA in 1890. He became a Clerk Maxwell Scholar and entered Trinity College, Cambridge, where he became a research student at the same time as Ernest Rutherford. At the Cavendish laboratory, he studied under J. J. Thomson. He developed the "Townsend's collision theory". Townsend supplied important work to the electrical conductivity of gases ("Townsend discharge" circa 1897). This work determined the elementary electrical charge with the droplet method. This method was improved later by Robert Andrews Millikan.
In 1900, Townsend became a Wykeham Professor of Physics at Oxford. In 1901, he discovered the ionization of molecules by ion impact and the dependence of the mean free path on electrons (in gases) of the energy (and his indepen
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https://en.wikipedia.org/wiki/Vant
|
Vant may refer to:
Vant (band), British punk band
Neil Vant, Canadian clergyman and politician
Turmite, a Turing machine in computer science
in India, the title for a high rank amongst the ennobled Hindu retainers of the Nizam of Hyderabad, equivalent to the Muslim nobiliary title Molk
See also
Vantaa
|
https://en.wikipedia.org/wiki/Principles%20of%20Neural%20Science
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First published in 1981 by Elsevier, Principles of Neural Science is an influential neuroscience textbook edited by Columbia University professors Eric R. Kandel, James H. Schwartz, and Thomas M. Jessell. The original edition was 468 pages; now on the sixth edition, the book has grown to 1646 pages. The second edition was published in 1985, third in 1991, fourth in 2000. The fifth was published on October 26, 2012 and included Steven A. Siegelbaum and A.J. Hudspeth as editors. The sixth and latest edition was published on March 8, 2021.
Authors
Editors
Kandel was one of the recipients of the 2000 Nobel Prize in Physiology or Medicine. He is currently a professor of biochemistry, molecular biophysics, physiology, cellular biophysics, and psychiatry at Columbia University. He is a senior investigator at the Howard Hughes Medical Institute and a recipient of the National Medal of Science.
Schwartz was a professor of physiology, cellular biophysics, neurology, and psychiatry at Columbia University.
Jessell became an editor of the book starting from the third edition. He was a professor of biochemistry and molecular biophysics at Columbia University, and an investigator at the Howard Hughes Medical Institute.
Hudspeth is a professor of sensory neuroscience at Rockefeller University. He is also an investigator at the Howard Hughes Medical Institute.
Siegelbaum is Chair of the Department of Neuroscience at Columbia University and is also an investigator at the Howard Hughes
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https://en.wikipedia.org/wiki/Bent%27s%20rule
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In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization of central atoms in molecules and the electronegativities of substituents. The rule was stated by Henry A. Bent as follows:
The chemical structure of a molecule is intimately related to its properties and reactivity. Valence bond theory proposes that molecular structures are due to covalent bonds between the atoms and that each bond consists of two overlapping and typically hybridised atomic orbitals. Traditionally, p-block elements in molecules are assumed to hybridise strictly as spn, where n is either 1, 2, or 3. In addition, the hybrid orbitals are all assumed to be equivalent (i.e. the spn orbitals have the same p character). Predictions using this approach are usually good, but they can be improved by allowing isovalent hybridization, in which the hybridised orbitals may have noninteger and unequal p character. Bent's rule provides a qualitative estimate as to how these hybridised orbitals should be constructed. Bent's rule is that in a molecule, a central atom bonded to multiple groups will hybridise so that orbitals with more s character are directed towards electropositive groups, while orbitals with more p character will be directed towards groups that are more electronegative. By removing the assumption that all hybrid orbitals are equivalent spn orbitals, better predictions and explanations of properties such as molecular geometry and bond strength can be obtain
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https://en.wikipedia.org/wiki/Constant%20fraction%20discriminator
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A constant fraction discriminator (CFD) is an electronic signal processing device, designed to mimic the mathematical operation of finding a maximum of a pulse by finding the zero of its slope. Some signals do not have a sharp maximum, but short rise times .
Typical input signals for CFDs are pulses from plastic scintillation counters, such as those used for lifetime measurement in positron annihilation experiments. The scintillator pulses have identical rise times that are much longer than the desired temporal resolution. This forbids simple threshold triggering, which causes a dependence of the trigger time on the signal's peak height, an effect called time walk (see diagram). Identical rise times and peak shapes permit triggering not on a fixed threshold but on a constant fraction of the total peak height, yielding trigger times independent from peak heights.
From another point of view
A time-to-digital converter assigns timestamps. The time-to-digital converter needs fast rising edges with normed height. The plastic scintillation counter delivers fast rising edge with varying heights. Theoretically, the signal could be split into two parts. One part would be delayed and the other low pass filtered, inverted and then used in a variable-gain amplifier to amplify the original signal to the desired height. Practically, it is difficult to achieve a high dynamic range for the variable-gain amplifier, and analog computers have problems with the inverse value.
Principle of o
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https://en.wikipedia.org/wiki/Sydney%20Shoemaker
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Sydney Sharpless Shoemaker (September 29, 1931 – September 3, 2022) was an American philosopher. He was the Susan Linn Sage Professor of Philosophy at Cornell University and is well known for his contributions to philosophy of mind and metaphysics.
Education and career
Shoemaker graduated with a Bachelor of Arts from Reed College and earned his Doctor of Philosophy from Cornell University in 1958 under the supervision of Norman Malcolm. He taught philosophy at Ohio State University from 1957 to 1960 then, in 1961, returned to Cornell as a faculty member of the philosophy department. In 1978 he was appointed the Susan Linn Sage Professor of Philosophy, a position he held until his retirement, as Professor Emeritus of Philosophy.
In 1971, he delivered the John Locke Lectures at Oxford University.
Shoemaker died on September 3, 2022, at the age of 90. He was buried in Greensprings Natural Cemetery Preserve in Newfield.
Philosophical work
Shoemaker worked primarily in the philosophy of mind and metaphysics, and published many classic papers in both of these areas (as well as their overlap). In "Functionalism and Qualia" (1975), for example, he argued that functionalism about mental states can account for the qualitative character (or 'raw feel') of mental states. In "Self-Reference and Self-Awareness" (1968), he argued that the phenomenon of absolute 'immunity to error through misidentification' is what distinguishes self-attributions of mental states (such as "I see a cana
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https://en.wikipedia.org/wiki/IGT
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IGT may refer to:
Biology and medicine
Impaired glucose tolerance, a term associated with diabetes
Insufficient Glandular Tissue, a term associated with low milk supply in breastfeeding
Information Governance Toolkit, an online system used in the NHS in the United Kingdom
Image Guided Therapy, a research area about navigated medical interventions (also see Computer-assisted interventions)
Technology
International Game Technology, a gaming systems manufacturer
International Game Technology (1975–2015), the original company superseded by merging with Gtech
Integrated Telecom Technology, or IgT, a former semiconductor company
Culture
Ireland's Got Talent, an Irish version of the Got Talent series
Indonesia's Got Talent, an Indonesian version of the Got Talent series
India's Got Talent, an Indian version of the Got Talent series
Other
Interlinear Glossed Text, a structured representation language text in various forms (usually for multilingual translations)
Indicazione Geografica Tipica, a class of Italian wine appellation ranking below Denominazione di Origine Controllata but above Vino da Tavola
Iowa gambling task, a psychological task thought to simulate real-life decision making
Magas Airport, IATA code IGT, is an airport in the Russian Republic of Ingushetia.
pt:IGT
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https://en.wikipedia.org/wiki/Indian%20rivers%20interlinking%20project
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The Indian Rivers Inter-link is a proposed large-scale civil engineering project that aims to effectively manage water resources in India by linking Indian rivers by a network of reservoirs and canals to enhance irrigation and groundwater recharge, reduce persistent floods in some parts and water shortages in other parts of India. India accounts for 18% of the world population and about 4% of the world’s water resources. One of the solutions to solve the country’s water woes is to link rivers and lakes.
The Inter-link project has been split into three parts: a northern Himalayan rivers inter-link component, a southern Peninsular component and starting 2005, an intrastate rivers linking component. The project is being managed by India's National Water Development Agency Ministry of Jal Shakti. NWDA has studied and prepared reports on 14 inter-link projects for Himalayan component, 16 inter-link projects for Peninsular component and 37 intrastate river linking projects.
The average rainfall in India is about 4,000 billion cubic metres, but most of India's rainfall comes over a 4-month period – June through September. Furthermore, the rain across the very large nation is not uniform, the east and north gets most of the rain, while the west and south get less. India also sees years of excess monsoons and floods, followed by below average or late monsoons with droughts. This geographical and time variance in availability of natural water versus the year round demand for irrigati
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https://en.wikipedia.org/wiki/Fritz%20Lenz
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Fritz Gottlieb Karl Lenz (9 March 1887 in Pflugrade, Pomerania – 6 July 1976 in Göttingen, Lower Saxony) was a German geneticist, member of the Nazi Party, and influential specialist in eugenics in Nazi Germany.
Biography
The pupil of Alfred Ploetz, Lenz took over the publication of the magazine "Archives for Racial and Social Biology" from 1913 to 1933 and received in 1923 the first chair in eugenics in Munich. In 1933 he came to Berlin where he established the first specific department devoted to eugenics, at the Kaiser Wilhelm Institute of Anthropology, Human Heredity, and Eugenics.
Lenz specialised in the field of the transmission of hereditary human diseases and "racial health". The results of his research were published in 1921 and 1932 in collaboration with Erwin Baur and Eugen Fischer in two volumes that were later combined under the title Human Heredity Theory and Racial Hygiene (1936).
This work and his theory of "race as a value principle" placed Lenz and his two colleagues in the position of Germany's leading racial theorists. Their ideas provided scientific justification for Nazi ideology, in particular its emphasis on the superiority of the "Nordic race" and the desirability of eliminating allegedly inferior strains of humanity – or "life unworthy of life" (Lebensunwertes Leben). Lenz was a member of the "Committee of Experts for Population and Racial Policy". He joined the Nazi party in 1937 while serving as the head of the Kaiser Wilhelm Institute of Anthr
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https://en.wikipedia.org/wiki/Strong%20prime
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In mathematics, a strong prime is a prime number with certain special properties. The definitions of strong primes are different in cryptography and number theory.
Definition in number theory
In number theory, a strong prime is a prime number that is greater than the arithmetic mean of the nearest prime above and below (in other words, it's closer to the following than to the preceding prime). Or to put it algebraically, writing the sequence of prime numbers as (p, p, p, ...) = (2, 3, 5, ...), p is a strong prime if . For example, 17 is the seventh prime: the sixth and eighth primes, 13 and 19, add up to 32, and half that is 16; 17 is greater than 16, so 17 is a strong prime.
The first few strong primes are
11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499 .
In a twin prime pair (p, p + 2) with p > 5, p is always a strong prime, since 3 must divide p − 2, which cannot be prime.
Definition in cryptography
In cryptography, a prime number p is said to be "strong" if the following conditions are satisfied.
p is sufficiently large to be useful in cryptography; typically this requires p to be too large for plausible computational resources to enable a cryptanalyst to factorise products of p with other strong primes.
p − 1 has large prime factors. That is, p = aq + 1 for some integer a and large prime q.
q − 1 has large prime fa
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https://en.wikipedia.org/wiki/Scalar%E2%80%93tensor%E2%80%93vector%20gravity
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Scalar–tensor–vector gravity (STVG) is a modified theory of gravity developed by John Moffat, a researcher at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. The theory is also often referred to by the acronym MOG (MOdified Gravity).
Overview
Scalar–tensor–vector gravity theory, also known as MOdified Gravity (MOG), is based on an action principle and postulates the existence of a vector field, while elevating the three constants of the theory to scalar fields. In the weak-field approximation, STVG produces a Yukawa-like modification of the gravitational force due to a point source. Intuitively, this result can be described as follows: far from a source gravity is stronger than the Newtonian prediction, but at shorter distances, it is counteracted by a repulsive fifth force due to the vector field.
STVG has been used successfully to explain galaxy rotation curves, the mass profiles of galaxy clusters, gravitational lensing in the Bullet Cluster, and cosmological observations without the need for dark matter. On a smaller scale, in the Solar System, STVG predicts no observable deviation from general relativity. The theory may also offer an explanation for the origin of inertia.
Mathematical details
STVG is formulated using the action principle. In the following discussion, a metric signature of will be used; the speed of light is set to , and we are using the following definition for the Ricci tensor:
We begin with the Einstein–Hilbert Lagrangian:
w
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https://en.wikipedia.org/wiki/Dorit%20Aharonov
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Dorit Aharonov (; born 1970) is an Israeli computer scientist specializing in quantum computing.
Aharonov was born in Washington and grew up in Haifa, the daughter of the mathematician Dov Aharonov and the niece of the physicist Yakir Aharonov.
Aharonov graduated from Weizmann Institute of Science with an MSc in physics. She received her doctorate for Computer Science in 1999 from the Hebrew University of Jerusalem, and her thesis was entitled Noisy Quantum Computation. She also did her post-doctorate in the mathematics department of Princeton University and in the computer science department of University of California Berkeley. She was a visiting scholar at the Institute for Advanced Study in 1998–99.
Aharonov was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Mathematical Aspects of Computer Science".
Research
Aharonov's research is mainly about quantum information processes, which includes:
quantum algorithms
quantum cryptography and computational complexity
quantum error corrections and fault tolerance
connections between quantum computation and quantum Markov chains and lattices
quantum Hamiltonian complexity and its connections to condensed matter physics
transition from quantum to classical physics
understanding entanglement by studying quantum complexity
References
External links
Aharonov's home page at the Hebrew University of Jerusalem
Profile in Nature
Dorit Aharonov in panel discussion, "Harnessing
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https://en.wikipedia.org/wiki/Nerve%20conduction%20velocity
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In neuroscience, nerve conduction velocity (CV) is the speed at which an electrochemical impulse propagates down a neural pathway. Conduction velocities are affected by a wide array of factors, which include age, sex, and various medical conditions. Studies allow for better diagnoses of various neuropathies, especially demyelinating diseases as these conditions result in reduced or non-existent conduction velocities. CV is an important aspect of nerve conduction studies.
Normal conduction velocities
Ultimately, conduction velocities are specific to each individual and depend largely on an axon's diameter and the degree to which that axon is myelinated, but the majority of 'normal' individuals fall within defined ranges.
Nerve impulses are extremely slow compared to the speed of electricity, where the electric field can propagate with a speed on the order of 50–99% of the speed of light; however, it is very fast compared to the speed of blood flow, with some myelinated neurons conducting at speeds up to 120 m/s (432 km/h or 275 mph).
Different sensory receptors are innervated by different types of nerve fibers. Proprioceptors are innervated by type Ia, Ib and II sensory fibers, mechanoreceptors by type II and III sensory fibers, and nociceptors and thermoreceptors by type III and IV sensory fibers.
Normal impulses in peripheral nerves of the legs travel at 40–45 m/s, and those in peripheral nerves of the arms at 50–65 m/s.
Largely generalized, normal conduction velocities
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https://en.wikipedia.org/wiki/Peter%20B.%20Kronheimer
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Peter Benedict Kronheimer (born 1963) is a British mathematician, known for his work on gauge theory and its applications to 3- and 4-dimensional topology. He is William Caspar Graustein Professor of Mathematics at Harvard University and former chair of the mathematics department.
Education
Kronheimer attended the City of London School. He completed his DPhil at Oxford University under the direction of Michael Atiyah. He has had a long association with Merton College, the oldest of the constituent colleges of Oxford University, being an undergraduate, graduate, and full fellow of the college.
Career
Kronheimer's early work was on gravitational instantons, in particular the classification of hyperkähler 4-manifolds with asymptotical locally Euclidean geometry (ALE spaces), leading to the papers "The construction of ALE spaces as hyper-Kähler quotients" and "A Torelli-type theorem for gravitational instantons." He and Hiraku Nakajima
gave a construction of instantons on ALE spaces generalizing the Atiyah–Hitchin–Drinfeld–Manin construction. This constructions identified these moduli spaces as moduli spaces for certain quivers (see "Yang-Mills instantons on ALE gravitational instantons.") He was the initial recipient of the Oberwolfach prize in 1998 on the basis of some of this work.
Kronheimer has frequently collaborated with Tomasz Mrowka from the Massachusetts Institute of Technology. Their collaboration began at the Mathematical Research Institute of Oberwolfach, and
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https://en.wikipedia.org/wiki/PSivida
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EyePoint Pharmaceuticals, Inc. (formerly pSivida Corp.) pSivida is a Watertown, Massachusetts company specialising in the application of microelectromechanical systems (MEMS) and nanotechnology to drug delivery.
pSivida obtained porous silicon technology from the British government Defence Evaluation and Research Agency (DERA, now QinetiQ). QinetiQ continues to be a strategic partner.
In June 2004, pSivida acquired full ownership of pSiMedica. In April 2018, pSivida purchased eye products firm Icon Bioscience.
See also
Alimera Sciences, pSvida's partner on Iluvien
References
External links
pSivida Mesoporous silicon patent
Qinetiq
Nanotechnology companies
Companies based in Middlesex County, Massachusetts
Drug delivery devices
Pharmaceutical companies of the United States
Health care companies based in Massachusetts
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https://en.wikipedia.org/wiki/Thom%20conjecture
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In mathematics, a smooth algebraic curve in the complex projective plane, of degree , has genus given by the genus–degree formula
.
The Thom conjecture, named after French mathematician René Thom, states that if is any smoothly embedded connected curve representing the same class in homology as , then the genus of satisfies the inequality
.
In particular, C is known as a genus minimizing representative of its homology class. It was first proved by Peter Kronheimer and Tomasz Mrowka in October 1994, using the then-new Seiberg–Witten invariants.
Assuming that has nonnegative self intersection number this was generalized to Kähler manifolds (an example being the complex projective plane) by John Morgan, Zoltán Szabó, and Clifford Taubes, also using the Seiberg–Witten invariants.
There is at least one generalization of this conjecture, known as the symplectic Thom conjecture (which is now a theorem, as proved for example by Peter Ozsváth and Szabó in 2000). It states that a symplectic surface of a symplectic 4-manifold is genus minimizing within its homology class. This would imply the previous result because algebraic curves (complex dimension 1, real dimension 2) are symplectic surfaces within the complex projective plane, which is a symplectic 4-manifold.
See also
Adjunction formula
Milnor conjecture (topology)
References
Four-dimensional geometry
4-manifolds
Algebraic surfaces
Conjectures that have been proved
Theorems in geometry
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https://en.wikipedia.org/wiki/Red%20Whittaker
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Red Whittaker (born 1948) is an American roboticist and research professor of robotics at Carnegie Mellon University. He led Tartan Racing to its first-place victory in the DARPA Grand Challenge (2007) Urban Challenge and brought Carnegie Mellon University the two million dollar prize. Previously, Whittaker also competed in the DARPA Grand Challenge, placing second and third place simultaneously in the Grand Challenge Races.
Whittaker is currently the Fredkin Research Professor at Carnegie Mellon University's Robotics Institute as well as the Director of the Field Robotics Center and Chief Scientist of the Robotics Engineering Consortium, both located at the university.
Red founded and led Carnegie Mellon University's team in the Google Lunar X Prize. from its inception in 2007 until its ultimate closure in 2018. Today, Whittaker continues this work through NASA contracts in the form of MoonRanger, a planetary rover in development designed to quickly and autonomously explore the surface of the Moon.
Biography
Whittaker spent his childhood in Hollidaysburg, Pennsylvania, where his father was an explosives salesman and his mother was a chemist. He matriculated at Princeton University, but interrupted his studies to join the United States Marines. He returned to Princeton to earn his bachelor's degree in civil engineering in 1973 and then attended Carnegie Mellon University, where he earned his master's degree in 1975 and his Ph.D. in 1979, both in civil engineering.
Roboti
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https://en.wikipedia.org/wiki/Lattice%20energy
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In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bind ionic solids. The size of the lattice energy is connected to many other physical properties including solubility, hardness, and volatility. Since it generally cannot be measured directly, the lattice energy is usually deduced from experimental data via the Born–Haber cycle.
Lattice energy and lattice enthalpy
The concept of lattice energy was originally applied to the formation of compounds with structures like rocksalt (NaCl) and sphalerite (ZnS) where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy change of the reaction
Na+ (g) + Cl− (g) → NaCl (s)
which amounts to −786 kJ/mol.
Some chemistry textbooks as well as the widely used CRC Handbook of Chemistry and Physics define lattice energy with the opposite sign, i.e. as the energy required to convert the crystal into infinitely separated gaseous ions in vacuum, an endothermic process. Following this convention, the lattice energy of NaCl would be +786 kJ/mol. Both sign conventions are widely used.
The relationship between the lattice energy and the lattice enthalpy at pressure is given by the following equation:
,
where is the lattice energy (i.e., the molar internal energy change), is the lattice enthalpy, and the
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https://en.wikipedia.org/wiki/Clemens%20C.%20J.%20Roothaan
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Clemens C. J. Roothaan (August 29, 1918 – June 17, 2019) was a Dutch physicist and chemist known for his development of the self-consistent field theory of molecular structure.
Biography
Roothaan was born in Nijmegen. He enrolled TU Delft in 1935 to study electrical engineering. During World War II he was first detained in a prisoner of war camp. Later he and his brother were sent to the Vught concentration camp for involvement with the Dutch Resistance. On September 5, 1944, the remaining prisoners of the camp (including the Roothaan brothers) were moved to the Sachsenhausen camp in Germany ahead of the advancing Allies. Near the end of the war, the Sachsenhausen inmates were sent on a death march which Roothaan's brother did not survive.
While a prisoner of war he was able to pursue his studies in physics together with other professors and students under the formal guidance of Philips. The work he was assigned to while cooperating with Philips was a foundation for his master's thesis. He obtained his master's degree in physics from TU Delft on October 14, 1945. After that he moved to USA, where he did his PhD thesis with Robert S. Mulliken from the University of Chicago, on semiempirical MO theory, while holding a post at The Catholic University of America in Washington, D.C.. He realised that the then current approach to molecular orbital theory was incorrect and changed his topic to what resulted in the development of the Roothaan equations. Prof. Mulliken mentions this
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https://en.wikipedia.org/wiki/George%20G.%20Hall
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George Garfield Hall (5 March 1925 – 6 May 2018) was a Northern Irish applied mathematician known for original work and contributions to the field of quantum chemistry. Independently from Clemens C. J. Roothaan, Hall discovered the Roothaan-Hall equations.
Education and career
For his work on the Roothaan-Hall equations, Hall was awarded a Ph.D. (1950) supervised by John Lennard-Jones. He then lectured at Cambridge University as Assistant in Research in Theoretical chemistry. He was elected to a Fellowship at St John's College, Cambridge in 1953. From 1955 to 1962 he lectured in Mathematics at the Imperial College, London. In 1957–58 he spent a year with Per-Olov Löwdin in Uppsala, Sweden. He became Professor of Mathematics at the University of Nottingham in 1962. In 1982 he took early retirement from Nottingham University and was appointed an emeritus professor. He moved in 1983 to Kyoto University, Japan, returning to Nottingham in 1988. He has collaborated with (inter alia) A.T. Amos, K. Collard, and D. Rees. He was Emeritus Professor and Senior Research Fellow in the Shell Centre for Mathematical Education at the University of Nottingham.
He was awarded several honorary degrees for his work: a DSc by Maynooth University (2004), a ScD by Cambridge University and a DEng by Kyoto University. He was a member of the International Academy of Quantum Molecular Science.
Hall had three children and six grandchildren. He died peacefully in Nottingham at the age of 93 on 6 Ma
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https://en.wikipedia.org/wiki/M.%20Brendan%20Fleming
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Martin Brendan Fleming (February 2, 1926 – May 28, 2016) was the mayor of Lowell, Massachusetts, from 1982 to 1984, and a member of the Lowell City Council for nine terms between the years of 1969 and 1992. Fleming was a faculty member in the mathematics department at Lowell Technological Institute and the University of Lowell for decades, retiring in 1996.
Life and career
In 1963, Fleming served on the Board of the Lowell Redevelopment Authority, chaired by Homer Bourgeois, President of the Lowell Union National Bank. During this time, the Lowell Redevelopment Authority initiated a Federal Urban Renewal project which would demolish Lowell's Little Canada neighborhood, Merrimack Manufacturing Company, and the Dutton Street Boardinghouses. Against Chairman Bourgeois' wishes, Fleming, along with several other LTI faculty members and community activist Lydia Howard, worked tirelessly to save and preserve the red brick Dutton Street Boardinghouses built in 1845. They failed, and shortly thereafter Chairman Bourgeois replaced Fleming on the Board of the Lowell Housing Authority.
Committed to the historic preservation of Lowell canal system and historic mill buildings, in 1966 Fleming went before the Lowell City Council and suggested the creation of the Lowell Historic Commission and was rejected, told that the history of Lowell best be forgotten. Fleming then ran for the Lowell City Council in 1967 and finished in 11th place of 18 candidates — missing a seat on the Lowell Cit
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https://en.wikipedia.org/wiki/Samuel%20Francis%20Boys
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Samuel Francis (Frank) Boys (20 December 1911 – 16 October 1972) was a British theoretical chemist.
Education
Boys was born in Pudsey, Yorkshire, England. He was educated at the Grammar School in Pudsey and then at Imperial College London. He graduated in Chemistry in 1932. He was awarded a PhD in 1937 from Cambridge for research conducted at Trinity College, supervised first by Martin Lowry, and then, after Lowry's 1936 death, by John Lennard-Jones. His thesis was "The Quantum Theory of Optical Rotation".
Career
In 1938, Boys was appointed an Assistant Lecturer in Mathematical Physics at Queen's University Belfast. He spent the whole of the Second World War working on explosives research with the Ministry of Supply at the Royal Arsenal, Woolwich, with Lennard-Jones as his supervisor. After the war, Boys accepted an ICI Fellowship at Imperial College, London. In 1949, he was appointed to a Lectureship in theoretical chemistry at the University of Cambridge. He remained at Cambridge until his death. He was only elected to a Cambridge College Fellowship at University College, now Wolfson College, Cambridge, shortly before his death.
Boys is best known for the introduction of Gaussian orbitals into ab initio quantum chemistry. Almost all basis sets used in computational chemistry now employ these orbitals. Frank Boys was also one of the first scientists to use digital computers for calculations on polyatomic molecules.
An International Conference, entitled "Molecular Quantu
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https://en.wikipedia.org/wiki/One-way%20compression%20function
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In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output. The transformation is "one-way", meaning that it is difficult given a particular output to compute inputs which compress to that output. One-way compression functions are not related to conventional data compression algorithms, which instead can be inverted exactly (lossless compression) or approximately (lossy compression) to the original data.
One-way compression functions are for instance used in the Merkle–Damgård construction inside cryptographic hash functions.
One-way compression functions are often built from block ciphers.
Some methods to turn any normal block cipher into a one-way compression function are Davies–Meyer, Matyas–Meyer–Oseas, Miyaguchi–Preneel (single-block-length compression functions) and MDC-2/Meyer–Schilling, MDC-4, Hirose (double-block-length compression functions). These methods are described in detail further down. (MDC-2 is also the name of a hash function patented by IBM.)
Another method is 2BOW (or NBOW in general), which is a "high-rate multi-block-length hash function based on block ciphers" and typically achieves (asymptotic) rates between 1 and 2 independent of the hash size (only with small constant overhead). This method has not yet seen any serious security analysis, so should be handled with care.
Compression
A compression function mixes two fixed length inputs and produces a single fixed length output
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https://en.wikipedia.org/wiki/Word%20problem%20%28mathematics%29
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In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well. A deep result of computational theory is that answering this question is in many important cases undecidable.
Background and motivation
In computer algebra one often wishes to encode mathematical expressions using an expression tree. But there are often multiple equivalent expression trees. The question naturally arises of whether there is an algorithm which, given as input two expressions, decides whether they represent the same element. Such an algorithm is called a solution to the word problem. For example, imagine that are symbols representing real numbers - then a relevant solution to the word problem would, given the input , produce the output EQUAL, and similarly produce NOT_EQUAL from .
The most direct solution to a word problem takes the form of a normal form theorem and algorithm which maps every element in an equivalence class of expressions to a single encoding known as the normal form - the word problem is then solved by comparing these normal forms via syntactic equality. For example one might decide that is the normal form of , , and , and devise a transformation system to rewrite those expressions to that form, in the process proving that all equivalent expressions will be rewritten to the same n
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https://en.wikipedia.org/wiki/Word%20problem
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Word problem may refer to:
Word problem (mathematics education), a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations
Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science
Word problem for groups, the problem of recognizing the identity element in a finitely presented group
Word problem (computability), a decision problem concerning formal languages
See also
Word-finding problem; problem using words; language problem: aphasia
Word game
Wordle
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https://en.wikipedia.org/wiki/Cryptovirology
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Cryptovirology refers to the use of cryptography to devise particularly powerful malware, such as ransomware and asymmetric backdoors. Traditionally, cryptography and its applications are defensive in nature, and provide privacy, authentication, and security to users. Cryptovirology employs a twist on cryptography, showing that it can also be used offensively. It can be used to mount extortion based attacks that cause loss of access to information, loss of confidentiality, and information leakage, tasks which cryptography typically prevents.
The field was born with the observation that public-key cryptography can be used to break the symmetry between what an antivirus analyst sees regarding malware and what the attacker sees. The antivirus analyst sees a public key contained in the malware, whereas the attacker sees the public key contained in the malware as well as the corresponding private key (outside the malware) since the attacker created the key pair for the attack. The public key allows the malware to perform trapdoor one-way operations on the victim's computer that only the attacker can undo.
Overview
The field encompasses covert malware attacks in which the attacker securely steals private information such as symmetric keys, private keys, PRNG state, and the victim's data. Examples of such covert attacks are asymmetric backdoors. An asymmetric backdoor is a backdoor (e.g., in a cryptosystem) that can be used only by the attacker, even after it is found. This contra
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https://en.wikipedia.org/wiki/Compact%20quantum%20group
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In mathematics, a compact quantum group is an abstract structure on a unital separable C*-algebra axiomatized from those that exist on the commutative C*-algebra of "continuous complex-valued functions" on a compact quantum group.
The basic motivation for this theory comes from the following analogy. The space of complex-valued functions on a compact Hausdorff topological space forms a commutative C*-algebra. On the other hand, by the Gelfand Theorem, a commutative C*-algebra is isomorphic to the C*-algebra of continuous complex-valued functions on a compact Hausdorff topological space, and the topological space is uniquely determined by the C*-algebra up to homeomorphism.
S. L. Woronowicz introduced the important concept of compact matrix quantum groups, which he initially called compact pseudogroups. Compact matrix quantum groups are abstract structures on which the "continuous functions" on the structure are given by elements of a C*-algebra. The geometry of a compact matrix quantum group is a special case of a noncommutative geometry.
Formulation
For a compact topological group, , there exists a C*-algebra homomorphism
where is the minimal C*-algebra tensor product — the completion of the algebraic tensor product of and ) — such that
for all , and for all , where
for all and all . There also exists a linear multiplicative mapping
,
such that
for all and all . Strictly speaking, this does not make into a Hopf algebra, unless is finite.
On the other hand,
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https://en.wikipedia.org/wiki/Kit%20Fine
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Kit Fine (born 26 March 1946) is a British philosopher, currently university professor and Silver Professor of Philosophy and Mathematics at New York University. Prior to joining the philosophy department of NYU in 1997, he taught at the University of Edinburgh, University of California, Irvine, University of Michigan and UCLA. The author of several books and dozens of articles in international academic journals, he has made notable contributions to the fields of philosophical logic, metaphysics, and the philosophy of language and also has written on ancient philosophy, in particular on Aristotle's account of logic and modality.
He is also a distinguished research professor in the Department of Philosophy, University of Birmingham, UK. Since 2018, Fine is visiting professor at the University of Italian Switzerland.
Education, family and career
After graduating from Balliol College, Oxford (B.A., 1967), Fine received his Ph.D. from the University of Warwick in 1969, under the supervision of A. N. Prior. He then taught at the University of Edinburgh, University of California, Irvine, University of Michigan, and UCLA, before moving to New York University.
He was elected a Corresponding Fellow of the British Academy in 2005 and a Fellow of the American Academy of Arts & Sciences in 2006. He has held fellowships from the John Simon Guggenheim Memorial Foundation and the American Council of Learned Societies and is a former editor of the Journal of Symbolic Logic.
Fine has two
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https://en.wikipedia.org/wiki/Microlensing%20Observations%20in%20Astrophysics
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Microlensing Observations in Astrophysics (MOA) is a collaborative project between researchers in New Zealand and Japan, led by Professor Yasushi Muraki of Nagoya University. They use microlensing to observe dark matter, extra-solar planets, and stellar atmospheres from the Southern Hemisphere. The group concentrates especially on the detection and observation of gravitational microlensing events of high magnification, of order 100 or more, as these provide the greatest sensitivity to extrasolar planets. They work with other groups in Australia, the United States and elsewhere. Observations are conducted at New Zealand's Mt. John University Observatory using a reflector telescope built for the project.
In September 2020, astronomers using microlensing techniques reported the detection, for the first time, of an earth-mass rogue planet unbounded by any star, and free floating in the Milky Way galaxy. In January 2022 in collaboration with Optical Gravitational Lensing Experiment (OGLE) they reported in a preprint the first rogue BH while there have been others candidates this is the most solid detection so far as their technique allowed to measure not only the amplification of light but also its deflection by the BH from the microlensing data.
MOA telescope mirror images
Planets discovered
The following planets have been announced by this survey, some in conjunction with other surveys.
See also
Optical Gravitational Lensing Experiment or OGLE, a similar microlensing surve
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https://en.wikipedia.org/wiki/Geir%20Ellingsrud
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Geir Ellingsrud (born 29 November 1948) is professor of mathematics at the University of Oslo, where he specialises in algebra and algebraic geometry.
He took the cand.real. degree at the University of Oslo in 1973, and the doctorate at Stockholm University in 1982. He was a lecturer at Stockholm University from 1982 to 1984, associate professor at the University of Oslo from 1984 to 1989, professor at the University of Bergen from 1989 to 1993 and at the University of Oslo since 1993. He has been a visiting scholar in Nice, Paris, Bonn and Chicago. He has edited the journals Acta Mathematica and Normat.
In 2005 Ellingsrud was elected to be rector of the University of Oslo for the period 2006-2009. His team also consisted of Inga Bostad and Haakon Breien Benestad. He did not seek reelection to a second term, and was succeeded by Ole Petter Ottersen.
References
1948 births
Living people
Algebraic geometers
University of Oslo alumni
Stockholm University alumni
Academic staff of Stockholm University
Academic staff of the University of Bergen
Academic staff of the University of Oslo
Rectors of the University of Oslo
Members of the Norwegian Academy of Science and Letters
20th-century Norwegian mathematicians
21st-century Norwegian mathematicians
Royal Norwegian Society of Sciences and Letters
Presidents of the Norwegian Mathematical Society
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https://en.wikipedia.org/wiki/No-slip%20condition
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In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary.
The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. Conceptually, one can think of the outermost molecules of fluid as stuck to the surfaces past which it flows. Because the solution is prescribed at given locations, this is an example of a Dirichlet boundary condition.
For highly viscous foodstuffs that contain a high level of fat, such as mayonnaise and melted cheese, the no-slip condition cannot be applied, due to their "self-lubricating" properties.
Physical justification
Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion.
At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero.
The no slip condition is only defined for viscous flows and where continuum concept is valid.
Exceptions
As with most of the engineering approximations, the no-slip condition does not always hold in reality. For example, at very low pressure (e.g. at high altitude), even when the continuum approximation still holds there may be so few molecules near the surface that they "bounce along" down the surface. A common approximation for fluid slip is:
where is the coordinate
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https://en.wikipedia.org/wiki/Giulio%20Ascoli
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Giulio Ascoli (20 January 1843, Trieste – 12 July 1896, Milan) was a Jewish-Italian mathematician. He was a student of the Scuola Normale di Pisa, where he graduated in 1868.
In 1872 he became Professor of Algebra and Calculus of the Politecnico di Milano University. From 1879 he was professor of mathematics at the Reale Istituto Tecnico Superiore, where, in 1901, was affixed a plaque that remembers him.
He was also a corresponding member of Istituto Lombardo.
He made contributions to the theory of functions of a real variable and to Fourier series. For example, Ascoli introduced equicontinuity in 1884, a topic regarded as one of the fundamental concepts in the theory of real functions. In 1889, Italian mathematician Cesare Arzelà generalized Ascoli's Theorem into the Arzelà–Ascoli theorem, a practical sequential compactness criterion of functions.
See also
Measure (mathematics)
Oscillation (mathematics)
Riemann Integral
Notes
Biographical references
.
(in Italian). Available from the website of the.
References
.
. "Riemann's conditions for integrability and their influence on the birth of the concept of measure" (English translation of title) is an article on the history of measure theory, analyzing deeply and comprehensively every early contribution to the field, starting from Riemann's work and going to the works of Hermann Hankel, Gaston Darboux, Giulio Ascoli, Henry John Stephen Smith, Ulisse Dini, Vito Volterra, Paul David Gustav du Bois-Reymond and Carl Gustav
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https://en.wikipedia.org/wiki/Atan2
|
In computing and mathematics, the function atan2 is the 2-argument arctangent. By definition, is the angle measure (in radians, with ) between the positive -axis and the ray from the origin to the point in the Cartesian plane. Equivalently, is the argument (also called phase or angle) of the complex number
The function first appeared in the programming language Fortran in 1961. It was originally intended to return a correct and unambiguous value for the angle in converting from Cartesian coordinates to polar coordinates . If and , then and
If , the desired angle measure is However, when , the angle is diametrically opposite the desired angle, and ± (a half turn) must be added to place the point in the correct quadrant. Using the function does away with this correction, simplifying code and mathematical formulas.
Motivation
The ordinary single-argument arctangent function only returns angle measures in the interval and when invoking it to find the angle measure between the -axis and an arbitrary vector in the Cartesian plane, there is no simple way to indicate a direction in the left half-plane (that is, a point with ). Diametrically opposite angle measures have the same tangent because so the tangent is not in itself sufficient to uniquely specify an angle.
To determine an angle measure using the arctangent function given a point or vector mathematical formulas or computer code must handle multiple cases; at least one for positive values of and one fo
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https://en.wikipedia.org/wiki/N%C3%B8rlund%E2%80%93Rice%20integral
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In mathematics, the Nørlund–Rice integral, sometimes called Rice's method, relates the nth forward difference of a function to a line integral on the complex plane. It commonly appears in the theory of finite differences and has also been applied in computer science and graph theory to estimate binary tree lengths. It is named in honour of Niels Erik Nørlund and Stephen O. Rice. Nørlund's contribution was to define the integral; Rice's contribution was to demonstrate its utility by applying saddle-point techniques to its evaluation.
Definition
The nth forward difference of a function f(x) is given by
where is the binomial coefficient.
The Nörlund–Rice integral is given by
where f is understood to be meromorphic, α is an integer, , and the contour of integration is understood to circle the poles located at the integers α, ..., n, but encircles neither integers 0, ..., nor any of the poles of f. The integral may also be written as
where B(a,b) is the Euler beta function. If the function is polynomially bounded on the right hand side of the complex plane, then the contour may be extended to infinity on the right hand side, allowing the transform to be written as
where the constant c is to the left of α.
Poisson–Mellin–Newton cycle
The Poisson–Mellin–Newton cycle, noted by Flajolet et al. in 1985, is the observation that the resemblance of the Nørlund–Rice integral to the Mellin transform is not accidental, but is related by means of the binomial transform and the New
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https://en.wikipedia.org/wiki/Pursuit%E2%80%93evasion
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Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically. In 1976, Torrence Parsons introduced a formulation whereby movement is constrained by a graph. The geometric formulation is sometimes called continuous pursuit–evasion, and the graph formulation discrete pursuit–evasion (also called graph searching). Current research is typically limited to one of these two formulations.
Discrete formulation
In the discrete formulation of the pursuit–evasion problem, the environment is modeled as a graph.
Problem definition
There are innumerable possible variants of pursuit–evasion, though they tend to share many elements. A typical, basic example is as follows (cops and robber games): Pursuers and evaders occupy nodes of a graph. The two sides take alternate turns, which consist of each member either staying put or moving along an edge to an adjacent node. If a pursuer occupies the same node as an evader the evader is captured and removed from the graph. The question usually posed is how many pursuers are necessary to ensure the eventual capture of all the evaders. If one pursuer suffices, the graph is called a cop-win graph. In this case, a single evader can always be captured in time linear to the number of n nodes of the graph.
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https://en.wikipedia.org/wiki/2-Norbornyl%20cation
|
In organic chemistry, the term 2-norbornyl cation (or 2-bicyclo[2.2.1]heptyl cation) describes one of the three carbocations formed from derivatives of norbornane. Though 1-norbornyl and 7-norbornyl cations have been studied, the most extensive studies and vigorous debates have been centered on the exact structure of the 2-norbornyl cation.
The 2-norbornyl cation has been formed from a variety of norbornane derivatives and reagents. First reports of its formation and reactivity published by Saul Winstein sparked controversy over the nature of its bonding, as he invoked a three-center two-electron bond to explain the stereochemical outcome of the reaction. Herbert C. Brown challenged this assertion on the grounds that classical resonance structures could explain these observations without needing to adapt a new perspective of bonding. Both researchers' views had its supporters, and dozens of scientists contributed ingeniously designed experiments to provide evidence for one viewpoint or the other. Over time, the dispute became increasingly bitter and acrimonious, and the debate took on a personal or ad hominem character.
Evidence of the non-classical nature of the 2-norbornyl cation grew over the course of several decades, mainly through spectroscopic data gathered using methods such as nuclear magnetic resonance (NMR). Crystallographic confirmation of its non-classical nature did not come until 2013. Although most chemists now agree that 2-norbornyl cation itself is non-
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https://en.wikipedia.org/wiki/Isaiah%20Shavitt
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Isaiah Shavitt was a Polish-born Israeli and American theoretical chemist.
He was born Isaiah Kruk on July 29, 1925, in Kutno, Poland but his family moved to what would become Israel in 1929. After undergraduate degrees in chemistry (1950) and chemical engineering (1951) from the Technion in Haifa, he started a Ph.D. in experimental physical chemistry, but shortly after traveled to Cambridge University on a British Council Scholarship and completed his Ph.D. (1957) under the aegis of pioneering computational chemist S. Francis Boys.
Following postdoctoral work with Joseph O. Hirschfelder, a stint as a temporary assistant professor at Brandeis University, and further postdoctoral research with Martin Karplus, he became a professor at his alma mater in 1962. In 1967 he moved to a senior research position at Battelle Memorial Institute in Columbus, Ohio, United States. In 1968 he also became a part-time faculty member at the department of chemistry at Ohio State University and moved there full-time in 1981. In 1994 he retired from this position and continued part-time as an emeritus professor. Until his death he was also an adjunct professor in the department of chemistry at the University of Illinois at Urbana-Champaign, US.
Shavitt's landmark achievements include being responsible for two of the first applications of the then newly available computer to chemistry; developing the Gaussian transform method for calculating multicenter integrals of Slater-type orbitals; coining
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https://en.wikipedia.org/wiki/T.%20Colin%20Campbell
|
Thomas Colin Campbell (born March 14, 1934) is an American biochemist who specializes in the effect of nutrition on long-term health. He is the Jacob Gould Schurman Professor Emeritus of Nutritional Biochemistry at Cornell University.
Campbell has become known for his advocacy of a low-fat, whole foods, plant-based diet. He coined the term "Plant-Based diet" to help present his research on diet at the National Institutes of Health in 1980. He is the author of over 300 research papers and four books: The China Study (2005), which was co-authored with his son, Thomas M. Campbell II, and became one of America's best-selling books about nutrition, Whole (2013), The Low-Carb Fraud (2014) and The Future of Nutrition: An Insider's Look at the Science, Why We Keep Getting It Wrong, and How to Start Getting It Right (2020). Campbell featured in the 2011 American documentary Forks Over Knives.
Campbell was one of the lead scientists of the China–Cornell–Oxford Project on diet and disease, set up in 1983 by Cornell University, the University of Oxford, and the Chinese Academy of Preventive Medicine to explore the relationship between nutrition and cancer, heart, and metabolic diseases. The study was described by The New York Times as "the Grand Prix of epidemiology".
Early life and education
Campbell grew up on a dairy farm. He studied pre-veterinary medicine at Pennsylvania State University, where he obtained his B.S. in 1956, then attended veterinary school at the University of G
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https://en.wikipedia.org/wiki/CADPAC
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CADPAC, the Cambridge Analytic Derivatives Package, is a suite of programs for ab initio computational chemistry calculations. It has been developed by R. D. Amos with contributions from I. L. Alberts, J. S. Andrews, S. M. Colwell, N. C. Handy, D. Jayatilaka, P. J. Knowles, R. Kobayashi, K. E. Laidig, G. Laming, A. M. Lee, P. E. Maslen, C. W. Murray, J. E. Rice, E. D. Simandiras, A. J. Stone, M.-D. Su and D. J. Tozer. at Cambridge University since 1981. It is capable of molecular Hartree–Fock calculations, Møller–Plesset calculations, various other correlated calculations and density functional theory calculations.
See also
Quantum chemistry computer programs
External links
Computational chemistry software
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https://en.wikipedia.org/wiki/Asperity%20%28materials%20science%29
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In materials science, asperity, defined as "unevenness of surface, roughness, ruggedness" (from the Latin asper—"rough"), has implications (for example) in physics and seismology. Smooth surfaces, even those polished to a mirror finish, are not truly smooth on a microscopic scale. They are rough, with sharp, rough or rugged projections, termed "asperities". Surface asperities exist across multiple scales, often in a self affine or fractal geometry. The fractal dimension of these structures has been correlated with the contact mechanics exhibited at an interface in terms of friction and contact stiffness.
When two macroscopically smooth surfaces come into contact, initially they only touch at a few of these asperity points. These cover only a very small portion of the surface area. Friction and wear originate at these points, and thus understanding their behavior becomes important when studying materials in contact. When the surfaces are subjected to a compressive load, the asperities deform through elastic and plastic modes, increasing the contact area between the two surfaces until the contact area is sufficient to support the load.
The relationship between frictional interactions and asperity geometry is complex and poorly understood. It has been reported that an increased roughness may under certain circumstances result in weaker frictional interactions while smoother surfaces may in fact exhibit high levels of friction owing to high levels of true contact.
The Archard
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https://en.wikipedia.org/wiki/D0
|
D0 may refer to:
d0, the d electron count of a transition metal complex
D0 meson
D0 experiment, at the Tevatron collider at Fermilab, in Batavia, Illinois, US
D0 motorway (Czech Republic), the partially complete outer ring road of Prague
Dangling bond, in chemistry
DHL Air Limited (IATA code)
See also
Do (disambiguation)
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https://en.wikipedia.org/wiki/Babylonian%20mathematics
|
Babylonian mathematics (also known as Assyro-Babylonian mathematics) are the mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited. With respect to time they fall in two distinct groups: one from the Old Babylonian period (1830–1531 BC), the other mainly Seleucid from the last three or four centuries BC. With respect to content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for over a millennium.
In contrast to the scarcity of sources in Egyptian mathematics, knowledge of Babylonian mathematics is derived from hundreds of clay tablets unearthed since the 1850s. Written in cuneiform, tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics that include fractions, algebra, quadratic and cubic equations and the Pythagorean theorem. The Babylonian tablet YBC 7289 gives an approximation to accurate to three significant sexagesimal digits (about six significant decimal digits).
Origins of Babylonian mathematics
Babylonian mathematics is a range of numeric and more advanced mathematical practices in the ancient Near East, written in cuneiform script. Study has historically focused on the Old Babylonian pe
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https://en.wikipedia.org/wiki/The%20Hive%20%28website%29
|
The Hive was a website that served as an information-sharing forum for individuals and groups interested in the practical synthesis, chemistry, biology, politics, and legal aspects of mind or body-altering drugs. Participants ranged from pure theorists to self-declared organized crime chemists (claimed to be retired but with excellent connections) as well as forensic chemists, who (much like their quarries) used the Hive to keep abreast of developments in clandestine chemistry. At its peak, the Hive had thousands of participants from all over the world.
History
Although it had been in operation since 1997, The Hive gained broader awareness in 2001 when a Dateline NBC special The "X" Files aired. This investigation into the use and production of MDMA featured the Hive and its founder, who operated under the pseudonym 'Strike' (Hobart Huson). Strike was the founder and site designer of the Hive as well as the author of several popular books (Total Synthesis I and II, and Sources) instructing readers how to synthesize a variety of amphetamines (specifically MDMA), obtain equipment and chemicals, and avoid prosecution. He remained anonymous until Dateline's investigation and interviews revealed that Hobart Huson (owner of the Strike-recommended laboratory supplier "Science Alliance") was the man behind Strike. The NBC program showed Huson/Strike at his office/chemical warehouse, complete with a stuffed bee sitting by his computer. The program led to Huson's arrest and imprison
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https://en.wikipedia.org/wiki/Composition%20algebra
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In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies
for all and in .
A composition algebra includes an involution called a conjugation: The quadratic form is called the norm of the algebra.
A composition algebra (A, ∗, N) is either a division algebra or a split algebra, depending on the existence of a non-zero v in A such that N(v) = 0, called a null vector. When x is not a null vector, the multiplicative inverse of x is When there is a non-zero null vector, N is an isotropic quadratic form, and "the algebra splits".
Structure theorem
Every unital composition algebra over a field can be obtained by repeated application of the Cayley–Dickson construction starting from (if the characteristic of is different from ) or a 2-dimensional composition subalgebra (if ). The possible dimensions of a composition algebra are , , , and .
1-dimensional composition algebras only exist when .
Composition algebras of dimension 1 and 2 are commutative and associative.
Composition algebras of dimension 2 are either quadratic field extensions of or isomorphic to .
Composition algebras of dimension 4 are called quaternion algebras. They are associative but not commutative.
Composition algebras of dimension 8 are called octonion algebras. They are neither associative nor commutative.
For consistent terminology, algebras of dimension 1 have been called unarion, and those of
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https://en.wikipedia.org/wiki/Split-octonion
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In mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers. Unlike the standard octonions, they contain non-zero elements which are non-invertible. Also the signatures of their quadratic forms differ: the split-octonions have a split signature (4,4) whereas the octonions have a positive-definite signature (8,0).
Up to isomorphism, the octonions and the split-octonions are the only two 8-dimensional composition algebras over the real numbers. They are also the only two octonion algebras over the real numbers. Split-octonion algebras analogous to the split-octonions can be defined over any field.
Definition
Cayley–Dickson construction
The octonions and the split-octonions can be obtained from the Cayley–Dickson construction by defining a multiplication on pairs of quaternions. We introduce a new imaginary unit ℓ and write a pair of quaternions (a, b) in the form a + ℓb. The product is defined by the rule:
where
If λ is chosen to be −1, we get the octonions. If, instead, it is taken to be +1 we get the split-octonions. One can also obtain the split-octonions via a Cayley–Dickson doubling of the split-quaternions. Here either choice of λ (±1) gives the split-octonions.
Multiplication table
A basis for the split-octonions is given by the set .
Every split-octonion can be written as a linear combination of the basis elements,
with real coefficients .
By linearity, multiplication of split-octonions is completely determined by
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https://en.wikipedia.org/wiki/H.%20Jay%20Melosh
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H. Jay Melosh (June 23, 1947 – September 11, 2020) was an American geophysicist specialising in impact cratering. He earned a degree in physics from Princeton University and a doctoral degree in physics and geology from Caltech in 1972. His PhD thesis concerned quarks. Melosh's research interests include impact craters, planetary tectonics, and the physics of earthquakes and landslides. His recent research includes studies of the giant impact origin of the Moon, the Chicxulub impact that is thought to have extinguished most dinosaurs, and studies of ejection of rocks from their parent bodies. He was active in astrobiological studies that relate chiefly to the exchange of microorganisms between the terrestrial planets (a process known as panspermia or transpermia).
Melosh was a member of the American Geophysical Union, Geological Society of America, Meteoritical Society, American Astronomical Society (Division of Planetary Sciences,) and the American Association for the Advancement of Science. He was the recipient of the Barringer Medal of the Meteoritical Society for his work on the physics of impact, and of the G. K. Gilbert Award from the Geological Society of America. He was elected to the National Academy of Sciences in 2003.
Awards and honors
Asteroid 8216 Melosh is named in his honor.
The American Geophysical Union 2008 Harry H. Hess Medal - for “outstanding achievements in research in the constitution and evolution of Earth and sister planets.”
Publications
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https://en.wikipedia.org/wiki/Point%20of%20zero%20charge
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The point of zero charge (pzc) is generally described as the pH at which the net charge of total particle surface (i.e. absorbent's surface) is equal to zero, which concept has been introduced in the studies dealt with colloidal flocculation to explain pH affecting the phenomenon.
A related concept in electrochemistry is the electrode potential at the point of zero charge. Generally, the pzc in electrochemistry is the value of the negative decimal logarithm of the activity of the potential-determining ion in the bulk fluid. The pzc is of fundamental importance in surface science. For example, in the field of environmental science, it determines how easily a substrate is able to adsorb potentially harmful ions. It also has countless applications in technology of colloids, e.g., flotation of minerals. Therefore, the pzc value has been examined in many application of adsorption to the environmental science. The pzc value is typically obtained by titrations and several titration method has been developed. Related values associated with the soil characteristics exist along with the pzc value, including zero point of charge (zpc), point of zero net charge (pznc), etc.
Term definition of point of zero charge
The point of zero charge is the pH for which the net surface charge of adsorbent is equal to zero. This concept has been introduced by an increase of interest in the pH of the solution during adsorption. The reason why pH has attracted much attention is that the adsorption o
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https://en.wikipedia.org/wiki/Yashavant%20Kanetkar
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Yashavant Kanetkar is an Indian computer science author, known for his books on programming languages. He has authored several books on C, C++, VC++, C#, .NET, DirectX and COM programming. He is also a speaker on various technology subjects and is a regular columnist for Express Computers and Developer 2.0. His best-known books include Let Us C, Understanding Pointers In C and Test Your C Skills.
He received the Microsoft Most Valuable Professional award for his work in programming from Microsoft for five consecutive years.
He obtained his B.E. from Veermata Jijabai Technological Institute and M.Tech from IIT Kanpur. He is the director of KICIT, a training company, and KSET. Both these companies are based in Nagpur.
Brief History
Yashavant originally specialized in mechanical engineering. He came to Delhi with the intention of starting a manufacturing business of making VIP suitcase locks. However, he was unable to receive a business loan from any banks. A bank manager told him about a computer scheme that the government had launched. For the benefits of the scheme, Yashavant decided to start a business in IT.
Bibliography (of selected books)
ASP.NET Web Services ()
Understanding Pointers in C()
C Column Collection ()
C Pearls ()
C Projects ()
C#.NET Fundas ()
C++.Net Fundas ()
C++. Net ()
Data Structure Through C ()
Data Structure Through C++ ()
Direct X Game Programming Fundas ()
Exploring C ()
Go Embedded ()
Graphics Under C ()
Introduction To OOPS & C++
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https://en.wikipedia.org/wiki/Georgios%20Souflias
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Georgios Ath. Souflias () (born July 7, 1941) is a Greek politician. He is a member of the New Democracy political party and was Minister for the Environment, Physical Planning and Public Works for the duration of the Karamanlis administration.
Born in Farsala, Larissa regional unit to a family of Sarakatsani, he graduated in civil engineering from the National Technical University of Athens and he successfully exercised the profession in Larisa from 1966 to 1974. In each election from 1974 to 1996, he was elected as a member of the Greek Parliament from Larissa. He was Deputy Minister for Interior Affairs from November 1977 to May 1980 and Deputy Minister for Coordination from May 1980 to September 1981. From July 1989 to October 1989, was Minister for the National Economy, and from November 1989 to February 1990, he was Minister for Finance. He served as Minister for the National Economy again from April 1990 to October 1990; he was also Minister for Tourism from April 1990 to May 1990, and from January 1991 to October 1993 he was Minister for National Education and Religious Affairs. He was a candidate for the presidency of New Democracy in 1997, but the presidency was won by Kostas Karamanlis. On February 4, 1998, he was expelled from the party, along with two other members of parliament, for failing to vote along with the party in its opposition to a government policy. He did not run in the 2000 parliamentary election. On the first day of the party's 5th Congress, March
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https://en.wikipedia.org/wiki/Symmetric%20monoidal%20category
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In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" is defined) such that the tensor product is symmetric (i.e. is, in a certain strict sense, naturally isomorphic to for all objects and of the category). One of the prototypical examples of a symmetric monoidal category is the category of vector spaces over some fixed field k, using the ordinary tensor product of vector spaces.
Definition
A symmetric monoidal category is a monoidal category (C, ⊗, I) such that, for every pair A, B of objects in C, there is an isomorphism called the swap map that is natural in both A and B and such that the following diagrams commute:
The unit coherence:
The associativity coherence:
The inverse law:
In the diagrams above, a, l, and r are the associativity isomorphism, the left unit isomorphism, and the right unit isomorphism respectively.
Examples
Some examples and non-examples of symmetric monoidal categories:
The category of sets. The tensor product is the set theoretic cartesian product, and any singleton can be fixed as the unit object.
The category of groups. Like before, the tensor product is just the cartesian product of groups, and the trivial group is the unit object.
More generally, any category with finite products, that is, a cartesian monoidal category, is symmetric monoidal. The tensor product is the direct product of objects, and any terminal object (empty product) is the un
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https://en.wikipedia.org/wiki/Genomic%20convergence
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Genomic convergence is a multifactor approach used in genetic research that combines different kinds of genetic data analysis to identify and prioritize susceptibility genes for a complex disease.
Early applications
In January 2003, Michael Hauser along with fellow researchers at the Duke Center for Human Genetics (CHG) coined the term “genomic convergence” to describe their endeavor to identify genes affecting the expression of Parkinson disease (PD). Their work successfully combined serial analysis of gene expression (SAGE) with genetic linkage analysis. The authors explain, “While both linkage and expression analyses are powerful on their own, the number of possible genes they present as candidates for PD or any complex disorder remains extremely large”. The convergence of the two methods allowed researchers to decrease the number of possible PD genes to consider for further study.
Their success prompted further use of the genomic convergence method at the CHG, and in July 2003 Yi-Ju Li, et al. published a paper revealing that glutathione S-transferase omega-1 (GSTO1) modifies the age-at-onset (AAO) of Alzheimer disease (AD) and PD.
In May 2004, Dr. Margaret Pericak-Vance, currently the director of the John P. Hussman Institute for Human Genomics at the University of Miami Miller School of Medicine and then the director of the CHG, articulated the value of the genomic convergence method at a New York Academy of Sciences (NYAS) keynote address entitled "Novel Methods in
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https://en.wikipedia.org/wiki/%2A-autonomous%20category
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In mathematics, a *-autonomous (read "star-autonomous") category C is a symmetric monoidal closed category equipped with a dualizing object . The concept is also referred to as Grothendieck—Verdier category in view of its relation to the notion of Verdier duality.
Definition
Let C be a symmetric monoidal closed category. For any object A and , there exists a morphism
defined as the image by the bijection defining the monoidal closure
of the morphism
where is the symmetry of the tensor product. An object of the category C is called dualizing when the associated morphism is an isomorphism for every object A of the category C.
Equivalently, a *-autonomous category is a symmetric monoidal category C together with a functor such that for every object A there is a natural isomorphism , and for every three objects A, B and C there is a natural bijection
.
The dualizing object of C is then defined by . The equivalence of the two definitions is shown by identifying .
Properties
Compact closed categories are *-autonomous, with the monoidal unit as the dualizing object. Conversely, if the unit of a *-autonomous category is a dualizing object then there is a canonical family of maps
.
These are all isomorphisms if and only if the *-autonomous category is compact closed.
Examples
A familiar example is the category of finite-dimensional vector spaces over any field k made monoidal with the usual tensor product of vector spaces. The dualizing object is k, the one-dimensi
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https://en.wikipedia.org/wiki/Dinatural%20transformation
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In category theory, a branch of mathematics, a dinatural transformation between two functors
written
is a function that to every object of associates an arrow
of
and satisfies the following coherence property: for every morphism of the diagram
commutes.
The composition of two dinatural transformations need not be dinatural.
See also
Extranatural transformation
Natural transformation
References
External links
Functors
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https://en.wikipedia.org/wiki/Evolution%40Home
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evolution@home was a volunteer computing project for evolutionary biology, launched in 2001. The aim of evolution@home is to improve understanding of evolutionary processes. This is achieved by simulating individual-based models. The Simulator005 module of evolution@home was designed to better predict the behaviour of Muller's ratchet.
The project was operated semi-automatically; participants had to manually download tasks from the webpage and submit results by email using this method of operation. yoyo@home used a BOINC wrapper to completely automate this project by automatically distributing tasks and collecting their results. Therefore, the BOINC version was a complete volunteer computing project. yoyo@home has declared its involvement in this project finished.
See also
Artificial life
Digital organism
Evolutionary computation
Folding@home
List of volunteer computing projects
References
Science in society
Free science software
Volunteer computing projects
Digital organisms
Bioinformatics
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https://en.wikipedia.org/wiki/Phosphite%20ester
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In organic chemistry, a phosphite ester or organophosphite usually refers to an organophosphorous compound with the formula P(OR)3. They can be considered as esters of an unobserved tautomer phosphorous acid, H3PO3, with the simplest example being trimethylphosphite, P(OCH3)3. Some phosphites can be considered esters of the dominant tautomer of phosphorous acid (HP(O)(OH)2). The simplest representative is dimethylphosphite with the formula HP(O)(OCH3)2. Both classes of phosphites are usually colorless liquids.
Synthesis
From PCl3
Phosphite esters are typically prepared by treating phosphorus trichloride with an alcohol. For alkyl alcohols the displaced chloride ion can attack the phosphite, causing dealkylation to give a dialkylphosphite and an organochlorine compound. The overall reaction is as follows:
PCl3 + 3 C2H5OH → (C2H5O)2P(O)H + 2 HCl + C2H5Cl
Alternatively, when the alcoholysis is conducted in the presence of proton acceptors (typically an amine base), one obtains the C3-symmetric trialkyl derivatives:
PCl3 + 3 C2H5OH + 3 R3N → (C2H5O)3P + 3 R3NHCl
A base is not essential when using aromatic alcohols such as phenols, as they are not susceptible to attack by chloride, however it does catalyse the esterification reaction and is therefore often included.
By transesterification
Phosphite esters can also be prepared by transesterification, as they undergo alcohol exchange upon heating with other alcohols. This process is reversible and can be
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https://en.wikipedia.org/wiki/Joaquim%20Pimenta%20de%20Castro
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Joaquim Pereira Pimenta de Castro, 10th Count of Pimenta de Castro (5 November 1846, in Pias, Monção – 14 May 1918, in Lisbon; ) was a Portuguese army officer and politician. He was a career military officer reaching the position of General, also graduated in mathematics by the University of Coimbra. In 1908, he was nominated commander of the 3rd Military Region, in Porto. After the proclamation of the Republic on 5 October 1910, he was Minister of War, for only two months, in 1911. He had to resign due to the monarchist incursion of Henrique de Paiva Couceiro. An independent, he was chosen by President Manuel de Arriaga to be the President of the Ministry (Prime Minister) of a government, who would rule without the parliament, where the Portuguese Republican Party, led by Afonso Costa had the majority. His government, with the support of the moderate Evolutionist Party and the Republican Union, and also conservative military factions, was in office from 28 January to 14 May 1915. It was overthrown by the military movement of 14 May 1915, supported by the Republican Party, which also caused the resignation of President Manuel de Arriaga.
References
1846 births
1918 deaths
Naval ministers of Portugal
People from Monção
Prime Ministers of Portugal
Finance ministers of Portugal
Portuguese military officers
University of Coimbra alumni
19th-century Portuguese people
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https://en.wikipedia.org/wiki/Table%20of%20Newtonian%20series
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In mathematics, a Newtonian series, named after Isaac Newton, is a sum over a sequence written in the form
where
is the binomial coefficient and is the falling factorial. Newtonian series often appear in relations of the form seen in umbral calculus.
List
The generalized binomial theorem gives
A proof for this identity can be obtained by showing that it satisfies the differential equation
The digamma function:
The Stirling numbers of the second kind are given by the finite sum
This formula is a special case of the kth forward difference of the monomial xn evaluated at x = 0:
A related identity forms the basis of the Nörlund–Rice integral:
where is the Gamma function and is the Beta function.
The trigonometric functions have umbral identities:
and
The umbral nature of these identities is a bit more clear by writing them in terms of the falling factorial . The first few terms of the sin series are
which can be recognized as resembling the Taylor series for sin x, with (s)n standing in the place of xn.
In analytic number theory it is of interest to sum
where B are the Bernoulli numbers. Employing the generating function its Borel sum can be evaluated as
The general relation gives the Newton series
where is the Hurwitz zeta function and the Bernoulli polynomial. The series does not converge, the identity holds formally.
Another identity is
which converges for . This follows from the general form of a Newton series for equidistant nodes (when it
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https://en.wikipedia.org/wiki/Lead%E2%80%93lag%20compensator
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A lead–lag compensator is a component in a control system that improves an undesirable frequency response in a feedback and control system. It is a fundamental building block in classical control theory.
Applications
Lead–lag compensators influence disciplines as varied as robotics,
satellite control, automobile diagnostics, LCDs and laser frequency stabilisation. They are an important building block in analog control systems, and
can also be used in digital control.
Given the control plant, desired specifications can be achieved using compensators. I, P, PI, PD, and PID, are optimizing controllers which are used to improve system parameters (such as reducing steady state error, reducing resonant peak, improving system response by reducing rise time). All these operations can be done by compensators as well,
used in cascade compensation technique.
Theory
Both lead compensators and lag compensators introduce a pole–zero pair into the open loop transfer function. The transfer function can be written in the Laplace domain as
where X is the input to the compensator, Y is the output, s is the complex Laplace transform variable, z is the zero frequency and p is the pole frequency. The pole and zero are both typically negative, or left of the origin in the complex plane. In a lead compensator, ,
while in a lag compensator .
A lead-lag compensator consists of a lead compensator cascaded with a lag compensator. The overall transfer function can be written as
Typ
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https://en.wikipedia.org/wiki/NBIC
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NBIC may refer to:
Acronym for the fields of Nanotechnology, Biotechnology, Information technology and Cognitive science
Namibia Business Innovation Center (see Namibia University of Science and Technology)
NanKang Biotech Incubation Center
Nano/Bio Interface Center, University of Pennsylvania
National Board Inspection Code (see National Board of Boiler and Pressure Vessel Inspectors)
Netherlands Bioinformatics Centre
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https://en.wikipedia.org/wiki/Synthetic%20differential%20geometry
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In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory. There are several insights that allow for such a reformulation. The first is that most of the analytic data for describing the class of smooth manifolds can be encoded into certain fibre bundles on manifolds: namely bundles of jets (see also jet bundle). The second insight is that the operation of assigning a bundle of jets to a smooth manifold is functorial in nature. The third insight is that over a certain category, these are representable functors. Furthermore, their representatives are related to the algebras of dual numbers, so that smooth infinitesimal analysis may be used.
Synthetic differential geometry can serve as a platform for formulating certain otherwise obscure or confusing notions from differential geometry. For example, the meaning of what it means to be natural (or invariant) has a particularly simple expression, even though the formulation in classical differential geometry may be quite difficult.
Further reading
John Lane Bell, Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets (PDF file)
F.W. Lawvere, Outline of synthetic differential geometry (PDF file)
Anders Kock, Synthetic Differential Geometry (PDF file), Cambridge University Press, 2nd Edition, 2006.
R. Lavendhomme, Basic Concepts of Synthetic Differential Geometry, Springer-Verlag, 1996.
Michael Shulman, Syn
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https://en.wikipedia.org/wiki/Solomon%20Pikelner
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Solomon Borisovich Pikelner () (February 6, 1921 - November 19, 1975) was a Soviet astronomer who made a significant contribution to the theory of the interstellar medium, solar plasma physics, stellar atmospheres, and magnetohydrodynamics. He was professor of astronomy at Moscow State University starting in 1959. The crater Pikelner on the Moon and asteroid 1975 Pikelner (see List of asteroids/1001–2000) bear his name.
External links
Biography
Soviet astronomers
1921 births
1975 deaths
Academic staff of Moscow State University
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https://en.wikipedia.org/wiki/Selected%20area%20diffraction
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Selected area (electron) diffraction (abbreviated as SAD or SAED) is a crystallographic experimental technique typically performed using a transmission electron microscope (TEM). It is a specific case of electron diffraction used primarily in material science and solid state physics as one of the most common experimental techniques. Especially with appropriate analytical software, SAD patterns (SADP) can be used to determine crystal orientation, measure lattice constants or examine its defects.
Principle
In transmission electron microscope, a thin crystalline sample is illuminated by parallel beam of electrons accelerated to energy of hundreds of kiloelectron volts. At these energies samples are transparent for the electrons if the sample is thinned enough (typically less than 100 nm). Due to the wave–particle duality, the high-energetic electrons behave as matter waves with wavelength of a few thousandths of a nanometer. The relativistic wavelength is given by
where is Planck's constant, is the electron rest mass, is the elementary charge, is the speed of light and is an electric potential accelerating the electrons (also called acceleration voltage). For instance the acceleration voltage of 200 000 kV results in a wavelength of 2.508 pm.
Since the spacing between atoms in crystals is about a hundred times larger, the electrons are diffracted on the crystal lattice, acting as a diffraction grating. Due to the diffraction, part of the electrons is scattered
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https://en.wikipedia.org/wiki/Static%20pressure
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In fluid mechanics the term static pressure has several uses:
In the design and operation of aircraft, static pressure is the air pressure in the aircraft's static pressure system.
In fluid dynamics, many authors use the term static pressure in preference to just pressure to avoid ambiguity. Often however, the word ‘static’ may be dropped and in that usage pressure is the same as static pressure at a nominated point in a fluid.
The term static pressure is also used by some authors in fluid statics.
Static pressure in design and operation of aircraft
An aircraft's static pressure system is the key input to its altimeter and, along with the pitot pressure system, also drives the airspeed indicator.
The static pressure system is open to the aircraft's exterior through a small opening called the static port, which allows sensing the ambient atmospheric pressure at the altitude at which the aircraft is flying. In flight, the air pressure varies slightly at different positions around the aircraft's exterior, so designers must select the static ports' locations carefully. Wherever they are located, the air pressure that the ports observe will generally be affected by the aircraft's instantaneous angle of attack. The difference between that observed pressure and the actual atmospheric pressure (at altitude) causes a small position error in the instruments' indicated altitude and airspeed. A designer's objective in locating the static port is to minimize the resulting position
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https://en.wikipedia.org/wiki/Zhu%E2%80%93Takaoka%20string%20matching%20algorithm
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In computer science, the Zhu–Takaoka string matching algorithm is a variant of the Boyer–Moore string-search algorithm. It uses two consecutive text characters to compute the bad-character shift. It is faster when the alphabet or pattern is small, but the skip table grows quickly, slowing the pre-processing phase.
References
http://www-igm.univ-mlv.fr/~lecroq/string/node20.html
String matching algorithms
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https://en.wikipedia.org/wiki/Bundle
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Bundle or Bundling may refer to:
Bundling (packaging), the process of using straps to bundle up items
Biology
Bundle of His, a collection of heart muscle cells specialized for electrical conduction
Bundle of Kent, an extra conduction pathway between the atria and ventricles in the heart
Hair bundle, a group of cellular processes resembling hair, characteristic of a hair cell
Computing
Bundle (OS X), a type of directory in NEXTSTEP and OS X
Bundle (software distribution), a package containing a software and everything it needs to operate
Bundle adjustment, a photogrammetry/computer vision technique
Economics
Bundled payment, a method for reimbursing health care providers
Product bundling, a marketing strategy that involves offering several products for sale as one combined product
Mathematics and engineering
Bundle (mathematics), a generalization of a fiber bundle dropping the condition of a local product structure
Bundle conductor (power engineering)
Fiber bundle, a topological space that looks locally like a product space
Optical fiber bundle, a cable consisting of a collection of fiber optics
Music
Bundles (album), a 1975 album by Soft Machine, including a song of the same title
The Bundles, an anti-folk supergroup
The Bundles (album), a 2010 album by the group
Politics
Bundling (fundraising), when donations from many individuals are collected by one person and presented to the recipient
Bundling (public choice), a similar concept to product bundlin
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https://en.wikipedia.org/wiki/Fr%C3%A9chet%20manifold
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In mathematics, in particular in nonlinear analysis, a Fréchet manifold is a topological space modeled on a Fréchet space in much the same way as a manifold is modeled on a Euclidean space.
More precisely, a Fréchet manifold consists of a Hausdorff space with an atlas of coordinate charts over Fréchet spaces whose transitions are smooth mappings. Thus has an open cover and a collection of homeomorphisms onto their images, where are Fréchet spaces, such that
is smooth for all pairs of indices
Classification up to homeomorphism
It is by no means true that a finite-dimensional manifold of dimension is homeomorphic to or even an open subset of However, in an infinite-dimensional setting, it is possible to classify "well-behaved" Fréchet manifolds up to homeomorphism quite nicely. A 1969 theorem of David Henderson states that every infinite-dimensional, separable, metric Fréchet manifold can be embedded as an open subset of the infinite-dimensional, separable Hilbert space, (up to linear isomorphism, there is only one such space).
The embedding homeomorphism can be used as a global chart for Thus, in the infinite-dimensional, separable, metric case, up to homeomorphism, the "only" topological Fréchet manifolds are the open subsets of the separable infinite-dimensional Hilbert space. But in the case of or Fréchet manifolds (up to the appropriate notion of diffeomorphism) this fails.
See also
, of which a Fréchet manifold is a generalization
References
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https://en.wikipedia.org/wiki/SDF-1
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SDF-1 may refer to:
Stromal cell-derived factor 1, a protein in cell biology
SDF-1 Macross, a fictional spaceship from the anime series The Super Dimension Fortress Macross
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https://en.wikipedia.org/wiki/Thial
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In organic chemistry, a thial or thioaldehyde is a functional group which is similar to an aldehyde, , in which a sulfur (S) atom replaces the oxygen (O) atom of the aldehyde (R represents an alkyl or aryl group). Thioaldehydes are even more reactive than thioketones. Unhindered thioaldehydes are generally too reactive to be isolated — for example, thioformaldehyde, , condenses to the cyclic trimer 1,3,5-trithiane. Thioacrolein, , formed by decomposition of allicin from garlic, undergoes a self Diels-Alder reaction giving isomeric vinyldithiins. While thioformaldehyde is highly reactive, it is found in interstellar space along with its mono- and di-deuterated isotopologues. With sufficient steric bulk, however, stable thioaldehydes can be isolated.
In early work, the existence of thioaldehydes was inferred by trapping processes. For instance the reaction of with benzaldehyde was proposed to form thiobenzaldehyde, which forms a cycloadduct with the dithiophosphine ylides to form a ring.
See also
Thioketone
Thioenol
Organosulfur compounds
References
Functional groups
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https://en.wikipedia.org/wiki/Simple%20%28abstract%20algebra%29
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In mathematics, the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element. Some examples are:
A group is called a simple group if it does not contain a nontrivial proper normal subgroup.
A ring is called a simple ring if it does not contain a nontrivial two sided ideal.
A module is called a simple module if it does not contain a nontrivial submodule.
An algebra is called a simple algebra if it does not contain a nontrivial two sided ideal.
The general pattern is that the structure admits no non-trivial congruence relations.
The term is used differently in semigroup theory. A semigroup is said to be simple if it has no nontrivial
ideals, or equivalently, if Green's relation J is
the universal relation. Not every congruence on a semigroup is associated with an ideal, so a simple semigroup may
have nontrivial congruences. A semigroup with no nontrivial congruences is called congruence simple.
See also
semisimple
simple universal algebra
Abstract algebra
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https://en.wikipedia.org/wiki/Brauer%20algebra
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In mathematics, a Brauer algebra is an associative algebra introduced by Richard Brauer in the context of the representation theory of the orthogonal group. It plays the same role that the symmetric group does for the representation theory of the general linear group in Schur–Weyl duality.
Structure
The Brauer algebra is a -algebra depending on the choice of a positive integer . Here is an indeterminate, but in practice is often specialised to the dimension of the fundamental representation of an orthogonal group . The Brauer algebra has the dimension
Diagrammatic definition
A basis of consists of all pairings on a set of elements (that is, all perfect matchings of a complete graph : any two of the elements may be matched to each other, regardless of their symbols). The elements are usually written in a row, with the elements beneath them.
The product of two basis elements and is obtained by concatenation: first identifying the endpoints in the bottom row of and the top row of (Figure AB in the diagram), then deleting the endpoints in the middle row and joining endpoints in the remaining two rows if they are joined, directly or by a path, in AB (Figure AB=nn in the diagram). Thereby all closed loops in the middle of AB are removed. The product of the basis elements is then defined to be the basis element corresponding to the new pairing multiplied by where is the number of deleted loops. In the example .
Generators and relations
can also be de
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https://en.wikipedia.org/wiki/Semisimple%20algebra
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In ring theory, a branch of mathematics, a semisimple algebra is an associative artinian algebra over a field which has trivial Jacobson radical (only the zero element of the algebra is in the Jacobson radical). If the algebra is finite-dimensional this is equivalent to saying that it can be expressed as a Cartesian product of simple subalgebras.
Definition
The Jacobson radical of an algebra over a field is the ideal consisting of all elements that annihilate every simple left-module. The radical contains all nilpotent ideals, and if the algebra is finite-dimensional, the radical itself is a nilpotent ideal. A finite-dimensional algebra is then said to be semisimple if its radical contains only the zero element.
An algebra A is called simple if it has no proper ideals and A2 = {ab | a, b ∈ A} ≠ {0}. As the terminology suggests, simple algebras are semisimple. The only possible ideals of a simple algebra A are A and {0}. Thus if A is simple, then A is not nilpotent. Because A2 is an ideal of A and A is simple, A2 = A. By induction, An = A for every positive integer n, i.e. A is not nilpotent.
Any self-adjoint subalgebra A of n × n matrices with complex entries is semisimple. Let Rad(A) be the radical of A. Suppose a matrix M is in Rad(A). Then M*M lies in some nilpotent ideals of A, therefore (M*M)k = 0 for some positive integer k. By positive-semidefiniteness of M*M, this implies M*M = 0. So M x is the zero vector for all x, i.e. M = 0.
If {Ai} is a finite collection of
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https://en.wikipedia.org/wiki/Stephen%20Hyde
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Professor Stephen Timothy Hyde is an Australian scientist who was appointed Fellow of the Australian Academy of Science in 2005.
He is professor and also the ARC Federation Fellow in the Department of Applied Mathematics, Research School of Physics, at the Australian National University. He holds the Barry Ninham Chair of Natural Sciences.
His speciality is in the field of theoretical physics: self-assembly of complex materials and systems.
From 1999 to 2002 he was Head of the Department of Applied Mathematics.
References
Fellows of the Australian Academy of Science
Living people
Academic staff of the Australian National University
Australian physicists
Theoretical physicists
Place of birth missing (living people)
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Describing%20function
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In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended by Ralph Kochenburger is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear time-invariant (LTI) transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is linear. Thus, this dependence on amplitude generates a family of linear systems that are combined in an attempt to capture salient features of the non-linear system behavior. The describing function is one of the few widely applicable methods for designing nonlinear systems, and is very widely used as a standard mathematical tool for analyzing limit cycles in closed-loop controllers, such as industrial process controls, servomechanisms, and electronic oscillators.
The method
Consider feedback around a discontinuous (but piecewise continuous) nonlinearity (e.g., an amplifier with saturation, or an element with deadband effects) cascaded with a slow stable linear system. The continuous region in which the feedback is presented to the nonlinearity depends on the amplitude of the output of the linear system. As the linear system's output amplitude decays, the nonlinearity may move in
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https://en.wikipedia.org/wiki/A.%20C.%20Heidebrecht
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Arthur C. Heidebrecht (born 1939) is a Canadian professor and civil engineer. He served as a faculty member at McMaster University from 1963 to 1997, dean of Engineering (1981–1989) and Vice-president Academic (1989–1994).
Born in Alberta, Canada, he studied at the University of Alberta and graduated with a B.Sc in Civil Engineering in 1960. He obtained his M.Sc and Ph.D. at Northwestern University in 1961 and 1963, respectively.
He is renowned for his research in earthquake engineering. In 2002, he was awarded an Honorary D.Sc degree from McMaster University.
References
1939 births
Living people
Canadian civil engineers
People from Alberta
Academic staff of McMaster University
Canadian people of German descent
University of Alberta alumni
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https://en.wikipedia.org/wiki/Tension%20%28physics%29
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In physics, tension is described as the pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements. Tension could be the opposite of compression.
At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing, the restoring force might create what is also called tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length.
Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in newtons in the International System of Units (or pounds-force in Imperial units). The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are also called "passive forces". There are two basic possibilities for systems of objects held by strings: either acceleration is zero and the system is therefore in equilibrium, or there is acceleration, and therefore a net force is present in the system.
Tension in one dimension
Tension in a string is a non-negative vector quantity. Zero tension is slack. A stri
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https://en.wikipedia.org/wiki/Coefficient%20%28disambiguation%29
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Coefficient could have one of the following meanings:
Mathematics
A coefficient is a constant multiplication of a function.
The term differential coefficient has been mostly displaced by the modern term derivative.
Computing
In computer arithmetics, the term coefficient (floating point number) is also sometimes used as a synonym for mantissa or significand.
Probability theory and Statistics
The coefficient of determination, denoted R2 and pronounced R squared, is the proportion of total variation of outcomes explained by a statistical model.
The coefficient of variation (CV) is a normalized measure of dispersion of a probability distribution or frequency distribution.
The correlation coefficient (Pearson's r) is a measure of the linear correlation (dependence) between two variables.
Science
In physics, a physical coefficient is an important number that characterizes some physical property of an object.
In chemistry, a stoichiometric coefficient is a number placed in front of a term in a chemical equation to indicate how many molecules (or atoms) take part in the reaction.
Other
UEFA coefficient, used by the governing body for association football in Europe to calculate ranking points for its member clubs and national federations
The Coefficients were an Edwardian London dining club.
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https://en.wikipedia.org/wiki/Second%20partial%20derivative%20test
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In mathematics, the second partial derivative test is a method in multivariable calculus used to determine if a critical point of a function is a local minimum, maximum or saddle point.
Functions of two variables
Suppose that is a differentiable real function of two variables whose second partial derivatives exist and are continuous. The Hessian matrix of is the 2 × 2 matrix of partial derivatives of :
Define to be the determinant
of . Finally, suppose that is a critical point of , that is, that . Then the second partial derivative test asserts the following:
If and then is a local minimum of .
If and then is a local maximum of .
If then is a saddle point of .
If then the point could be any of a minimum, maximum, or saddle point (that is, the test is inconclusive).
Sometimes other equivalent versions of the test are used. In cases 1 and 2, the requirement that is positive at implies that and have the same sign there. Therefore, the second condition, that be greater (or less) than zero, could equivalently be that or be greater (or less) than zero at that point.
A condition implicit in the statement of the test is that if or , it must be the case that and therefore only cases 3 or 4 are possible.
Functions of many variables
For a function f of three or more variables, there is a generalization of the rule above. In this context, instead of examining the determinant of the Hessian matrix, one must look at the eigenvalues of the Hessian matrix
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https://en.wikipedia.org/wiki/Polynomial%20transformation
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In mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of a polynomial. Polynomial transformations such as Tschirnhaus transformations are often used to simplify the solution of algebraic equations.
Simple examples
Translating the roots
Let
be a polynomial, and
be its complex roots (not necessarily distinct).
For any constant , the polynomial whose roots are
is
If the coefficients of are integers and the constant is a rational number, the coefficients of may be not integers, but the polynomial has integer coefficients and has the same roots as .
A special case is when The resulting polynomial does not have any term in .
Reciprocals of the roots
Let
be a polynomial. The polynomial whose roots are the reciprocals of the roots of as roots is its reciprocal polynomial
Scaling the roots
Let
be a polynomial, and be a non-zero constant. A polynomial whose roots are the product by of the roots of is
The factor appears here because, if and the coefficients of are integers or belong to some integral domain, the same is true for the coefficients of .
In the special case where , all coefficients of are multiple of , and is a monic polynomial, whose coefficients belong to any integral domain containing and the coefficients of . This polynomial transformation is often used to reduce questions on algebraic numbers to questions on algebraic integers.
Combining this with a translat
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https://en.wikipedia.org/wiki/J.%20Fuller
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J. Fuller was a publisher in 18th-century England.
Publications
"A Lover of the Mathematics". A Mathematical Miscellany in Four Parts. 2nd ed., S. Fuller, Dublin, 1735. The First Part is: An Essay towards the Probable Solution of the Forty five Surprising PARADOXES, in GORDON's Geography.
Gentleman's Diary or The Mathematical Repository (1741-1745)
English publishers (people)
Businesspeople from Dublin (city)
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