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https://en.wikipedia.org/wiki/1722%20in%20science
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The year 1722 in science and technology involved some significant events.
Chemistry
René Antoine Ferchault de Réaumur publishes his work on metallurgy, L'Art de convertir le fer forge en acier, which describes how to convert iron into steel.
Exploration
April 5 (Easter Sunday) – Jacob Roggeveen lands on Easter Island.
Mathematics
Abraham de Moivre states de Moivre's formula, connecting complex numbers and trigonometry.
Meteorology
A continuous series of weather records is begun in Uppsala by Anders Celsius; it will be maintained for at least 300 years.
Physics
Willem 's Gravesande publishes experimental evidence that the formula for kinetic energy of a body in motion is .
Technology
October – In clockmaking, George Graham demonstrates that his experiments, begun in December 1721, with mercurial compensation of the pendulum result in greater accuracy in timekeeping under conditions of variable temperature.
Births
May 11 – Petrus Camper, Dutch comparative anatomist (died 1789)
November 19 – Leopold Auenbrugger, Austrian physician (died 1809)
December 28 – Eliza Lucas, American agronomist (died 1793)
Thomas Barker, English meteorologist (died 1809)
Deaths
May 20 – Sébastien Vaillant, French botanist (born 1669)
References
18th century in science
1720s in science
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https://en.wikipedia.org/wiki/Invertible%20%28disambiguation%29
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Invertible may refer to
Mathematics
Invertible element
Invertible function
Invertible ideal
Invertible knot
Invertible jet
Invertible matrix
Invertible module
Invertible sheaf
Others
Invertible counterpoint
See also
Inverse (disambiguation)
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https://en.wikipedia.org/wiki/James%20Clark%20%28programmer%29
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James Clark (born 23 February 1964) is a software engineer and creator of various open-source software including groff, expat and several XML specifications.
Education and early life
Clark was born in London and educated at Charterhouse School and Merton College, Oxford where he studied Mathematics and Philosophy.
Career
Clark has lived in Bangkok, Thailand since 1995, and is permanent Thai resident. He owns a company called Thai Open Source Software Center, which provides him a legal framework for his open-source activities. Clark is the author and creator of groff, as well as an XML editing mode for GNU Emacs.
Work on XML
Clark served as technical lead of the working group that developed XML—notably contributing the self-closing, empty element tag syntax, and the name XML. His contributions to XML are cited in dozens of books on the subject. Clark is the author or co-author of a number of influential specifications and implementations, including:
DSSSL: An SGML transformation and styling language.
Expat: An open-source XML parser.
XSLT: XSL Transformations, a part of the XSL family. He was the editor of the XSLT 1.0 specification.
XPath: Path language for addressing XML documents; used by XSLT but also as a free-standing language. He was the editor of the XPath 1.0 specification.
TREX: Tree regular experessions for XML (TREX) is a schema language for XML. TREX has been merged with RELAX to create RELAX NG.
RELAX NG: an XML Schema language, with both an explicit
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https://en.wikipedia.org/wiki/Fractional%20ideal
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In mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains. In some sense, fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both under discussion, the latter are sometimes termed integral ideals for clarity.
Definition and basic results
Let be an integral domain, and let be its field of fractions.
A fractional ideal of is an -submodule of such that there exists a non-zero such that . The element can be thought of as clearing out the denominators in , hence the name fractional ideal.
The principal fractional ideals are those -submodules of generated by a single nonzero element of . A fractional ideal is contained in if and only if it is an (integral) ideal of .
A fractional ideal is called invertible if there is another fractional ideal such that
where
is the product of the two fractional ideals.
In this case, the fractional ideal is uniquely determined and equal to the generalized ideal quotient
The set of invertible fractional ideals form an abelian group with respect to the above product, where the identity is the unit ideal itself. This group is called the group of fractional ideals of . The principal fractional ideals form a subgroup. A (nonzero) fractional ideal is invertible if and only if it is projective as an
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https://en.wikipedia.org/wiki/Derived%20set
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A derived set may refer to:
Derived set (mathematics), a construction in point-set topology
Derived row, a concept in musical set theory
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https://en.wikipedia.org/wiki/Scalar%20potential
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In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.
A scalar potential is a fundamental concept in vector analysis and physics (the adjective scalar is frequently omitted if there is no danger of confusion with vector potential). The scalar potential is an example of a scalar field. Given a vector field , the scalar potential is defined such that:
where is the gradient of and the second part of the equation is minus the gradient for a function of the Cartesian coordinates . In some cases, mathematicians may use a positive sign in front of the gradient to define the potential. Because of this definition of in terms of the gradient, the direction of at any point is the direction of the steepest decrease of at that point, its magnitude is the rate of that decrease per unit length.
In order for to be described in terms of a scalar potential only, any of the following equivalent statements have to be true:
where the integration is over a Jordan arc passing from location to location and is evaluated at location .
where the integral is over any simple closed path, otherwise known
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https://en.wikipedia.org/wiki/ARF
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ARF may refer to:
Organizations
Advertising Research Foundation
Animal Rescue Foundation
Armenian Revolutionary Federation
ASEAN Regional Forum
People
Cahit Arf (1910–1997), Turkish mathematician
Science, medicine, and mathematics
Acute renal failure
Acute rheumatic fever
ADP ribosylation factor, a small GTP-binding protein
The Arf invariant in mathematics
Argon fluoride laser or ArF laser
Atomic Resonance Filter or atomic line filter
Auxin Response Factors in plants
p14arf or ARF tumor suppressor
Other uses
Arf (Nanoha), character in Magical Girl Lyrical Nanoha
Abuse Reporting Format
Almost-Ready-to-Fly model aircraft
The Azkena Rock Festival, Vitoria-Gasteiz, Spain
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https://en.wikipedia.org/wiki/Eddington%20number
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In astrophysics, the Eddington number, , is the number of protons in the observable universe. Eddington originally calculated it as about ; current estimates make it approximately .
The term is named for British astrophysicist Arthur Eddington, who in 1940 was the first to propose a value of and to explain why this number might be important for physical cosmology and the foundations of physics.
History
Eddington argued that the value of the fine-structure constant, α, could be obtained by pure deduction. He related α to the Eddington number, which was his estimate of the number of protons in the universe. This led him in 1929 to conjecture that α was exactly 1/136. He devised a "proof" that NEdd = 136 × 2256, or about 1.57×1079. Other physicists did not adopt this conjecture and did not accept his argument.
In the late 1930s, the best experimental value of the fine-structure constant, α, was approximately 1/137. Eddington then argued, from aesthetic and numerological considerations, that α should be exactly 1/137.
Current estimates of NEdd point to a value of about . These estimates assume that all matter can be taken to be hydrogen and require assumed values for the number and size of galaxies and stars in the universe.
Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time.
During a course of lectures that he delivered in 1938 as Tarner Lecturer at Trinity College, Cambridge, Eddington averred that:
This large n
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https://en.wikipedia.org/wiki/Vanish%20at%20infinity
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In mathematics, a function is said to vanish at infinity if its values approach 0 as the input grows without bounds. There are two different ways to define this with one definition applying to functions defined on normed vector spaces and the other applying to functions defined on locally compact spaces.
Aside from this difference, both of these notions correspond to the intuitive notion of adding a point at infinity, and requiring the values of the function to get arbitrarily close to zero as one approaches it. This definition can be formalized in many cases by adding an (actual) point at infinity.
Definitions
A function on a normed vector space is said to if the function approaches as the input grows without bounds (that is, as ). Or,
in the specific case of functions on the real line.
For example, the function
defined on the real line vanishes at infinity.
Alternatively, a function on a locally compact space , if given any positive number , there exists a compact subset such that
whenever the point lies outside of In other words, for each positive number the set has compact closure.
For a given locally compact space the set of such functions
valued in which is either or forms a -vector space with respect to pointwise scalar multiplication and addition, which is often denoted
As an example, the function
where and are reals greater or equal 1 and correspond to the point on vanishes at infinity.
A normed space is locally compact if and onl
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https://en.wikipedia.org/wiki/Standard%20basis
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In mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs of real numbers, the standard basis is formed by the vectors
Similarly, the standard basis for the three-dimensional space is formed by vectors
Here the vector ex points in the x direction, the vector ey points in the y direction, and the vector ez points in the z direction. There are several common notations for standard-basis vectors, including {ex, ey, ez}, {e1, e2, e3}, {i, j, k}, and {x, y, z}. These vectors are sometimes written with a hat to emphasize their status as unit vectors (standard unit vectors).
These vectors are a basis in the sense that any other vector can be expressed uniquely as a linear combination of these. For example, every vector v in three-dimensional space can be written uniquely as
the scalars , , being the scalar components of the vector v.
In the -dimensional Euclidean space , the standard basis consists of n distinct vectors
where ei denotes the vector with a 1 in the th coordinate and 0's elsewhere.
Standard bases can be defined for other vector spaces, whose definition involves coefficients, such as polynomials and matrices. In both cases, the standard basis consists of the elements of the space such that all coefficients but one are 0 and the non-zero
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https://en.wikipedia.org/wiki/1718%20in%20science
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This is a list of significant events that occurred in the year 1718 in science.
Astronomy
Edmond Halley discovers the proper motion of stars.
Chemistry
Étienne François Geoffroy presents the first ever table of chemical affinity (based on displacement reactions) to the French Academy of Sciences.
Mathematics
Abraham de Moivre publishes The Doctrine of Chances: a method of calculating the probabilities of events in play in English, which goes through several editions.
Medicine
The Charitable Infirmary, Dublin, is founded by six surgeons in Ireland, the first public voluntary hospital in the British Isles.
Technology
May 15 – James Puckle patents the Puckle Gun, in England.
Births
May 16 – Maria Gaetana Agnesi, Italian mathematician (died 1799)
May 23 – William Hunter, Scottish anatomist (died 1783)
August 17 – Francis Willis, English physician specialising in mental disorders (died 1807)
Salomée Halpir (née Rusiecki), Lithuanian physician (died after 1763)
Deaths
March 11 – Guy-Crescent Fagon, French physician and botanist (born 1638)
April – James Petiver, English naturalist and apothecary (born c. 1665)
December 9 – Vincenzo Coronelli, Italian cartographer and encyclopedist (born 1650)
December 11 – Pierre Dionis, French surgeon and anatomist (born 1643)
References
18th century in science
1710s in science
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https://en.wikipedia.org/wiki/1717%20in%20science
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The year 1717 in science and technology involved few significant events.
Biology
Thomas Fairchild, a nurseryman at Hoxton in the East End of London, becomes the first person to produce a successful scientific plant hybrid, Dianthus Caryophyllus barbatus, known as "Fairchild's Mule".
James Petiver publishes Papilionum Brittaniae Icones, the first book devoted exclusively to British butterflies, giving English names to a number of species.
Births
June 5 – Emanuel Mendes da Costa, English botanist (died 1791)
June 28 – Matthew Stewart, Scottish mathematician (died 1785)
September 11 – Pehr Wilhelm Wargentin, Swedish astronomer (died 1783)
November 16 – Jean le Rond d'Alembert, French mathematician (died 1783)
Pierre Le Roy, French clockmaker (died 1785)
Wilhelm Friedrich von Gleichen, German microscopist (died 1783)
Deaths
January 13 – Maria Sibylla Merian, German-born naturalist (born 1647)
March 8 – Abraham Darby I, English ironmaster (born 1678)
References
18th century in science
1710s in science
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https://en.wikipedia.org/wiki/1716%20in%20science
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The year 1716 in science and technology involved some significant events.
Chemistry
Johann von Löwenstern-Kunckel publishes his handbook of experimental chemistry, Collegium physico-chymicum experimentale, oder, Laboratorium chymicum, in Germany.
Events
Tsar Peter the Great of Russia studies with the physician Herman Boerhaave at Leiden University.
Births
January 12 – Antonio de Ulloa, Spanish explorer (died 1795)
March 6 – Pehr Kalm, Swedish botanist and explorer (died 1779)
May 29 – Louis-Jean-Marie Daubenton, French naturalist (died 1799)
c. August 18 – Johan Maurits Mohr, Dutch astronomer (died 1775)
October 3 – Giovanni Battista Beccaria, Italian physicist (died 1781)
October 4 – James Lind, Scottish-born pioneer of hygiene in the British Royal Navy (died 1794)
December 27 – Leonardo Ximenes, Tuscan polymath (died 1786)
James Brindley, English engineer (died 1772)
Deaths
November 14 – Gottfried Leibniz, German scientist and mathematician (born 1646)
18th century in science
1710s in science
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https://en.wikipedia.org/wiki/1714%20in%20science
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The year 1714 in science and technology involved some significant events.
Mathematics
March – Roger Cotes publishes Logometrica in the Philosophical Transactions of the Royal Society. He provides the first proof of what is now known as Euler's formula and constructs the logarithmic spiral.
May – Brook Taylor publishes a paper, written in 1708, in the Philosophical Transactions of the Royal Society which describes his solution to the center of oscillation problem.
Gottfried Leibniz discusses the harmonic triangle.
Medicine
April 14 – Anne, Queen of Great Britain, performs the last touching for the "King's evil".
Dominique Anel uses the first fine-pointed syringe in surgery, later known as "Anel's syringe".
Herman Boerhaave introduces a modern system of clinical teaching at the University of Leiden.
The anatomical engravings of Bartolomeo Eustachi (died 1574) are published for the first time as Tabulae anatomicae by Giovanni Maria Lancisi.
Technology
Henry Mill obtains a British patent for a machine resembling a typewriter.
Events
July – The Parliament of Great Britain offers the Longitude prize to anyone who can solve the problem of accurately determining a ship's longitude.
Births
January 21 – Anna Morandi, Bolognese anatomist (died 1774)
January 6 – Percivall Pott, English surgeon (died 1788)
June 17 – César-François Cassini de Thury, French astronomer (died 1784)
September 6 – Robert Whytt, Scottish physician (died 1766)
October 16 – Giovanni Arduino, Ita
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https://en.wikipedia.org/wiki/1713%20in%20science
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The year 1713 in science and technology involved some significant events.
Astronomy
John Rowley of London produces an orrery to a commission by Charles Boyle, 4th Earl of Orrery.
Mathematics
September 9 – Nicolas Bernoulli first describes the St. Petersburg paradox in a letter to Pierre Raymond de Montmort.
November 13 – James Waldegrave provides the first known minimax mixed strategy solution to a two-person game, in a letter to de Montmort.
Jacob Bernoulli's best known work, Ars Conjectandi (The Art of Conjecture), is published posthumously by his nephew. It contains a mathematical proof of the law of large numbers, the Bernoulli numbers, and other important research in probability theory and enumeration.
Medicine
William Cheselden publishes Anatomy of the Human Body and it becomes a popular work on anatomy, at least in part due to it being written in English rather than Latin.
Italian Bernardino Ramazzini provides one of the first descriptions of task-specific dystonia in his book of occupational diseases, Morbis Artificum, noting in chapter II of its Supplementum that "Scribes and Notaries" may develop "incessant movement of the hand, always in the same direction … the continuous and almost tonic strain on the muscles... that results in failure of power in the right hand".
Physics
The second edition of Isaac Newton's Principia Mathematica is published with an introduction by Roger Cotes and an essay by Newton titled General Scholium where he famously states "Hy
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https://en.wikipedia.org/wiki/1712%20in%20science
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The year 1712 in science and technology involved some significant events.
Astronomy
John Flamsteed's Historia Coelestis is first published, against his will and without credit by Isaac Newton and Edmond Halley with the influence of John Arbuthnot. (A final version, approved by Flamsteed, is published posthumously in 1725.)
Mathematics
Seki Takakazu's discovery of what become known as Bernoulli numbers is first published in his posthumous Katsuyo Sanpō.
Giacomo F. Maraldi experimentally obtains the angle in the rhombic dodecahedron shape, which becomes known as the Maraldi angle.
Technology
The first known working Newcomen steam engine is built by Thomas Newcomen with John Calley to pump water out of mines in the Black Country of England.
Births
March 8 – John Fothergill, English physician (died 1780)
March 27 – Claude Bourgelat, French veterinary surgeon (died 1779)
June 15 – Andrew Gordon, Scottish-born Benedictine monk, physicist and inventor (died 1751)
undated
Angélique du Coudray, French pioneer of modern midwifery (died 1789)
Bartholomew Mosse, Irish surgeon and impresario (died 1759)
Deaths
February 2 – Martin Lister, English naturalist (born 1639)
March 25 – Nehemiah Grew, English naturalist (born 1641)
August 29 – Gregory King, English statistician (born 1648)
September 14 – Giovanni Cassini, Italian-born astronomer (born 1625)
References
18th century in science
1710s in science
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https://en.wikipedia.org/wiki/1711%20in%20science
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The year 1711 in science and technology involved some significant events.
Biology
Luigi Ferdinando Marsigli shows that coral is an animal rather than a plant as previously thought.
Mathematics
Giovanni Ceva publishes De Re Nummeraria (Concerning Money Matters), one of the first books on mathematical economics.
John Keill, writing in the journal of the Royal Society and with Isaac Newton's presumed blessing, accuses Gottfried Leibniz of having plagiarized Newton's calculus, formally starting the Leibniz and Newton calculus controversy.
Technology
John Shore invents the tuning fork
Births
May 18 – Ruđer Bošković, Ragusan polymath (died 1787)
July 22 – Georg Wilhelm Richmann, Russian physicist (died 1753)
September 22 – Thomas Wright, English astronomer, mathematician, instrument maker, architect, garden designer, antiquary and genealogist (died 1786)
October 31 – Laura Bassi, Italian scientist (died 1778)
November 19 – Mikhail Lomonosov, Russian scientist (died 1765)
18th century in science
1710s in science
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https://en.wikipedia.org/wiki/Tunel
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Tunel or Tünel may refer to:
TUNEL assay (Terminal deoxynucleotidyl transferase mediated dUTP Nick End Labeling assay), in genetics, a method for detecting DNA fragmentation
Tunel (band), Yugoslav rock band
Tunel (railroad station), railroad station in Poland
Tünel, a historical underground funicular in Istanbul, Turkey
Tünel, Khövsgöl, a Mongolian sum
Tunel, a brand of Herbs de Majorca
See also
Tunnel (disambiguation)
Tune (disambiguation)
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https://en.wikipedia.org/wiki/Particle%20in%20a%20one-dimensional%20lattice
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In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside the lattice. It is a generalization of the free electron model, which assumes zero potential inside the lattice.
Problem definition
When talking about solid materials, the discussion is mainly around crystals – periodic lattices. Here we will discuss a 1D lattice of positive ions. Assuming the spacing between two ions is , the potential in the lattice will look something like this:
The mathematical representation of the potential is a periodic function with a period . According to Bloch's theorem, the wavefunction solution of the Schrödinger equation when the potential is periodic, can be written as:
where is a periodic function which satisfies . It is the Bloch factor with Floquet exponent which gives rise to the band structure of the energy spectrum of the Schrödinger equation with a periodic potential like the Kronig–Penney potential or a cosine function as in the Mathieu equation.
When nearing the edges of the lattice, there are problems with the boundary condition. Therefore, we can represent the ion lattice as a ring following the Born–von Karman boundary conditions. If is the length of the lattice so that , then the number of ions in the lattice is so big, that when consi
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https://en.wikipedia.org/wiki/Richard%20Bolt
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Richard Henry Bolt (April 22, 1911 – January 13, 2002) was an American physics professor at MIT with an interest in acoustics. He was one of the founders of the company Bolt, Beranek and Newman, which built the ARPANET, a forerunner of the Internet.
Early life
Bolt was born in Peking, China, where his parents were medical missionaries. His family returned to the U.S. in 1916 and settled in California.
Bolt graduated from Berkeley High School, California in 1928 and went to college and graduate school at the University of California, Berkeley.
Although he initially expected to major in either music or graphical design, he decided on architecture, in which he attained a BA in 1933. At that time, he had already developed an interest in acoustics, combining his interests for music, design and architecture.
After his marriage to Katherine Mary Smith, right after his graduation in 1933, they made a honeymoon to Europe, where he became acquainted with a number of scientists from Berlin, and the honeymoon was extended to ten months while Bolt learned German and studied acoustics.
Berkeley
Returning to Berkeley in 1934, he entered the graduate physics program, and, earning an M.A. in 1937 and qualifying for Berkeley's Physics Ph.D. program, which he completed in 1939. He performed his research at UCLA, given the fact that Berkeley had no acoustics research facilities at that time. After attaining his PhD in 1939 he worked at MIT for a year on the transmission of sound in various
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https://en.wikipedia.org/wiki/Baryogenesis
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In physical cosmology, baryogenesis (also known as baryosynthesis) is the physical process that is hypothesized to have taken place during the early universe to produce baryonic asymmetry, i.e. the imbalance of matter (baryons) and antimatter (antibaryons) in the observed universe.
One of the outstanding problems in modern physics is the predominance of matter over antimatter in the universe. The universe, as a whole, seems to have a nonzero positive baryon number density. Since it is assumed in cosmology that the particles we see were created using the same physics we measure today, it would normally be expected that the overall baryon number should be zero, as matter and antimatter should have been created in equal amounts. A number of theoretical mechanisms are proposed to account for this discrepancy, namely identifying conditions that favour symmetry breaking and the creation of normal matter (as opposed to antimatter). This imbalance has to be exceptionally small, on the order of 1 in every (≈) particles a small fraction of a second after the Big Bang. After most of the matter and antimatter was annihilated, what remained was all the baryonic matter in the current universe, along with a much greater number of bosons. Experiments reported in 2010 at Fermilab, however, seem to show that this imbalance is much greater than previously assumed. These experiments involved a series of particle collisions and found that the amount of generated matter was approximately 1% larg
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https://en.wikipedia.org/wiki/1709%20in%20science
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The year 1709 in science and technology involved some significant events.
Meteorology
January – Great Frost in Western Europe.
Physics
Francis Hauksbee publishes Physico-Mechanical Experiments on Various Subjects, summarizing the results of his many experiments with electricity and other topics.
Technology
January 10 – Industrial Revolution: Abraham Darby I successfully produces cast iron using coke fuel at his Coalbrookdale blast furnace in Shropshire, England.
February 5 – Dramatist John Dennis devises the thundersheet as a new method of producing theatrical thunder for his tragedy Appius and Virginia at the Theatre Royal, Drury Lane, London.
March 28 – Johann Friedrich Böttger reports the first production of hard-paste porcelain in Europe, at Dresden.
July 13 – Johann Maria Farina founds the first Eau de Cologne and perfume factory in Cologne, Germany.
August 8 – Hot air balloon of Bartholome de Gusmão flies in Portugal.
A collapsible umbrella is introduced in Paris.
Awards
April 9 – Sir Godfrey Copley, 2nd Baronet dies and in his will provides funding to the Royal Society for the annual Copley Medal honoring achievement in science (first awarded in 1731).
Births
February 24 – Jacques de Vaucanson, French engineer and inventor (died 1782)
March 3 – Andreas Sigismund Marggraf, German chemist (died 1782)
March 10 – Georg Steller, German naturalist (died 1746)
April 17 – Giovanni Domenico Maraldi, French-Italian astronomer (died 1788)
July 11 – Johan Gottsc
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https://en.wikipedia.org/wiki/1707%20in%20science
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The year 1707 in science and technology involved some significant events.
Geophysics
May 23 – Volcanic eruption in the Santorini caldera begins.
October 28 – The Hōei earthquake ruptures all segments of the Nankai megathrust simultaneously – the only earthquake known to have done this. It is the most powerful in Japan until 2011, with an estimated local magnitude of 8.6.
December 16 – Hōei eruption, the last eruption of Mount Fuji in Japan, begins.
Mathematics
Publication of Arithmetica universalis, the collected works of Isaac Newton on algebra.
Abraham de Moivre derives de Moivre's formula.
Medicine
John Floyer, in The Physician's Pulse Watch, introduces counting of pulse rate during one minute.
Giovanni Maria Lancisi publishes De Subitaneis Mortibus (On Sudden Death), an early work in cardiology.
Georg Ernst Stahl publishes .
Births
January 11 – Vincenzo Riccati, Italian mathematician (died 1775)
April 10 – John Pringle, Scottish physician (died 1782)
April 15 – Leonhard Euler, Swiss mathematician (died 1783)
April 26 – Johannes Burman, Dutch botanist (died 1780)
May 23 – Carl Linnaeus, Swedish naturalist (died 1778)
June 22 (bapt.) – Elizabeth Blackwell, Scottish-born botanical illustrator (died 1758)
September 7 – Georges-Louis Leclerc, Comte de Buffon, French naturalist (died 1788)
December 22 – Johann Amman, Swiss-Russian botanist (died 1741)
date unknown – Benjamin Robins, English scientist and engineer (died 1751)
Deaths
March 30 – Marquis de V
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https://en.wikipedia.org/wiki/1704%20in%20science
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The year 1704 in science and technology involved some significant events.
Astronomy
approx. date – The first modern orrery is built by George Graham and Thomas Tompion.
Earth sciences
An earthquake strikes Gondar in Ethiopia.
Meteorology
Daniel Defoe documents the Great Storm of 1703 with eyewitness testimonies in The Storm (London).
Physics
Isaac Newton releases a record of experiments and the deductions made from them in Opticks, a major contribution in study of optics and refraction of light.
Pierre Varignon invents the U-tube manometer, a device capable of measuring rarefaction in gases.
Technology
The second electric machine is invented by British engineer Francis Hauksbee the elder (1660–1713): it is a sphere of glass rotated by a wheel.
For watch movements, Peter Debaufre invents the Debaufre escapement, the first frictional rest watch escapement produced: the escapement consists of two saw-tooth escape wheels of the same count.
For watch bearings, a jewel bearing made of ruby, comprising a ring (the "hole") with a sink for oil, is invented by Nicholas Facio with Peter and Jacob Debaufre, who use pierced natural rubies. Other gemstones are used subsequently, including garnet (which is too soft) and diamond; in the 20th century, synthetic ruby or sapphire becomes universal for jewel bearings.
In oil painting, colormaker Diesbach of Berlin (Germany) accidentally invents the pigment Prussian blue, a powerful dark blue pigment with greenish undertones (made f
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https://en.wikipedia.org/wiki/1703%20in%20science
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The year 1703 in science and technology involved some significant events.
Biology
Charles Plumier's Nova plantarum Americanarum genera begins publication in Paris. This includes descriptions of Fuchsia, discovered by him on Hispaniola, and naming of the genus Magnolia, applied to species from Martinique.
Chemistry
Georg Ernst Stahl, professor of medicine and chemistry at the University of Halle, proposes phlogiston theory in the way it comes to be generally understood.
Mathematics
Gottfried Leibniz first publishes a description of binary numbers in the West.
Leonty Magnitsky's Arithmetic (Арифметика) is published, a scientific book in the Russian language.
Meteorology
November 24 – December 2 – The Great Storm of 1703, an Atlantic hurricane, ravages southern England and the English Channel, killing nearly 8000, mostly at sea.
Technology
An early, crude seismograph is developed by the French physicist Abbé Jean de Hautefeuille.
Appointments
November 30 – Isaac Newton is elected president of the Royal Society in London, a position he will hold until his death in 1727.
Births
January 8 – André Levret, French obstetrician (died 1780)
January 15 – Johann Ernst Hebenstreit, German physician and naturalist (died 1757)
June 21 – Joseph Lieutaud, French physician (died 1780)
August 23 – Robert James, English physician (died 1776)
September 15 – Guillaume-François Rouelle, French chemist and apothecary (died 1770)
October 28 – Antoine Deparcieux, French mathematici
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https://en.wikipedia.org/wiki/BTB
|
BTB may refer to:
In biology:
Blood–testis barrier in testicular anatomy
Blood–thymus barrier
Bovine tuberculosis or Mycobacterium bovis, a disease originating in cattle
Breakthrough bleeding, of the menstrual period
Bromothymol blue, a chemical indicator for weak acids and bases
BTB/POZ domain, a protein domain
In other uses:
Belgian Union of Transport Workers, a trade union in Belgium
Branch target buffer, a computer processor element
Bétou Airport, in the Republic of the Congo (IATA airport code: BTB)
Basil Temple Blackwood (1870–1917), British book illustrator (credited as B.T.B.)
Bob the Builder, British children's television series
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https://en.wikipedia.org/wiki/Harmonic%20divisor%20number
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In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are
1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 .
Harmonic divisor numbers were introduced by Øystein Ore, who showed that every perfect number is a harmonic divisor number and conjectured that there are no odd harmonic divisor numbers other than 1.
Examples
The number 6 has the four divisors 1, 2, 3, and 6. Their harmonic mean is an integer:
Thus 6 is a harmonic divisor number. Similarly, the number 140 has divisors 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. Their harmonic mean is
Since 5 is an integer, 140 a harmonic divisor number.
Factorization of the harmonic mean
The harmonic mean of the divisors of any number can be expressed as the formula
where is the sum of th powers of the divisors of : is the number of divisors, and is the sum of divisors .
All of the terms in this formula are multiplicative, but not completely multiplicative.
Therefore, the harmonic mean is also multiplicative.
This means that, for any positive integer , the harmonic mean can be expressed as the product of the harmonic means of the prime powers in the factorization of .
For instance, we have
and
Harmonic divisor numbers and perfect numbers
For any integer M, as Ore observed, the product of the harmonic mean and arithmetic mean of its divisors equals M itself, as can be seen from the defini
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https://en.wikipedia.org/wiki/Conditional%20%28computer%20programming%29
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In computer science, conditionals (that is, conditional statements, conditional expressions and conditional constructs) are programming language commands for handling decisions. Specifically, conditionals perform different computations or actions depending on whether a programmer-defined Boolean condition evaluates to true or false. In terms of control flow, the decision is always achieved by selectively altering the control flow based on some condition (apart from the case of branch predication).
Although dynamic dispatch is not usually classified as a conditional construct, it is another way to select between alternatives at runtime. Conditional statements are the checkpoints in the programe that determines behaviour according to situation.
Terminology
In imperative programming languages, the term "conditional statement" is usually used, whereas in functional programming, the terms "conditional expression" or "conditional construct" are preferred, because these terms all have distinct meanings.
If–then(–else)
The if–then construct (sometimes called if–then–else) is common across many programming languages. Although the syntax varies from language to language, the basic structure (in pseudocode form) looks like this:
If (boolean condition) Then
(consequent)
Else
(alternative)
End If
For example:
If stock=0 Then
message= order new stock
Else
message= there is stock
End If
In the example code above, the part represented by (boolean condition) con
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https://en.wikipedia.org/wiki/Body%20image
|
Body image is a person's thoughts, feelings and perception of the aesthetics or sexual attractiveness of their own body. The concept of body image is used in a number of disciplines, including neuroscience, psychology, medicine, psychiatry, psychoanalysis, philosophy, cultural and feminist studies; the media also often uses the term. Across these disciplines, there is no single consensus definition, but broadly speaking body image consists of the ways people view themselves; their memories, experiences, assumptions, and comparisons about their own appearances; and their overall attitudes towards their own respective heights, shapes, and weights—all of which are shaped by prevalent social and cultural ideals.
Body image can be negative ("body negativity") or positive ("body positivity"). A person with a negative body image may feel self-conscious or ashamed, and may feel that others are more attractive. In a time where social media holds a very important place and is used frequently in our daily lives, people of different ages are affected emotionally and mentally by the appearance and body size/shape ideals set by the society they live in. These standards created and changed by society created a world filled with body shaming; the act of humiliating an individual by mocking or making critical comments about a person's physiological appearance.
Aside from having low self-esteem, sufferers typically fixate on altering their physical appearances. Such behavior creates body di
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https://en.wikipedia.org/wiki/144%20%28number%29
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144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross.
In mathematics
144 is the square of 12. It is also the twelfth Fibonacci number, following 89 and preceding 233, and the only Fibonacci number (other than 0, and 1) to also be a square. 144 is the smallest number with exactly 15 divisors, but it is not highly composite since the smaller number 120 contains 16. 144 is also equal to the sum of the eighth twin prime pair, (71 + 73). It is divisible by the value of its φ function, which returns 48 in its case, and there are 21 solutions to the equation φ(x) = 144. This is more than any integer below it, which makes it a highly totient number.
As a square number in decimal notation, 144 = 12 × 12, and if each number is reversed the equation still holds: 21 × 21 = 441. 169 shares this property, 13 × 13 = 169, while 31 × 31 = 961. Also in decimal, 144 is the largest of only four sum-product numbers, and it is a Harshad number, since 1 + 4 + 4 = 9, which divides 144.
144 is the smallest number whose fifth power is a sum of four (smaller) fifth powers. This solution was found in 1966 by L. J. Lander and T. R. Parkin, and disproved Euler's sum of powers conjecture. It was famously published in a paper by both authors, whose body consisted of only two sentences:
A regular ten-sided decagon has an internal angle of 144 degrees, which is equal to four times its own central angle, and equivalently twice the cen
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https://en.wikipedia.org/wiki/666%20%28number%29
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666 (six hundred [and] sixty-six) is the natural number following 665 and preceding 667.
In Christianity, 666 is referred to in (most manuscripts of) chapter 13 of the Book of Revelation of the New Testament as the "number of the beast."
In mathematics
666 is the sum of the first thirty-six natural numbers, which makes it a triangular number:
.
Since 36 is also triangular, 666 is a doubly triangular number. Also, where 15 and 21 are triangular as well, whose squares ( and ) add to 666 and have a difference of .
The number of integers which are relatively prime to 666 is also 216, ; and for an angle measured in degrees, (where here is the golden ratio).
666 is also the sum of the squares of the first seven primes , while the number of twin primes less than is 666.
A prime reciprocal magic square based on in decimal has a magic constant of 666. The twelfth pair of twin primes is (149, 151), with 151 the thirty-sixth prime number.
666 is a Smith number and Harshad number in base ten. The 27th indexed unique prime in decimal features a "666" in the middle of its sequence of digits.
The Roman numeral for 666, DCLXVI, has exactly one occurrence of all symbols whose value is less than 1000 in decreasing order (D = 500, C = 100, L = 50, X = 10, V = 5, I = 1).
In religion
Number of the beast
In the Textus Receptus manuscripts of the New Testament, the Book of Revelation () cryptically asserts 666 to be "the man's number" or "the number of a man" (depending on ho
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https://en.wikipedia.org/wiki/Addition%20polymer
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In polymer chemistry, an addition polymer is a polymer that forms by simple linking of monomers without the co-generation of other products. Addition polymerization differs from condensation polymerization, which does co-generate a product, usually water. Addition polymers can be formed by chain polymerization, when the polymer is formed by the sequential addition of monomer units to an active site in a chain reaction, or by polyaddition, when the polymer is formed by addition reactions between species of all degrees of polymerization. Addition polymers are formed by the addition of some simple monomer units repeatedly. Generally polymers are unsaturated compounds like alkenes, alkalines etc. The addition polymerization mainly takes place in free radical mechanism. The free radical mechanism of addition polymerization completed by three steps i.e. Initiation of free radical, Chain propagation, Termination of chain.
Polyolefins
Many common addition polymers are formed from unsaturated monomers (usually having a C=C double bond). The most prevalent addition polymers are polyolefins, i.e. polymers derived by the conversion of olefins (alkenes) to long-chain alkanes. The stoichiometry is simple:
n RCH=CH2 → [RCH-CH2]n
This conversion can be induced by a variety of catalysts including free radicals, acids, carbanions and metal complexes.
Examples of such polyolefins are polyethenes, polypropylene, PVC, Teflon, Buna rubbers, polyacrylates, polystyrene, and PCTFE.
Copolymer
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https://en.wikipedia.org/wiki/Kikuchi
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Kikuchi, often written 菊池 or 菊地, may refer to:
Places
Kikuchi, Kumamoto
Kikuchi River, Kumamoto
Kikuchi District, Kumamoto
People
Kikuchi (surname)
Kikuchi clan
Yoshihiko Kikuchi
Yusei Kikuchi
Other
Kikuchi disease, a rare, non-cancerous enlargement of the lymph nodes
Kikuchi line (solid state physics), a line in an electron diffraction pattern for a crystal
Kikuchi Line (Kumaden), a railway line in Kumamoto Prefecture connecting Kami-Kumamoto Station to Miyoshi Station
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https://en.wikipedia.org/wiki/Metric%20signature
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In mathematics, the signature of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix of the metric tensor with respect to a basis. In relativistic physics, the v represents the time or virtual dimension, and the p for the space and physical dimension. Alternatively, it can be defined as the dimensions of a maximal positive and null subspace. By Sylvester's law of inertia these numbers do not depend on the choice of basis and thus can be used to classify the metric. The signature is often denoted by a pair of integers implying r= 0, or as an explicit list of signs of eigenvalues such as or for the signatures and , respectively.
The signature is said to be indefinite or mixed if both v and p are nonzero, and degenerate if r is nonzero. A Riemannian metric is a metric with a positive definite signature . A Lorentzian metric is a metric with signature , or .
There is another notion of signature of a nondegenerate metric tensor given by a single number s defined as , where v and p are as above, which is equivalent to the above definition when the dimension n = v + p is given or implicit. For example, s = 1 − 3 = −2 for and its mirroring s' = −s = +2 for .
Definition
The signature of a metric tensor is defined as the signature of the corresponding quadratic form. It is
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https://en.wikipedia.org/wiki/Jon%20Speelman
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Jonathan Simon Speelman (born 2 October 1956) is a British chess player and author. He was awarded the title of Grandmaster in 1980.
Early life and education
Speelman was educated at St Paul's School, London and Worcester College, Oxford, where he read mathematics.
Career
A winner of the British Chess Championship in 1978, 1985 and 1986, Speelman has been a regular member of the English team for the Chess Olympiad, an international biennial chess tournament organised by FIDE, the World Chess Federation.
He qualified for two Candidates Tournaments:
In the 1989–1990 cycle, Speelman qualified by placing third in the 1987 interzonal tournament held in Subotica, Yugoslavia. After beating Yasser Seirawan in his first round 4–1, and Nigel Short in the second round 3½–1½, he lost to Jan Timman at the semi-final stage 4½–3½.
In the following 1990–93 championship cycle, he lost 5½–4½ in the first round to Short, the eventual challenger for Garry Kasparov's crown.
In 1989, Speelman beat Kasparov in a televised speed tournament and then went on to win the event.
On December 7, 1990, Speelman was featured in an experimental interactive BBC2 broadcast called Your Move, which was hosted by Rob Curling and commentated by chess writer William Hartston. In the groundbreaking one-off episode, Speelman was pitted against the audience, who would use a special telephone line to submit their moves, with the move played by the viewers being decided by a democratic vote. Speelman won the match,
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https://en.wikipedia.org/wiki/Space%20group
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In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions. In dimensions other than 3, they are sometimes called Bieberbach groups.
In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography .
History
Space groups in 2 dimensions are the 17 wallpaper groups which have been known for several centuries, though the proof that the list was complete was only given in 1891, after the much more difficult classification of space groups had largely been completed.
In 1879 the German mathematician Leonhard Sohncke listed the 65 space groups (called Sohncke groups) whose elements preserve the chirality. More accurately, he listed 66 groups, but both the Russian mathematician and crystallographer Evgraf Fedorov and the German mathematician Arthur Moritz Schoenflies noticed that two of them were really the same. The space groups in three dimensions were
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https://en.wikipedia.org/wiki/Life%20on%20Mars
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The possibility of life on Mars is a subject of interest in astrobiology due to the planet's proximity and similarities to Earth. To date, no proof of past or present life has been found on Mars. Cumulative evidence suggests that during the ancient Noachian time period, the surface environment of Mars had liquid water and may have been habitable for microorganisms, but habitable conditions do not necessarily indicate life.
Scientific searches for evidence of life began in the 19th century and continue today via telescopic investigations and deployed probes, searching for water, chemical biosignatures in the soil and rocks at the planet's surface, and biomarker gases in the atmosphere.
Mars is of particular interest for the study of the origins of life because of its similarity to the early Earth. This is especially true since Mars has a cold climate and lacks plate tectonics or continental drift, so it has remained almost unchanged since the end of the Hesperian period. At least two-thirds of Mars's surface is more than 3.5 billion years old, and it could have been habitable since 4.48 billion years ago, 500 million years before the earliest known Earth lifeforms; Mars may thus hold the best record of the prebiotic conditions leading to life, even if life does not or has never existed there.
Following the confirmation of the past existence of surface liquid water, the Curiosity, Perseverance and Opportunity rovers started searching for evidence of past life, including a pa
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https://en.wikipedia.org/wiki/555%20%28number%29
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555 (five hundred [and] fifty-five) is the natural number following 554 and preceding 556.
In mathematics
555 is a sphenic number. In base 10, it is a repdigit, and because it is divisible by the sum of its digits, it is a Harshad number. It is also a Harshad number in binary, base 11, base 13 and hexadecimal.
It is the sum of the first triplet of three-digit permutable primes in decimal:
.
It is the twenty-sixth number such that its Euler totient (288) is equal to the totient value of its sum-of-divisors: .
Telephone numbers
The NANP reserves telephone numbers in many dialing areas in the 555 local block for fictional purposes, such as 1-308-555-3485.
References
External links
Integers
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https://en.wikipedia.org/wiki/Antiholomorphic%20function
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In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions.
A function of the complex variable z defined on an open set in the complex plane is said to be antiholomorphic if its derivative with respect to exists in the neighbourhood of each and every point in that set, where is the complex conjugate.
A definition of antiholomorphic function follows: "[a] function of one or more complex variables [is said to be anti-holomorphic if (and only if) it] is the complex conjugate of a holomorphic function ."
One can show that if f(z) is a holomorphic function on an open set D, then f() is an antiholomorphic function on , where is the reflection against the x-axis of D, or in other words, is the set of complex conjugates of elements of D. Moreover, any antiholomorphic function can be obtained in this manner from a holomorphic function. This implies that a function is antiholomorphic if and only if it can be expanded in a power series in in a neighborhood of each point in its domain. Also, a function f(z) is antiholomorphic on an open set D if and only if the function is holomorphic on D.
If a function is both holomorphic and antiholomorphic, then it is constant on any connected component of its domain.
References
Complex analysis
Types of functions
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https://en.wikipedia.org/wiki/African%20spoonbill
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The African spoonbill (Platalea alba) is a long-legged wading bird of the ibis and spoonbill family Threskiornithidae. The species is widespread across Africa and Madagascar, including Botswana, Kenya, Mozambique, Namibia, South Africa, and Zimbabwe.
Biology
It lives in marshy wetlands with some open shallow water and nests in colonies in trees or reedbeds. They usually don't share colonies with storks or herons. The African spoonbill feeds in shallow water, and fishes for various fish, molluscs, amphibians, crustaceans, insects and larvae. The animal uses its open bill to catch foods by swinging it from side-to-side in the water, which catches foods in its mouth. Long legs and thin, pointed toes enable it to walk easily through varying depths of water.
The African spoonbill is almost unmistakable through most of its range. The breeding bird is all white except for its red legs and face and long grey spatulate bill. It has no crest, unlike the common spoonbill. Immature birds lack the red face and have a yellow bill. Unlike herons, spoonbills fly with their necks outstretched.
Breeding
The African spoonbill begins breeding in the winter, which lasts until spring. During the breeding season, adult male African Spoonbills develop more plumage and brighter coloration. The spoonbill's nest, generally located in trees above water, is built from sticks and reeds and lined with leaves. Three to five eggs are laid by the female birds, usually during the months of April or May.
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https://en.wikipedia.org/wiki/Electroacoustic%20music
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Electroacoustic music is a genre of popular and Western art music in which composers use technology to manipulate the timbres of acoustic sounds, sometimes by using audio signal processing, such as reverb or harmonizing, on acoustical instruments. It originated around the middle of the 20th century, following the incorporation of electric sound production into compositional practice. The initial developments in electroacoustic music composition to fixed media during the 20th century are associated with the activities of the at the ORTF in Paris, the home of musique concrète, the Studio for Electronic Music in Cologne, where the focus was on the composition of elektronische Musik, and the Columbia-Princeton Electronic Music Center in New York City, where tape music, electronic music, and computer music were all explored. Practical electronic music instruments began to appear in the early 20th century.
Tape music
Tape music is an integral part of musique concrète, which uses the tape recorder as its central musical source. The music can utilise pre-recorded sound fragments and the creation of loops, which can be altered and manipulated through techniques such as editing and playback speed manipulation. The work of Halim El-Dabh is perhaps the earliest example of tape (or, in this case, Wire recording) music. El-Dabh's The Expression of Zaar, first presented in Cairo, Egypt, in 1944, was an early work using musique concrète–like techniques similar to those developed in Paris
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https://en.wikipedia.org/wiki/E.%20B.%20Ford
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Edmund Brisco "Henry" Ford (23 April 1901 – 2 January 1988) was a British ecological geneticist. He was a leader among those British biologists who investigated the role of natural selection in nature. As a schoolboy Ford became interested in lepidoptera, the group of insects which includes butterflies and moths. He went on to study the genetics of natural populations, and invented the field of ecological genetics. Ford was awarded the Royal Society's Darwin Medal in 1954. In the wider world his best known work is Butterflies (1945).
Education
Ford was born in Dalton-in-Furness, near Ulverston, in Lancashire, England, in 1901. He was the only child of Harold Dodsworth Ford (1864–1943), a classics teacher turned Anglican clergyman, and his wife (and second cousin) Gertrude Emma Bennett. His paternal grandfather, Dr Henry Edmund Ford (1821–1909), was a "professor" (= teacher) of music at Carlisle and the organist of Carlisle Cathedral from 1842 to 1902. Ford was educated at St Bees School, Cumberland (now Cumbria), and read zoology at Wadham College, Oxford, (where his father had also studied), graduating B.A. in 1924, upgraded to M.A. 1927, B.Sc. (a research degree) in 1927, and taking a D.Sc in 1943.
Career and research
Ford's career was based entirely at the University of Oxford. The biologist Arthur Cain said Ford took a degree in classics before turning to zoology. Ford read zoology at Oxford, and was taught genetics by Julian Huxley. "The lecturer whose interests most
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https://en.wikipedia.org/wiki/NCD
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NCD may refer to:
Language
Nemine contradicente (or N.C.D.), for 'with no one speaking against'
Non-convergent discourse, an asymmetricly bilingual conversation
Mathematics
Normalized compression distance, in statistics and information theory
Nearly completely decomposable Markov chain, in probability theory
Medicine
Non-communicable disease, that cannot be transmitted
National coverage determination, American public healthcare guidance
Neurocognitive disorder, a class of mental illness
Organisations in government and politics
National Council on Disability, United States
National Center for Digitization, Serbia
Naval Construction Division of the U.S. Navy Seabees
New Centre-Right, Italy
Other uses
National Cleavage Day
National Commission On Disabilities, an organization based in Liberia
Naval Combat Dress, a uniform of the Canadian Forces
Network Computing Devices, a company
No claim discount on insurance policies
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https://en.wikipedia.org/wiki/Sperner%27s%20lemma
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In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring (described below) of a triangulation of an simplex contains a cell whose vertices all have different colors.
The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points and in root-finding algorithms, and are applied in fair division (cake cutting) algorithms.
According to the Soviet Mathematical Encyclopaedia (ed. I.M. Vinogradov), a related 1929 theorem (of Knaster, Borsuk and Mazurkiewicz) had also become known as the Sperner lemma – this point is discussed in the English translation (ed. M. Hazewinkel). It is now commonly known as the Knaster–Kuratowski–Mazurkiewicz lemma.
Statement
One-dimensional case
In one dimension, Sperner's Lemma can be regarded as a discrete version of the intermediate value theorem. In this case, it essentially says that if a discrete function takes only the values 0 and 1, begins at the value 0 and ends at the value 1, then it must switch values an odd number of times.
Two-dimensional case
The two-dimensional case is the one referred to most frequently. It is stated as follows:
Subdivide a triangle arbitrarily into a triangulation consisting of smaller triangles meeting edge to edge. Then a Sperner coloring of
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https://en.wikipedia.org/wiki/D%27Alembert%27s%20paradox
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In fluid dynamics, d'Alembert's paradox (or the hydrodynamic paradox) is a contradiction reached in 1752 by French mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to the fluid. Zero drag is in direct contradiction to the observation of substantial drag on bodies moving relative to fluids, such as air and water; especially at high velocities corresponding with high Reynolds numbers. It is a particular example of the reversibility paradox.
D’Alembert, working on a 1749 Prize Problem of the Berlin Academy on flow drag, concluded: "It seems to me that the theory (potential flow), developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future Geometers [i.e. mathematicians - the two terms were used interchangeably at that time] to elucidate". A physical paradox indicates flaws in the theory.
Fluid mechanics was thus discredited by engineers from the start, which resulted in an unfortunate split – between the field of hydraulics, observing phenomena which could not be explained, and theoretical fluid mechanics explaining phenomena which could not be observed – in the words of the Chemistry Nobel Laureate Sir Cyril Hinshelwood.
According to scientific consensus, the occurrence of the paradox is due to the neglected effects of viscosity. In conjunction with scientifi
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https://en.wikipedia.org/wiki/Excitatory%20postsynaptic%20potential
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In neuroscience, an excitatory postsynaptic potential (EPSP) is a postsynaptic potential that makes the postsynaptic neuron more likely to fire an action potential. This temporary depolarization of postsynaptic membrane potential, caused by the flow of positively charged ions into the postsynaptic cell, is a result of opening ligand-gated ion channels. These are the opposite of inhibitory postsynaptic potentials (IPSPs), which usually result from the flow of negative ions into the cell or positive ions out of the cell. EPSPs can also result from a decrease in outgoing positive charges, while IPSPs are sometimes caused by an increase in positive charge outflow. The flow of ions that causes an EPSP is an excitatory postsynaptic current (EPSC).
EPSPs, like IPSPs, are graded (i.e. they have an additive effect). When multiple EPSPs occur on a single patch of postsynaptic membrane, their combined effect is the sum of the individual EPSPs. Larger EPSPs result in greater membrane depolarization and thus increase the likelihood that the postsynaptic cell reaches the threshold for firing an action potential.
EPSPs in living cells are caused chemically. When an active presynaptic cell releases neurotransmitters into the synapse, some of them bind to receptors on the postsynaptic cell. Many of these receptors contain an ion channel capable of passing positively charged ions either into or out of the cell (such receptors are called ionotropic receptors). At excitatory synapses, the ion
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https://en.wikipedia.org/wiki/Chrysiogenes%20arsenatis
|
Chrysiogenes arsenatis is a species of bacterium in the family Chrysiogenaceae. It has a unique biochemistry. Instead of respiring with oxygen, it respires using the most oxidized form of arsenic, arsenate. It uses arsenate as its terminal electron acceptor. Arsenic is usually toxic to life. Bacteria like Chrysiogenes arsenatis are found in anoxic arsenic-contaminated environments.
References
External links
Type strain of Chrysiogenes arsenatis at BacDive - the Bacterial Diversity Metadatabase
Chrysiogenetes
Bacteria described in 1996
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https://en.wikipedia.org/wiki/William%20Hung
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William Hing Cheung Hung (; born January 13, 1983) is a Hong Kong motivational speaker and former singer who gained fame in 2004 as a result of his unsuccessful audition singing Ricky Martin's hit song "She Bangs" on the third season of the television series American Idol.
At the time of his audition, Hung was a civil engineering student at UC Berkeley. After his spirited audition to be the next American Idol, he won the support of many fans, ironically, based on his perceived lack of musical talent. Hung voluntarily left university to pursue a music career. His recording career was marked by negative critical reaction.
He brought his own career as a musician to an end when in 2011 he accepted a job opportunity as a technical crime analyst for the Los Angeles County Sheriff's Department, and decided to pursue law enforcement. Since then, Hung has reflected positively on his pop music career.
Personal life
Hung is a 73rd-generation descendant of Confucius.
After growing up in the Sha Tin district of British Hong Kong, Hung moved with his family to the Van Nuys area in Los Angeles, California, at age 11. He was a civil engineering student at University of California, Berkeley, when he competed on the US television contest series American Idol. He exited college to pursue his music career and later graduated from California State University, Northridge with a degree in mathematics. Hung later completed an MBA from Marist College.
Hung was married to Jian Teng on June 18,
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https://en.wikipedia.org/wiki/1654%20in%20science
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The year 1654 in science and technology involved some significant events.
Astronomy
Sicilian astronomer Giovanni Battista Hodierna publishes De systemate orbis cometici, deque admirandis coeli characteribus including a catalog of comets and nebulae.
Mathematics
At the prompting of the Chevalier de Méré, Blaise Pascal corresponds with Pierre de Fermat on gambling problems, from which is born the theory of probability.
Physics
May 8 – Otto von Guericke demonstrates the effectiveness of his vacuum pump and the power of atmospheric pressure using the Magdeburg hemispheres before Ferdinand III, Holy Roman Emperor, in Regensburg.
Births
December 27 – Jakob Bernoulli, Swiss mathematician (died 1705).
John Banister, English missionary and botanist (died 1692).
prob. date – Eleanor Glanville, English entomologist (died 1709).
Deaths
August 31 – Ole Worm, Danish physician, natural historian and antiquary (born 1588)
October 18 – Nicholas Culpeper, English herbalist (born 1616)
Giovanni de Galliano Pieroni, Italian military engineer and astronomer (born 1586)
References
17th century in science
1650s in science
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https://en.wikipedia.org/wiki/Decoding
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Decoding or decode may refer to: is the process of converting code into plain text or any format that is useful for subsequent processes.
Science and technology
Decoding, the reverse of encoding
Parsing, in computer science
Digital-to-analog converter, "decoding" of a digital signal
Phonics, decoding in communication theory
Decode (Oracle)
Other uses
deCODE genetics, a biopharmaceutical company based in Iceland
"Decode" (song), a 2008 song by Paramore
”Decode”, a song by Sabrina Carpenter from the album Emails I Can't Send
Decoding (semiotics), the interpreting of a message communicated to a receiver
See also
Code (disambiguation)
Decoder (disambiguation)
Decoding methods, methods in communication theory for decoding codewords sent over a noisy channel
Codec, a coder-decoder
Recode (disambiguation)
Video decoder, an electronic circuit
es:Descodificador
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https://en.wikipedia.org/wiki/Books%20on%20cryptography
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Books on cryptography have been published sporadically and with highly variable quality for a long time. This is despite the tempting, though superficial, paradox that secrecy is of the essence in sending confidential messages — see Kerckhoffs' principle.
In contrast, the revolutions in cryptography and secure communications since the 1970s are well covered in the available literature.
Early history
An early example of a book about cryptography was a Roman work, now lost and known only by references. Many early cryptographic works were esoteric, mystical, and/or reputation-promoting; cryptography being mysterious, there was much opportunity for such things. At least one work by Trithemius was banned by the Catholic Church and put on the Index Librorum Prohibitorum as being about black magic or witchcraft. Many writers claimed to have invented unbreakable ciphers. None were, though it sometimes took a long while to establish this.
In the 19th century, the general standard improved somewhat (e.g., works by Auguste Kerckhoffs, Friedrich Kasiski, and Étienne Bazeries). Colonel Parker Hitt and William Friedman in the early 20th century also wrote books on cryptography. These authors, and others, mostly abandoned any mystical or magical tone.
Open literature versus classified literature
With the invention of radio, much of military communications went wireless, allowing the possibility of enemy interception much more readily than tapping into a landline. This increased the nee
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https://en.wikipedia.org/wiki/Onsager
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Onsager is a surname. Notable people with the surname include:
Lars Onsager (1903–1976), Norwegian–American physical chemist and theoretical physicist
Søren Onsager (1878–1946), Norwegian painter
See also
Onsager Medal, an award in the fields of chemistry, physics and mathematics
Onsager reciprocal relations, certain relations between flows and forces in thermodynamic systems
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https://en.wikipedia.org/wiki/Flow
|
Flow may refer to:
Science and technology
Fluid flow, the motion of a gas or liquid
Flow (geomorphology), a type of mass wasting or slope movement in geomorphology
Flow (mathematics), a group action of the real numbers on a set
Flow (psychology), a mental state of being fully immersed and focused
Flow, a spacecraft of NASA's GRAIL program
Computing
Flow network, graph-theoretic version of a mathematical flow
Flow analysis
Calligra Flow, free diagramming software
Dataflow, a broad concept in computer systems with many different meanings
Microsoft Flow (renamed to Power Automate in 2019), a workflow toolkit in Microsoft Dynamics
Neos Flow, a free and open source web application framework written in PHP
webMethods Flow, a graphical programming language
FLOW (programming language), an educational programming language from the 1970s
Flow (web browser), a web browser with a proprietary rendering engine
Arts, entertainment and media
Flow (journal), an online journal of television and media studies
The Flow (book), a 2022 non-fiction book by Amy-Jane Beer
Flow (video game)
Flow (comics), a fictional character in the International Ultramarine Corps
Flow 93.5, the Canadian radio station CFXJ-FM
Flow FM (Australia), a radio station
Flow (Argentina), a cable television operator
Film and television
Flow (television), the sequencing of TV material from one element to the next
Flow TV, a network of Ripe Digital Entertainment
Flow: For Love of Water, a 2008 docume
|
https://en.wikipedia.org/wiki/Assembler
|
Assembler may refer to:
Arts and media
Nobukazu Takemura, avant-garde electronic musician, stage name Assembler
Assemblers, a fictional race in the Star Wars universe
Assemblers, an alternative name of the superhero group Champions of Angor
Biology
Assembler (bioinformatics), a program to perform genome assembly
Assembler (nanotechnology), a conjectured construction machine that would manipulate and build with individual atoms or molecules
Computing
Assembler (computing), a computer program which translates assembly language to machine language
Assembly language, a more readable interpretation of a processor's machine code, allowing easier understanding and programming by humans, sometimes erroneously referenced as 'assembler' after the program which translates it
Other uses
a worker on an assembly line
See also
Assemble (disambiguation)
Assembly (disambiguation)
Constructor (disambiguation)
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https://en.wikipedia.org/wiki/1644%20in%20science
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The year 1644 AD in science and technology involved some significant events.
Mathematics
The Basel problem is posed by Pietro Mengoli, and will puzzle mathematicians until solved by Leonhard Euler in 1735.
Technology
Jacob van Eyck collaborates with the bellfounding duo Pieter and François Hemony to create the first tuned carillon in Zutphen.
Publications
Jan Baptist van Helmont publishes Dageraad ofte Nieuwe Opkomst der Geneeskunst ("Daybreak, or the New Rise of Medicine").
Births
25 September – Ole Rømer, Danish astronomer who makes the first quantitative measurements of the speed of light (died 1710)
Deaths
2 July – William Gascoigne, English scientist (born 1610)
30 December – Jan Baptist van Helmont, Flemish chemist (born 1580)
References
17th century in science
1640s in science
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https://en.wikipedia.org/wiki/1625%20in%20science
|
The year 1625 in science and technology involved some significant events.
Chemistry
First description of hydrogen by Johann Baptista van Helmont. First to use the word "gas".
Johann Rudolf Glauber discovers sodium sulfate (sal mirabilis or "Glauber's salt", used as a laxative) in Austrian spring water.
Births
June 8 – Giovanni Cassini, Italian astronomer (died 1712)
March 25 – John Collins, English mathematician (died 1683)
August 13 – Rasmus Bartholin, Danish scientist (died 1698)
December 16 – Erhard Weigel, German mathematician and scientific populariser (died 1699)
December 20 – David Gregory, Scottish physician and inventor (died 1720)
Samuel Morland, English inventor (died 1695)
Deaths
March 7 – Johann Bayer, German uranographer (born 1572)
April 7 – Adriaan van den Spiegel, Flemish-born anatomist and botanist (born 1578)
May 6 – George Bruce of Carnock, Scottish coal mining engineer (born c.1550)
Ferrante Imperato, Neapolitan natural historian (born 1550)
Willem Schouten, Dutch navigator, died at sea (born c. 1567)
References
17th century in science
1620s in science
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https://en.wikipedia.org/wiki/1667%20in%20science
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The year 1667 in science and technology involved some significant events.
Astronomy
June 24 – The site of the Paris Observatory is located on the Paris Meridian.
Chemistry
Johann Joachim Becher originates what will become known as phlogiston theory in his Physical Education.
History and philosophy of science
Thomas Sprat publishes The History of the Royal-Society of London, for the Improving of Natural Knowledge.
Mathematics
James Gregory demonstrates the transcendence of π.
Physiology and medicine
June 15 – Jean-Baptiste Denys performs the first blood transfusion from a lamb into a boy.
Robert Hooke demonstrates that the alteration of the blood in the lungs is essential for respiration.
Thomas Willis publishes Pathologicae Cerebri, et nervosi generis specimen.
Publications
Nicolas Steno publishes Elementorum Myologiae Specimen, seu Musculi Descriptio Geometrica. Cui accedunt canis carchariae dissectum caput, et dissectus piscis ex canum genere in Florence, providing a foundation for the study of muscle mechanics, the ovary (based on his dissection of dogfish), and the sedimentary theory of geology.
Births
April 29 (bapt.) – John Arbuthnot, Scottish-born polymath (died 1735)
May 2 – Jacob Christoph Le Blon, German inventor of four-colour printing (died 1741)
May 26 – Abraham de Moivre, French mathematician (died 1754)
July 27 – Johann Bernoulli, Swiss mathematician (died 1748)
Deaths
April 3 – Edward Somerset, 2nd Marquess of Worcester, English inventor
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https://en.wikipedia.org/wiki/1679%20in%20science
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The year 1679 in science and technology involved some significant events.
Botany
Establishment of Hortus Botanicus (Amsterdam).
Mathematics
Samuel Morland publishes The Doctrine of Interest, both Simple & Compound, probably the first tables produced with the aid of a calculating machine.
Medicine
Great Plague of Vienna.
Franciscus Sylvius' Opera Medica, published posthumously, recognizes scrofula and phthisis as forms of tuberculosis.
Technology
Pierre-Paul Riquet excavates Malpas Tunnel on the Canal du Midi in Hérault, France, Europe's first navigable canal tunnel (165 m, concrete lined).
Publications
Publication in Paris of the first of Edme Mariotte's Essays de physique: De la végétation des plantes, a pioneering discussion of plant physiology; and De la nature de l'air, a statement of Boyle's law.
Publication by the Paris Observatory of the world's first national ephemeris almanac, the Connaissance des tems, compiled by Jean Picard.
Births
January 2 - Pierre Fauchard, French physician (died 1761).
January 24 – Christian Wolff, German philosopher, mathematician and scientist (died 1754)
Deaths
January 14 – Jacques de Billy, French Jesuit mathematician (born 1602)
References
17th century in science
1670s in science
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https://en.wikipedia.org/wiki/1677%20in%20science
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The year 1677 in science and technology involved some significant events.
Astronomy
Publication of the first English star atlas, John Seller's Atlas Coelestis.
Mathematics
Publication of Cocker's Arithmetick: Being a Plain and Familiar Method Suitable to the Meanest Capacity for the Full Understanding of That Incomparable Art, As It Is Now Taught by the Ablest School-Masters in City and Country, attributed to Edward Cocker (died 1676). It will remain a standard grammar school textbook in England for more than 150 years.
Medicine
January 21 – A pamphlet on smallpox published in Boston becomes the first medical publication in the British colonies in North America.
Microbiology
Antonie van Leeuwenhoek discovers the spermatozoon.
Paleontology
Robert Plot publishes The Natural History of Oxford-shire, Being an Essay Toward the Natural History of England, in which he describes the fossilised femur of a human giant, now known to be from the dinosaur Megalosaurus.
Births
February 8 – Jacques Cassini, French astronomer (died 1756)
September 17 – Stephen Hales, English physiologist and clergyman (died 1761)
September 27 – Johann Gabriel Doppelmayr, German mathematician, astronomer and cartographer (died 1750)
Deaths
May 4 – Isaac Barrow, English mathematician (born 1630)
May 23 (bur.) – John Kersey, English mathematician (born 1677)
October 11 – Sir Cornelius Vermuyden, Dutch-born drainage engineer (born 1595).
October 14 – Francis Glisson, English physician (born 15
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https://en.wikipedia.org/wiki/1683%20in%20science
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The year 1683 in science and technology involved some significant events.
Geography
Vincenzo Coronelli completes terrestrial and celestial globes for Louis XIV of France.
Biology
September 17 – Antonie van Leeuwenhoek writes a letter to the Royal Society of London describing "animalcules" – the first known description of protozoa.
Mathematics
Based on his discovery of the resultant, Seki Takakazu starts to develop elimination theory in the Kai-fukudai-no-hō (解伏題之法,); and to express the resultant, he develops the notion of the determinant.
Jacob Bernoulli discovers the mathematical constant e.
Medicine
Dutch physician Willem ten Rhijne publishes Dissertatio de Arthritide: Mantissa Schematica: De Acupunctura in London, introducing the West to acupuncture and moxibustion.
Technology
Vauban's manual on fortification, Le Directeur-Général des fortifications, begins publication at The Hague.
Institutions
May 24 – The Ashmolean Museum opens in Broad Street, Oxford (England) as the world's first purpose-built university museum, including accommodation for the teaching of natural philosophy and a chemistry laboratory. Naturalist Dr. Robert Plot is the first keeper and first professor of chemistry.
October 15 – First meeting of the Dublin Philosophical Society, established by William Molyneux.
Births
February 28 – Rene Antoine Ferchault de Reaumur, French physicist (died 1757)
December 23 – François Nicole, French mathematician (died 1758)
Approximate date
Giovanni P
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https://en.wikipedia.org/wiki/Thermal%20energy
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The term "thermal energy" is used loosely in various contexts in physics and engineering, generally related to the kinetic energy of vibrating and colliding atoms in a substance. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, defined as a type of energy transfer (as is thermodynamic work); and the characteristic energy of a degree of freedom, , in a system that is described in terms of its microscopic particulate constituents (where denotes temperature and denotes the Boltzmann constant).
Relation to heat and internal energy
In thermodynamics, heat is energy transferred to or from a thermodynamic system by mechanisms other than thermodynamic work or transfer of matter, such as conduction, radiation, and friction. Heat refers to a quantity transferred between systems, not to a property of any one system, or "contained" within it. On the other hand, internal energy and enthalpy are properties of a single system. Heat and work depend on the way in which an energy transfer occurred, whereas internal energy is a property of the state of a system and can thus be understood without knowing how the energy got there.
Macroscopic thermal energy
The internal energy of a body can change in a process in which chemical potential energy is converted into non-chemical energy. In such a process, the thermodynamic system can change its internal energy by doing work on its surroundi
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https://en.wikipedia.org/wiki/Ivan%20Vinogradov
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Ivan Matveevich Vinogradov (; 14 September 1891 – 20 March 1983) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR. He was born in the Velikiye Luki district, Pskov Oblast. He graduated from the University of St. Petersburg, where in 1920 he became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics, a position he held for the rest of his life, except for the five-year period (1941–1946) when the institute was directed by Academician Sergei Sobolev. In 1941 he was awarded the Stalin Prize. He was elected to the American Philosophical Society in 1942. In 1951 he became a foreign member of the Polish Academy of Sciences and Letters in Kraków.
Mathematical contributions
In analytic number theory, Vinogradov's method refers to his main problem-solving technique, applied to central questions involving the estimation of exponential sums. In its most basic form, it is used to estimate sums over prime numbers, or Weyl sums. It is a reduction from a complicated sum to a number of smaller sums which are then simplified. The canonical form for prime number sums is
With the help of this method, Vinogradov tackled questions such as the ternary Goldbach problem in 1937 (using Vinogradov's theorem), and the zero-free region for the Riemann zeta function. His own use of it was inimitable; in terms of later techniques, it is recognised as a prototype of the large si
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https://en.wikipedia.org/wiki/1687%20in%20science
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The year 1687 in science and technology involved some significant events.
Astronomy
The constellation Triangulum Minus is named by Johannes Hevelius.
Biology
Alida Withoos at the house of Agnes Block makes a painting of the first pineapple bred in Europe.
Medicine
Dutch physician Willem ten Rhijne publishes Verhandelinge van de Asiatise Melaatsheid na een naaukeuriger ondersoek ten dienste van het gemeen in Amsterdam, explaining Asian leprosy to the West.
Physics
July 5 – Isaac Newton's Philosophiæ Naturalis Principia Mathematica, known as the Principia, is published by the Royal Society of London. In it, Newton describes his theory of universal gravitation, explains the laws of mechanics (including Newton's laws of motion), gives a formula for the speed of sound and demonstrates that Earth is an oblate spheroid. The concepts in the Principia become the foundations of modern physics.
Births
October 14 – Robert Simson, Scottish mathematician (died 1768).
Deaths
January 28 – Johannes Hevelius, German astronomer (born 1611).
17th century in science
1680s in science
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https://en.wikipedia.org/wiki/1688%20in%20science
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The year 1688 in science and technology included a number of events, some of which are listed here.
Astronomy
The constellation Sceptrum Brandenburgicum is named by Gottfried Kirch.
Exploration
A French Jesuit scientific mission led by Jean de Fontaney arrives in China.
Mathematics
Simon de la Loubère introduces the Siamese method for constructing any size of n-odd magic square to Western Europe.
Technology
Earliest known mention of the balalaika.
Births
January 29 – Emanuel Swedenborg, Swedish scientist and theologian (died 1772)
April 4 – Joseph-Nicolas Delisle, French astronomer (died 1768)
August 14 – Johann Leonhard Rost, German astronomer (died 1727)
September 26 – Willem 's Gravesande, Dutch polymath (died 1742)
November 15 – Louis Bertrand Castel, French Jesuit mathematician and physicist (died 1757)
Deaths
January 28 – Ferdinand Verbiest, Flemish Jesuit astronomer in China (born 1623)
October 9 – Claude Perrault, French architect and physicist (born 1613)
November 11 – Jean-Baptiste de La Quintinie, French horticulturalist (born 1626)
References
17th century in science
1680s in science
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https://en.wikipedia.org/wiki/1692%20in%20science
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The year 1692 in science and technology:
Events
In the American colonies, the Salem witch trials develop, following 250 years of witch-hunts in Europe.
Mathematics
The tractrix, sometimes called a tractory or equitangential curve, is first studied by Christiaan Huygens, who gives it its name.
John Arbuthnot publishes Of the Laws of Chance (translated from Huygens' De ratiociniis in ludo aleae), the first work on probability theory in English.
Medicine
Thomas Sydenham's Processus integri ("The Process of Healing") is published posthumously.
Births
April 22 – James Stirling, Scottish mathematician (died 1770)
Deaths
May – John Banister, English missionary and botanist, accidentally shot (born 1654)
References
17th century in science
1690s in science
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https://en.wikipedia.org/wiki/1699%20in%20science
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The year 1699 in science and technology involved some significant events.
Biology
English physician Edward Tyson publishes Orang-Outang, sive Homo Sylvestris: or, the Anatomy of a Pygmie Compared with that of a Monkey, an Ape, and a Man, a pioneering work of comparative anatomy.
Exploration
July 26 – William Dampier's expedition to New Holland (Australia) in HMS Roebuck reaches Dirk Hartog Island at the mouth of what he calls Shark Bay in Western Australia and begins producing the first known detailed record of Australian flora and fauna.
approx. date – Sir Isaac Newton develops a reflecting quadrant.
Mathematics
Abraham Sharp calculates π to 72 digits using an arctan sequence (although only 71 are correct).
Paleontology
Edward Lhuyd produces the first published scientific treatment of what would now be recognized as a dinosaur, describing and naming a sauropod tooth, "Rutellum implicatum" found at Caswell, near Witney, Oxfordshire, England.
Births
March 23 – John Bartram, naturalist and explorer, "father of American botany" (died 1777)
August 17 – Bernard de Jussieu, French botanist (died 1777)
September 12 – John Martyn, English botanist (died 1768)
Deaths
March 21 – Erhard Weigel, German mathematician and scientific populariser (born 1625)
November 18 – Pierre Pomet, French pharmacist (born 1658)
References
17th century in science
1690s in science
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https://en.wikipedia.org/wiki/1640%20in%20science
|
The year 1640 in science and technology involved some significant events.
Botany
John Parkinson publishes Theatrum Botanicum:The Theater of Plants, or, An Herbal of a Large Extent.
Mathematics
The 16-year-old Blaise Pascal demonstrates the properties of the hexagrammum mysticum in his Essai pour les coniques which he sends to Mersenne.
October 18 – Fermat states his "little theorem" in a letter to Frénicle de Bessy: if p is a prime number, then for any integer a, a p − a will be divisible by p.
December 25 – Fermat claims a proof of the theorem on sums of two squares in a letter to Mersenne ("Fermat's Christmas Theorem"): an odd prime p is expressible as the sum of two squares.
Technology
The micrometer is developed.
A form of bayonet is invented; in later years it will gradually replace the pike.
The reticle telescope is developed and initiates the birth of sharpshooting.
Births
April 1 – Georg Mohr, Danish mathematician (died 1697)
December 13 (bapt.) – Robert Plot, English naturalist and chemist (died 1696)
Elias Tillandz, Swedish physician and botanist in Finland (died 1693)
Deaths
December 22 – Jean de Beaugrand, French mathematician (born c. 1584)
References
17th century in science
1640s in science
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https://en.wikipedia.org/wiki/1629%20in%20science
|
The year 1629 in science and technology involved some significant events.
Botany
In London, John Parkinson publishes .
Chemistry
English alchemist Arthur Dee, court physician to Michael I of Russia, compiles Fasciculus Chemicus, Chymical Collections. Expressing the Ingress, Progress, and Egress, of the Secret Hermetick Science out of the choicest and most famous authors.
Medicine
Plague breaks out in Mantua and spreads to Milan.
In Toulouse, Niall Ó Glacáin publishes Tractatus de Peste.
Technology
In Rome, Giovanni Branca publishes .
Births
April 14 – Christiaan Huygens, Dutch mathematician and physicist (died 1695)
Laurent Cassegrain, French priest and physicist (died 1693)
Jan Commelijn, Dutch botanist (died 1692)
Christophe Glaser, Swiss pharmacian (died 1672)
Johann Glaser, Swiss anatomist (died 1675)
Agnes Block, Dutch horticulturalist (died 1704)
Deaths
July 13 – Caspar Bartholin the Elder, Danish polymath, physician and theologian (born 1585)
Giovanni Faber, German papal doctor and botanist (born 1574)
References
17th century in science
1620s in science
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https://en.wikipedia.org/wiki/1664%20in%20science
|
The year 1664 in science and technology involved some significant events.
Astronomy
May 9 – Robert Hooke discovers Jupiter's Great Red Spot.
Biology
Francesco Redi writes Osservazioni intorno alle vipere ("Observations about the Viper"), demonstrating that popular beliefs about venom are untrue.
Mathematics
January 18 – Isaac Barrow is appointed first Lucasian Professor of Mathematics at the University of Cambridge.
Blaise Pascal's paper on the properties of the triangle is published posthumously.
Medicine
Thomas Willis publishes Cerebri Anatome, cui accessit nervorum descriptio et usus in London, including illustrations by Christopher Wren. This contains an accurate account of the nervous system and introduces the term "neurology".
Births
February 24 – Thomas Newcomen, English inventor (died 1729)
September 22 – Catherine Jérémie, French-Canadian botanist (died 1744)
Deaths
July 11 (bur.) – Jan Janssonius, Dutch cartographer (born 1588)
August 22 – Maria Cunitz, Silesian astronomer (born 1610)
References
17th century in science
1660s in science
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https://en.wikipedia.org/wiki/1623%20in%20science
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The year 1623 in science and technology involved some significant events.
Astronomy
July 16 – Great conjunction of Jupiter and Saturn, the closest together the two planets come until 2020.
Biology
Apple orchard at Grönsö Manor in Sweden planted; it will still be productive into the 21st century.
Psychology
Erotomania is first mentioned in a psychiatric treatise.
Technology
Wilhelm Schickard draws a calculating clock on a letter to Kepler. This will be the first of five unsuccessful attempts at designing a direct entry calculating clock in the 17th century (including the designs of Tito Burattini, Samuel Morland and René Grillet).
Births
June 19 – Blaise Pascal, French mathematician and physicist (died 1662)
July 12 – Elizabeth Walker, English pharmacist (died 1690)
August 26 – Johann Sigismund Elsholtz, German naturalist and physician (died 1688)
September 1 – Caspar Schamberger, German surgeon and merchant (died 1706)
September 23 – Georg Balthasar Metzger, German physician and scientist (died 1687)
October 9 – Ferdinand Verbiest, Flemish Jesuit Sinologist and astronomer (died 1688)
Margaret Lucas, later Margaret Cavendish, Duchess of Newcastle-upon-Tyne, English natural philosopher (died 1673)
Deaths
May 26 – Francis Anthony, English apothecary and physician (born 1550)
December 24 – Michiel Coignet, Flemish engineer, cosmographer, mathematician and scientific instrument-maker (born 1549)
References
17th century in science
1620s in science
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https://en.wikipedia.org/wiki/A13
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A13 or A-13 may refer to:
Biology
ATC code A13 Tonics, a subgroup of the Anatomical Therapeutic Chemical Classification System
British NVC community A13 (Potamogeton perfoliatus - Myriophyllum alterniflorum community)
Subfamily A13, a rhodopsin-like receptors subfamily
Transportation
A13 road, in several countries
Archambault A13, a French sailboat design
Antonov A-13, a 1958 Soviet acrobatic sailplane
Chery A13, a subcompact car
, a British A-class submarine of the Royal Navy
A-13 (tank), the General Staff specification covering three British cruiser tanks designed and built before and during the Second World War
Cruiser Mk III
Cruiser Mk IV
Covenanter tank
Other uses
A13, one of the Encyclopaedia of Chess Openings codes for the English Opening in chess
Apple A13, a system on a chip mobile processor designed by Apple
Samsung Galaxy A13, a smartphone manufactured by Samsung Electronics
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https://en.wikipedia.org/wiki/1659%20in%20science
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The year 1659 in science and technology involved some significant events.
Astronomy
Christiaan Huygens publishes Systema Saturnium, including the first illustration of the Orion Nebula.
Mathematics
First known use of the term Abscissa, by Stefano degli Angeli.
Swiss mathematician Johann Rahn publishes Teutsche Algebra, containing the first printed use of the 'division sign' (÷, a repurposed obelus variant) as a mathematical symbol for division and of the 'therefore sign' (∴).
Medicine
Thomas Willis publishes De Febribus.
Physics
Christiaan Huygens derives the formula for centripedal force.
Births
February 27 – William Sherard, English botanist (died 1728)
June 3 – David Gregory, Scottish astronomer (died 1708)
Deaths
October 10 – Abel Tasman, Dutch explorer (born 1603)
References
17th century in science
1650s in science
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https://en.wikipedia.org/wiki/1658%20in%20science
|
The year 1658 in science and technology involved some significant events.
Astronomy
approx. date – Kamalakara compiles his major work, Siddhāntatattvaviveka, in Varanasi.
Life sciences
Jan Swammerdam observes red blood cells (in the frog) with the aid of a microscope.
Samuel Volckertzoon observes a quokka on Rottnest Island.
Mathematics
Christopher Wren gives the first published proof of the arc length of a cycloid.
Publication
Posthumous publication of Arzneibüchlein, pharmacopoeia compiled by Anna von Diesbach.
Births
March 5 – Antoine Laumet de La Mothe, sieur de Cadillac, French explorer (died 1730)
April 2 - Pierre Pomet, French pharmacist (died 1699)
April 8 - Georges Mareschal, French surgeon (died 1736)
unknown date – Nicolas Andry, French physician (died 1742)
Deaths
January 9 - Pierre-Jean Fabre, French physician and alchemist (born 1588)
October 22 – Charles Bouvard, French herbalist (born 1572)
References
17th century in science
1650s in science
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https://en.wikipedia.org/wiki/Shift%20operator
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In mathematics, and in particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function
to its translation . In time series analysis, the shift operator is called the lag operator.
Shift operators are examples of linear operators, important for their simplicity and natural occurrence. The shift operator action on functions of a real variable plays an important role in harmonic analysis, for example, it appears in the definitions of almost periodic functions, positive-definite functions, derivatives, and convolution. Shifts of sequences (functions of an integer variable) appear in diverse areas such as Hardy spaces, the theory of abelian varieties, and the theory of symbolic dynamics, for which the baker's map is an explicit representation. The notion of triangulated category is a categorified analogue of the shift operator.
Definition
Functions of a real variable
The shift operator (where ) takes a function on to its translation ,
A practical operational calculus representation of the linear operator in terms of the plain derivative was introduced by Lagrange,
which may be interpreted operationally through its formal Taylor expansion in ; and whose action on the monomial is evident by the binomial theorem, and hence on all series in , and so all functions as above. This, then, is a formal encoding of the Taylor expansion in Heaviside's calculus.
The operator thus provides the prototype
for Li
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https://en.wikipedia.org/wiki/Potential%20gradient
|
In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux.
Definition
One dimension
The simplest definition for a potential gradient F in one dimension is the following:
where is some type of scalar potential and is displacement (not distance) in the direction, the subscripts label two different positions , and potentials at those points, . In the limit of infinitesimal displacements, the ratio of differences becomes a ratio of differentials:
The direction of the electric potential gradient is from to .
Three dimensions
In three dimensions, Cartesian coordinates make it clear that the resultant potential gradient is the sum of the potential gradients in each direction:
where are unit vectors in the directions. This can be compactly written in terms of the gradient operator ,
although this final form holds in any curvilinear coordinate system, not just Cartesian.
This expression represents a significant feature of any conservative vector field , namely has a corresponding potential .
Using Stokes' theorem, this is equivalently stated as
meaning the curl, denoted ∇×, of the vector field vanishes.
Physics
Newtonian gravitation
In the case of the gravitational field , which can be shown to be conservative, it is equal to the gradient in gravitati
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https://en.wikipedia.org/wiki/1696%20in%20science
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The year 1696 in science and technology involved some significant events.
History of science
Daniel Le Clerc publishes Histoire de la médecine in Geneva, the first comprehensive work on the subject.
Mathematics
Guillaume de l'Hôpital publishes Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes, the first textbook on differential calculus, including a statement of his rule for the computation of certain limits.
Jakob Bernoulli and Johann Bernoulli solve the brachistochrone curve problem, the first result in the calculus of variations.
Births
unknown date – Christine Kirch, German astronomer (d. 1782)
Deaths
April 30 – Robert Plot, English naturalist and chemist (born 1640)
Jean Richer, French astronomer (born 1630)
References
17th century in science
1690s in science
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https://en.wikipedia.org/wiki/1661%20in%20science
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The year 1661 in science and technology involved some significant events.
Biology
Marcello Malpighi is the first to observe and correctly describe capillaries when he discovers them in a frog's lung.
Chemistry
Robert Boyle's The Sceptical Chymist is published in London.
Environment
John Evelyn's pamphlet Fumifugium is one of the earliest descriptions of air pollution.
Publications
Abraham Cowley's pamphlet The Advancement of Experimental Philosophy.
Johann Sperling's handbook Zoologia physica (posthumous).
Births
May 3 – Antonio Vallisneri, Italian physician and natural scientist (died 1730)
December 18 – Christopher Polhem, Swedish scientist and inventor (died 1751)
Guillaume François Antoine, Marquis de l'Hôpital, French mathematician (died 1704)
approx. date – Alida Withoos, Dutch botanical artist (died 1730)
Events
Isaac Newton is admitted to Trinity College, Cambridge, as a sizar (June)
Deaths
October – Gérard Desargues, French geometer (born 1591)
References
17th century in science
1660s in science
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https://en.wikipedia.org/wiki/1638%20in%20science
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The year 1638 in science and technology involved some significant events.
Astronomy
December 21 – Total eclipse of the Moon falls on the same day as the winter solstice, for the first time in the Common Era.
Geology
(Italy).
. The epicentre was in Crotone.
Physics
The final book of the now-blind Galileo, Discorsi e dimostrazioni matematiche, intorno à due nuove scienze is published in Leiden, dealing with the strength of materials and the motion of objects. In it, he discusses the square–cube law, the law of falling bodies and infinity. He also discusses his experimental method for measuring the speed of light; he has been unable to determine it over a short distance.
Publications
Publication of The Man in the Moone, or the Discovrse of a Voyage thither "by Domingo Gonsales" (actually by Francis Godwin, Bishop of Hereford (died 1633)), an early example of science fiction.
Births
January 1 (NS January 11) – Nicolas Steno, Danish pioneer of geology (died 1686)
March 28 – Frederik Ruysch, Dutch physician and anatomist (died 1731)
April 19 - Niccolao Manucci, Italian physician, writer and traveller (died 1717)
May 11 – Guy-Crescent Fagon, French physician and botanist (died 1718)
June 8 – Pierre Magnol, French botanist (died 1715)
June 29 - Heinrich Meibom, German physician and scholar (died 1700)
July 22 - Theodor Kerckring, Dutch anatomist and chemical physician (died 1693)
November 21 - Luca Tozzi, Italian physician (died 1717)
November – James Gregory, Sco
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https://en.wikipedia.org/wiki/1685%20in%20science
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The year 1685 in science and technology involved some significant events.
Mathematics
Adam Adamandy Kochański publishes an approximation for squaring the circle.
Physiology and medicine
Charles Allen publishes the first book in English on dentistry, The Operator for the Teeth.
Govert Bidloo publishes an atlas of human anatomy, Ontleding des menschelyken lichaams, with plates by Gerard de Lairesse.
Technology
Menno van Coehoorn publishes his principal treatise on fortification, Nieuwe Vestingbouw op een natte of lage horisont, in Leeuwarden.
Births
August 18 – Brook Taylor, English mathematician (died 1731)
November 17 – Pierre Gaultier de Varennes et de la Vérendrye, French Canadian explorer (died 1749)
Deaths
February 2 – Pierre Bourdelot, French physician, anatomist, freethinker, abbé and libertine (born 1610)
November 23 – Bernard de Gomme, military engineer in England (born 1620)
December 12 – John Pell, English mathematician (born 1610)
References
17th century in science
1680s in science
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https://en.wikipedia.org/wiki/1684%20in%20science
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The year 1684 in science and technology involved some significant events.
Astronomy
December 10 – Edmond Halley presents the paper De motu corporum in gyrum, containing Isaac Newton's derivation of Kepler's laws of planetary motion (incorporating inverse-square force) from his theory of gravity, to the Royal Society in London.
Mathematics
Gottfried Leibniz publishes the first account of differential calculus.
Publications
Robert Boyle publishes Experiments and Considerations about the Porosity of Bodies, the first work on this topic.
Raymond Vieussens publishes Neurographia universalis, a "pioneering work" on the nervous system.
Births
Celia Grillo Borromeo, Italian scientist and mathematician (died 1777)
Deaths
April 5 – William Brouncker, 2nd Viscount Brouncker, English mathematician (born 1620)
May 11 – Daniel Whistler, English physician (born c. 1619)
May 12 – Edme Mariotte, French physicist known for his recognition of Boyle's law (born 1620)
October – Dud Dudley, English metallurgist (born 1600?)
References
17th century in science
1680s in science
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https://en.wikipedia.org/wiki/Transactional%20interpretation
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The transactional interpretation of quantum mechanics (TIQM) takes the wave function of the standard quantum formalism, and its complex conjugate, to be retarded (forward in time) and advanced (backward in time) waves that form a quantum interaction as a Wheeler–Feynman handshake or transaction. It was first proposed in 1986 by John G. Cramer, who argues that it helps in developing intuition for quantum processes. He also suggests that it avoids the philosophical problems with the Copenhagen interpretation and the role of the observer, and also resolves various quantum paradoxes. TIQM formed a minor plot point in his science fiction novel Einstein's Bridge.
More recently, he has also argued TIQM to be consistent with the Afshar experiment, while claiming that the Copenhagen interpretation and the many-worlds interpretation are not.
The existence of both advanced and retarded waves as admissible solutions to Maxwell's equations was explored in the Wheeler–Feynman absorber theory. Cramer revived their idea of two waves for his transactional interpretation of quantum theory. While the ordinary Schrödinger equation does not admit advanced solutions, its relativistic version does, and these advanced solutions are the ones used by TIQM.
In TIQM, the source emits a usual (retarded) wave forward in time, but it also emits an advanced wave backward in time; furthermore, the receiver, who is later in time, also emits an advanced wave backward in time and a retarded wave forward in t
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https://en.wikipedia.org/wiki/1680%20in%20science
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The year 1680 in science and technology involved some significant events.
Astronomy
14 November NS – Great Comet of 1680 observed by Gottfried Kirch, the first comet discovered by telescope.
Biology
English comparative anatomist Edward Tyson publishes Phocæna, or The anatomy of a porpess, dissected at Gresham Colledge, concluding that the porpoise is a mammal.g
Robert Morison publishes Plantarum Historiae Universalis Oxoniensis, Pars Secunda, seu Herbarum Distributio Nova per Tabulas Cognationis et Affinitatis ex Libro Naturae observata et detecta, utilising his method of taxonomy.
Chemistry
30 September – Robert Boyle reports to the Royal Society of London his manufacture of phosphorus. He uses it to ignite sulfur-tipped wooden splints, forerunners of the match.
Physics
8 July – Robert Hooke observes the nodal patterns associated with the vibrations of glass plates.
Births
Deaths
17 February – Jan Swammerdam, Dutch naturalist, founder of both comparative anatomy and entomology (born 1637)
22 March – François Cureau de La Chambre, French physician (born 1630)
Marie Meurdrac, French chemist and alchemist (born 1610)
References
17th century in science
1680s in science
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https://en.wikipedia.org/wiki/1637%20in%20science
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The year 1637 in science and technology involved some significant events.
Mathematics
René Descartes promotes intellectual rigour in Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences and introduces the Cartesian coordinate system in its appendix La Géométrie (published in Leiden).
Pierre de Fermat conjectures Fermat's Last Theorem.
Publications
May – Chinese encyclopedist Song Yingxing publishes his Tiangong Kaiwu ("Exploitation of the Works of Nature").
Births
February 12 – Jan Swammerdam, Dutch naturalist, pioneer of comparative anatomy and entomology (died 1680)
François Mauriceau, French obstetrician (died 1709)
Deaths
June 24 – Nicolas-Claude Fabri de Peiresc, French astronomer (born 1580)
May 19 – Isaac Beeckman, Dutch philosopher and scientist (born 1588)
Henry Gellibrand, English mathematician (born 1597)
References
17th century in science
1630s in science
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https://en.wikipedia.org/wiki/F%C3%A9lix%20d%27H%C3%A9relle
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Félix d'Hérelle (25 April 1873 – 22 February 1949) was a French microbiologist. He was co-discoverer of bacteriophages (viruses that infect bacteria) and experimented with the possibility of phage therapy. D'Hérelle has also been credited for his contributions to the larger concept of applied microbiology.
d'Hérelle was a self-taught microbiologist. In 1917 he discovered that "an invisible antagonist", when added to bacteria on agar, would produce areas of dead bacteria. The antagonist, now known to be a bacteriophage, could pass through a Chamberland filter. He accurately diluted a suspension of these viruses and discovered that the highest dilutions (lowest virus concentrations), rather than killing all the bacteria, formed discrete areas of dead organisms. Counting these areas and multiplying by the dilution factor allowed him to calculate the number of viruses in the original suspension. He realised that he had discovered a new form of virus and later coined the term "bacteriophage".
Between 1918 and 1921 d'Herelle discovered different types of bacteriophages that could infect several other species of bacteria including Vibrio cholerae. Bacteriophages were heralded as a potential treatment for diseases such as typhoid and cholera, but their promise was forgotten with the development of penicillin. Since the early 1970s, bacteria have continued to develop resistance to antibiotics such as penicillin, and this has led to a renewed interest in the use of bacteriophages to
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https://en.wikipedia.org/wiki/1678%20in%20science
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The year 1678 in science and technology involved some significant events.
Astronomy
Edmund Halley publishes a catalogue of 341 southern stars—the first systematic southern sky survey.
Physics
Christiaan Huygens publishes his Traité de la Lumière/Treatise on Light, which states his principle of wavefront sources.
Robert Hooke discovers the fundamental law of elasticity when he finds that the stress (force) exerted is proportional to the strain (elongation) produced.
Zoology
Publication of English Spiders by Martin Lister, the first book devoted to spiders.
Births
April 14 – Abraham Darby I, ironmaster (died 1717)
July 16 – Jakob Hermann, mathematician (died 1733)
October 27 – Pierre Raymond de Montmort, mathematician (died 1719)
November 26 – Jean-Jacques d'Ortous de Mairan, geophysicist (died 1771)
December 2 – Nicolaas Kruik (Cruquius), cartographer and meteorologist (died 1754)
unknown – Pierre Fauchard, physician and "father of modern dentistry" (died 1761)
Deaths
November 28 – Willem Piso, physician and naturalist (born 1611)
17th century in science
1670s in science
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https://en.wikipedia.org/wiki/169%20%28number%29
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169 (one hundred [and] sixty-nine) is the natural number following 168 and preceding 170.
In mathematics
169 is an odd number, a composite number, and a deficient number.
169 is a square number: 13 × 13 = 169, and if each number is reversed the equation is still true: 31 × 31 = 961. 144 shares this property: 12 × 12 = 144, 21 × 21 = 441.
169 is one of the few squares to also be a centered hexagonal number. Like all odd squares, it is a centered octagonal number. 169 is an odd-indexed Pell number, thus it is also a Markov number, appearing in the solutions (2, 169, 985), (2, 29, 169), (29, 169, 14701), etc. 169 is the sum of seven consecutive primes: 13 + 17 + 19 + 23 + 29 + 31 + 37. 169 is a difference in consecutive cubes, equaling
In astronomy
169 Zelia is a bright main belt asteroid
Gliese 169 is an orange, main sequence (K7 V) star in the constellation Taurus
QSO B0307+169 is a quasar in the constellation Aries
Sayh al Uhaymir 169 is a 206g lunar meteorite found in Sultanate of Oman
In the military
was a United States Navy technical research ship during the 1960s
was a United States Navy during World War II
was a United States Navy during World War II
was a United States Navy following World War I
was a United States Navy during World War II
was a United States Navy submarine during World War II
169th Battalion, CEF unit in the Canadian Expeditionary Force during the World War I
169th Fires Brigade the US Army National Guard artillery brigade,
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https://en.wikipedia.org/wiki/Partial%20discharge
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In electrical engineering, partial discharge (PD) is a localized dielectric breakdown (DB) (which does not completely bridge the space between the two conductors) of a small portion of a solid or fluid electrical insulation (EI) system under high voltage (HV) stress.
While a corona discharge (CD) is usually revealed by a relatively steady glow or brush discharge (BD) in air, partial discharges within solid insulation system are not visible.
PD can occur in a gaseous, liquid, or solid insulating medium. It often starts within gas voids, such as voids in solid epoxy insulation or bubbles in transformer oil. Protracted partial discharge can erode solid insulation and eventually lead to breakdown of insulation.
Discharge mechanism
PD usually begins within voids, cracks, or inclusions within a solid dielectric, at conductor-dielectric interfaces within solid or liquid dielectrics, or in bubbles within liquid dielectrics. Since PDs are limited to only a portion of the insulation, the discharges only partially bridge the distance between electrodes. PD can also occur along the boundary between different insulating materials.
Partial discharges within an insulating material are usually initiated within gas-filled voids within the dielectric. Because the dielectric constant of the void is considerably less than the surrounding dielectric, the electric field across the void is significantly higher than that across an equivalent distance of dielectric. If the voltage stress acro
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https://en.wikipedia.org/wiki/Electrophile
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In chemistry, an electrophile is a chemical species that forms bonds with nucleophiles by accepting an electron pair. Because electrophiles accept electrons, they are Lewis acids. Most electrophiles are positively charged, have an atom that carries a partial positive charge, or have an atom that does not have an octet of electrons.
Electrophiles mainly interact with nucleophiles through addition and substitution reactions. Frequently seen electrophiles in organic syntheses include cations such as H+ and NO+, polarized neutral molecules such as HCl, alkyl halides, acyl halides, and carbonyl compounds, polarizable neutral molecules such as Cl2 and Br2, oxidizing agents such as organic peracids, chemical species that do not satisfy the octet rule such as carbenes and radicals, and some Lewis acids such as BH3 and DIBAL.
Organic chemistry
Addition of halogens
These occur between alkenes and electrophiles, often halogens as in halogen addition reactions. Common reactions include use of bromine water to titrate against a sample to deduce the number of double bonds present. For example, ethene + bromine → 1,2-dibromoethane:
C2H4 + Br2 → BrCH2CH2Br
This takes the form of 3 main steps shown below;
Forming of a π-complex
The electrophilic Br-Br molecule interacts with electron-rich alkene molecule to form a π-complex 1.
Forming of a three-membered bromonium ion
The alkene is working as an electron donor and bromine as an electrophile. The three-membered bromonium ion 2 consist
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https://en.wikipedia.org/wiki/DMC
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DMC may refer to:
Computer science and information technology
Data Matrix Code, laser etched square code, often used for marking products in the production area
Diffusion Monte Carlo method
Digital Media Controller, a category within the DLNA standard (for sharing digital media among multimedia devices) tasked with finding content on digital media servers
Discrete memoryless channel
Dynamic Markov Compression algorithm
Dynamic Mesh Communication, a mesh-based intercom system developed for motorcycle communication
Media and entertainment
Digital mixing console, used in audio mixing
Darryl McDaniels, a member of hip hop group Run–DMC
Devil May Cry, a Japanese video game series
Devil May Cry (video game), the first game in the series
DmC: Devil May Cry, a reboot of the series
Detroit Metal City, a manga franchise
Disco Mix Club, a remix label
Dhammakaya Media Channel, a Thai television channel
Deathmatch Classic, a Half-Life mod
Drummond Money-Coutts, an English magician
DMC (Egyptian TV channel), an Arabic-language channel
Motor vehicles
DeLorean Motor Company, former American automobile manufacturer (1975-1982)
DeLorean Motor Company (Texas), company founded in 1995 supplying parts and services to owners of DeLoreans
Daelim Motor Company, a South Korean motorcycle, motorscooter and ATV manufacturer
Organizations
Damak Multiple Campus, Jhapa, Nepal
Dhaka Medical College, Bangladesh
Diabetes Management Center, Services Hospital Lahore
Divisional Mod
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https://en.wikipedia.org/wiki/Systems%20biology
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Systems biology is the computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems, using a holistic approach (holism instead of the more traditional reductionism) to biological research.
Particularly from the year 2000 onwards, the concept has been used widely in biology in a variety of contexts. The Human Genome Project is an example of applied systems thinking in biology which has led to new, collaborative ways of working on problems in the biological field of genetics. One of the aims of systems biology is to model and discover emergent properties, properties of cells, tissues and organisms functioning as a system whose theoretical description is only possible using techniques of systems biology. These typically involve metabolic networks or cell signaling networks.
Overview
Systems biology can be considered from a number of different aspects.
As a field of study, particularly, the study of the interactions between the components of biological systems, and how these interactions give rise to the function and behavior of that system (for example, the enzymes and metabolites in a metabolic pathway or the heart beats).
As a paradigm, systems biology is usually defined in antithesis to the so-called reductionist paradigm (biological organisation), although it is consistent with the scientific method. The distinction between the tw
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https://en.wikipedia.org/wiki/FASTA%20format
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In bioinformatics and biochemistry, the FASTA format is a text-based format for representing either nucleotide sequences or amino acid (protein) sequences, in which nucleotides or amino acids are represented using single-letter codes.
The format allows for sequence names and comments to precede the sequences. It originated from the FASTA software package but has now become a near-universal standard in the field of bioinformatics.
The simplicity of FASTA format makes it easy to manipulate and parse sequences using text-processing tools and scripting languages.
Overview
A sequence begins with a greater-than character (">") followed by a description of the sequence (all in a single line). The next lines immediately following the description line are the sequence representation, with one letter per amino acid or nucleic acid, and are typically no more than 80 characters in length.
For example:
>MCHU - Calmodulin - Human, rabbit, bovine, rat, and chicken
MADQLTEEQIAEFKEAFSLFDKDGDGTITTKELGTVMRSLGQNPTEAELQDMINEVDADGNGTID
FPEFLTMMARKMKDTDSEEEIREAFRVFDKDGNGYISAAELRHVMTNLGEKLTDEEVDEMIREA
DIDGDGQVNYEEFVQMMTAK*
Original format
The original FASTA/Pearson format is described in the documentation for the FASTA suite of programs. It can be downloaded with any free distribution of FASTA (see fasta20.doc, fastaVN.doc, or fastaVN.me—where VN is the Version Number).
In the original format, a sequence was represented as a series of lines, each of which was no longer than 120 characters a
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https://en.wikipedia.org/wiki/Mask%20%28computing%29
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In computer science, a mask or bitmask is data that is used for bitwise operations, particularly in a bit field. Using a mask, multiple bits in a byte, nibble, word, etc. can be set either on or off, or inverted from on to off (or vice versa) in a single bitwise operation. An additional use of masking involves predication in vector processing, where the bitmask is used to select which element operations in the vector are to be executed (mask bit is enabled) and which are not (mask bit is clear).
Common bitmask functions
Masking bits to 1
To turn certain bits on, the bitwise OR operation can be used, following the principle that Y OR 1 = 1 and Y OR 0 = Y. Therefore, to make sure a bit is on, OR can be used with a 1. To leave a bit unchanged, OR is used with a 0.
Example: Masking on the higher nibble (bits 4, 5, 6, 7) while leaving the lower nibble (bits 0, 1, 2, 3) unchanged.
10010101 10100101
OR 11110000 11110000
= 11110101 11110101
Masking bits to 0
More often in practice, bits are "masked off" (or masked to 0) than "masked on" (or masked to 1). When a bit is ANDed with a 0, the result is always 0, i.e. Y AND 0 = 0. To leave the other bits as they were originally, they can be ANDed with 1 as Y AND 1 = Y
Example: Masking off the higher nibble (bits 4, 5, 6, 7) while leaving the lower nibble (bits 0, 1, 2, 3) unchanged.
10010101 10100101
AND 00001111 00001111
= 00000101 00000101
Querying the status of a bit
It is possible to use bitmask
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https://en.wikipedia.org/wiki/Nagell%E2%80%93Lutz%20theorem
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In mathematics, the Nagell–Lutz theorem is a result in the diophantine geometry of elliptic curves, which describes rational torsion points on elliptic curves over the integers.
It is named for Trygve Nagell and Élisabeth Lutz.
Definition of the terms
Suppose that the equation
defines a non-singular cubic curve with integer coefficients a, b, c, and let D be the discriminant of the cubic polynomial on the right side:
Statement of the theorem
If P = (x,y) is a rational point of finite order on C, for the elliptic curve group law, then:
1) x and y are integers
2) either y = 0, in which case P has order two, or else y divides D, which immediately implies that y2 divides D.
Generalizations
The Nagell–Lutz theorem generalizes to arbitrary number fields and more
general cubic equations.
For curves over the rationals, the
generalization says that, for a nonsingular cubic curve
whose Weierstrass form
has integer coefficients, any rational point P=(x,y) of finite
order must have integer coordinates, or else have order 2 and
coordinates of the form x=m/4, y=n/8, for m and n integers.
History
The result is named for its two independent discoverers, the Norwegian Trygve Nagell (1895–1988) who published it in 1935, and Élisabeth Lutz (1937).
See also
Mordell–Weil theorem
References
Joseph H. Silverman, John Tate (1994), "Rational Points on Elliptic Curves", Springer, .
Elliptic curves
Theorems in number theory
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https://en.wikipedia.org/wiki/Purely%20functional
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Purely functional may refer to:
Computer science
Pure function, a function that does not have side effects
Purely functional data structure, a persistent data structure that does not rely on mutable state
Purely functional programming, a programming paradigm that does not rely on mutable state
Law
Functionality doctrine, in intellectual property law
See also
Referential transparency
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https://en.wikipedia.org/wiki/European%20Committee%20for%20Electrotechnical%20Standardization
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CENELEC (; ) is responsible for European standardization in the area of electrical engineering. Together with ETSI (telecommunications) and CEN (other technical areas), it forms the European system for technical standardization. Standards harmonised by these agencies are regularly adopted in many countries outside Europe which follow European technical standards. Although CENELEC works closely with the European Union, it is not an EU institution. Nevertheless, its standards are "EN" EU (and EEA) standards, thanks to EU Regulation 1025/2012.
CENELEC was founded in 1973. Before that two organizations were responsible for electrotechnical standardization: CENELCOM and CENEL. CENELEC is a non-profit organization under Belgian law, based in Brussels. The members are the national electrotechnical standardization bodies of most European countries.
Agreement types
Members
The current members of CENELEC are: Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, North Macedonia, Norway, Poland, Portugal, Romania, Serbia, Spain, Slovakia, Slovenia, Sweden, Switzerland, Turkey and the United Kingdom.
Affiliates
Albania, Belarus, Bosnia/Herzegovina, Egypt, Georgia, Israel, Jordan, Libya, Moldova, Montenegro, Morocco, Tunisia and Ukraine are currently "affiliate members" with a view to becoming full members.
Others
CENELEC has coopera
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https://en.wikipedia.org/wiki/Discrete%20group
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In mathematics, a topological group G is called a discrete group if there is no limit point in it (i.e., for each element in G, there is a neighborhood which only contains that element). Equivalently, the group G is discrete if and only if its identity is isolated.
A subgroup H of a topological group G is a discrete subgroup if H is discrete when endowed with the subspace topology from G. In other words there is a neighbourhood of the identity in G containing no other element of H. For example, the integers, Z, form a discrete subgroup of the reals, R (with the standard metric topology), but the rational numbers, Q, do not.
Any group can be endowed with the discrete topology, making it a discrete topological group. Since every map from a discrete space is continuous, the topological homomorphisms between discrete groups are exactly the group homomorphisms between the underlying groups. Hence, there is an isomorphism between the category of groups and the category of discrete groups. Discrete groups can therefore be identified with their underlying (non-topological) groups.
There are some occasions when a topological group or Lie group is usefully endowed with the discrete topology, 'against nature'. This happens for example in the theory of the Bohr compactification, and in group cohomology theory of Lie groups.
A discrete isometry group is an isometry group such that for every point of the metric space the set of images of the point under the isometries is a discrete s
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https://en.wikipedia.org/wiki/Edison%20Denisov
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Edison Vasilievich Denisov (, 6 April 1929 – 24 November 1996) was a Russian composer in the so-called "Underground", "alternative" or "nonconformist" division of Soviet music.
Biography
Denisov was born in Tomsk, Siberia. He studied mathematics before deciding to spend his life composing. This decision was enthusiastically supported by Dmitri Shostakovich, who gave him lessons in composition.
In 1951–56 Denisov studied at the Moscow Conservatory: composition with Vissarion Shebalin, orchestration with Nikolai Rakov, analysis with Viktor Tsukkerman and piano with Vladimir Belov. In 1956–59 he composed the opera Ivan-Soldat (Soldier Ivan) in three acts based on Russian folk fairy tales.
He began his own study of scores that were difficult to obtain in the USSR at that time, including music by composers ranging from Mahler and Debussy to Boulez and Stockhausen. He wrote a series of articles giving a detailed analysis of different aspects of contemporary compositional techniques and at same time actively experimented as a composer, trying to find his own way.
After graduating from the Moscow Conservatory, he taught orchestration and later composition there. His pupils included the composers Dmitri Smirnov, Elena Firsova, Dilorom Saidaminova, Vladimir Tarnopolsky, Sergey Pavlenko, Ivan Sokolov, Yuri Kasparov. He supported and encouraged Dmitri Capyrin and Alexander Shchetynsky who have never been his pupils.
In 1979, at the Sixth Congress of the Union of Soviet Composers
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https://en.wikipedia.org/wiki/List%20of%20curves
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This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine, biology, psychology, ecology, etc.
Mathematics (Geometry)
Algebraic curves
Rational curves
Rational curves are subdivided according to the degree of the polynomial.
Degree 1
Line
Degree 2
Plane curves of degree 2 are known as conics or conic sections and include
Circle
Unit circle
Ellipse
Parabola
Hyperbola
Unit hyperbola
Degree 3
Cubic plane curves include
Cubic parabola
Folium of Descartes
Cissoid of Diocles
Conchoid of de Sluze
Right strophoid
Semicubical parabola
Serpentine curve
Trident curve
Trisectrix of Maclaurin
Tschirnhausen cubic
Witch of Agnesi
Degree 4
Quartic plane curves include
Ampersand curve
Bean curve
Bicorn
Bow curve
Bullet-nose curve
Cartesian oval
Cruciform curve
Deltoid curve
Devil's curve
Hippopede
Kampyle of Eudoxus
Kappa curve
Lemniscate
Lemniscate of Booth
Lemniscate of Gerono
Lemniscate of Bernoulli
Limaçon
Cardioid
Limaçon trisectrix
Ovals of Cassini
Squircle
Trifolium Curve
Degree 5
Degree 6
Astroid
Atriphtaloid
Nephroid
Quadrifolium
Curve families of variable degree
Epicycloid
Epispiral
Epitrochoid
Hypocycloid
Lissajous curve
Poinsot's spirals
Rational normal curve
Rose curve
Curves with genus 1
Bicuspid curve
Cassinoide
Cubic curve
Elliptic curve
Watt's curve
Curves with genus > 1
Bolza surface (genus 2)
Klein quartic (genus 3)
Bring's curve
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https://en.wikipedia.org/wiki/Fisher%20equation
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In financial mathematics and economics, the Fisher equation expresses the relationship between nominal interest rates, real interest rates, and inflation. Named after Irving Fisher, an American economist, it can be expressed as real interest rate ≈ nominal interest rate − inflation rate.
In more formal terms, where equals the real interest rate, equals the nominal interest rate, and equals the inflation rate, then . The approximation of is often used instead since the nominal interest rate, real interest rate, and inflation rate are usually close to zero.
Applications
Borrowing, lending and the time value of money
When loans are made, the amount borrowed and the repayments due to the lender are normally stated in nominal terms, before inflation. However, when inflation occurs, a dollar repaid in the future is worth less than a dollar borrowed today. To calculate the true economics of the loan, it is necessary to adjust the nominal cash flows to account for future inflation.
Inflation-indexed bonds
The Fisher equation can be used in the analysis of bonds. The real return on a bond is roughly equivalent to the nominal interest rate minus the expected inflation rate. But if actual inflation exceeds expected inflation during the life of the bond, the bondholder's real return will suffer. This risk is one of the reasons inflation-indexed bonds such as U.S. Treasury Inflation-Protected Securities were created to eliminate inflation uncertainty. Holders of indexed bonds are
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https://en.wikipedia.org/wiki/For%20loop
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In computer science a for-loop or for loop is a control flow statement for specifying iteration. Specifically, a for loop functions by running a section of code repeatedly until a certain condition has been satisfied.
For-loops have two parts: a header and a body. The header defines the iteration and the body is the code that is executed once per iteration. The header often declares an explicit loop counter or loop variable. This allows the body to know which iteration is being executed. For-loops are typically used when the number of iterations is known before entering the loop. For-loops can be thought of as shorthands for while-loops which increment and test a loop variable.
Various keywords are used to indicate the usage of a for loop: descendants of ALGOL use "", while descendants of Fortran use "". There are other possibilities, for example COBOL which uses .
The name for-loop comes from the word for. For is used as the keyword in many programming languages to introduce a for-loop. The term in English dates to ALGOL 58 and was popularized in ALGOL 60. It is the direct translation of the earlier German and was used in Superplan (1949–1951) by Heinz Rutishauser. Rutishauser was involved in defining ALGOL 58 and ALGOL 60. The loop body is executed "for" the given values of the loop variable. This is more explicit in ALGOL versions of the for statement where a list of possible values and increments can be specified.
In Fortran and PL/I, the keyword is used for the
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