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83,600 | There are many developmental questions to be considered, but Edelman is able to succinctly summarize the problem in a way that will show a clear explanatory path forward for him. The developmental genetic question defines the problem - and, the theoretical approach for him. "How does a one-dimensional genetic code spec... | Neuronal group selection | 0.783719 |
83,601 | It seeks to provide an explanation of how the diversity of neuronal group phenotypes emerge from the organism's genotype via genetic and epigenetic influences that manifest themselves mechano-chemically at the cell surface and determine connectivity. Edelman list the following as vital to the formation of the primary r... | Neuronal group selection | 0.783719 |
83,602 | sculpt the organism over geological evolutionary time scales; but, Edelmans approach is more mechanical, and in the here and now – focusing on the genetically constrained mechano-chemistry of the selection processes that guide epigenetic behaviors on the part of cells within the embryo and adult over developmental time... | Neuronal group selection | 0.783719 |
83,603 | One of his goals is reconciling the relationships between genes in a population (genome) which lie in the germ line (sperm, egg, and fertilized egg); and the individuals in a population who develop degenerate phenotypes (soma) as they transform from an embryo into an adult who will eventually procreate if adaptive. Sel... | Neuronal group selection | 0.783719 |
83,604 | Edelman, and his team, were positioned in time and space to fully capitalize on these technical developments and scientific challenges – as his research progressed deeper and deeper into the cellular and molecular underpinnings of the neurophysiological aspects of behavior and cognition from a Darwinian perspective. Ed... | Neuronal group selection | 0.783719 |
83,605 | The modern synthesis was greatly accelerated and expanded with the rise of the genomic sciences, molecular biology, as well as, advances in computational techniques and the power to model population dynamics. But, for evolutionary-developmental biologists, there was something very important missing... – and, that was t... | Neuronal group selection | 0.783719 |
83,606 | Things had changed by the early 1900s, the Neodarwinian synthesis had unified the population biology of Mendelian inheritance with Darwinian natural selection. By the 1940s, the theories had been shown to be mutually consistent and coherent with paleontology and comparative morphology. The theory came to be known as th... | Neuronal group selection | 0.783719 |
83,607 | An account of how behavior is enabled and constrained by morphology. An account of how morphogenesis occurs in development and evolution.It is important to notice that these requirements are not directly stated in terms of genes, but heredity instead. This is understandable considering that Darwin himself appears to no... | Neuronal group selection | 0.783719 |
83,608 | How adaptive fitness can explain selection that leads to emergence of complex body structures.Later, In Bright Air, Brilliant Fire, Edelman describes what he calls Darwin's Program for obtaining a complete understanding of the rules of behavior and form in evolutionary biology. He identifies four necessary requirements... | Neuronal group selection | 0.783719 |
83,609 | In Topobiology, Edelman reflects upon Darwin's search for the connections between morphology and embryology in his theory of natural selection. He identifies four unresolved problems in the development and evolution of morphology that Darwin thought important: Explaining the finite number of body plans manifested since... | Neuronal group selection | 0.783719 |
83,610 | Edelman was inspired by the successes of fellow Nobel laureate Frank MacFarlane Burnet and his clonal selection theory (CST) of acquired antigen immunity by differential amplification of pre-existing variation within the finite pool of lymphocytes in the immune system. The population of variant lymphocytes within the b... | Neuronal group selection | 0.783719 |
83,611 | During a foray into molecular embryology and neuroscience, in 1975, Edelman and his team went on to isolate the first neural cell-adhesion molecule (N-CAM), one of the many molecules that hold the animal nervous system together. N-CAM turned out to be an important molecule in guiding the development and differentiation... | Neuronal group selection | 0.783719 |
83,612 | Edelman would draw inspiration from the mechano-chemical aspects of antigen/antibody/lymphocyte interaction in relation to recognition of self-nonself; the degenerate population of lymphocytes in their physiological context; and the bio-theoretical foundations of this work in Darwinian terms. By 1974, Edelman felt that... | Neuronal group selection | 0.783719 |
83,613 | Francis Crick based his criticism on the basis that neuronal groups are instructed by the environment rather than undergoing blind variation. In 1988, the neurophysiologist William Calvin had proposed true replication in the brain, whereas Edelman opposed the idea of true replicators in the brain. Stephen Smoliar publi... | Neuronal group selection | 0.783719 |
83,614 | The other two volumes are Topobiology – An Introduction to Molecular Embryology (1988) with its morpho-regulatory hypothesis of animal body plan development and evolutionary diversification via differential expression of cell surface molecules during development; and The Remembered Present – A Biological Theory of Cons... | Neuronal group selection | 0.783719 |
83,615 | Neural Darwinism is really the neural part of the natural philosophical and explanatory framework Edelman employs for much of his work – Somatic selective systems. Neural Darwinism is the backdrop for a comprehensive set of biological hypotheses and theories Edelman, and his team, devised that seek to reconcile vertebr... | Neuronal group selection | 0.783719 |
83,616 | In the aftermath of his publication of Neural Darwinism, Edelman continued to develop and extend his TNGS theory as well as his regulator hypothesis. Edelman would deal with the morphological issues in Topobiology and begin to extend the TNGS theory in The Remembered Present. Periodically over the intervening years, Ed... | Neuronal group selection | 0.783719 |
83,617 | Significant benefits result from the ability to boot a physical computer from a virtual hard drive: Ease of deployment: IT organizations can deploy standardized, 'pre-built' configurations on a single VHD. As an example, software engineering organizations that need a specific set of tools for a particular project could... | VHD (file format) | 0.783719 |
83,618 | Since June 2005, Lustre has consistently been used by at least half of the top ten, and more than 60 of the top 100 fastest supercomputers in the world, including the world's No. 1 ranked TOP500 supercomputer in November 2022, Frontier, as well as previous top supercomputers such as Fugaku, Titan and Sequoia.Lustre fil... | Cluster File Systems | 0.783719 |
83,619 | The Lustre File System ChecK (LFSCK) feature can verify and repair the MDS Object Index (OI) while the file system is in use, after a file-level backup/restore or in case of MDS corruption. The server-side IO statistics were enhanced to allow integration with batch job schedulers such as SLURM to track per-job statisti... | Cluster File Systems | 0.783719 |
83,620 | The state of primitive simplicity is followed by a period of growth, which eventually slows and gives way to a period of decay (1874:4): As man has developed, so also has his language (...): even the simplest language is the product of a gradual growth: all higher forms of language have come out of simpler ones.... Lan... | Schleicher theories | 0.783717 |
83,621 | It is central to the field of comparative linguistics, which involves using evidence from known languages and observed rules of language feature evolution to identify and describe the hypothetical proto-languages ancestral to each language family, such as Proto-Indo-European and the Indo-European languages. However, th... | Schleicher theories | 0.783717 |
83,622 | 206). Terms introduced by the Swiss geologist Émile Argand in 1924 (Krill 2011). Moreover, most of the blistering attacks were aimed at Wegener himself, an outsider (PhD in Astronomy) who seemed to be attacking the very foundations of geology. | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,623 | 1 cm/year). This implies a certain plasticity under the crust (Flint 1947).The alpine geology with its theory of thrusting (as geosyncline hypothesis; today's thrust tectonics) accepted horizontal movements. (Suess 1875) cited in (Holmes 1929a) 1848 Arnold Escher shows Roderick Murchison the Glarus thrust at the Pass d... | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,624 | ((Lyell 1875, p. 258) cited in (Summerhayes 1990)) Quote, Wallace about Dana: "In 1856, in articles in the American Journal, he discussed the development of the American continent, and argued for its general permanence; and in his Manual of Geology in 1863 and later editions, the same views were more fully enforced and... | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,625 | It was a mistake to state the continents "plowed" through the sea, although it isn't sure that this fixist quote is true in the original in German. He was an outsider with a doctorate in astronomy attacking an established theory between 'geophysicists'. The geophysicists were right to state that the Earth is solid, and... | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,626 | Journal of Geology. 52 (suppl): 1. Bibcode:1948JG.....56..497.. doi:10.1086/625552. | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,627 | Journal of Geology. 39 (1): 54–67. Bibcode:1931JG.....39...54P. | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,628 | Alexander du Toit's book. (du Toit 1937) In 1923, he received a grant from the Carnegie Institution of Washington, and used this to travel to eastern South America to study the geology of Argentina, Paraguay and Brazil. 1931: Peacock named the calc-alkaline igneous rock series. | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,629 | (Hellman 1998b), (Sullivan 1991, p. 15) Quote, Bailey Willis: "further discussion of it merely incumbers the literature and befogs the mind of fellow students. (It is) as antiquated as pre-Curie physics". | Timeline of the development of tectonophysics (before 1954) | 0.783716 |
83,630 | In mathematics, specifically Riemannian geometry, Synge's theorem is a classical result relating the curvature of a Riemannian manifold to its topology. It is named for John Lighton Synge, who proved it in 1936. | Synge theorem | 0.783715 |
83,631 | This reduces to a problem of pure linear algebra: let V be a finite-dimensional real inner product space with T: V → V an orthogonal linear map with an eigenvector v with eigenvalue one. If the determinant of T is positive and the dimension of V is even, or alternatively if the determinant of T is negative and the dime... | Synge theorem | 0.783715 |
83,632 | Let M be a closed Riemannian manifold with positive sectional curvature. The theorem asserts: If M is even-dimensional and orientable, then M is simply connected. If M is odd-dimensional, then it is orientable.In particular, a closed manifold of even dimension can support a positively curved Riemannian metric only if i... | Synge theorem | 0.783715 |
83,633 | Ergodic Ramsey theory arose shortly after Endre Szemerédi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, when Hillel Furstenberg gave a new proof of this theorem using ergodic theory. It has since produced combinatorial results, some of which have yet to be obtained by o... | Ergodic Ramsey theory | 0.783712 |
83,634 | Szemerédi's theorem is a result in arithmetic combinatorics, concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every set of integers A with positive natural density contains a k term arithmetic progression for every k. This conjecture, which became Szemerédi's theo... | Ergodic Ramsey theory | 0.783712 |
83,635 | The Kyoto Prize in Basic Sciences is awarded on a rotating basis to researchers in the following four fields: Mathematical sciences (including pure mathematics) Biological sciences (evolution, behavior, ecology, environment) Earth and planetary sciences, astronomy and astrophysics Cognitive science/Life sciences (molec... | Kyoto Prize in Basic Sciences | 0.783712 |
83,636 | Some feel that there are other elements, such as potassium, sulfur, zinc, copper, and iron which are also important in the ocean chemistry.In particular, iron (Fe) was considered of great importance as early biological oceanographers hypothesized that iron may also be a limiting factor for primary production in the oce... | Redfield ratio | 0.783711 |
83,637 | The research that resulted in this ratio has become a fundamental feature in the understanding of the biogeochemical cycles of the oceans, and one of the key tenets of biogeochemistry. The Redfield ratio is instrumental in estimating carbon and nutrient fluxes in global circulation models. They also help in determining... | Redfield ratio | 0.783711 |
83,638 | Redfield discovered the remarkable congruence between the chemistry of the deep ocean and the chemistry of living things such as phytoplankton in the surface ocean. Both have N:P ratios of about 16:1 in terms of atoms. When nutrients are not limiting, the molar elemental ratio C:N:P in most phytoplankton is 106:16:1. R... | Redfield ratio | 0.783711 |
83,639 | The Goldreich-Kylafis (GK) effect is a quantum mechanical effect with applications in Astrophysics. The theoretical background of the work was published by Peter Goldreich and his at the time postdoc Nick Kylafis in a series of two papers in The Astrophysical Journal. The GK effect predicts that, under special conditio... | Goldreich-Kylafis effect | 0.783711 |
83,640 | A coupled map lattice (CML) is a dynamical system that models the behavior of non-linear systems (especially partial differential equations). They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems. This includes the dynamics of spatiotemporal chaos where the number of effe... | Coupled map lattices | 0.783709 |
83,641 | Paul Erlich (born 1972) is a guitarist and music theorist living near Boston, Massachusetts. He is known for his seminal role in developing the theory of regular temperaments, including being the first to define pajara temperament and its decatonic scales in 22-ET. He holds a Bachelor of Science degree in physics from ... | Harmonic entropy | 0.783707 |
83,642 | Suppose that X and Y are two plane projective curves defined over a field F that do not have a common component (this condition means that X and Y are defined by polynomials, without common divisor of positive degree). Then the total number of intersection points of X and Y with coordinates in an algebraically closed f... | Bezouts theorem | 0.783707 |
83,643 | For stating the general result, one has to recall that the intersection points form an algebraic set, and that there is a finite number of intersection points if and only if all component of the intersection have a zero dimension (an algebraic set of positive dimension has an infinity of points over an algebraically cl... | Bezouts theorem | 0.783707 |
83,644 | The affine case of the theorem is the following statement, that has been proven in 1983 by David Masser and Gisbert Wüstholz.Let n affine hypersurfaces which are defined over an algebraically closed field by n polynomials in n variables, of degrees d 1 , … , d n . {\displaystyle d_{1},\ldots ,d_{n}.} Then either the nu... | Bezouts theorem | 0.783707 |
83,645 | The above technical condition ensures that β {\displaystyle \beta } is unique. The first above technical condition means that the degrees used in the definition of the resultant are p and q; this implies that the degree of R is pq (see Resultant § Homogeneity). As R is a homogeneous polynomial in two indeterminates, th... | Bezouts theorem | 0.783707 |
83,646 | Sponge aquaculture for spongin or metabolite production capitalises on the high regenerative abilities of the totipotent sponge cells by using explants (cut pieces of a parent sponge, which will then regrow into a full sponge) as a means of culturing sponges. Sponges have indeterminate growth, with maximum growth deter... | Sea sponge aquaculture | 0.783707 |
83,647 | OKA (Russian: ОКА — Опыты с КАонами, literal translation "Observations of KAons") is a particle physics detector experiment at the U-70 accelerator in the Institute for High Energy Physics located in Protvino near Moscow (Russia). OKA is specialized experiment with separated charge kaons beam. Superconducting high radi... | OKA (experiment) | 0.783705 |
83,648 | The transition temperature Tg in silicates is related to the energy required to break and re-form covalent bonds in an amorphous (or random network) lattice of covalent bonds. The Tg is clearly influenced by the chemistry of the glass. For example, addition of elements such as B, Na, K or Ca to a silica glass, which ha... | Dynamic arrest | 0.783704 |
83,649 | In mathematics, and particularly category theory, a coherence condition is a collection of conditions requiring that various compositions of elementary morphisms are equal. Typically the elementary morphisms are part of the data of the category. A coherence theorem states that, in order to be assured that all these equ... | Coherence axiom | 0.783704 |
83,650 | In some cases, artists who consider themselves space artists use more than illustration and painting to communicate astronomy or works depicting space, with some working directly with space flight technology and scientists in attempts to expand the arts, humanities, and cultural expression relative to space exploration... | Astronomical art | 0.783704 |
83,651 | Astronomical art is an aspect of space art devoted to visualizing outer space. A major emphasis of such art is the space environment as a new frontier for humanity. Many other works portray alien worlds, extremes of matter such as black holes, and concepts arising from inspiration derived from astronomy. | Astronomical art | 0.783704 |
83,652 | The top layer remained still in weightlessness, while the middle and bottom layers spun at different speeds to produce centripetal accelerations that mimicked lunar gravity and Martian gravity, respectively. Each layer carried six pockets that held the projects. Each pocket was a container with a diameter of 10 mm and ... | Astronomical art | 0.783704 |
83,653 | There are several forms of research: scientific, humanities, artistic, economic, social, business, marketing, practitioner research, life, technological, etc. The scientific study of research practices is known as meta-research. A researcher is a person engaged in conducting research, possibly recognized as an occupati... | Research ethics | 0.783701 |
83,654 | A simple example of a non-empirical task is the prototyping of a new drug using a differentiated application of existing knowledge; another is the development of a business process in the form of a flow chart and texts where all the ingredients are from established knowledge. Much of cosmological research is theoretica... | Research ethics | 0.783701 |
83,655 | Quantitative research This involves systematic empirical investigation of quantitative properties and phenomena and their relationships, by asking a narrow question and collecting numerical data to analyze it utilizing statistical methods. The quantitative research designs are experimental, correlational, and survey (o... | Research ethics | 0.783701 |
83,656 | The Lehmstedt–Tanasescu reaction is a method in organic chemistry for the organic synthesis of acridone derivatives (3) from a 2-nitrobenzaldehyde (1) and an arene compound (2): The reaction is named after two chemists who devoted part of their careers to research into this synthetic method, the German chemist Kurt Leh... | Lehmstedt–Tanasescu reaction | 0.783701 |
83,657 | In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V → W {\displaystyle V\to W} between two vector spaces that preserves the operations of vector addition and scalar mult... | Linear endomorphism | 0.783699 |
83,658 | In the mathematical field of graph theory, a self-complementary graph is a graph which is isomorphic to its complement. The simplest non-trivial self-complementary graphs are the 4-vertex path graph and the 5-vertex cycle graph. There is no known characterization of self-complementary graphs. | Self-complementary graph | 0.783698 |
83,659 | In plane geometry, an automedian triangle is a triangle in which the lengths of the three medians (the line segments connecting each vertex to the midpoint of the opposite side) are proportional to the lengths of the three sides, in a different order. The three medians of an automedian triangle may be translated to for... | Automedian triangle | 0.783696 |
83,660 | The side lengths of an automedian triangle satisfy the formula 2 a 2 = b 2 + c 2 {\displaystyle 2a^{2}=b^{2}+c^{2}} or a permutation thereof, analogous to the Pythagorean theorem characterizing right triangles as the triangles satisfying the formula a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} . Equivalently, in o... | Automedian triangle | 0.783696 |
83,661 | This property of automedian triangles stands in contrast to the Steiner–Lehmus theorem, according to which the only triangles two of whose angle bisectors have equal length are the isosceles triangles.Additionally, suppose that A B C {\displaystyle ABC} is an automedian triangle, in which vertex A {\displaystyle A} sta... | Automedian triangle | 0.783696 |
83,662 | Later, ATI developed a successor to the original Rage 128, called the Rage 128 Pro. This chip carried several enhancements, including an enhanced triangle setup engine that doubled geometry throughput to eight million triangles/s, better texture filtering, DirectX 6.0 texture compression, AGP 4×, DVI support, and a Rag... | ATI Rage | 0.783694 |
83,663 | The presence of lead is used in glasses absorbing gamma radiation and X-rays, used in radiation shielding as a form of lead shielding (e.g. in cathode ray tubes, thus lowering the exposure of the viewer to soft X-rays). In particle physics, the combination of the low radiation length resulting from the high density and... | Lead Crystal | 0.783694 |
83,664 | The company is a member of the Robotics Industries Association (RIA), of the International Federation of Robotics (IFR) and the German engineering association VDMA. In 1996, KUKA Schweissanlagen GmbH became an independent company and, two years later, the leader among European welding equipment manufacturers. The suppl... | Intelligent industrial work assistant | 0.783694 |
83,665 | These welding systems were then further expanded to adhesive bonding and sealing technologies in the following year. Around the same time, KUKA took over the tools & equipment manufacturers Schwarzenberg GmbH and expanded its business to China and the USA in the following years. In 1995, the company was split into KUKA... | Intelligent industrial work assistant | 0.783694 |
83,666 | A domain ontology (or domain-specific ontology) represents concepts which belong to a realm of the world, such as biology or politics. Each domain ontology typically models domain-specific definitions of terms. For example, the word card has many different meanings. An ontology about the domain of poker would model the... | Domain ontology | 0.783692 |
83,667 | Program abstraction taxonomy Protein Ontology for proteomics RXNO Ontology, for name reactions in chemistry SCDO, the Sickle Cell Disease Ontology, facilitates data sharing and collaborations within the SDC community, amongst other applications (see list on SCDO website). Sequence Ontology, for representing genomic fea... | Domain ontology | 0.783692 |
83,668 | LPL, Landmark Pattern Language NCBO Bioportal, biological and biomedical ontologies and associated tools to search, browse and visualise NIFSTD Ontologies from the Neuroscience Information Framework: a modular set of ontologies for the neuroscience domain. OBO-Edit, an ontology browser for most of the Open Biological a... | Domain ontology | 0.783692 |
83,669 | It started as a merger of the basic elements of the OpenCyc and SUMO ontologies, and has been supplemented with other ontology elements (types, relations) so as to include representations of all of the words in the Longman dictionary defining vocabulary. Computer Science Ontology, an automatically generated ontology of... | Domain ontology | 0.783692 |
83,670 | Some researchers, drawing inspiration from philosophical ontologies, viewed computational ontology as a kind of applied philosophy. In 1993, the widely cited web page and paper "Toward Principles for the Design of Ontologies Used for Knowledge Sharing" by Tom Gruber used ontology as a technical term in computer science... | Domain ontology | 0.783692 |
83,671 | Since the mid-1970s, researchers in the field of artificial intelligence (AI) have recognized that knowledge engineering is the key to building large and powerful AI systems. AI researchers argued that they could create new ontologies as computational models that enable certain kinds of automated reasoning, which was o... | Domain ontology | 0.783692 |
83,672 | Ontology is a branch of philosophy and intersects areas such as metaphysics, epistemology, and philosophy of language, as it considers how knowledge, language, and perception relate to the nature of reality. Metaphysics deals with questions like "what exists?" and "what is the nature of reality?". One of five tradition... | Domain ontology | 0.783692 |
83,673 | (Benzene)chromium tricarbonyl is an organometallic compound with the formula Cr(C6H6)(CO)3. This yellow crystalline solid compound is soluble in common nonpolar organic solvents. The molecule adopts a geometry known as “piano stool” because of the planar arrangement of the aryl group and the presence of three CO ligand... | (Benzene)chromium tricarbonyl | 0.783691 |
83,674 | In polymer chemistry, materials science, and food science, bloom refers to the migration of one component of a solid mixture to the surface of an article. The process is an example of phase separation or phase aggregation. | Bloom (phase) | 0.78369 |
83,675 | Such lookups take one instruction and two instruction cycles. Many functions can be modeled in this way. Optimization is facilitated by the relatively large program space of the PIC (e.g. 4096 × 14-bit words on the 16F690) and by the design of the instruction set, which allows embedded constants. | PIC microcontrollers | 0.783689 |
83,676 | Microchip provides a freeware IDE package called MPLAB X, which includes an assembler, linker, software simulator, and debugger. They also sell C compilers for the PIC10, PIC12, PIC16, PIC18, PIC24, PIC32 and dsPIC, which integrate cleanly with MPLAB X. Free versions of the C compilers are also available with all featu... | PIC microcontrollers | 0.783689 |
83,677 | The International Renewable Energy Agency has reported that 14,438 megawatts (MW) of geothermal power was online worldwide at the end of 2020, generating 94,949 GWh of electricity. In theory, the world's geothermal resources are sufficient to supply humans with energy. However, only a tiny fraction of the world's geoth... | Flash steam power station | 0.783688 |
83,678 | Over the past 60 years, net fluid production has been in excess of 2.5 km3. Subsidence at Wairakei-Tauhara has been an issue in a number of formal hearings related to environmental consents for expanded development of the system as a source of renewable energy.In 1960, Pacific Gas and Electric began operation of the fi... | Flash steam power station | 0.783688 |
83,679 | The validity of the Heckscher–Ohlin model has been questioned since the classical Leontief paradox. Indeed, Feenstra called the Heckscher–Ohlin model "hopelessly inadequate as an explanation for historical and modern trade patterns". As for the Stolper–Samuelson theorem itself, Davis and Mishra recently stated, "It is ... | Stolper–Samuelson theorem | 0.783687 |
83,680 | Considering a two-good economy that produces only wheat and cloth, with labor and land being the only factors of production, wheat a land-intensive industry and cloth a labor-intensive one, and assuming that the price of each product equals its marginal cost, the theorem can be derived. The price of cloth should be: (1... | Stolper–Samuelson theorem | 0.783687 |
83,681 | The Stolper–Samuelson theorem is a basic theorem in Heckscher–Ohlin trade theory. It describes the relationship between relative prices of output and relative factor rewards—specifically, real wages and real returns to capital. The theorem states that—under specific economic assumptions (constant returns to scale, perf... | Stolper–Samuelson theorem | 0.783687 |
83,682 | It was derived in 1941 from within the framework of the Heckscher–Ohlin model by Wolfgang Stolper and Paul Samuelson, but has subsequently been derived in less restricted models. As a term, it is applied to all cases where the effect is seen. Ronald W. Jones and José Scheinkman show that under very general conditions t... | Stolper–Samuelson theorem | 0.783687 |
83,683 | Therefore, the early versions of the theorem could make no predictions about the effect on the unskilled labor force in a high-income country under trade liberalization. However, more sophisticated models with multiple classes of worker productivity have been shown to produce the Stolper–Samuelson effect within each cl... | Stolper–Samuelson theorem | 0.783687 |
83,684 | If considering the change in real returns under increased international trade a robust finding of the theorem is that returns to the scarce factor will go down, ceteris paribus. An additional robust corollary of the theorem is that a compensation to the scarce factor exists which will overcome this effect and make incr... | Stolper–Samuelson theorem | 0.783687 |
83,685 | Liberman's lemma is a theorem used in studying intrinsic geometry of convex surface. It is named after Joseph Liberman. | Liberman's lemma | 0.783685 |
83,686 | The storm was an important event in the field of heliophysics, the study of space weather, with numerous studies published in the next few years and throughout the 1970s and 1980s, as well as leading to several influential internal investigations and to significant policy changes. Almost fifty years after the fact, the... | August 1972 solar storms | 0.783685 |
83,687 | utilities in these regions reported no disturbances, with the presence of igneous rock geology a suspected factor, as well as geomagnetic latitude and differences in operational characteristics of respective electrical grids. Manitoba Hydro reported that power going the other way, from Manitoba to the U.S., plummeted 1... | August 1972 solar storms | 0.783685 |
83,688 | In mathematics, the slice genus of a smooth knot K in S3 (sometimes called its Murasugi genus or 4-ball genus) is the least integer g such that K is the boundary of a connected, orientable 2-manifold S of genus g properly embedded in the 4-ball D4 bounded by S3. More precisely, if S is required to be smoothly embedded,... | Slice genus | 0.783684 |
83,689 | Tilting theory may be seen as a generalization of Morita equivalence which is recovered if T is a projective generator; in that case T = mod − A {\displaystyle {\mathcal {T}}=\operatorname {mod} -A} and Y = mod − B {\displaystyle {\mathcal {Y}}=\operatorname {mod} -B} . If A has finite global dimension, then B also has... | Coxeter functor | 0.783683 |
83,690 | Suppose A is a finite-dimensional algebra, T is a tilting module over A, and B = EndA(T ). Write F = HomA(T,−), F′ = Ext1A(T,−), G = −⊗BT, and G′ = TorB1(−,T). F is right adjoint to G and F′ is right adjoint to G′. Brenner & Butler (1980) showed that tilting functors give equivalences between certain subcategories of m... | Coxeter functor | 0.783683 |
83,691 | In mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras using so-called tilting modules and associated tilting functors. Here, the second algebra is the endomorphism algebra of a tilting module over the first algebra. Tilting theory was motivate... | Coxeter functor | 0.783683 |
83,692 | In 2013, the Buchwald group reported a copper-catalyzed hydroamination method for synthesizing chiral tertiary amines; similar work was disclosed by the Miura group (Osaka University) in the same year. For about a decade, the group had published numerous papers employing ligated copper (I) hydride in 1,4-reductions of ... | Hydrocupration | 0.783683 |
83,693 | For hydroalkylations (and hydroacylations), the generated organocuprate (after initial migratory insertion) can perform nucleophilic substitution chemistry (SN2) with alkyl halides, carbonyls, and various other classical electrophiles; in this instance (and in the case of reactivity with an alkyl halide) a copper (I) h... | Hydrocupration | 0.783683 |
83,694 | ( ∂ ∂ x ) k − 1 ( f ( x ) k ) {\displaystyle v=x+\sum _{k=1}^{\infty }{\frac {y^{k}}{k! }}\left({\frac {\partial }{\partial x}}\right)^{k-1}\left(f(x)^{k}\right)} In which case the equation can be derived using perturbation theory. In 1770, Joseph Louis Lagrange (1736–1813) published his power series solution of the im... | Lagrange reversion theorem | 0.783683 |
83,695 | In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions. Let v be a function of x and y in terms of another function f such that v = x + y f ( v ) {\displaystyle v=x+yf(v)} Then for any function g,... | Lagrange reversion theorem | 0.783683 |
83,696 | Given a nilpotent square matrix A {\displaystyle A} of order n {\displaystyle n} over an algebraically closed field F {\displaystyle F} , the following algorithm produces an invertible matrix C {\displaystyle C} and a Weyr matrix W {\displaystyle W} such that W = C − 1 A C {\displaystyle W=C^{-1}AC} . Step 1 Let A 1 = ... | Weyr canonical form | 0.783682 |
83,697 | That the Weyr form is a canonical form of a matrix is a consequence of the following result: Each square matrix A {\displaystyle A} over an algebraically closed field is similar to a Weyr matrix W {\displaystyle W} which is unique up to permutation of its basic blocks. The matrix W {\displaystyle W} is called the Weyr ... | Weyr canonical form | 0.783682 |
83,698 | Some well-known applications of the Weyr form are listed below: The Weyr form can be used to simplify the proof of Gerstenhaber’s Theorem which asserts that the subalgebra generated by two commuting n × n {\displaystyle n\times n} matrices has dimension at most n {\displaystyle n} . A set of finite matrices is said to ... | Weyr canonical form | 0.783682 |
83,699 | Let A {\displaystyle A} be a square matrix of order n {\displaystyle n} over an algebraically closed field and let the distinct eigenvalues of A {\displaystyle A} be λ 1 , λ 2 , … , λ k {\displaystyle \lambda _{1},\lambda _{2},\ldots ,\lambda _{k}} . The Jordan–Chevalley decomposition theorem states that A {\displaysty... | Weyr canonical form | 0.783682 |
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