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https://en.wikipedia.org/wiki/John%20Ellis%20%28physicist%2C%20born%201946%29
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Jonathan Richard Ellis (born 1 July 1946) is a British theoretical physicist who is currently Clerk Maxwell Professor of Theoretical Physics at King's College London.
After completing his secondary education at Highgate School, he attended King's College, Cambridge, earning his PhD in theoretical (high-energy) particle physics in 1971. After brief post-doc positions in the SLAC Theory Group and Caltech, he went to CERN and has held an indefinite contract there since 1978. He was awarded the Maxwell Medal and the Paul Dirac Prize by the Institute of Physics in 1982 and 2005 respectively, and is an Elected Fellow of the Royal Society of London since 1985 and of the Institute of Physics since 1991. He was awarded an Honorary Doctorate from the University of Southampton, and twice won the First Award in the Gravity Research Foundation essay competition (in 1999 and 2005). He is also Honorary Doctor at Uppsala University.
Ellis' activities at CERN are wide-ranging. He was twice Deputy Division Leader for the theory ("TH") division, and served as Division Leader for 1988–1994. He was a founding member of the LEPC and of the LHCC; currently he is chair of the committee to investigate physics opportunities for future proton accelerators, and is a member of the extended CLIC (Compact Linear Collider) Steering Committee.
Ellis was appointed Commander of the Order of the British Empire (CBE) in the 2012 Birthday Honours for services to science and technology.
Scientific research
E
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https://en.wikipedia.org/wiki/Organoselenium%20chemistry
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Organoselenium chemistry is the science exploring the properties and reactivity of organoselenium compounds, chemical compounds containing carbon-to-selenium chemical bonds. Selenium belongs with oxygen and sulfur to the group 16 elements or chalcogens, and similarities in chemistry are to be expected. Organoselenium compounds are found at trace levels in ambient waters, soils and sediments.
Selenium can exist with oxidation state −2, +2, +4, +6. Se(II) is the dominant form in organoselenium chemistry. Down the group 16 column, the bond strength becomes increasingly weaker (234 kJ/mol for the C−Se bond and 272 kJ/mol for the C−S bond) and the bond lengths longer (C−Se 198 pm, C−S 181 pm and C−O 141 pm). Selenium compounds are more nucleophilic than the corresponding sulfur compounds and also more acidic. The pKa values of XH2 are 16 for oxygen, 7 for sulfur and 3.8 for selenium. In contrast to sulfoxides, the corresponding selenoxides are unstable in the presence of β-protons and this property is utilized in many organic reactions of selenium, notably in selenoxide oxidations and in selenoxide eliminations.
The first organoselenium compound to be isolated was diethyl selenide in 1836.
Structural classification of organoselenium compounds
Selenols (RSeH) are the selenium equivalents of alcohols and thiols. These compounds are relatively unstable and generally have an unpleasant smell. Benzeneselenol (also called selenophenol or PhSeH) is more acidic (pKa 5.9) than thioph
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https://en.wikipedia.org/wiki/Helicity
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Helicity may refer to:
Helicity (fluid mechanics), the extent to which corkscrew-like motion occurs
Helicity (particle physics), the projection of the spin onto the direction of momentum
Magnetic helicity, the extent to which a magnetic field "wraps around itself"
Circular dichroism, the differential absorption of left and right circularly polarized light
A form of axial chirality
A former name for inherent chirality
See also
Helix
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https://en.wikipedia.org/wiki/Cayley%E2%80%93Bacharach%20theorem
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In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane . The original form states:
Assume that two cubics and in the projective plane meet in nine (different) points, as they do in general over an algebraically closed field. Then every cubic that passes through any eight of the points also passes through the ninth point.
A more intrinsic form of the Cayley–Bacharach theorem reads as follows:
Every cubic curve over an algebraically closed field that passes through a given set of eight points also passes through (counting multiplicities) a ninth point which depends only on .
A related result on conics was first proved by the French geometer Michel Chasles and later generalized to cubics by Arthur Cayley and Isaak Bacharach.
Details
If seven of the points lie on a conic, then the ninth point can be chosen on that conic, since will always contain the whole conic on account of Bézout's theorem. In other cases, we have the following.
If no seven points out of are co-conic, then the vector space of cubic homogeneous polynomials that vanish on (the affine cones of) (with multiplicity for double points) has dimension two.
In that case, every cubic through also passes through the intersection of any two different cubics through , which has at least nine points (over the algebraic closure) on account of Bézout's theorem. These points cannot be covered by only, which gives us .
Since degene
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https://en.wikipedia.org/wiki/Pitch%20axis
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Pitch axis may refer to:
In music
Pitch axis (music), the center about which a melody is inverted
Pitch axis theory, a musical technique used in constructing chord progressions
In mathematics and engineering
Aircraft principal axes, the axes of an airplane in flight
Yaw, pitch, and roll, a specific kind of Euler angles
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https://en.wikipedia.org/wiki/The%20Roots%20of%20Coincidence
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The Roots of Coincidence is a 1972 book by Arthur Koestler. It is an introduction to theories of parapsychology, including extrasensory perception and psychokinesis. Koestler postulates links between modern physics, their interaction with time and paranormal phenomena. It is influenced by Carl Jung's concept of synchronicity and the seriality of Paul Kammerer.
In the book Koestler argues that science needs to take the possibility of the occurrence of phenomena that are outside our common sense view of the world more seriously and study them. He concludes that paranormal events are rare, unpredictable and capricious and need a paradoxical combination of skillful scientific experiment with a childlike excitement to be seen and recorded.
The psychologist David Marks initially was critical of Koestler's book for endorsing pseudoscience. Marks noted that Koestler uncritically accepted ESP experiments and ignored evidence that did not fit his hypothesis. In The Psychology of the Psychic Marks coined the term "Koestler's Fallacy" as the assumption that odd matches of random events cannot arise by chance. Marks illustrates the fact that such odd matches do regularly occur with examples from his own experience. In "Psychology and the Paranormal: Exploring Anomalous Experience" Marks (2020) modifies his position by suggesting that a few coincidences are so extremely improbable that they warrant more serious scientific attention. Subjective anomalous experiences defy scientific explan
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https://en.wikipedia.org/wiki/Carlos%20Simmerling
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Carlos Simmerling is a full professor of chemistry at the State University of New York at Stony Brook. He is associate director of the Louis and Beatrice Laufer Center for Physical and Quantitative Biology. Simmerling received his Bachelor of Arts in 1991 from the University of Illinois at Chicago and then his doctorate in 1994 from the same institution. His postdoctoral work was performed at the University of California, San Francisco under the direction of Peter Kollman. His primary field of interest is computational structural biology with a focus on methods of conformational sampling and protein structure prediction. He is a member of the AMBER development team.
Research
Simmerling is leading a team of researchers in the development of new algorithms and programs for accurate and efficient simulation of large biomolecular systems using state-of-the-art computers. Their groundbreaking basic work in the field of computational chemistry and structural biology already is having a tremendous impact in biotechnology, medicinal chemistry and drug design. Using computer simulations in 2002, the team correctly predicted how a protein folds into its final shape purely from its genetic code. By forecasting what these molecules of life look like from their gene sequence, the team received worldwide attention for solving one of the most important challenges in post-genomic biology.
The significance of Simmerling's discovery lies in the protein's shape, which dictates its func
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https://en.wikipedia.org/wiki/Keith%20Edward%20Bullen
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Keith Edward Bullen FAA FRS (29 June 1906 – 23 September 1976) was a New Zealand-born mathematician and geophysicist. He is noted for his seismological interpretation of the deep structure of the Earth's mantle and core. He was Professor of Applied Mathematics at the University of Sydney in Australia from 1945 until 1971.
Personal life
Bullen married Florence Mary Pressley (known as Mary) in Auckland in 1935 and they had two children, a son named John born in Auckland in 1936, and a daughter named Anne born in Melbourne in 1943.
Career
Bullen went to St John's College, Cambridge in 1931, and became a research student, with Harold Jeffreys as his supervisor. Jeffreys was working on the revision of the travel time of the seismic waves from earthquakes and Bullen worked with Jeffreys on this project throughout his years in Cambridge. Jeffreys remarks of this period that 'Bullen's energy was phenomenal'.
Bullen wrote prolifically. There are 290 papers in his list of publications. The topics are diverse apart from the many research papers there are scientific biographies, articles in encyclopaedias and dictionaries of science, and articles on education, especially mathematical education.
His first book, Introduction to the Theory of Seismology, was published by the Cambridge University Press in 1947 and has been a standard text for seismology ever since. The third edition was published in 1975 and Turkish, Chinese, and Russian translations were published in 1960, 1965, and 196
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https://en.wikipedia.org/wiki/Heisenberg%27s%20microscope
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Heisenberg's microscope is a thought experiment proposed by Werner Heisenberg that has served as the nucleus of some commonly held ideas about quantum mechanics. In particular, it provides an argument for the uncertainty principle on the basis of the principles of classical optics.
The concept was criticized by Heisenberg's mentor Niels Bohr, and theoretical and experimental developments have suggested that Heisenberg's intuitive explanation of his mathematical result might be misleading. While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument when measured at the level of an individual state. The formal mathematical result remains valid, however, and the original intuitive argument has also been vindicated mathematically when the notion of disturbance is expanded to be independent of any specific state.
Heisenberg's argument
Heisenberg supposes that an electron is like a classical particle, moving in the direction along a line below the microscope. Let the cone of light rays leaving the microscope lens and focusing on the electron make an angle with the electron. Let be the wavelength of the light rays. Then, according to the laws of classical optics, the microscope can only resolve the position of the electron up to an accuracy of
An observer perceives an image of the particle because the light rays strike the particle and bounce back through the microscope to the observer's eye. We know from
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https://en.wikipedia.org/wiki/Chan%20King-ming
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Chan King-ming is a Hong Kong politician and academic. He served as the vice-chairman of the Democratic Party of Hong Kong from 2004 to 2006. He is also an associate professor in the department of biochemistry and Environmental Science Program of the Chinese University of Hong Kong.
Academic career
Chan King-ming earned his Bachelor of Science and Master of Philosophy degrees at the Chinese University of Hong Kong, and his doctoral degree from Memorial University of Newfoundland in St. John's, Newfoundland, Canada.
He is now director of the Environmental Science Program at the Chinese University of Hong Kong. He teaches many different courses including Current Environmental Issues, Biochemical Toxicology and Introduction to Environmental Science in the Environmental Science Program and Molecular Endocrinology in the Biochemistry Programme. Trained as a molecular biologist for his PhD and post-doctoral research, Professor Chan's research interests include gene regulation, aquatic toxicology, marine biotechnology and environmental biochemistry and environmental policy. Prof. Chan is also chairman of CUTA (Chinese University Teachers Association), trustee of Shaw College Board of trustees, Member of Assembly of Fellows, Shaw College, and warden of Hostel 2, Shaw College.
Political career
Chan is a founding member of the Democratic Party. He was elected as chairman of the New Territories East Branch in 1999, and later became the party's minister of organization affairs and c
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https://en.wikipedia.org/wiki/Sandy%20Douglas
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Alexander Shafto "Sandy" Douglas CBE (21 May 1921 – 29 April 2010) was a British professor of computer science, credited with creating the first graphical computer game, OXO, a version of noughts and crosses, in 1952 on the EDSAC computer at University of Cambridge.
Biography
Early life
Douglas was born on 21 May 1921 in London. At age eight, his family moved to Cromwell Road, near what would become the London Air Terminal.
A 74 bus ride for one old penny took me to Exhibition Road, from which I could go towards South Kensington station to my father's office (which is still there) and workshop (now demolished) down by what became the Lycée Français. Alternatively, I could turn north to the Science Museum – a trip I took often.
In the winter of 1938–39, Douglas and his future wife Andrey Parker made a snowman in the grounds of the Natural History Museum. Douglas and his wife would go on to have two children and at least two grandsons.
During the Blitz, in 1940–41, Douglas's Home Guard Unit, 'C' Company of the Chelsea and Kensington Battalion of the KRRC, had its headquarters in the basement of the Royal School of Mines, just the other side of Exhibition Road from the museums. He appeared to commission into the Corps of Royal Engineers on 7 March 1943 as a second lieutenant, but this was later corrected to show that he actually commissioned into the Royal Corps of Signals.
Cambridge
Douglas attended the University of Cambridge in 1950. In 1952, while working towards ea
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https://en.wikipedia.org/wiki/Bruce%20L.%20Gordon
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Bruce L. Gordon is a Canadian philosopher of science (physics), metaphysician and philosopher of religion. He is a proponent of intelligent design and has been affiliated with the Discovery Institute since 1997.
Biography
Early life and education
Gordon was born in Calgary, Alberta, Canada in 1963.
Gordon earned two undergraduate degrees, one in piano performance at the Royal Conservatory of Music at the University of Toronto in 1982 and another in applied mathematics at the University of Calgary in 1986. He was awarded a master's degree in analytic philosophy from the University of Calgary in 1988. He moved to the United States for graduate study in 1988, and has been a permanent resident ever since. In 1990, Gordon received a master's degree in apologetics and systematic theology from Westminster Theological Seminary in Philadelphia. Finally, he was awarded a Ph.D. from Northwestern University in Evanston, Illinois in the history and philosophy of science (physics) in 1998.
Career
In 1997 he became an affiliate of the Discovery Institute.
He was a visiting assistant professor of philosophy at the University of Notre Dame and a Fellow in the Center for Philosophy of Religion at Notre Dame in 1998–99.
In 1999 he was appointed as a non-tenured associate research professor at Baylor University, and was appointed as associate director of the short-lived Michael Polanyi Center there, which was directed by William Dembski. The center was a step forward in the Discovery Inst
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https://en.wikipedia.org/wiki/Enumerative%20geometry
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In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory.
History
The problem of Apollonius is one of the earliest examples of enumerative geometry. This problem asks for the number and construction of circles that are tangent to three given circles, points or lines. In general, the problem for three given circles has eight solutions, which can be seen as 23, each tangency condition imposing a quadratic condition on the space of circles. However, for special arrangements of the given circles, the number of solutions may also be any integer from 0 (no solutions) to six; there is no arrangement for which there are seven solutions to Apollonius' problem.
Key tools
A number of tools, ranging from the elementary to the more advanced, include:
Dimension counting
Bézout's theorem
Schubert calculus, and more generally characteristic classes in cohomology
The connection of counting intersections with cohomology is Poincaré duality
The study of moduli spaces of curves, maps and other geometric objects, sometimes via the theory of quantum cohomology. The study of quantum cohomology, Gromov–Witten invariants and mirror symmetry gave a significant progress in Clemens conjecture.
Enumerative geometry is very closely tied to intersection theory.
Schubert calculus
Enumerative geometry saw spectacular development towards the end of the nineteenth century, a
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https://en.wikipedia.org/wiki/Jacques%20Mehler
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Jacques Mehler (17 August 1936 – 11 February 2020) was a cognitive psychologist specializing in language acquisition.
Education
Mehler studied chemistry and obtained his Licenciatura en Ciencias Quimicas at the Universidad de Buenos Aires from 1952 to 1958. After that, he went to Oxford University and University College of London where he obtained his B.Sc. degree in 1959.
From 1961 to 1964, he studied at Harvard University, at the time of the cognitive revolution, where he worked with George A. Miller and obtained a PhD. in psychology.
Career
Mehler was Emeritus at the École des Hautes Études en Sciences Sociales, where he directed the Laboratoire de Sciences Cognitives et Psycholinguistique (LSCP); he was also the head of the Language, Cognition and Development lab at the International School for Advanced Studies (SISSA) in Trieste (Italy). In 1982, He became a member of the Max Planck Institute for Psycholinguistics' Scientific Council in 1982. He was editor-in-chief of the journal Cognition until 2007. Mehler was elected a foreign honorary member of the American Academy of Arts and Sciences in 2001, a Fellow of the American Association for the Advancement of Science in 2003, and an international member of the American Philosophical Society in 2009.
Research
Jacques Mehler devoted most of his career to language processing and language acquisition. Early on, he and his colleagues discovered that 2-year-olds display previously unsuspected cognitive capacities, providin
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https://en.wikipedia.org/wiki/Formula%20unit
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In chemistry, a formula unit is the smallest unit of any Ionic compound or covalent network solid or metal (not for molecular substances). . And it can also refer to the chemical formula for that unit. Those structures do not consist of discrete molecules, and so for them, the term formula unit is used. In contrast, the terms molecule or molecular formula are applied to molecules. The formula unit is used as an independent entity for stoichiometric calculations. Examples of formula units, include ionic compounds such as and and covalent networks such as and C (as diamond or graphite).
In most cases the formula representing a formula unit, will also be an empirical formula e.g. calcium carbonate or sodium chloride but this isn't always the case. For example the ionic compound Potassium persulfate has formula unit which isn't an empirical formula. And the ionic compound is not an empirical formula as you see those compounds have formula units with ratios that are not in simplest/reduced form. The empirical formulae for those ionic compounds would be and respectively.
In mineralogy, as minerals are almost exclusively either ionic or network solids, the formula unit is used. The number of formula units (Z) and the dimensions of the crystallographic axes are used in defining the unit cell.
References
Chemical formulas
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https://en.wikipedia.org/wiki/High%20Flux%20Isotope%20Reactor
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The High Flux Isotope Reactor (HFIR) is a nuclear research reactor at Oak Ridge National Laboratory (ORNL) in Oak Ridge, Tennessee, United States. Operating at 85 MW, HFIR is one of the highest flux reactor-based sources of neutrons for condensed matter physics research in the United States, and it has one of the highest steady-state neutron fluxes of any research reactor in the world. The thermal and cold neutrons produced by HFIR are used to study physics, chemistry, materials science, engineering, and biology. The intense neutron flux, constant power density, and constant-length fuel cycles are used by more than 500 researchers each year for neutron scattering research into the fundamental properties of condensed matter. HFIR has about 600 users each year for both scattering and in-core research.
The neutron scattering research facilities at HFIR contain a world-class collection of instruments used for fundamental and applied research on the structure and dynamics of matter. The reactor is also used for medical, industrial, and research isotope production; research on severe neutron damage to materials; and neutron activation to examine trace elements in the environment. Additionally, the building houses a gamma irradiation facility that uses spent fuel assemblies and is capable of accommodating high gamma dose experiments.
With projected regular operations, the next major shutdown for a beryllium reflector replacement will not be necessary until about 2023. This ou
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https://en.wikipedia.org/wiki/Ekmeleddin%20%C4%B0hsano%C4%9Flu
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Ekmeleddin Mehmet İhsanoğlu (; born 26 December 1943) is a Turkish chemistry and science history professor, academician, diplomat and politician who was Secretary-General of the Organisation of Islamic Cooperation (OIC) from 2004 to 2014. He is also an author and editor of academic journals and advocate of intercultural dialogue.
İhsanoğlu studied science at the Ain Shams University, where he received his BSc in 1966. He remained in Cairo and obtained his MSc in 1970 from Al-Azhar University. İhsanoğlu received his PhD from the Faculty of Science at the Ankara University in 1974. İhsanoğlu's academic work has focused on the history of scientific activity and institutions of learning within Islam, cultural exchanges between Islam and the West, the relationship between science and religion, and the development of science in its socio-cultural environment.
İhsanoğlu was the founder of the Department of History of Science at the Faculty of Letters of Istanbul University, and he remained the chairman of that department between 1984 and 2003. He was also a lecturer and a visiting professor at various universities, including Ankara University, the university of Exeter, United Kingdom (1975–1977), Inönü University (1970–1980), the university of Malatya (1978–1980), and Ludwig Maximilians University of Munich, Germany (2003).
After taking the office as the ninth Secretary General of the OIC in January 2005, İhsanoğlu coordinated the drafting and implementation of a reform program f
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https://en.wikipedia.org/wiki/Evolving%20classification%20function
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Evolving classification functions (ECF), evolving classifier functions or evolving classifiers are used for classifying and clustering in the field of machine learning and artificial intelligence, typically employed for data stream mining tasks in dynamic and changing environments.
See also
Supervised Classification on Data Streams
Evolving fuzzy rule-based Classifier (eClass )
Evolving Takagi-Sugeno fuzzy systems (eTS )
Evolving All-Pairs (ensembled) classifiers (EFC-AP )
Evolving Connectionist Systems (ECOS)
Dynamic Evolving Neuro-Fuzzy Inference Systems (DENFIS)
Evolving Fuzzy Neural Networks (EFuNN)
Evolving Self-Organising Maps
neuro-fuzzy techniques
hybrid intelligent systems
fuzzy clustering
Growing Neural Gas
References
Classification algorithms
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https://en.wikipedia.org/wiki/Winthrop%20E.%20Stone
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Winthrop Ellsworth Stone (June 12, 1862 – July 17, 1921) was a professor of chemistry and served as the president of Purdue University from 1900–1921.
Biography
Youth and career
Born in Chesterfield, New Hampshire, to Frederick L. Stone and Ann Butler, he was the older brother of Chief Justice Harlan Fiske Stone.
He moved to Amherst, Massachusetts in 1874, and attended Amherst High School and Massachusetts Agricultural College (now the University of Massachusetts Amherst), where he received his bachelor's degree in 1882.
Stone studied chemistry and biology at Boston University, while also serving as an assistant chemist to the Massachusetts State Agricultural Experiment Station from 1884–1886. He then studied at the University of Göttingen, receiving his Ph.D. there in 1888. From 1888 to 1889, he was a chemist at the Tennessee Agricultural Experiment Station.
In 1889 he joined Purdue University as a professor of chemistry and conducted research in the chemistry of carbohydrates. After serving as Purdue's first vice president from 1892–1900, he became president of the university upon the death of James Henry Smart in 1900.
During Stone's tenure, Purdue's schools of agriculture and engineering grew rapidly. President Stone was present at one of Purdue's worst tragedies, the Purdue Wreck train collision in 1903, tending to those who were injured or dying. Stone was also instrumental in the founding of Purdue's school of medicine, which would be active from 1905 to 1
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https://en.wikipedia.org/wiki/Gravitational%20acceleration
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In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies; the measurement and analysis of these rates is known as gravimetry.
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. At different points on Earth's surface, the free fall acceleration ranges from , depending on altitude, latitude, and longitude. A conventional standard value is defined exactly as 9.80665 m/s² (about 32.1740 ft/s²). Locations of significant variation from this value are known as gravity anomalies. This does not take into account other effects, such as buoyancy or drag.
Relation to the Universal Law
Newton's law of universal gravitation states that there is a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other. The formula is:
where and are any two masses, is the gravitational constant, and is the distance between the two point-like masses.
Using the integral form of Gauss's Law, this formula can be extended to any pair of objects of which one is far more massive than the other — like a planet relative to any man-scale art
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https://en.wikipedia.org/wiki/Long-toed%20salamander
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The long-toed salamander (Ambystoma macrodactylum) is a mole salamander in the family Ambystomatidae. This species, typically long when mature, is characterized by its mottled black, brown, and yellow pigmentation, and its long outer fourth toe on the hind limbs. Analysis of fossil records, genetics, and biogeography suggest A. macrodactylum and A. laterale are descended from a common ancestor that gained access to the western Cordillera with the loss of the mid-continental seaway toward the Paleocene.
The distribution of the long-toed salamander is primarily in the Pacific Northwest, with an altitudinal range of up to . It lives in a variety of habitats, including temperate rainforests, coniferous forests, montane riparian zones, sagebrush plains, red fir forests, semiarid sagebrush, cheatgrass plains, and alpine meadows along the rocky shores of mountain lakes. It lives in slow-moving streams, ponds, and lakes during its aquatic breeding phase. The long-toed salamander hibernates during the cold winter months, surviving on energy reserves stored in the skin and tail.
The five subspecies have different genetic and ecological histories, phenotypically expressed in a range of color and skin patterns. Although the long-toed salamander is classified as a species of Least Concern by the IUCN, many forms of land development threaten and negatively affect the salamander's habitat.
Taxonomy
Ambystoma macrodactylum is a member of the Ambystomatidae, also known as the mole salama
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https://en.wikipedia.org/wiki/Metal%20carbonyl
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Metal carbonyls are coordination complexes of transition metals with carbon monoxide ligands. Metal carbonyls are useful in organic synthesis and as catalysts or catalyst precursors in homogeneous catalysis, such as hydroformylation and Reppe chemistry. In the Mond process, nickel tetracarbonyl is used to produce pure nickel. In organometallic chemistry, metal carbonyls serve as precursors for the preparation of other organometallic complexes.
Metal carbonyls are toxic by skin contact, inhalation or ingestion, in part because of their ability to carbonylate hemoglobin to give carboxyhemoglobin, which prevents the binding of oxygen.
Nomenclature and terminology
The nomenclature of the metal carbonyls depends on the charge of the complex, the number and type of central atoms, and the number and type of ligands and their binding modes. They occur as neutral complexes, as positively-charged metal carbonyl cations or as negatively charged metal carbonylates. The carbon monoxide ligand may be bound terminally to a single metal atom or bridging to two or more metal atoms. These complexes may be homoleptic, containing only CO ligands, such as nickel tetracarbonyl (Ni(CO)4), but more commonly metal carbonyls are heteroleptic and contain a mixture of ligands.
Mononuclear metal carbonyls contain only one metal atom as the central atom. Except vanadium hexacarbonyl, only metals with even atomic number, such as chromium, iron, nickel, and their homologs, build neutral mononuclear compl
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https://en.wikipedia.org/wiki/Roy%20McWeeny
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Roy McWeeny (19 May 1924 – 29 April 2021) was a British academic physicist and chemist.
McWeeny was born in Bradford, Yorkshire in May 1924. His first degree was in physics from the University of Leeds. He then obtained a D.Phil. in mathematical physics and quantum theory under the supervision of Charles Coulson at the Mathematical Institute, University of Oxford.
From 1948 to 1957 he was lecturer in physical chemistry at King's College, University of Durham (King's College is now the University of Newcastle upon Tyne). From 1957 to 1965 he was at the University of Keele rising to Professor of Theoretical Physics and Theoretical Chemistry. From 1966 to 1982 he was Professor of Theoretical Chemistry at the University of Sheffield. In 1982 he moved to the University of Pisa, Italy where he remained an Emeritus Professor until his death.
In 1996 a celebratory festschrift volume was published in his honour containing original
papers by 132 scientists from 19 countries. He was awarded the 2006 Spiers Memorial Medal by the Faraday Division of the Royal Society of Chemistry and the Medal Lecture, "Quantum chemistry: The first seventy years", was published in Faraday Discussions. He has served on the editorial board of Molecular Physics, Chemical Physics Letters and International Journal of Quantum Chemistry.
He has written many scientific papers and seven books, of which perhaps the best known are Coulson's Valence in 1979, an update of the famous book by Charles Coulson origin
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https://en.wikipedia.org/wiki/363%20%28number%29
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363 (three hundred [and] sixty-three) is the natural number following 362 and preceding 364.
In mathematics
It is an odd, composite, positive, real integer, composed of a prime (3) and a prime squared (112).
363 is a deficient number and a perfect totient number.
363 is a palindromic number in bases 3, 10, 11 and 32.
363 is a repdigit (BB) in base 32.
The Mertens function returns 0.
Any subset of its digits is divisible by three.
363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).
363 can be expressed as the sum of three squares in four different ways: 112 + 112 + 112, 52 + 72 + 172, 12 + 12 + 192, and 132 + 132 + 52.
363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter .
References
Integers
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https://en.wikipedia.org/wiki/Elliptic%20surface
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In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex numbers, these fibers are elliptic curves, perhaps without a chosen origin.) This is equivalent to the generic fiber being a smooth curve of genus one. This follows from proper base change.
The surface and the base curve are assumed to be non-singular (complex manifolds or regular schemes, depending on the context). The fibers that are not elliptic curves are called the singular fibers and were classified by Kunihiko Kodaira. Both elliptic and singular fibers are important in string theory, especially in F-theory.
Elliptic surfaces form a large class of surfaces that contains many of the interesting examples of surfaces, and are relatively well understood in the theories of complex manifolds and smooth 4-manifolds. They are similar to (have analogies with, that is), elliptic curves over number fields.
Examples
The product of any elliptic curve with any curve is an elliptic surface (with no singular fibers).
All surfaces of Kodaira dimension 1 are elliptic surfaces.
Every complex Enriques surface is elliptic, and has an elliptic fibration over the projective line.
Kodaira surfaces
Dolgachev surfaces
Shioda modular surfaces
Kodaira's table of singular fibers
Most of the fibers of an elliptic fibration are
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https://en.wikipedia.org/wiki/Impenetrability
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In metaphysics, impenetrability is the name given to that quality of matter whereby two bodies cannot occupy the same space at the same time. The philosopher John Toland argued that impenetrability and extension were sufficient to define matter, a contention strongly disputed by Gottfried Wilhelm von Leibniz.
Locke considered impenetrability to be "more a consequence of solidity, than solidity itself."
See also
Locke's views on extension
Interpenetration (disambiguation)
Notes
References
Heinemann, F. H. "Toland and Leibniz." The Philosophical Review, Vol. 54, No. 5. (September, 1945), pp. 437–457.
Metaphysical properties
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https://en.wikipedia.org/wiki/Henry%20Harris%20%28scientist%29
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Sir Henry Harris (28 January 1925 – 31 October 2014) was an Australian professor of medicine at the University of Oxford who led pioneering work on cancer and human genetics in the 2000s.
Early life and education
Harris was born in 1925 to a Jewish family in the Soviet Union. In 1929, his family emigrated to Australia. Harris studied at Sydney Boys High School from 1937 to 1941. In 1941, he first read modern languages, but was subsequently attracted to medicine through his literary interests. He studied medicine at the Royal Prince Alfred Hospital and began a career in medical research rather than in clinical practice.
Career
In the early 1950s, Harris moved to England to study at the Sir William Dunn School of Pathology in Oxford under Howard Florey. He completed his DPhil in 1954 and settled down to a career of academic research. In 1960, he was appointed the head of the new department of cell biology at the John Innes Institute, and, in 1964, he succeeded Florey as head of the Dunn School. In 1979, he was appointed as Oxford's Regius Professor of Medicine, succeeding Richard Doll.
Harris's research interests were primarily focused on cancer cells and their differences from normal cells. He later studied the possibility of genetic modification of human cell lines with the material of other species to increase the range of genetic markers. Harris and his colleagues developed some of the basic techniques for investigating and measuring genes along the human chromosome.
I
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https://en.wikipedia.org/wiki/Partial%20order%20reduction
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In computer science, partial order reduction is a technique for reducing the size of the state-space to be searched by a model checking or automated planning and scheduling algorithm. It exploits the commutativity of concurrently executed transitions that result in the same state when executed in different orders.
In explicit state space exploration, partial order reduction usually refers to the specific technique of expanding a representative subset of all enabled transitions. This technique has also been described as model checking with representatives. There are various versions of the method, the so-called stubborn set method, ample set method, and persistent set method.
Ample sets
Ample sets are an example of model checking with representatives. Their formulation relies on a separate notion of dependency. Two transitions are considered independent only if they cannot disable another whenever they are mutually enabled. The execution of both results in a unique state regardless of the order in which they are executed. Transitions that are not independent, are dependent. In practice dependency is approximated using static analysis.
Ample sets for different purposes can be defined by giving conditions as to when a set of transitions is "ample" in a given state.
C0
C1 If a transition depends on some transition relation in , this transition cannot be invoked until some transition in the ample set is executed.
Conditions C0 and C1 are sufficient for preserving all the
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https://en.wikipedia.org/wiki/ARGUS%20distribution
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In physics, the ARGUS distribution, named after the particle physics experiment ARGUS, is the probability distribution of the reconstructed invariant mass of a decayed particle candidate in continuum background.
Definition
The probability density function (pdf) of the ARGUS distribution is:
for . Here and are parameters of the distribution and
where and are the cumulative distribution and probability density functions of the standard normal distribution, respectively.
Cumulative distribution function
The cumulative distribution function (cdf) of the ARGUS distribution is
.
Parameter estimation
Parameter c is assumed to be known (the kinematic limit of the invariant mass distribution), whereas χ can be estimated from the sample X1, …, Xn using the maximum likelihood approach. The estimator is a function of sample second moment, and is given as a solution to the non-linear equation
.
The solution exists and is unique, provided that the right-hand side is greater than 0.4; the resulting estimator is consistent and asymptotically normal.
Generalized ARGUS distribution
Sometimes a more general form is used to describe a more peaking-like distribution:
where Γ(·) is the gamma function, and Γ(·,·) is the upper incomplete gamma function.
Here parameters c, χ, p represent the cutoff, curvature, and power respectively.
The mode is:
The mean is:
where M(·,·,·) is the Kummer's confluent hypergeometric function.
The variance is:
p = 0.5 gives a regular ARGUS, listed
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https://en.wikipedia.org/wiki/High%20School%20for%20Health%20Professions%20and%20Human%20Services
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The High School for Health Professions and Human Services is a public high school in Manhattan, New York City. It is specialized for students preparing for careers in the healthcare and human resources fields.
The curriculum emphasizes the academic preparation necessary for these fields. Students take four years of both mathematics and science, and there are elective research programs and college level courses in both the sciences and the humanities. The High School for Health Professions and Human Services offers a range of science courses as part of a traditional high school curriculum. Top students may conduct research with mentors at nearby hospitals and a few may even compete in the Intel Science Talent Search. The school also offers courses in nutrition, forensics, and a combined art and anatomy class.
School life
Housed in the old Stuyvesant High School building, Health Professions can be very crowded at times. Starting times are staggered from 7:20 to 9 a.m. to accommodate triple sessions. Seniors may leave as early as noon; other grades stay until 3:10 p.m, depending on class periods. Physical education classes such as gym have about 50 students. The attendance and graduation rates are higher than the citywide average, and kids say they feel safe. There are no metal detectors and the bathrooms are unlocked. The school is about 70% female.
Two other schools are housed in the building at 345 East 15th Street. PS 226, a school for students with moderate to severe de
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https://en.wikipedia.org/wiki/Chin%20Dae-je
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Chin Dae-je is a South-Korean businessman and former politician. He was born on January 20, 1952, in Uiryeong, South Gyeongsang Province.
Biography
He attended Gyeonggi High School and then studied Electrical Engineering at Seoul National University (B.S. and M.S.), the University of Massachusetts Amherst (M.S.) and Stanford (Ph.D). From 1985 he worked for Samsung, and served as president of their Digital Media Business from 2000–2003.
He became Minister of Information and Communication in February, 2003.
He resigned from the government in early 2006, and ran for the governorship of Gyeonggi Province on the ruling Uri Party ticket. However he lost to Kim Moon-soo, the candidate of Grand National Party, as part of the widespread electoral revolt against the incumbent ruling party. He was however the only candidate to collect more than 30% of the votes by a ruling Uri-party candidate in all of the contests in the whole nation, except Governor Kim Wan-ju of Jeollabukdo.
He gave a plenary talk at International Solid State Circuit Conference (ISSCC), 2005.
Chin was elected a member of the National Academy of Engineering in 2020 for innovations and industry leadership in semiconductor technology.
External links
korea.net profile
businessweek.com article
References
1952 births
Living people
Seoul National University alumni
Stanford University alumni
University of Massachusetts Amherst College of Engineering alumni
Uri Party politicians
Government ministers of South Kore
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https://en.wikipedia.org/wiki/Enrico%20Verson
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Enrico Verson (25 April 1845 in Padua – 15 February 1927 in Padua) was an Italian entomologist,
A physician, Verson worked initially at the experimental station of Gorizia before founding the second research station on the silkworm in the world, the Stazione Bacologica Sperimentale in 1871. Verson made many observations on the biology of the silkworm and made anatomical discoveries such as the cells of Verson (apical cells of the genital apparatus of certain insects) and glands of Verson (glands of the exoskeleton (skin) of the caterpillars playing an important part in the moult).
He had a considerable influence on the Italian entomologists of his and the following generation like Antonio Berlese (1863–1927), Adolfo Targioni Tozzetti (1823–1902) and Filippo Silvestri (1873–1949).
1845 births
1927 deaths
Italian entomologists
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https://en.wikipedia.org/wiki/Fenchel%27s%20duality%20theorem
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In mathematics, Fenchel's duality theorem is a result in the theory of convex functions named after Werner Fenchel.
Let ƒ be a proper convex function on Rn and let g be a proper concave function on Rn. Then, if regularity conditions are satisfied,
where ƒ * is the convex conjugate of ƒ (also referred to as the Fenchel–Legendre transform) and g * is the concave conjugate of g. That is,
Mathematical theorem
Let X and Y be Banach spaces, and be convex functions and be a bounded linear map. Then the Fenchel problems:
satisfy weak duality, i.e. . Note that are the convex conjugates of f,g respectively, and is the adjoint operator. The perturbation function for this dual problem is given by .
Suppose that f,g, and A satisfy either
f and g are lower semi-continuous and where is the algebraic interior and , where h is some function, is the set , or
where are the points where the function is continuous.
Then strong duality holds, i.e. . If then supremum is attained.
One-dimensional illustration
In the following figure, the minimization problem on the left side of the equation is illustrated. One seeks to vary x such that the vertical distance between the convex and concave curves at x is as small as possible. The position of the vertical line in the figure is the (approximate) optimum.
The next figure illustrates the maximization problem on the right hand side of the above equation. Tangents are drawn to each of the two curves such that both tangents have th
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https://en.wikipedia.org/wiki/Ramond%E2%80%93Ramond%20field
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In theoretical physics, Ramond–Ramond fields are differential form fields in the 10-dimensional spacetime of type II supergravity theories, which are the classical limits of type II string theory. The ranks of the fields depend on which type II theory is considered. As Joseph Polchinski argued in 1995, D-branes are the charged objects that act as sources for these fields, according to the rules of p-form electrodynamics. It has been conjectured that quantum RR fields are not differential forms, but instead are classified by twisted K-theory.
The adjective "Ramond–Ramond" reflects the fact that in the RNS formalism, these fields appear in the Ramond–Ramond sector in which all vector fermions are periodic. Both uses of the word "Ramond" refer to Pierre Ramond, who studied such boundary conditions (the so-called Ramond boundary conditions) and the fields that satisfy them in 1971.
Defining the fields
The fields in each theory
As in Maxwell's theory of electromagnetism and its generalization, p-form electrodynamics, Ramond–Ramond (RR) fields come in pairs consisting of a p-form potential Cp and a (p + 1)-form field strength Gp+1. The field strength is, as usual defined to be the exterior derivative of the potential Gp+1 = dCp.
As is usual in such theories, if one allows topologically nontrivial configurations or charged matter (D-branes) then the connections are only defined on each coordinate patch of spacetime, and the values on various patches are glued using transiti
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https://en.wikipedia.org/wiki/Charles%20LeGeyt%20Fortescue
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Charles LeGeyt Fortescue (1876–1936) was an electrical engineer. He was born in York Factory, in what is now Manitoba where the Hayes River enters Hudson Bay. He was the son of a Hudson's Bay Company fur trading factor and was among the first graduates of the Queen's University electrical engineering program in 1898.
On graduation Fortescue joined the Westinghouse Corporation at East Pittsburgh, Pennsylvania, where he spent his entire professional career. In 1901 he joined the Transformer Engineering Department and worked on many problems arising from the use of high voltage. In 1913 Fortescue published the AIEE paper "The Application of a Theorem of Electrostatics to Insulator Problems". Also in that year he was one of the authors of a paper on measurement of high voltage by the breakdown of a gap between two conductive spheres, which is a technique still used in high-voltage laboratories today.
In a paper presented in 1918, Fortescue demonstrated that any set of N unbalanced phasors — that is, any such "polyphase" signal — could be expressed as the sum of N symmetrical sets of balanced phasors known as symmetrical components. The paper was judged to be the most important power engineering paper in the twentieth century.
He was awarded the Franklin Institute's 1932 Elliott Cresson Medal for his contributions to the field of electrical engineering.
A fellowship awarded every year by the IEEE in his name commemorates his contributions to electrical engineering.
Patents
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https://en.wikipedia.org/wiki/Hobbs%20Observatory
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Hobbs Observatory is an astronomical observatory owned and operated by University of Wisconsin–Eau Claire's Department of Physics and Astronomy and home to the Chippewa Valley Astronomical Society. It is located in the Beaver Creek Reserve four miles North of Fall Creek, Wisconsin. It is named after the Hobbs Foundation, a local philanthropic organization which provided money for the initial construction in 1978 and the purchase of a Navy telescope.
See also
List of astronomical observatories
References
External links
Official website
Hobbs Observatory Clear Sky Clock Forecasts of observing conditions.
Astronomical observatories in Wisconsin
Buildings and structures in Eau Claire County, Wisconsin
Tourist attractions in Eau Claire County, Wisconsin
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https://en.wikipedia.org/wiki/Stuart%20Newman
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Stuart Alan Newman (born April 4, 1945 in New York City) is a professor of cell biology and anatomy at New York Medical College in Valhalla, NY, United States. His research centers around three program areas: cellular and molecular mechanisms of vertebrate limb development, physical mechanisms of morphogenesis, and mechanisms of morphological evolution. He also writes about social and cultural aspects of biological research and technology.
Career
Stuart Newman graduated from Jamaica High School in Queens, New York. He received an A.B. from Columbia College of Columbia University in 1965, and a Ph.D. in chemical physics from the University of Chicago in 1970, where he worked with the theoretical chemist, Stuart A. Rice. He was a postdoctoral fellow in the Department of Theoretical Biology, University of Chicago and the School of Biological Sciences, University of Sussex, UK, and before joining New York Medical College was an instructor in anatomy at the University of Pennsylvania and an assistant professor of biological sciences at the State University of New York at Albany.
He has been a visiting professor at the Pasteur Institute, Paris, the Commissariat à l'Energie Atomique-Saclay, the Indian Institute of Science, Bangalore, the University of Tokyo, Komaba, and was a Fogarty Senior International Fellow at Monash University, Australia. He is a member of the External Faculty of the Konrad Lorenz Institute for Evolution and Cognition Research, Klosterneuburg, Austria and in
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https://en.wikipedia.org/wiki/Origination%20of%20Organismal%20Form
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Origination of Organismal Form: Beyond the Gene in Developmental and Evolutionary Biology is an anthology published in 2003 edited by Gerd B. Müller and Stuart A. Newman. The book is the outcome of the 4th Altenberg Workshop in Theoretical Biology on "Origins of Organismal Form: Beyond the Gene Paradigm", hosted in 1999 at the Konrad Lorenz Institute for Evolution and Cognition Research. It has been cited over 200 times and has a major influence on extended evolutionary synthesis research.
Description of the book
The book explores the multiple factors that may have been responsible for the origination of biological form in multicellular life. These biological forms include limbs, segmented structures, and different body symmetries.
It explores why the basic body plans of nearly all multicellular life arose in the relatively short time span of the Cambrian Explosion. The authors focus on physical factors (structuralism) other than changes in an organism's genome that may have caused multicellular life to form new structures. These physical factors include differential adhesion of cells and feedback oscillations between cells.
The book also presents recent experimental results that examine how the same embryonic tissues or tumor cells can be coaxed into forming dramatically different structures under different environmental conditions.
One of the goals of the book is to stimulate research that may lead to a more comprehensive theory of evolution. It is frequently cited as
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https://en.wikipedia.org/wiki/Joseph%20Nelson%20Rose
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Joseph Nelson Rose (January 11, 1862 – May 4, 1928) was an American botanist. He was born in Union County, Indiana. His father died serving during the Civil War when Joseph Rose was a young boy. He later graduated from high school in Liberty, Indiana.
He received his Ph.D. in Biology from Wabash College in 1889. having received his B.A. in Biology and M.A. Paleobotany earlier at the same institute. He married Lou Beatrice Sims in 1888 and produced with her three sons and three daughters.
Rose worked for the U.S. Department of Agriculture and became an assistant curator at the Smithsonian in 1896.
While Rose was employed by the national museum, he was an authority on several plants families, including Apiaceae (Parsley Family) and Cactaceae (Cactus Family). He made several field trips to Mexico, and presented specimens to the Smithsonian and the New York Botanical Garden.
With Nathaniel Lord Britton, Rose published many articles on the Crassulaceae. He took a leave of absence from the Smithsonian to do further fieldwork in South America and publish with Britton, the four-volume work, The Cactaceae (1919–1923), illustrated by Mary Emily Eaton (1873–1961).
Rose returned to work afterwards at the Smithsonian, making further contributions to Botany.
Honors
Astroblepus rosei is a species of catfish of the family Astroblepidae that was named after Rose. It can be found on Cajamarca, Peru.
In 1890, botanist S.Watson published Rhodosciadium, a genus of flowering plants fr
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https://en.wikipedia.org/wiki/TASI
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TASI can mean:
Technical Advisory Service for Images
Time-assignment speech interpolation
Theoretical Advanced Study Institute (TASI), best known for the TASI lectures in astrophysics and high energy physics
Tadawul All Share Index of the Saudi Stock Exchange
The Animation Society of India (TASI), a non-profit organisation (see Indian animation industry)
See also
Tasi a Greek neighbourhood in the city of Patras
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https://en.wikipedia.org/wiki/George%20F.%20Pinder
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George Francis Pinder (born 1942) is an American environmental engineer who is Professor of Civil and Environmental Engineering with a secondary appointment in Mathematics and Statistics at the University of Vermont. He also served as a professional witness in various notable environmental cases including Love Canal and the Woburn groundwater contamination incident.
He was elected a member of the National Academy of Engineering in 2010 for leadership in groundwater modeling applied to diverse problems in water resources. He is founding editor of the journal "Advances in Water Resources", and he served as editor-in-chief of the journal Numerical Methods for Partial Differential Equations.
Pinder's principal research interest is in the development of numerical methods to solve complex problems pertaining to groundwater contamination and supply. He has published approximately one hundred and thirty five papers in refereed journals in the area of quantitative analysis of subsurface flow and transport, as well as twelve books.
In popular culture
Pinder was featured as a character in the movie A Civil Action, based on the Woburn toxic waste case and starring John Travolta. He was portrayed by British actor Stephen Fry. He and his wife Phyllis were also featured in the book on which the film is based.
References
External links
George Pinder at the University of Vermont
Official George Pinder Website
Environmental engineers
American civil engineers
Engineering educators
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https://en.wikipedia.org/wiki/Semi-differentiability
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In calculus, a branch of mathematics, the notions of one-sided differentiability and semi-differentiability of a real-valued function f of a real variable are weaker than differentiability. Specifically, the function f is said to be right differentiable at a point a if, roughly speaking, a derivative can be defined as the function's argument x moves to a from the right, and left differentiable at a if the derivative can be defined as x moves to a from the left.
One-dimensional case
In mathematics, a left derivative and a right derivative are derivatives (rates of change of a function) defined for movement in one direction only (left or right; that is, to lower or higher values) by the argument of a function.
Definitions
Let f denote a real-valued function defined on a subset I of the real numbers.
If is a limit point of and the one-sided limit
exists as a real number, then f is called right differentiable at a and the limit ∂+f(a) is called the right derivative of f at a.
If is a limit point of and the one-sided limit
exists as a real number, then f is called left differentiable at a and the limit ∂–f(a) is called the left derivative of f at a.
If is a limit point of and and if f is left and right differentiable at a, then f is called semi-differentiable at a.
If the left and right derivatives are equal, then they have the same value as the usual ("bidirectional") derivative. One can also define a symmetric derivative, which equals the arithmetic mean of t
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https://en.wikipedia.org/wiki/Hermann%20Jacobi
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Hermann Georg Jacobi (11 February 1850 – 19 October 1937) was an eminent German Indologist.
Education
Jacobi was born in Köln (Cologne) on 11 February 1850. He was educated in the gymnasium of Cologne and then went to the University of Berlin, where initially he studied mathematics, but later, probably under the influence of Albrecht Weber, switched to Sanskrit and comparative linguistics, which he studied under Weber and Johann Gildemeister. He obtained his doctorate from the University of Bonn. The subject of his thesis, written in 1872, was the origin of the term "hora" in Indian astrology.
Jacobi was able to visit London for a year, 1872–1873, where he examined the Indian manuscripts available there. The next year, with Georg Buehler, he visited Rajasthan, India, where manuscripts were being collected. At Jaisalmer Library, he came across Jain Manuscripts, which were of abiding interest to him for the rest of his life. He later edited and translated many of them, both into German and English, including those for Max Mueller's Sacred Books of the East.
Academic appointments
In 1875, he became a docent in Sanskrit at Bonn; from 1876-85 was professor extraordinarius of Sanskrit and Comparative Philology at Münster, Westphalia; in 1885 was made professor ordinarius of Sanskrit at Kiel; and in 1889 was appointed professor of Sanskrit at Bonn. He served as professor in Bonn until his retirement in 1922. After his retirement, Jacobi remained active, lecturing and writing til
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https://en.wikipedia.org/wiki/Serre%20spectral%20sequence
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In mathematics, the Serre spectral sequence (sometimes Leray–Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important tool in algebraic topology. It expresses, in the language of homological algebra, the singular (co)homology of the total space X of a (Serre) fibration in terms of the (co)homology of the base space B and the fiber F. The result is due to Jean-Pierre Serre in his doctoral dissertation.
Cohomology spectral sequence
Let be a Serre fibration of topological spaces, and let F be the (path-connected) fiber. The Serre cohomology spectral sequence is the following:
Here, at least under standard simplifying conditions, the coefficient group in the -term is the q-th integral cohomology group of F, and the outer group is the singular cohomology of B with coefficients in that group.
Strictly speaking, what is meant is cohomology with respect to the local coefficient system on B given by the cohomology of the various fibers. Assuming for example, that B is simply connected, this collapses to the usual cohomology. For a path connected base, all the different fibers are homotopy equivalent. In particular, their cohomology is isomorphic, so the choice of "the" fiber does not give any ambiguity.
The abutment means integral cohomology of the total space X.
This spectral sequence can be derived from an exact couple built out of the long exact sequences of the cohomology of the pair , where is the restriction of the
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https://en.wikipedia.org/wiki/Gibbs%20measure
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In mathematics, the Gibbs measure, named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory and statistical mechanics. It is a generalization of the canonical ensemble to infinite systems.
The canonical ensemble gives the probability of the system X being in state x (equivalently, of the random variable X having value x) as
Here, is a function from the space of states to the real numbers; in physics applications, is interpreted as the energy of the configuration x. The parameter is a free parameter; in physics, it is the inverse temperature. The normalizing constant is the partition function. However, in infinite systems, the total energy is no longer a finite number and cannot be used in the traditional construction of the probability distribution of a canonical ensemble. Traditional approaches in statistical physics studied the limit of intensive properties as the size of a finite system approaches infinity (the thermodynamic limit). When the energy function can be written as a sum of terms that each involve only variables from a finite subsystem, the notion of a Gibbs measure provides an alternative approach. Gibbs measures were proposed by probability theorists such as Dobrushin, Lanford, and Ruelle and provided a framework to directly study infinite systems, instead of taking the limit of finite systems.
A measure is a Gibbs measure if the conditional probabilities it induces on each finite subsystem satisfy
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https://en.wikipedia.org/wiki/Burr%E2%80%93Erd%C5%91s%20conjecture
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In mathematics, the Burr–Erdős conjecture was a problem concerning the Ramsey number of sparse graphs. The conjecture is named after Stefan Burr and Paul Erdős, and is one of many conjectures named after Erdős; it states that the Ramsey number of graphs in any sparse family of graphs should grow linearly in the number of vertices of the graph.
The conjecture was proven by Choongbum Lee. Thus it is now a theorem.
Definitions
If G is an undirected graph, then the degeneracy of G is the minimum number p such that every subgraph of G contains a vertex of degree p or smaller. A graph with degeneracy p is called p-degenerate. Equivalently, a p-degenerate graph is a graph that can be reduced to the empty graph by repeatedly removing a vertex of degree p or smaller.
It follows from Ramsey's theorem that for any graph G there exists a least integer
, the Ramsey number of G, such that any complete graph on at least vertices whose edges are coloured red or blue contains a monochromatic copy of G. For instance, the Ramsey number of a triangle is 6: no matter how the edges of a complete graph on six vertices are colored red or blue, there is always either a red triangle or a blue triangle.
The conjecture
In 1973, Stefan Burr and Paul Erdős made the following conjecture:
For every integer p there exists a constant cp so that any p-degenerate graph G on n vertices has Ramsey number at most cp n.
That is, if an n-vertex graph G is p-degenerate, then a monochromatic copy of G should
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https://en.wikipedia.org/wiki/Eddy%20Zemach
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Eddy M. Zemach (1935 – 21 May 2021) was an Israeli philosopher, born in Jerusalem, Mandatory Palestine.
He was Ahad Ha'am Professor Emeritus in the Department of Philosophy at the Hebrew University of Jerusalem. He received his Ph.D. from Yale University in 1965. His main research interests were aesthetics, metaphysics, epistemology, philosophy of psychology, and philosophy of language.
Major works
1970: Analytic Aesthetics, Daga (in Hebrew).
1976: Aesthetics, Institute for Poetics & Semiotics (in Hebrew).
1992: The Reality of Meaning and the Meaning of 'Reality''', Brown U. Press.
1992: Types: Essays in Metaphysics, E. J. Brill Publishers.
1997: Real Beauty, Penn State Press....
2001: Mind and Right'', Magnes Press (in Hebrew).
References
External links
Recent article in "Iton Tel-Aviv" (in Hebrew)
Works by Eddy Zemach, PhilPapers
Recent translation of two papers about Ontology by Matthieu Dubost for Klesis (in french)
1935 births
2021 deaths
21st-century Israeli philosophers
Analytic philosophers
Epistemologists
Academic staff of the Hebrew University of Jerusalem
Israeli philosophers
Metaphysicians
Philosophers of art
Philosophers of language
Philosophers of psychology
Yale University alumni
People from Jerusalem
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https://en.wikipedia.org/wiki/Nagata%E2%80%93Biran%20conjecture
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In mathematics, the Nagata–Biran conjecture, named after Masayoshi Nagata and Paul Biran, is a generalisation of Nagata's conjecture on curves to arbitrary polarised surfaces.
Statement
Let X be a smooth algebraic surface and L be an ample line bundle on X of degree d. The Nagata–Biran conjecture states that for sufficiently large r the Seshadri constant satisfies
References
.
. See in particular page 3 of the pdf.
Algebraic surfaces
Conjectures
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https://en.wikipedia.org/wiki/Fujita%20conjecture
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In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, unsolved . It is named after Takao Fujita, who formulated it in 1985.
Statement
In complex geometry, the conjecture states that for a positive holomorphic line bundle L on a compact complex manifold M, the line bundle KM ⊗ L⊗m (where KM is a canonical line bundle of M) is
spanned by sections when m ≥ n + 1 ;
very ample when m ≥ n + 2,
where n is the complex dimension of M.
Note that for large m the line bundle KM ⊗ L⊗m is very ample by the standard Serre's vanishing theorem (and its complex analytic variant). Fujita conjecture provides an explicit bound on m, which is optimal for projective spaces.
Known cases
For surfaces the Fujita conjecture follows from Reider's theorem. For three-dimensional algebraic varieties, Ein and Lazarsfeld in 1993 proved the first part of the Fujita conjecture, i.e. that m≥4 implies global generation.
See also
Ohsawa–Takegoshi L2 extension theorem
References
.
.
.
.
.
External links
supporting facts to fujita conjecture
Algebraic geometry
Complex manifolds
Conjectures
Unsolved problems in geometry
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https://en.wikipedia.org/wiki/KRP%20%28biochemistry%29
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KRP stands for kinesin related proteins. bimC is a subfamily of KRPs and its function is to separate the duplicated centrosomes during mitosis.
Role in mitotic repair
Kinesin-13 MCAK (Mitotic Centromere-Associated Kinesin) is a KRP that is involved in resolving errors during mitosis involving kinetochore-microtubules. This process is associated with Aurora B Protein Kinase. When Aurora B's function is disrupted, MCAK ability to locate centromeres, which play a critical role in separation of chromosomes during mitosis, was suppressed. There are other environments in which MCAK's function is impaired, absent impact on its associated kinase. For example, alpha-tubulin detyrosination has been demonstrated to impact MCAK's mitotic repair capabilities, suggesting a potential cause of chromosomal instability.
References
Proteins
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https://en.wikipedia.org/wiki/Turbulence%20modeling
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In fluid dynamics, turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real-life scenarios, including the flow of blood through the cardiovascular system, the airflow over an aircraft wing, the re-entry of space vehicles, besides others. In spite of decades of research, there is no analytical theory to predict the evolution of these turbulent flows. The equations governing turbulent flows can only be solved directly for simple cases of flow. For most real-life turbulent flows, CFD simulations use turbulent models to predict the evolution of turbulence. These turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows.
Closure problem
The Navier–Stokes equations govern the velocity and pressure of a fluid flow. In a turbulent flow, each of these quantities may be decomposed into a mean part and a fluctuating part. Averaging the equations gives the Reynolds-averaged Navier–Stokes (RANS) equations, which govern the mean flow. However, the nonlinearity of the Navier–Stokes equations means that the velocity fluctuations still appear in the RANS equations, in the nonlinear term from the convective acceleration. This term is known as the Reynolds stress, . Its effect on the mean flow is like that of a stress term, such as from pressure or viscosity.
To obtain equations containing only the mean velocity and pressure, we need to cl
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https://en.wikipedia.org/wiki/American%20Mathematical%20Association%20of%20Two-Year%20Colleges
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The American Mathematical Association of Two-Year Colleges (AMATYC) is an organization dedicated to the improvement of education in the first two years of college mathematics in the United States and Canada. AMATYC hosts an annual conference, summer institutes, workshops and mentoring for teachers in and outside math, and a semiannual math competition. AMATYC publishes one refereed journal, MathAMATYC Educator, and issues position statements on matters of mathematics education.
The math competition is held in spring and fall semester each year and is limited to problems in precalculus. Only students enrolled in two-year colleges are eligible to participate. Only students who haven't received any degree/diploma, including within or outside of the U.S, can enter the competition.
AMATYC was founded in 1974. Its office is at Southwest Tennessee Community College in Memphis, Tennessee.
AMATYC is divided into eight regions: Central, Mid-Atlantic, Midwest, Northeast, Northwest, Southeast, Southwest, and West. A vice president is assigned to each region.
See also
Mathematical Association of America
National Council of Teachers of Mathematics
External links
Student Math League home page
Mathematics education in the United States
1974 establishments in Tennessee
Organizations based in Memphis, Tennessee
Organizations established in 1974
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https://en.wikipedia.org/wiki/Topological%20order
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In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.
Various topologically ordered states have interesting properties, such as (1) topological degeneracy and fractional statistics or non-Abelian statistics that can be used to realize a topological quantum computer; (2) perfect conducting edge states that may have important device applications; (3) emergent gauge field and Fermi statistics that suggest a quantum information origin of elementary particles; (4) topological entanglement entropy that reveals the entanglement origin of topological order, etc. Topological order is important in the study of several physical systems such as spin liquids and the quantum Hall effect, along with potential applications to fault-tolerant quantum computation.
Topological insulators and topological superconductors (beyond 1D) do not have topological order as defined above, their entanglements being only short-ranged.
Background
Matter composed of atoms can have different properties and appear in different forms, s
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https://en.wikipedia.org/wiki/Twiddle
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Twiddle or twiddling may refer to:
Twiddle (band), an American rock band
Twiddle factor, used in fast Fourier transforms in mathematics
Thumb twiddling, action of the hands
Twiddly bits, English idiom
Tilde character ( ~ ), sometimes referred to as "twiddle" or "squiggle"
Mr Twiddle, zookeeper character in Wally Gator animated TV series
"Twiddling", the constant fine-tuning of online platforms that is part of the enshittification process
See also
Bit twiddler (disambiguation), for various uses in computing
Twiddler, a one-handed input device
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https://en.wikipedia.org/wiki/Texas%20A%26M%20Astronomical%20Observatory
|
Texas A&M Astronomical Observatory is an astronomical observatory owned and operated by Texas A&M University's Department of Physics. It is located in College Station, Texas, USA.
Latitude: N 30° 34' 21.78"
Longitude: W 96° 21' 59.94"
Elevation: 283 ft. (86.2584 m)
See also
List of observatories
References
Astronomical observatories in Texas
Buildings and structures in Brazos County, Texas
Texas A&M University
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https://en.wikipedia.org/wiki/Scission
|
Scission may refer to:
Scission (chemistry), bond cleavage, the splitting of chemical bonds
Chain scission, the degradation of a polymer main chain
Beta scission, reaction in thermal cracking of hydrocarbons
Scission and Other Stories, a 1985 collection of short stories
Instruction scission, opcode overlapping in computing
See also
Scission (a cut-out piece), term involved in development of senses of word "sect"
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https://en.wikipedia.org/wiki/Crunode
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In mathematics, a crunode (archaic) or node is a point where a curve intersects itself so that both branches of the curve have distinct tangent lines at the point of intersection. A crunode is also known as an ordinary double point.
For a plane curve, defined as the locus of points , where is a smooth function of variables and ranging over the real numbers, a crunode of the curve is a singularity of the function , where both partial derivatives and vanish. Further the Hessian matrix of second derivatives will have both positive and negative eigenvalues.
See also
Singular point of a curve
Acnode
Cusp
Tacnode
Saddle point
References
Curves
Algebraic curves
es:Punto singular de una curva#Crunodos
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https://en.wikipedia.org/wiki/Pad%C3%A9%20approximant
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In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating. The technique was developed around 1890 by Henri Padé, but goes back to Georg Frobenius, who introduced the idea and investigated the features of rational approximations of power series.
The Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. For these reasons Padé approximants are used extensively in computer calculations. They have also been used as auxiliary functions in Diophantine approximation and transcendental number theory, though for sharp results ad hoc methods—in some sense inspired by the Padé theory—typically replace them. Since Padé approximant is a rational function, an artificial singular point may occur as an approximation, but this can be avoided by Borel–Padé analysis.
The reason the Padé approximant tends to be a better approximation than a truncating Taylor series is clear from the viewpoint of the multi-point summation method. Since there are many cases in which the asymptotic expansion at infinity becomes 0 or a constant, it can be interpreted as the "incomplete two-point Padé approximation", in which the ordinary Padé approximation improves the method truncating a Taylor series.
Defin
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https://en.wikipedia.org/wiki/Peachtree%20Ridge%20High%20School
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Peachtree Ridge High School (PRHS) is a public high school in Gwinnett County, in Suwanee, Georgia, United States. It is a part of Gwinnett County Public Schools. It is one of three public schools in the county to use block scheduling, the others being Shiloh High School and the Gwinnett School of Mathematics, Science, and Technology.
History
Peachtree Ridge High School is located on Old Peachtree Road. It is located on land which belonged to the heirs of Eugene Baynes. A lake behind the school is named Lake Louella after Mrs. Louise Ella Baynes, as is Lake Louella Road near the school. A few hundred yards from the school is the Goodwin home, which was built in 1823 and is the oldest building in Suwanee.
Construction of the school's main facility commenced in March 2001. PRHS was constructed to relieve overcrowding at four neighboring high schools. When its doors opened for the 2003–2004 academic year, almost all of the sophomores, juniors, and seniors came from either Duluth High School in Duluth, Collins Hill High School in Suwanee, or North Gwinnett High School in Suwanee.
The school officially opened for classes on Monday, August 11, 2003, with enrollment topping 1,900 students. By November of the same year, another of athletic facilities (field house) were nearing completion.
Clubs
Robotics
Peachtree Ridge High School Robotics (Team 1261 Robo Lions) was established in the 2003–2004 school year.
Team 1261's main platform is the FIRST Robotics Competition, which ta
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https://en.wikipedia.org/wiki/EOM
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Eom or EOM may refer to:
People
Eom (Korean surname)
Science and technology
Electro-optic modulator
End of message
Enterprise output management
Equations of motion
Ensemble optimization method; see Biological small-angle scattering
Other uses
Employee of the month (program)
Encyclopedia of Mathematics
Encyclopedia of Mormonism
English-only movement, a political movement in the United States
Estatuto Orgânico de Macau, an organic statute of Portuguese Macau
End Of Month
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https://en.wikipedia.org/wiki/Michael%20Harrison%20%28musician%29
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Michael Harrison is an American contemporary classical music composer and pianist living in New York City. He was a Guggenheim Fellow for the academic year 2018–2019.
Early years
Born in Bryn Mawr, PA, Harrison grew up in Eugene, OR, where his father, David Kent Harrison was a professor of mathematics at the University of Oregon and a Guggenheim Fellow for the academic year 1963–1964. As a child and teenager, he spent summers in both Chatham and Concord, MA with his grandfather, George R. Harrison, a professor of experimental physics at the Massachusetts Institute of Technology (1930), and Dean of Science (1942–64).
He studied piano from the age of 6, composition from the age of 17, and North Indian classical vocal music from the age of 18, and attended Phillips Academy Andover. Early passions also included backpacking and mountain climbing in the Oregon Cascades and Himalayas, downhill and cross-country skiing, and chess. He graduated from the University of Oregon with a B.M. in Composition, where he later received the Distinguished Alumnus of the Year Award, and then moved to New York City to study with La Monte Young through a Dia Art Foundation Apprenticeship-in Residency. He later received an M.M. in composition from the Manhattan School of Music, studying with Reiko Fueting.
Career
In 1986, Harrison designed and produced the "harmonic piano", an extensively modified grand piano with the ability to play 24 notes per octave. Critic Kyle Gann referred to it as "an indi
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https://en.wikipedia.org/wiki/Intermediate%20Jacobian
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In mathematics, the intermediate Jacobian of a compact Kähler manifold or Hodge structure is a complex torus that is a common generalization of the Jacobian variety of a curve and the Picard variety and the Albanese variety. It is obtained by putting a complex structure on the torus for n odd. There are several different natural ways to put a complex structure on this torus, giving several different sorts of intermediate Jacobians, including one due to and one due to . The ones constructed by Weil have natural polarizations if M is projective, and so are abelian varieties, while the ones constructed by Griffiths behave well under holomorphic deformations.
A complex structure on a real vector space is given by an automorphism I with square . The complex structures on are defined using the Hodge decomposition
On the Weil complex structure is multiplication by , while the Griffiths complex structure is multiplication by if and if . Both these complex structures map into itself and so defined complex structures on it.
For the intermediate Jacobian is the Picard variety, and for it is the Albanese variety. In these two extreme cases the constructions of Weil and Griffiths are equivalent.
used intermediate Jacobians to show that non-singular cubic threefolds are not rational, even though they are unirational.
See also
Deligne cohomology
References
Hodge theory
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https://en.wikipedia.org/wiki/Colby%20Miller
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Colby Miller (born February 19, 1980) is an MTV VJ for MTV Asia. He began his career as an MTV VJ after winning the Philippine MTV VJ Hunt 2005.
Biography
Early life
Miller was born in Spanaway, Washington. He graduated in 2004 from Central Washington University with a degree in Biology. He was born to an American father of German and Irish descent and a Filipino mother.
Career
Miller began his career as an MTV VJ after winning the Philippine MTV VJ Hunt 2005. He also won the first ever ASEAN MTV VJ Hunt held in Bali, Indonesia, where he competed against other winners of MTV VJ Hunts from around the region. Colby is currently based in Singapore where he hosts for MTV Asia in shows such as Pop Inc.
Personal life
Miller enjoys basketball, hiking, outdoor activities as well as visiting the gym. He is also the brother of Troy Montero and KC Montero.
Television series
2004: MTV Supahstar: The Supahsearch
References
1980 births
Living people
American people of Irish descent
American people of German descent
American people of Filipino descent
Filipino people of American descent
Filipino people of German descent
Filipino people of Irish descent
Participants in Philippine reality television series
VJs (media personalities)
People from Spanaway, Washington
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https://en.wikipedia.org/wiki/Richard%20Currie
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Richard James Currie (born 1937 in Saint John, New Brunswick) is a Canadian businessman.
Education
He entered the University of New Brunswick in 1955 on a Beaverbrook Scholarship and was elected president of the first-year class. He later received a Bachelor of Engineering in Chemistry degree from the Technical University of Nova Scotia in 1960. He worked as an engineer until 1968, when he entered Harvard University to earn a Master of Business Administration degree in 1970.
Career
In 1960, he joined Atlantic Sugar Refineries as a Process Engineer and was a Refining Superintendent from 1963 to 1968. After graduating from Harvard in 1970, he became a Senior Associate at McKinsey & Co., a management consultant firm based in New York City.
In 1972, he joined Loblaws as a Vice-President, becoming Executive Vice-President in 1974, and President in 1976. Loblaws increased its market share over 350 times in 25 years while under his control, reaching $14 billion before he stepped down on December 31, 2000. Through this, it became the largest private sector employer in Canada.
In 1996, he was appointed President of Loblaws parent company, George Weston Ltd., where he increased the share price from $16 to $123. In 2002 he stepped down from Weston and was appointed Chairman of BCE Inc. on April 24 of that year.
He, along with Lynton Wilson, Anthony S. Fell, James Fleck, Hal Jackman and John McArthur, helped establish a chair in Canadian business history at the Joseph L. Rotman S
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https://en.wikipedia.org/wiki/Jind%C5%99ich%20Ba%C4%8Dkovsk%C3%BD
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Jindřich Bačkovský (; May 4, 1912 – 2000) was an eminent Czechoslovak physicist whose work focused on X-ray spectroscopy, the structure of crystals, vacuum techniques, radiometry and the physics of high pressures. Many of his findings are used in industry, especially in the manufacture of semiconductor parts and synthetic diamonds.
External links
Czech archives
Short Biography (Czech)
Czechoslovak physicists
1912 births
2000 deaths
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https://en.wikipedia.org/wiki/Tight%20binding
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In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method (linear combination of atomic orbitals method) used in chemistry. Tight-binding models are applied to a wide variety of solids. The model gives good qualitative results in many cases and can be combined with other models that give better results where the tight-binding model fails. Though the tight-binding model is a one-electron model, the model also provides a basis for more advanced calculations like the calculation of surface states and application to various kinds of many-body problem and quasiparticle calculations.
Introduction
The name "tight binding" of this electronic band structure model suggests that this quantum mechanical model describes the properties of tightly bound electrons in solids. The electrons in this model should be tightly bound to the atom to which they belong and they should have limited interaction with states and potentials on surrounding atoms of the solid. As a result, the wave function of the electron will be rather similar to the atomic orbital of the free atom to which it belongs. The energy of the electron will also be rather close to the ionization energy of the electron in the free atom or ion because the interaction with potentials and
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https://en.wikipedia.org/wiki/Castelnuovo%E2%80%93de%20Franchis%20theorem
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In mathematics, the Castelnuovo–de Franchis theorem is a classical result on complex algebraic surfaces. Let X be such a surface, projective and non-singular, and let
ω1 and ω2
be two differentials of the first kind on X which are linearly independent but with wedge product 0. Then this data can be represented as a pullback of an algebraic curve: there is a non-singular algebraic curve C, a morphism
φ: X → C,
and differentials of the first kind ω1 and ω2 on C such that
φ*(1) = ω1 and φ*(2) = ω2.
This result is due to Guido Castelnuovo and Michele de Franchis (1875–1946).
The converse, that two such pullbacks would have wedge 0, is immediate.
See also
de Franchis theorem
References
.
Algebraic surfaces
Theorems in geometry
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https://en.wikipedia.org/wiki/Charge%20conservation
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In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved. Charge conservation, considered as a physical conservation law, implies that the change in the amount of electric charge in any volume of space is exactly equal to the amount of charge flowing into the volume minus the amount of charge flowing out of the volume. In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that region, given by a continuity equation between charge density and current density .
This does not mean that individual positive and negative charges cannot be created or destroyed. Electric charge is carried by subatomic particles such as electrons and protons. Charged particles can be created and destroyed in elementary particle reactions. In particle physics, charge conservation means that in reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Similarly, when particles are destroyed, equal numbers of positive and negative charges are destroyed. This property is supported without exception by all empirical observations so far.
Although conservation of charge requires that the total quantity of charge in the uni
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https://en.wikipedia.org/wiki/De%20Franchis%20theorem
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In mathematics, the de Franchis theorem is one of a number of closely related statements applying to compact Riemann surfaces, or, more generally, algebraic curves, X and Y, in the case of genus g > 1. The simplest is that the automorphism group of X is finite (see though Hurwitz's automorphisms theorem). More generally,
the set of non-constant morphisms from X to Y is finite;
fixing X, for all but a finite number of such Y, there is no non-constant morphism from X to Y.
These results are named for (1875–1946). It is sometimes referenced as the De Franchis-Severi theorem. It was used in an important way by Gerd Faltings to prove the Mordell conjecture.
See also
Castelnuovo–de Franchis theorem
References
M. De Franchis: Un teorema sulle involuzioni irrazionali, Rend. Circ. Mat Palermo 36 (1913), 368
Algebraic curves
Riemann surfaces
Theorems in algebraic geometry
Theorems in algebraic topology
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https://en.wikipedia.org/wiki/Enriques%20surface
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In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0.
Over fields of characteristic not 2 they are quotients of K3 surfaces by a group of order 2 acting without fixed points and their theory is similar to that of algebraic K3 surfaces. Enriques surfaces were first studied in detail by as an answer to a question discussed by about whether a surface with q = pg = 0 is necessarily rational, though some of the Reye congruences introduced earlier by are also examples of Enriques surfaces.
Enriques surfaces can also be defined over other fields.
Over fields of characteristic other than 2, showed that the theory is similar to that over the complex numbers. Over fields of characteristic 2 the definition is modified, and there are two new families, called singular and supersingular Enriques surfaces, described by . These two extra families are related to the two non-discrete algebraic group schemes of order 2 in characteristic 2.
Invariants of complex Enriques surfaces
The plurigenera Pn are 1 if n is even and 0 if n is odd. The fundamental group has order 2. The second cohomology group H2(X, Z) is isomorphic to the sum of the unique even unimodular lattice II1,9 of dimension 10 and signature -8 and a group of order 2.
Hodge diamond:
Marked Enriqu
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https://en.wikipedia.org/wiki/Tate%20module
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In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made in the following situation: G is a commutative group scheme over a field K, Ks is the separable closure of K, and A = G(Ks) (the Ks-valued points of G). In this case, the Tate module of A is equipped with an action of the absolute Galois group of K, and it is referred to as the Tate module of G.
Definition
Given an abelian group A and a prime number p, the p-adic Tate module of A is
where A[pn] is the pn torsion of A (i.e. the kernel of the multiplication-by-pn map), and the inverse limit is over positive integers n with transition morphisms given by the multiplication-by-p map A[pn+1] → A[pn]. Thus, the Tate module encodes all the p-power torsion of A. It is equipped with the structure of a Zp-module via
Examples
The Tate module
When the abelian group A is the group of roots of unity in a separable closure Ks of K, the p-adic Tate module of A is sometimes referred to as the Tate module (where the choice of p and K are tacitly understood). It is a free rank one module over Zp with a linear action of the absolute Galois group GK of K. Thus, it is a Galois representation also referred to as the p-adic cyclotomic character of K. It can also be considered as the Tate module of the multiplicative group scheme Gm,K over K.
The Tate module of an abelian variety
Given an abelian variety G over a field K, the Ks-valued points of
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https://en.wikipedia.org/wiki/Michael%20Eisen
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Michael Bruce Eisen (born April 13, 1967) is an American computational biologist and the former editor-in-chief of the journal eLife. He is a professor of genetics, genomics and development at University of California, Berkeley. He is a leading advocate of open access scientific publishing and is co-founder of Public Library of Science (PLOS). In 2018, Eisen announced his candidacy U.S. Senate from California as an Independent, though he failed to qualify for the ballot.
Early life and education
Born in Boston, Eisen and his brother Jonathan were raised in a family of scientists. Their grandfather was an x-ray crystallographer, their father, Howard Eisen a physician, and mother, Laura a biochemist. They moved to Bethesda, Maryland when Eisen was four or five years old. The brothers spent summers in Long Island with their grandparents. Eisen states that he loved frogs and salamanders '"Even more than I have a frog fetish, I have a swamp fetish. I really like being in swamps."' He was also very interested in math and was captain of the high school math team. Eisen graduated from Walt Whitman High School in 1985. Intending to major in mathematics at Harvard University, he realized that there [he may encounter] other more brilliant math students, it was a Good Will Hunting moment and he decided that he did not want to major in mathematics, '"You don't want to be Salieri to Mozart."' During his years at Harvard, Eisen worked on "unlocking the three-dimensional structures of pro
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https://en.wikipedia.org/wiki/Timothy%20Kanold
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Dr. Timothy D. Kanold is a mathematics educator and author of textbooks. He was the president of the National Council of Supervisors of Mathematics (NCSM) from 2008 to 2009.
Dr. Kanold holds a bachelor's degree in Education and a master's degree in Mathematics from the University of Illinois, and a doctorate in Educational Leadership and Counseling Psychology from Loyola University Chicago. In 2007, he retired from his position as Superintendent at Adlai E. Stevenson High School in Lincolnshire, Illinois, where for 17 years, he served as Director of Mathematics and Science.
With Ron Larson, Dr. Kanold is co-author of 27 mathematics textbooks grades 6-12, written for Houghton Mifflin/McDougal Littell Publishing Company from 1988 to the present. Additionally, since 2001 he has authored and co-authored 18 books on K-12 mathematics and school leadership, published with Solution Tree Press. He continues to write and present for the National Council of Teachers of Mathematics on the Principles and Standards for School Mathematics, as well as for AASA and NASSP. He is the lead author for NCTM's update of the Teaching Performance Standards Document, and has presented more than 600 talks and seminars nationally and internationally over the past decade, with the primary focus on the creation of equitable learning experiences for all children in mathematics.
Dr. Kanold is the 1986 recipient of the Presidential Award for Excellence in Mathematics Teaching, the 1991 recipient of the
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https://en.wikipedia.org/wiki/Noether%27s%20theorem%20on%20rationality%20for%20surfaces
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In mathematics, Noether's theorem on rationality for surfaces is a classical result of Max Noether on complex algebraic surfaces, giving a criterion for a rational surface. Let S be an algebraic surface that is non-singular and projective. Suppose there is a morphism φ from S to the projective line, with general fibre also a projective line. Then the theorem states that S is rational.
See also
Hirzebruch surface
List of complex and algebraic surfaces
References
Castelnuovo’s Theorem
Notes
Algebraic surfaces
Theorems in algebraic geometry
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https://en.wikipedia.org/wiki/Kennon%20Observatory
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Kennon Observatory is an astronomical observatory owned and operated by the University of Mississippi. Built in 1939 and located on the university's campus in Oxford, Mississippi, it was named after William Lee Kennon, a long-serving chair of the Department of Physics and Astronomy. It consists of two copper-roofed domes with the main entrance of the observatory facing south, and the building precisely aligned east to west. A small tube in the south wall is oriented such that direct rays of the sun shine through it to the floor only twice a year, at noon on the vernal and autumnal equinoxes.
See also
Barnard Observatory - Univ. of Mississippi's first observatory.
List of observatories
References
External links
Kennon Observatory Clear Sky Clock Forecasts of observing conditions.
Astronomical observatories in Mississippi
Buildings and structures at the University of Mississippi
University and college buildings completed in 1939
1939 establishments in Mississippi
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https://en.wikipedia.org/wiki/Nehari
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Zeev Nehari, mathematician
Nehari manifold in mathematics
Nihari, South Asian stew
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https://en.wikipedia.org/wiki/Axiality%20and%20rhombicity
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In physics and mathematics, axiality and rhombicity are two characteristics of a symmetric second-rank tensor in three-dimensional Euclidean space, describing its directional asymmetry.
Let A denote a second-rank tensor in R3, which can be represented by a 3-by-3 matrix. We assume that A is symmetric. This implies that A has three real eigenvalues, which we denote by , and . We assume that they are ordered such that
The axiality of A is defined by
The rhombicity is the difference between the smallest and the second-smallest eigenvalue:
Other definitions of axiality and rhombicity differ from the ones given above by constant factors which depend on the context. For example, when using them as parameters in the irreducible spherical tensor expansion, it is most convenient to divide the above definition of axiality by and that of rhombicity by .
Applications
The description of physical interactions in terms of axiality and rhombicity is frequently encountered in spin dynamics and, in particular, in spin relaxation theory, where many traceless bilinear interaction Hamiltonians, having the (eigenframe) form
(hats denote spin projection operators) may be conveniently rotated using rank 2 irreducible spherical tensor operators:
where are Wigner functions, are Euler angles, and the expressions for the rank 2 irreducible spherical tensor operators are:
Defining Hamiltonian rotations in this way (axiality, rhombicity, three angles) significantly simplifies calculations, si
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https://en.wikipedia.org/wiki/University%20of%20North%20Alabama%20Planetarium%20and%20Observatory
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UNA Observatory is an astronomical observatory owned and operated by the University of North Alabama. It is located in Florence, Alabama (USA). It has 2 telescopes, a Celestron 0.35 m Schmidt–Cassegrain telescope. The UNA Planetarium is a 65-seat planetarium with a Spitz A3P projector and East Cost Control Systems controller.
History
Construction
Construction of the UNA Planetarium and Observatory was done in two stages, with the observatory being constructed first. In 1964 what would eventually become University of North Alabama was then known as Florence State College. It was proposed that the College acquire an observatory and planetarium. At the time, the space race was well under way and investments were being made across the country in math and science.
The first stage of the project was construction of the observatory. The building was constructed and the dome hoisted into place on March 15, 1964. The event was the culmination of a four-year effort on the part of the local Florence Astronomy Club. The group wanted a telescope that would provide public views of the sky that was accessible and did not require driving long distances. Conversations with the college led to the project. Florence State College was interested in a planetarium and observatory and it was a natural alliance.
The show piece of the observatory was the 14.5 inch telescope that was to be the second largest telescope in the state. The mirror was ground by hand by members of the Astronomy club,
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https://en.wikipedia.org/wiki/The%20Number%20Devil
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The Number Devil: A Mathematical Adventure () is a book for children and young adults that explores mathematics. It was originally written in 1997 in German by Hans Magnus Enzensberger and illustrated by Rotraut Susanne Berner. The book follows a young boy named Robert, who is taught mathematics by a sly "number devil" called Teplotaxl over the course of twelve dreams.
The book was met with mostly positive reviews from critics, approving its description of math while praising its simplicity. Its colorful use of fictional mathematical terms and its creative descriptions of concepts have made it a suggested book for both children and adults troubled with math. The Number Devil was a bestseller in Europe, and has been translated into English by Michael Henry Heim.
Plot
Robert is a young boy who suffers from mathematical anxiety due to his boredom in school. His mother is Mrs. Wilson. He also experiences recurring dreams—including falling down an endless slide or being eaten by a giant fish—but is interrupted from this sleep habit one night by a small devil creature who introduces himself as the Number Devil. Although there are many Number Devils (from Number Heaven), Robert only knows him as the Number Devil before learning of his actual name, Teplotaxl, later in the story.
Over the course of twelve dreams, the Number Devil teaches Robert mathematical principles. On the first night, the Number Devil appears to Robert in an oversized world and introduces the number one. The ne
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https://en.wikipedia.org/wiki/Zariski%20surface
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In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic p > 0 such that there is a dominant inseparable map of degree p from the projective plane to the surface. In particular, all Zariski surfaces are unirational. They were named by Piotr Blass in 1977 after Oscar Zariski who used them in 1958 to give examples of unirational surfaces in characteristic p > 0 that are not rational. (In characteristic 0 by contrast, Castelnuovo's theorem implies that all unirational surfaces are rational.)
Zariski surfaces are birational to surfaces in affine 3-space A3 defined by irreducible polynomials of the form
The following problem was posed by Oscar Zariski in 1971: Let S be a Zariski surface with vanishing geometric genus. Is S necessarily a rational surface? For p = 2 and for p = 3 the answer to the above problem is negative as shown in 1977 by Piotr Blass in his University of Michigan Ph.D. thesis and by William E. Lang in his Harvard Ph.D. thesis in 1978. announced further examples giving a negative answer to Zariski's question in every characteristic p>0 .
His method however is non constructive at the moment and we do not have explicit equations for p>3.
See also
List of algebraic surfaces
References
Algebraic surfaces
University of Michigan
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https://en.wikipedia.org/wiki/Pine%20Mountain%20Observatory
|
Pine Mountain Observatory (PMO) is an astronomical observatory owned and operated by University of Oregon Department of Physics. The facility is located 26 miles (42 km) southeast of Bend, Oregon (USA) in the Deschutes National Forest near the summit of Pine Mountain.
PMO supports a wide variety of programs with an emphasis on projects that allow undergraduate students to be involved with many aspects of facility operations. PMO also has robust programs centered on K-12 education and public outreach.
The site was discovered and characterized by professors Russ Donnelly and E.G. Ebbinghausen in 1965 when they determined that the sky conditions were excellent and worthy of an observatory being built on Pine Mountain. The first telescope became operational in 1967.
Former programs gave high-school students the opportunity to not only observe at PMO, but also analyze data and prepare of a paper for publication. Early programs at PMO helped develop older software programs that allowed K-12 teachers to perform observations remotely and process the data for classroom use.
Past research projects included research on white dwarf stars and examining the large-scale structure of galaxies.
Telescopes
Planewave 14" Telescope
The Planewave 14” Corrected Dall-Kirkham telescope and dome are the newest on the Mountain. Construction on the site started in 2015 and the entire system was commissioned over the next two summer seasons, and in Fall 2018 the Planewave started observations. U
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https://en.wikipedia.org/wiki/Supernova%20%28disambiguation%29
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A supernova is an astronomical event, a type of stellar explosion.
Supernova or Super Nova may also refer to:
Astrophysics
Type Ia supernova
Type Ib and Ic supernovae
Type II supernova
Supernova impostor
Supernova remnant
Pair-instability supernova
Films and television
Supernova, a film production company created by Oleg Mavromati
Supernova (2000 film), an MGM/UA science fiction film
Supernova (2005 film), a Hallmark Channel science fiction TV movie
Supernova (2020 film), a British drama film
2012: Supernova, an Asylum science fiction film
Supernova (British TV series), a BBC TV comedy series
Supernova (Latvian TV series), a singing competition show
Rock Star: Supernova, a U.S. reality TV series
Super Nova, the second TV movie from the science fiction show Lexx
Music
Festivals
Supernova Sukkot Gathering, the Israeli edition of psytrance festival Universo Paralello
Bands
Supernova (American band), a pop/punk trio
Supernova (Chilean band), a pop band
Supernova (South Korean band), a boy band
Superknova, American queer pop artist
Albums
Supernova (Alice Nine album), 2014
Supernova (The Echoing Green album) or the title song, 2000
Supernova (Gonzalo Rubalcaba Trio album) or the title song, 2001
Supernova (Granrodeo album) or the title song, 2011
Supernova (Lisa Lopes album), 2001
Supernova (Nova Twins album), 2022
Supernova (Ray LaMontagne album) or the title song, 2014
Supernova (Supernova album), by the Chilean band, 1999
Supernova (Today Is the Day album), 1993
Super N
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https://en.wikipedia.org/wiki/The%20Only%20Possible%20Argument%20in%20Support%20of%20a%20Demonstration%20of%20the%20Existence%20of%20God
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The Only Possible Argument in Support of a Demonstration of the Existence of God () is a book by Immanuel Kant, published in 1763. It was published during the earlier period of Kant's philosophy, often referred to as the "pre-critical" period, during which he expressed little doubt about the possibility of rational metaphysics as conducted in the Leibnizian-Wolffian philosophical system which dominated German philosophy during that time. Kant later came to view this period of his philosophical career as a "dogmatic slumber".
Contents
In The Only Possible Argument, Kant questions both the ontological argument for God (as proposed by Saint Anselm) and the argument from design. Kant argues that the internal possibility of all things presupposes some existence:
Accordingly, there must be something whose nonexistence would cancel all internal possibility whatsoever. This is a necessary thing.
Kant then argues that this necessary thing must have all the characteristics commonly ascribed to God. Therefore, God necessarily exists. This a priori step in Kant's argument is followed by a step a posteriori, in which he establishes the necessity of an absolutely necessary being. He argues that matter itself contains the principles which give rise to an ordered universe, and this leads us to the concept of God as a Supreme Being, which "embraces within itself everything which can be thought by man." "God includes all that is possible or real."
Reception
"[T]he very substantial and fav
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https://en.wikipedia.org/wiki/Clarence%20Hiskey
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Clarence Francis Hiskey (1912–1998), born Clarence Szczechowski, was a Soviet espionage agent in the United States. He became active in the Communist Party USA (CPUSA) when he attended graduate school at the University of Wisconsin. He became a professor of chemistry at the University of Tennessee, Columbia University and Brooklyn Polytechnic Institute. For a time, Hiskey worked at the Tennessee Valley Authority and the University of Chicago Metallurgical Laboratory, part of the Manhattan Project. He was the father of Nicholas Sand.
Metallurgical Laboratory
Hiskey joined the Chicago Metallurgical Laboratory in September 1943.
In May 1944, a message sent by New York KGB to Moscow Venona project was intercepted and decrypted. The message contained information reporting that Bernard Schuster, member of the CPUSA secret apparatus, working for Soviet intelligence, had traveled to Chicago on the KGB's instructions. The message recorded Schuster's description of those he had come in contact with, including Rose Olsen, and stating Olsen had been meeting with Hiskey on the instructions of the organization. In July, it appears Joseph Katz had been assigned to the Hiskey case.
On 28 April 1944, Army counter-intelligence (G-2) observed a meeting between Clarence Hiskey and Soviet Military Intelligence (GRU) officer Arthur Adams. Hiskey was removed from the Manhattan Project by drafting him into the Army, and stationing him in Canada for the duration of the conflict. While en r
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https://en.wikipedia.org/wiki/Gravity%20Dreams
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Gravity Dreams is a 1999 science fiction novel by L. E. Modesitt, Jr.
Synopsis
The novel is set in the year 4512, when humans have achieved spaceflight faster than the speed of light, along with nanotechnology. Gravity Dreams centers around main character, Tyndel, who was raised in Dorcha, whose culture uses the philosophy of Dzin as a means of social control. Dzin preaches that what you see is, and not to ask questions that a scientist normally would. Tyndel is a master of Dzin. One day he is attacked and infected with nanites. This brands him as a 'Demon' because Dorcha has rejected technology, as the cause of a major ecological collapse centuries before.
After escaping from prison, Tyndel returns to his wife, and sees her killed by the people who he thought were meant to protect her. After taking revenge by killing the man who infected him with the nanites, Tyndel flees north to the "Demon Nation" of Rykasha, which still retains high technology and uses nanites.
He is taken to a medical facility after experiencing weird lights across his vision, and told that he was infected with an ancient strain of nanites that would have killed him. They are replaced with more balanced nanites adjusted to his system. He is introduced to his handler Cerrelle, who explains that it is her duty to help him adjust to their society and become a productive citizen so that he can repay his debt for their help.
Tyndel is riddled with guilt over his wife's death and sees many of her attribute
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https://en.wikipedia.org/wiki/Kerala%20school%20of%20astronomy%20and%20mathematics
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The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and its original discoveries seem to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa (), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha.
Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series).
Background
Islamic scholars nearly developed a general formula for finding integrals of polynomials by 1000 AD —and evidently could find such a formula for any polynomial in which they were interested. But, it ap
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https://en.wikipedia.org/wiki/Gonality%20of%20an%20algebraic%20curve
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In mathematics, the gonality of an algebraic curve C is defined as the lowest degree of a nonconstant rational map from C to the projective line. In more algebraic terms, if C is defined over the field K and K(C) denotes the function field of C, then the gonality is the minimum value taken by the degrees of field extensions
K(C)/K(f)
of the function field over its subfields generated by single functions f.
If K is algebraically closed, then the gonality is 1 precisely for curves of genus 0. The gonality is 2 for curves of genus 1 (elliptic curves) and for hyperelliptic curves (this includes all curves of genus 2). For genus g ≥ 3 it is no longer the case that the genus determines the gonality. The gonality of the generic curve of genus g is the floor function of
(g + 3)/2.
Trigonal curves are those with gonality 3, and this case gave rise to the name in general. Trigonal curves include the Picard curves, of genus three and given by an equation
y3 = Q(x)
where Q is of degree 4.
The gonality conjecture, of M. Green and R. Lazarsfeld, predicts that the gonality of the algebraic curve C can be calculated by homological algebra means, from a minimal resolution of an invertible sheaf of high degree. In many cases the gonality is two more than the Clifford index. The Green–Lazarsfeld conjecture is an exact formula in terms of the graded Betti numbers for a degree d embedding in r dimensions, for d large with respect to the genus. Writing b(C), with respect to a given such em
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https://en.wikipedia.org/wiki/K%C3%B6the%20conjecture
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In mathematics, the Köthe conjecture is a problem in ring theory, open . It is formulated in various ways. Suppose that R is a ring. One way to state the conjecture is that if R has no nil ideal, other than {0}, then it has no nil one-sided ideal, other than {0}.
This question was posed in 1930 by Gottfried Köthe (1905–1989). The Köthe conjecture has been shown to be true for various classes of rings, such as polynomial identity rings and right Noetherian rings, but a general solution remains elusive.
Equivalent formulations
The conjecture has several different formulations:
(Köthe conjecture) In any ring, the sum of two nil left ideals is nil.
In any ring, the sum of two one-sided nil ideals is nil.
In any ring, every nil left or right ideal of the ring is contained in the upper nil radical of the ring.
For any ring R and for any nil ideal J of R, the matrix ideal Mn(J) is a nil ideal of Mn(R) for every n.
For any ring R and for any nil ideal J of R, the matrix ideal M2(J) is a nil ideal of M2(R).
For any ring R, the upper nilradical of Mn(R) is the set of matrices with entries from the upper nilradical of R for every positive integer n.
For any ring R and for any nil ideal J of R, the polynomials with indeterminate x and coefficients from J lie in the Jacobson radical of the polynomial ring R[x].
For any ring R, the Jacobson radical of R[x] consists of the polynomials with coefficients from the upper nilradical of R.
Related problems
A conjecture by Amitsur read
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https://en.wikipedia.org/wiki/Nil%20ideal
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In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent.
The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring maximal with respect to the property of being nil. Unfortunately the set of nil elements does not always form an ideal for noncommutative rings. Nil ideals are still associated with interesting open questions, especially the unsolved Köthe conjecture.
Commutative rings
In commutative rings, the nil ideals are better understood than in noncommutative rings, primarily because in commutative rings, products involving nilpotent elements and sums of nilpotent elements are both nilpotent. This is because if a and b are nilpotent elements of R with an = 0 and bm = 0, and r is any element of R, then (a·r)n = an·r n = 0, and by the binomial theorem, (a+b)m+n = 0. Therefore, the set of all nilpotent elements forms an ideal known as the nil radical of a ring. Because the nil radical contains every nilpotent element, an ideal of a commutative ring is nil if and only if it is a subset of the nil radical, and so the nil radical is maximal among non-nil ideals. Furthermore, for any nilpotent element a of a commutative ring R, the ideal aR is nil. For a non commutative ring however, it is not in general true that the set of nilpotent elements forms an ideal, or that a ·R is a nil (one-sided) ideal, even if a is nilpotent.
Nonco
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https://en.wikipedia.org/wiki/Ruziewicz%20problem
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In mathematics, the Ruziewicz problem (sometimes Banach–Ruziewicz problem) in measure theory asks whether the usual Lebesgue measure on the n-sphere is characterised, up to proportionality, by its properties of being finitely additive, invariant under rotations, and defined on all Lebesgue measurable sets.
This was answered affirmatively and independently for n ≥ 4 by Grigory Margulis and Dennis Sullivan around 1980, and for n = 2 and 3 by Vladimir Drinfeld (published 1984). It fails for the circle.
The problem is named after Stanisław Ruziewicz.
References
.
.
.
.
Survey of the area by Hee Oh
Measure theory
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https://en.wikipedia.org/wiki/Radiation%20chemistry
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Radiation chemistry is a subdivision of nuclear chemistry which studies the chemical effects of ionizing radiation on matter. This is quite different from radiochemistry, as no radioactivity needs to be present in the material which is being chemically changed by the radiation. An example is the conversion of water into hydrogen gas and hydrogen peroxide.
Radiation interactions with matter
As ionizing radiation moves through matter its energy is deposited through interactions with the electrons of the absorber. The result of an interaction between the radiation and the absorbing species is removal of an electron from an atom or molecular bond to form radicals and excited species. The radical species then proceed to react with each other or with other molecules in their vicinity. It is the reactions of the radical species that are responsible for the changes observed following irradiation of a chemical system.
Charged radiation species (α and β particles) interact through Coulombic forces between the charges of the electrons in the absorbing medium and the charged radiation particle. These interactions occur continuously along the path of the incident particle until the kinetic energy of the particle is sufficiently depleted. Uncharged species (γ photons, x-rays) undergo a single event per photon, totally consuming the energy of the photon and leading to the ejection of an electron from a single atom. Electrons with sufficient energy proceed to interact with the absorbing me
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https://en.wikipedia.org/wiki/Ore%20condition
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In mathematics, especially in the area of algebra known as ring theory, the Ore condition is a condition introduced by Øystein Ore, in connection with the question of extending beyond commutative rings the construction of a field of fractions, or more generally localization of a ring. The right Ore condition for a multiplicative subset S of a ring R is that for and , the intersection . A (non-commutative) domain for which the set of non-zero elements satisfies the right Ore condition is called a right Ore domain. The left case is defined similarly.
General idea
The goal is to construct the right ring of fractions R[S−1] with respect to a multiplicative subset S. In other words, we want to work with elements of the form as−1 and have a ring structure on the set R[S−1]. The problem is that there is no obvious interpretation of the product (as−1)(bt−1); indeed, we need a method to "move" s−1 past b. This means that we need to be able to rewrite s−1b as a product b1s1−1. Suppose then multiplying on the left by s and on the right by s1, we get . Hence we see the necessity, for a given a and s, of the existence of a1 and s1 with and such that .
Application
Since it is well known that each integral domain is a subring of a field of fractions (via an embedding) in such a way that every element is of the form rs−1 with s nonzero, it is natural to ask if the same construction can take a noncommutative domain and associate a division ring (a noncommutative field) with the same pr
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https://en.wikipedia.org/wiki/Quasiregular%20representation
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This article addresses the notion of quasiregularity in the context of representation theory and topological algebra. For other notions of quasiregularity in mathematics, see the disambiguation page quasiregular.
In mathematics, quasiregular representation is a concept of representation theory, for a locally compact group G and a homogeneous space G/H where H is a closed subgroup.
In line with the concepts of regular representation and induced representation, G acts on functions on G/H. If however Haar measures give rise only to a quasi-invariant measure on G/H, certain 'correction factors' have to be made to the action on functions, for
L2(G/H)
to afford a unitary representation of G on square-integrable functions. With appropriate scaling factors, therefore, introduced into the action of G, this is the quasiregular representation or modified induced representation.
Unitary representation theory
Topological groups
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https://en.wikipedia.org/wiki/Vector%20fields%20on%20spheres
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In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras.
Specifically, the question is how many linearly independent smooth nowhere-zero vector fields can be constructed on a sphere in -dimensional Euclidean space. A definitive answer was provided in 1962 by Frank Adams. It was already known, by direct construction using Clifford algebras, that there were at least such fields (see definition below). Adams applied homotopy theory and topological K-theory to prove that no more independent vector fields could be found. Hence is the exact number of pointwise linearly independent vector fields that exist on an ()-dimensional sphere.
Technical details
In detail, the question applies to the 'round spheres' and to their tangent bundles: in fact since all exotic spheres have isomorphic tangent bundles, the Radon–Hurwitz numbers determine the maximum number of linearly independent sections of the tangent bundle of any homotopy sphere. The case of odd is taken care of by the Poincaré–Hopf index theorem (see hairy ball theorem), so the case even is an extension of that. Adams showed that the maximum number of continuous (smooth would be no different here) pointwise linearly-independent vector fields on the ()-sphere is exactly .
The construction of the fields is related to the real Clifford algebras, which is a theory with a perio
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https://en.wikipedia.org/wiki/Chris%20Maslanka
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Christopher M. Maslanka (born 27 October 1954) is a British writer and broadcaster, specialising in puzzles and problem solving.
He was born in Clapham, London, but was brought up by his uncle and aunt in Lowdham, Nottingham. He was educated at The Becket School, Nottingham, where he was a successful chess player, and went on to study physics at St Catherine's College, Oxford.
His first book – The Pyrgic Puzzler – a collection of 80 puzzles with illustrations by Michael Harrington, was written without any particular view to publication, but was taken up by Iris Murdoch who wrote an introduction for it in which she said that although she's not a great solver of puzzles, the book may be 'read as literature' just as in the case of Wittgenstein's Tractatus Logico-Philosophicus and the Bible.
He was invited by Alan Rusbridger to submit puzzles to Weekend Guardian and his two puzzle columns: Wordplay and Pyrgic Puzzles have appeared in the Saturday edition of the newspaper for 20 years. Maslanka is also the quizmaster for New Humanist magazine.
A book interview with David Freeman at BBC Radio Oxford led to Maslanka's contributing anecdotes and puzzles to many programmes and in 1992-3 he co-hosted the Saturday afternoon show PDQ 95.2 with Andrew Peach.
He was also invited by the World Service to broadcast his humorous puzzle anecdotes to the hostages during the Gulf War.
Maslanka designed the puzzles for Harry Horse's 1996 computer game, Drowned God.
He presented the BBC Radi
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https://en.wikipedia.org/wiki/William%20Markby
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Sir William Markby, KCIE (31 May 182915 October 1914) was an English judge and legal writer.
Career
Markby was born on 31 May 1829, the fourth son of the Rev. William Henry Markby, Rector of Duxford in Cambridgeshire. He was educated at Bury St. Edmunds and from 1846 at Merton College, Oxford, where he took his degree in Mathematics 1850. He was called to the bar in 1850 (or 1853?), and in 1865 he became recorder of Buckingham. In 1866, Markby went to India as judge of the Calcutta High Court. This post he held for twelve years. He also became the Vice Chancellor of the University of Calcutta. On his retirement in 1878, he was knighted and appointed as Reader in Indian Law at Oxford University, a post he held until 1900. He was also Tutor and Senior Bursar of Balliol College. In February 1900 he was appointed perpetual curator of the Indian Institute, in recognition of his long and valuable service to the University.
He was a member of the Commission to inquire into the administration of justice at Trinidad and Tobago. Besides Lectures on Indian Law, he wrote Elements of Law considered with reference to the General Principles of Jurisprudence. The latter, being intended in the first place for Indian students, calls attention to many difficulties in the definition and application of legal conceptions which are usually passed over in textbooks, and it ranks as one of the few books on the philosophy of law which are both useful to beginners and profitable to teachers and think
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https://en.wikipedia.org/wiki/Barlow%20surface
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In mathematics, a Barlow surface is one of the complex surfaces introduced by . They are simply connected surfaces of general type with pg = 0. They are homeomorphic but not diffeomorphic to a projective plane blown up in 8 points. The Hodge diamond for the Barlow surfaces is:
See also
Hodge theory
References
Algebraic surfaces
Complex surfaces
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https://en.wikipedia.org/wiki/Godeaux%20surface
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In mathematics, a Godeaux surface is one of the surfaces of general type introduced by Lucien Godeaux in 1931.
Other surfaces constructed in a similar way with the same Hodge numbers are also sometimes called Godeaux surfaces. Surfaces with the same Hodge numbers (such as Barlow surfaces) are called numerical Godeaux surfaces.
Construction
The cyclic group of order 5 acts freely on the Fermat surface of points (w : x : y : z)
in P3 satisfying w5 + x5 + y5 + z5 = 0 by mapping (w : x : y : z) to (w:ρx:ρ2y:ρ3z) where ρ is a fifth root of 1. The quotient by this action is the original Godeaux surface.
Invariants
The fundamental group (of the original Godeaux surface) is cyclic of order 5.
It has invariants like rational surfaces do, though it is not rational. The square of the first Chern class (and moreover the canonical class is ample).
See also
Hodge theory
References
Algebraic surfaces
Complex surfaces
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https://en.wikipedia.org/wiki/Contiguity
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Contiguity or contiguous may refer to:
Contiguous data storage, in computer science
Contiguity (probability theory)
Contiguity (psychology)
Contiguous distribution of species, in biogeography
Geographic contiguity of territorial land
Contiguous zone in territorial waters
See also
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https://en.wikipedia.org/wiki/Ring-closing%20metathesis
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Ring-closing metathesis (RCM) is a widely used variation of olefin metathesis in organic chemistry for the synthesis of various unsaturated rings via the intramolecular metathesis of two terminal alkenes, which forms the cycloalkene as the E- or Z- isomers and volatile ethylene.
The most commonly synthesized ring sizes are between 5-7 atoms; however, reported syntheses include 45- up to 90- membered macroheterocycles. These reactions are metal-catalyzed and proceed through a metallacyclobutane intermediate. It was first published by Dider Villemin in 1980 describing the synthesis of an Exaltolide precursor, and later become popularized by Robert H. Grubbs and Richard R. Schrock, who shared the Nobel Prize in Chemistry, along with Yves Chauvin, in 2005 for their combined work in olefin metathesis. RCM is a favorite among organic chemists due to its synthetic utility in the formation of rings, which were previously difficult to access efficiently, and broad substrate scope. Since the only major by-product is ethylene, these reactions may also be considered atom economic, an increasingly important concern in the development of green chemistry.
There are several reviews published on ring-closing metathesis.
History
The first example of ring-closing metathesis was reported by Dider Villemin in 1980 when he synthesized an Exaltolide precursor using a WCl6/Me4Sn catalyzed metathesis cyclization in 60-65% yield depending on ring size (A). In the following months, Jiro Tsuji rep
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