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86,000 | The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime fa... | RSA Factoring Challenge | 0.798678 |
86,001 | Pauli and Jung's approach to dual-aspect monism has a very specific further feature, namely that different aspects may show a complementarity in a quantum physical sense. That is, the Pauli-Jung conjecture implies that with regard to mental and physical states there may be incompatible descriptions of different parts t... | Double-aspect theory | 0.798677 |
86,002 | The U-resultant is a homogeneous polynomial in k . {\displaystyle k.} It is zero if and only if the common zeros of P 1 , … , P n − 1 {\displaystyle P_{1},\ldots ,P_{n-1}} form a projective algebraic set of positive dimension (that is, there are infinitely many projective zeros over an algebraically closed extension o... | Multivariate resultant | 0.798677 |
86,003 | Other products exist independently to manage across arrays and/or server DAS storage. Virtual volumes (VVols), a proposal from VMware for a more transparent mapping between large volumes and the VM disk images within them, to allow better performance and data management optimizations. This does not reflect a new capabi... | Software Defined Storage | 0.798676 |
86,004 | In response to concerns about publication bias and p-hacking, more than 140 psychology journals have adopted result-blind peer review, in which studies are pre-registered and published without regard for their outcome. An analysis of these reforms estimated that 61 percent of result-blind studies produce null results, ... | Metascience | 0.798676 |
86,005 | Examples include the giant panda, the Bengal tiger, and the blue whale. Compare flagship species. chemical ecology A branch of ecology which studies the use by organisms of naturally occurring chemical compounds for various purposes, e.g. in defense against predators. | Glossary of ecology | 0.798676 |
86,006 | If the observed strength of the weak force is then vital for the emergence of observers, this would explain why the weak force is indeed observed with this strength. Barr and others argued that if one only allows the electroweak symmetry breaking scale to vary between universes, keeping all other parameters fixed, atom... | Weakless Universe | 0.798676 |
86,007 | Wisdom (Whitewater Interactive System Development with Object Models) is a software development process and method to design software-intensive interactive systems. It is based on object modelling, and focuses human-computer interaction (HCI) in order to model the software architecture of the system i.e. it is architec... | Whitewater Interactive System Development with Object Models | 0.798676 |
86,008 | The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph. A sequen... | Erdős–Gallai theorem | 0.798676 |
86,009 | The Hiroshima Synchrotron Radiation Center, also known as Hiroshima Synchrotron Orbital Radiation (HiSOR), at Hiroshima University is a national user research facility in Japan. It was founded in 1996 by the University Science Council at Hiroshima University initially as a combined educational and research facility bef... | Hiroshima Synchrotron Radiation Center | 0.798676 |
86,010 | The results of the experiment could then be compared to what was predicted by local realism and those predicted by quantum mechanics.In theory, the results could be "coincidentally" consistent with both. To address this problem, Bell proposed a mathematical description of local realism that placed a statistical limit o... | Loopholes in Bell tests | 0.798676 |
86,011 | The Cleveland open-cup method is one of three main methods in chemistry for determining the flash point of a petroleum product using a Cleveland open-cup apparatus, also known as a Cleveland open-cup tester. First, the test cup of the apparatus (usually brass) is filled to a certain level with a portion of the product.... | Cleveland open cup method | 0.798675 |
86,012 | In formal terms, the difference quotient is a linear operator which takes a function as its input and produces a second function as its output. This is more abstract than many of the processes studied in elementary algebra, where functions usually input a number and output another number. For example, if the doubling f... | Discrete calculus | 0.798675 |
86,013 | Using this sequence, he constructs nested intervals whose intersection contains a real number not in the sequence. Since every sequence of real numbers can be used to construct a real not in the sequence, the real numbers cannot be written as a sequence – that is, the real numbers are not countable. By applying his con... | Georg Cantor | 0.798675 |
86,014 | Skew partitions form one of the key components of a structural decomposition of perfect graphs used by Chudnovsky et al. (2006) as part of their proof of the strong perfect graph theorem. Chudnovsky et al. showed that every perfect graph either belongs to one of five basic classes of perfect graphs, or it has one of fo... | Skew partition | 0.798674 |
86,015 | Risk assessments can be done in individual cases, including in patient and physician interactions. In the narrow sense chemical risk assessment is the assessment of a health risk in response to environmental exposures. The ways statistics are expressed and communicated to an individual, both through words and numbers i... | Risk assessments | 0.798674 |
86,016 | However, Hicks' third law of demand gives us ϵ H H = − ϵ H L {\displaystyle \epsilon _{HH}=-\epsilon _{HL}} and ϵ L H = − ϵ L L {\displaystyle \epsilon _{LH}=-\epsilon _{LL}} . To see why this is, suppose that we take a more general version of the compensated demand function with n {\displaystyle n} goods and compensat... | Iron law of prohibition | 0.798674 |
86,017 | At least one species of bacterium in the genus Nocardia can degrade PET with an esterase enzyme. Esterases are enzymes able to cleave the ester bond. Also, the initial degradation of PET can be esterases expressed by Bacillus and Nocardia.Japanese scientists have isolated a bacterium Ideonella sakaiensis that possesses... | Flexible substrate | 0.798674 |
86,018 | Two Greek philosophers, Leucippus (first half of the 5th century BC) and Democritus came up with the notion that there were two real entities: atoms, which were small indivisible particles of matter, and the void, which was the empty space in which matter was located. Although all the explanations from Thales to Democr... | Greek science | 0.798673 |
86,019 | The first application of the pump–probe technique in biology was in vitro imaging of stimulated emission of a dye-labelled cell. Pump–probe imaging is now widely used for melanin imaging to differentiate between the two main forms of melanin – eumelanin (brown/black) and pheomelanin (red/yellow). In melanoma, eumelanin... | Pump–probe microscopy | 0.798673 |
86,020 | In natural language processing, language identification or language guessing is the problem of determining which natural language given content is in. Computational approaches to this problem view it as a special case of text categorization, solved with various statistical methods. | Language identification | 0.798672 |
86,021 | More concretely, DeepMind aims to combine insights from systems neuroscience with new developments in machine learning and computing hardware to unlock increasingly powerful general-purpose learning algorithms that will work towards the creation of an artificial general intelligence (AGI). The company has focused on tr... | Demis Hassabis | 0.798672 |
86,022 | Synthetic biology is an outgrowth of biotechnology distinguished by the use of biological pathways or organisms not found in nature. This contrasts with "traditional" genetically modified organisms created by transferring existing genes from one cell type to another. Major goals of synthetic biology include re-designin... | Hazards of synthetic biology | 0.798672 |
86,023 | In 4-dimensional geometry, the octahedral pyramid is bounded by one octahedron on the base and 8 triangular pyramid cells which meet at the apex. Since an octahedron has a circumradius divided by edge length less than one, the triangular pyramids can be made with regular faces (as regular tetrahedrons) by computing the... | Octahedral pyramid | 0.798672 |
86,024 | Stuart Alan Rice (born January 6, 1932) is an American theoretical chemist and physical chemist. He is well known as a theoretical chemist who also does experimental research, having spent much of his career working in multiple areas of physical chemistry. He is currently the Frank P. Hixon Distinguished Service Profes... | Stuart A. Rice | 0.798671 |
86,025 | —; Frank Ayres, Jr (1999). Schaum's Outline of Calculus (paperback). Schaum's Outlines (5th ed.). | Elliott Mendelson | 0.798671 |
86,026 | Edelman explicitly rejects computational approaches to explaining biology as non-biological. Edelman acknowledges that there is a conservation of phylogenetic organization and structure within the vertebrate nervous system, but also points out that locally natural diversity, variation and degeneracy abound. This variat... | Neural Darwinism | 0.798671 |
86,027 | Automatic taxonomy construction (ATC) is the use of software programs to generate taxonomical classifications from a body of texts called a corpus. ATC is a branch of natural language processing, which in turn is a branch of artificial intelligence. A taxonomy (or taxonomical classification) is a scheme of classificati... | Automatic taxonomy construction | 0.798671 |
86,028 | Mincer: A software package using FORM to compute massless propagator diagrams with up to three loops. FORM has been the essential tool to calculate the higher-order QCD beta function. The mathematical structure of multiple zeta values has been researched with dedicated FORM programs. The software package FormCalc which... | FORM (symbolic manipulation system) | 0.79867 |
86,029 | At the age of 16, he sat two examinations for university scholarships, and won both of them.Chadwick chose to attend Victoria University of Manchester, which he entered in 1908. He meant to study mathematics, but enrolled in physics by mistake. Like most students, he lived at home, walking the 4 miles (6.4 km) to the u... | James Chadwick | 0.79867 |
86,030 | In 1572 Rafael Bombelli published his L'Algebra in which he showed how to deal with the imaginary quantities that could appear in Cardano's formula for solving cubic equations. Simon Stevin's book De Thiende ('the art of tenths'), published in Dutch in 1585, contained a systematic treatment of decimal notation, which i... | History of mathematical notation | 0.79867 |
86,031 | These bridges must be able to withstand their own weight, as well as the trucks and any force they impart when landing on the bridge. Elements from Portal require the player to guide the trucks across the bridges, navigate through portals, cross over buttons to open doors or other actions, avoid coming in sight of sent... | Bridge Constructor Portal | 0.798669 |
86,032 | In bioinformatics, a spaced seed is a pattern of relevant and irrelevant positions in a biosequence and a method of approximate string matching that allows for substitutions. They are a straightforward modification to the earliest heuristic-based alignment efforts that allow for minor differences between the sequences ... | Spaced seed | 0.798669 |
86,033 | in philosophy in 1993. His dissertation topic was entitled, Measurement and the Disunity of Quantum Physics. He was also a visiting graduate student at Harvard University. | Hasok Chang | 0.798669 |
86,034 | The overwhelmingly dominant circuit topology during this period was the single-ended triode gain stage, operating in class A, which gave very good sound (and reasonable measured distortion performance) despite extremely simple circuitry with very few components: important at a time when components were handmade and ext... | Valve amplifiers | 0.798669 |
86,035 | In organic chemistry, tolyl groups are functional groups related to toluene. They have the general formula CH3C6H4−R, the change of the relative position of the methyl and the R substituent on the aromatic ring can generate three possible structural isomers 1,2 (ortho), 1,3 (meta), and 1,4 (para). Tolyl groups are aryl... | Tolyl groups | 0.798669 |
86,036 | Tuple-versioning (also called point-in-time) is a mechanism used in a relational database management system to store past states of a relation. Normally, only the current state is captured. Using tuple-versioning techniques, typically two values for time are stored along with each tuple: a start time and an end time. T... | Tuple-versioning | 0.798669 |
86,037 | Joseph grew up in the village of Vieille Case in Dominica. Her mother was a nurse and her father worked a variety of jobs. She graduated in 2012 with a BSc in Chemistry and mathematics from the University of the West Indies. This was followed by an MPhil in Chemistry at the same institution, graduating in 2014. | Jerelle Joseph | 0.798668 |
86,038 | In particle physics and astrophysics, the term is used in two ways, one broader and the other more specific. The broader meaning is just quark matter that contains three flavors of quarks: up, down, and strange. In this definition, there is a critical pressure and an associated critical density, and when nuclear matter... | Corporeal substance | 0.798668 |
86,039 | This representation emerged simultaneously with the 2 when William Rowan Hamilton introduced versors, his term for elements of SU(2). Note that Hamilton did not use standard group theory terminology since his work preceded Lie group developments. The m = 3 {\displaystyle m=3} (i.e. l = 3 / 2 {\displaystyle l=3/2} ) rep... | Representation theory of SU(2) | 0.798668 |
86,040 | Hamiltonian truncation computations are normally performed using a computer algebra system, or a programming language like Python or C++. The number of low-energy states N ( Λ ) {\displaystyle N(\Lambda )} tends to grow rapidly with the UV cutoff, and it is common to perform Hamiltonian truncation computations taking i... | Hamiltonian truncation | 0.798668 |
86,041 | The first reaction is a Barbier reaction with propargylic bromide in water (green chemistry) and the second reaction is a Sonogashira coupling. Substrates may vary in these sequences and in this way a chemical library of new compounds can be realized. == References == | Noncovalent solid-phase organic synthesis | 0.798667 |
86,042 | Abell 2597 is a galaxy cluster located about a billion light years from Earth in the constellation of Aquarius. It is a giant elliptical galaxy that is surrounded by a sprawling cluster of other galaxies. In 2018, the National Radio Astronomy Observatory (NRAO) captured cosmic weather event using the Atacama Large Mill... | Abell 2597 | 0.798667 |
86,043 | Data on experimental inquiry published in Deutsche Landwirthschafts-Zeitung provided immediate practical industry benefits in the form of the Tuberculin test as an aide to diagnosis in both sick and healthy cattle. Tuberculin proved to be an ineffective means of immunization but in 1908, Charles Mantoux found it was an... | History of tuberculosis | 0.798666 |
86,044 | Since C {\displaystyle \mathbb {C} } is algebraically closed, every homomorphism R → F {\displaystyle R\to \mathbb {F} } must factor through C {\displaystyle \mathbb {C} } , so we only have to compute the intersection of { ker ( Φ ): Φ ∈ Hom ( R , C ) } {\displaystyle \{\ker(\Phi ):\Phi \in \operatorname {Hom} (R,\... | Radical of an ideal | 0.798666 |
86,045 | The number of the common zeros of the polynomials in a Gröbner basis is strongly related to the number of monomials that are irreducibles by the basis. Namely, the number of common zeros is infinite if and only if the same is true for the irreducible monomials; if the two numbers are finite, the number of irreducible m... | Projective Nullstellensatz | 0.798666 |
86,046 | The diffusive gradients in thin films (DGT) technique is an environmental chemistry technique for the detection of elements and compounds in aqueous environments, including natural waters, sediments and soils. It is well suited to in situ detection of bioavailable toxic trace metal contaminants. The technique involves ... | Diffusive gradients in thin films | 0.798666 |
86,047 | For most reactions, the rate decreases as the reaction proceeds. A reaction's rate can be determined by measuring the changes in concentration over time. Chemical kinetics is the part of physical chemistry that concerns how rates of chemical reactions are measured and predicted, and how reaction-rate data can be used t... | Reaction rates | 0.798666 |
86,048 | The module structure of a representation of a Hopf algebra H is simply its structure as a module for the underlying associative algebra. The main use of considering the additional structure of a Hopf algebra is when considering all H-modules as a category. The additional structure is also used to define invariant eleme... | Representation theory of Hopf algebras | 0.798666 |
86,049 | However, this conclusion is not a mathematical certainty; there exist undirected graphs (such as the graph formed by removing a single edge from a large complete graph) that are unlikely to arise as social networks but in which most vertices have higher degree than the average of their neighbors' degrees. The Friendshi... | Friendship paradox | 0.798665 |
86,050 | S2CID 689632.Hande MP, Azizova TV, Geard CR, Burak LE, Mitchell CR, Khokhryakov VF, Vasilenko EK, Brenner DJ (2003). "Past exposure to densely ionizing radiation leaves a unique permanent signature in the genome". American Journal of Human Genetics. | Valentin Fedorovich Khokhryakov | 0.798665 |
86,051 | The virtualization that ODBC offers is no longer a strong requirement, and development of ODBC is no longer as active as it once was. But while ODBC is no longer a strong requirement for client-server programming, it is now more important for access, virtualization, and integration in analytics and data science scenari... | ODBC driver | 0.798664 |
86,052 | In set theory, the random algebra or random real algebra is the Boolean algebra of Borel sets of the unit interval modulo the ideal of measure zero sets. It is used in random forcing to add random reals to a model of set theory. The random algebra was studied by John von Neumann in 1935 (in work later published as Neum... | Random algebra | 0.798664 |
86,053 | On the invitation of Arnold Sommerfeld, he worked at the University of Munich, and on the creation by the Rockefeller Foundation of the Institute of Physics and Chemistry (Madrid), in 1930 he was named head of the Spectroscopy Section. He was invited numerous times to work in the laboratories of the National Bureau of ... | Miguel A. Catalán | 0.798663 |
86,054 | Formally, let X be a variety defined over an algebraically closed field of characteristic zero: hence X is defined over a finitely generated field E. If the set of points X(F) is finite for any finitely generated field extension F of E, then X is Mordellic. | Algebraic hyperbolicity | 0.798663 |
86,055 | substrate Also substratum; plural substrata. The surface or base upon which a lichen grows or is attached. Although the terms substratum and substrate are often used equivalently in lichenology, the latter term has different meanings in microbiology and in enzymology. | Glossary of lichen terms | 0.798663 |
86,056 | Another example of an indolamine is melatonin. In biochemistry, indolamines are substituted indole compounds that contain an amino group. Examples of indolamines include the lysergamides. | Indolamines | 0.798663 |
86,057 | Semidefinite programming subsumes SOCPs as the SOCP constraints can be written as linear matrix inequalities (LMI) and can be reformulated as an instance of semidefinite program. The converse, however, is not valid: there are positive semidefinite cones that do not admit any second-order cone representation. In fact, w... | Second-order cone programming | 0.798663 |
86,058 | The ancients – unlike Prof. Tait – knew not, and did not worship Quaternions. Neither matrices nor quaternions and ordinary vectors were banished from these ten chapters. For, in spite of the uncontested power of the modern Tensor Calculus, those older mathematical languages continue, in my opinion, to offer conspicuo... | Norm of a quaternion | 0.798662 |
86,059 | Melvin Hochster (born August 2, 1943) is an American mathematician working in commutative algebra. He is currently the Jack E. McLaughlin Distinguished University Professor of Mathematics at the University of Michigan. | Melvin Hochster | 0.798662 |
86,060 | Sagan served as Chairman of the Division for Planetary Science of the American Astronomical Society, as President of the Planetology Section of the American Geophysical Union, and as Chairman of the Astronomy Section of the American Association for the Advancement of Science (AAAS). At the height of the Cold War, Sagan... | Carl Sagan | 0.798662 |
86,061 | Pseudospectral methods, also known as orthogonal collocation methods, in optimal control arose from spectral methods which were traditionally used to solve fluid dynamics problems. Seminal work in orthogonal collocation methods for optimal control problems date back to 1979 with the work of Reddien and some of the firs... | Gauss pseudospectral method | 0.798662 |
86,062 | As used in astrophysics, a flux tube generally means an area of space through which a strong magnetic field passes, in which the behavior of matter (usually ionized gas or plasma) is strongly influenced by the field. They are commonly found around stars, including the Sun, which has many flux tubes from tens to hundred... | Magnetic flux tube | 0.798662 |
86,063 | Deep learning and computer vision techniques are then employed to learn the location of the body parts in the training data. Next, the trained model is used to predict the location of the body parts in each frame on newly collected videos. The resulting time series data consists of the positions of the visible body par... | Study of animal locomotion | 0.798662 |
86,064 | As a strictly geographical concept, sympatric speciation is defined as one species diverging into two while the ranges of both nascent species overlap entirely – this definition is not specific enough about the original population to be useful in modeling.Definitions based on population genetics are not necessarily spa... | Sympatric speciation | 0.798662 |
86,065 | The result is known as the Gauss–Wantzel theorem: A regular n-gon can be constructed with compass and straightedge if and only if n is a power of 2 or the product of a power of 2 and any number of distinct Fermat primes.A Fermat prime is a prime number of the form 2 ( 2 m ) + 1. {\displaystyle 2^{(2^{m})}+1.} In order ... | Constructible polygon | 0.798662 |
86,066 | Analytical model can be created using the ribbon-based user interface, by editing the command file or by importing several other files types like dxf, cis/2 etc. The model geometry can even be generated from the data of macro-enabled applications (like Microsoft Excel, Microstation etc.) by using Macros. | STAAD | 0.798661 |
86,067 | In five-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 5-demicubic honeycomb, and a quarter of the vertices of a 5-cube honeycomb. Its facets are 5-demicubes and runcinated 5-demicubes. | Quarter 5-cubic honeycomb | 0.798661 |
86,068 | The Xerox software, called processors, available for CP-V in 1978 included: Terminal Executive Language (TEL) command language Control Command Interpreter (CCI) batch counterpart of TEL File system management processors — backup/restore (fill, fsave and fres) EASY — online Interactive Debugging Environment for Fortran ... | SDS Sigma series | 0.798661 |
86,069 | As a result, provinces like Quebec, Alberta and Manitoba have put almost the full costs of IVF on the public healthcare bill. Dr. Santiago Munne, developer of the first PGD test for Down's syndrome and founder of Reprogenetics, saw these provincial decisions as an opportunity for his company to grow and open more Repro... | Blastocyst biopsy | 0.798661 |
86,070 | Speciation from assortative mating has occurred in the Middle East blind mole rat, cicadas, and the European corn borer.Like other animals, humans also display these genetic results of assortative mating. What makes humans unique, however, is the tendency towards seeking mates that are not only similar to them in genet... | Assortative mating | 0.79866 |
86,071 | 129–136, MR 0278980. Halin, R. (1974), "A note on Menger's theorem for infinite locally finite graphs", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 40: 111–114, doi:10.1007/BF02993589, MR 0335355, S2CID 120915644. Halin, R. (1976), "S-functions for graphs", Journal of Geometry, 8 (1–2): 171–186... | Rudolf Halin | 0.79866 |
86,072 | In the usual cumulative hierarchy Vα of ZFC set theory (for ordinals α), any one of the sets Vα for α a limit ordinal larger than the first infinite ordinal ω (such as Vω·2) forms a model of Zermelo set theory. So the consistency of Zermelo set theory is a theorem of ZFC set theory. As V ω ⋅ 2 {\displaystyle V_{\omega ... | Zermelo set theory | 0.79866 |
86,073 | Asano contractions can be used in statistical physics to gain information about a system from its subsystems. For example, suppose we have a system with a finite set Λ {\displaystyle \Lambda } of particles with magnetic spin either 1 or -1. For each site, we have a complex variable z x {\displaystyle z_{x}} Then we can... | Asano contraction | 0.79866 |
86,074 | Its PHOENIX software delivered "virtual classrooms" to many corporate networks. Pathlore was acquired by SumTotal Systems in 2005. The National Science Foundation releases its evaluation of the MITRE TICCIT project demonstration, giving a mixed review of the success of using the computer-television system as the primar... | History of virtual learning environments | 0.79866 |
86,075 | In contrast to the above mechanisms, a delivery with magnetic fields does not strongly depend on the biochemistry of the brain. In this case, nanoparticles are literally pulled across the BBB via application of a magnetic field gradient. The nanoparticles can be pulled in as well as removed from the brain merely by con... | Nanoparticles for drug delivery to the brain | 0.798659 |
86,076 | The Weierstrass–Erdmann condition is a mathematical result from the calculus of variations, which specifies sufficient conditions for broken extremals (that is, an extremal which is constrained to be smooth except at a finite number of "corners"). | Weierstrass–Erdmann condition | 0.798659 |
86,077 | Allen studied the Natural Sciences Tripos at the University of Cambridge, graduating with a Bachelor of Arts (BA) and Master of Science (MSci) degrees in 1999. She was an undergraduate student at Emmanuel College, Cambridge. She moved to America for further postgraduate study, earning another master's degree (MS) in ch... | Rosalind J. Allen | 0.798658 |
86,078 | In neuroscience, repolarization refers to the change in membrane potential that returns it to a negative value just after the depolarization phase of an action potential which has changed the membrane potential to a positive value. The repolarization phase usually returns the membrane potential back to the resting memb... | Repolarization | 0.798658 |
86,079 | Dyson and Lenard did not consider the extreme magnetic or gravitational forces that occur in some astronomical objects. In 1995 Elliott Lieb and coworkers showed that the Pauli principle still leads to stability in intense magnetic fields such as in neutron stars, although at a much higher density than in ordinary matt... | Pauli exclusive principle | 0.798658 |
86,080 | After a one-year study in aircraft design at Tsinghua University, he left Mainland China in August 1935 and went to the Massachusetts Institute of Technology (MIT) for a master's program in mechanical engineering. He received a Master of Science in aeronautical engineering from MIT on 18 December 1936.While at MIT, he ... | Qian Xuesen | 0.798658 |
86,081 | CALET is an astrophysics mission that searches for signatures of dark matter and provides the highest energy direct measurements of the cosmic ray electron spectrum in order to observe discrete sources of high-energy particle acceleration in our local region of the galaxy. The mission was developed and sponsored by the... | Calorimetric Electron Telescope | 0.798657 |
86,082 | The precise mathematical expression for a statistical ensemble depends on the kind of mechanics under consideration—quantum or classical—since the notion of a "microstate" is considerably different in these two cases. In quantum mechanics, the canonical ensemble affords a simple description since diagonalization provid... | Gibbs canonical ensemble | 0.798657 |
86,083 | Thus, in the presence of matter, space-time becomes non-Euclidean, resolving the apparent conflict between Newton's proof of the conservation of angular momentum and Einstein's theory of special relativity.Mach's question regarding the bulging of rotating bodies is resolved because local space-time geometry is informin... | Action at a distance | 0.798656 |
86,084 | This equivalence relation is an abstraction of the germ equivalence described above. Interpreting germs through sheaves also gives a general explanation for the presence of algebraic structures on sets of germs. The reason is that formation of stalks preserves finite limits. This implies that if T is a Lawvere theory a... | Set germ | 0.798656 |
86,085 | So π is unitarily equivalent to a subrepresentation of πg ⊕ πg' . This shows that π is irreducible if and only if any such πg is unitarily equivalent to π, i.e. g is a scalar multiple of f, which proves the theorem. Extremal states are usually called pure states. Note that a state is a pure state if and only if it is e... | GNS theorem | 0.798656 |
86,086 | The book is generally acknowledged as a key element in awakening the genius of Ramanujan.Carr acknowledged the main sources of his book in its preface: ... In the Algebra, Theory of Equations, and Trigonometry sections, I am largely indebted to Todhunter's well-known treatises ... In the section entitled Elementary Geo... | Synopsis of Pure Mathematics | 0.798656 |
86,087 | Klein-Seetharaman was born in Germany. She completed her undergraduate training at the University of Cologne, where she earned dual honours in biology and chemistry. After earning her doctorate, she moved to the United States, where she worked in the laboratory of Har Gobind Khorana at the Massachusetts Institute of Te... | Judith Klein-Seetharaman | 0.798656 |
86,088 | (E. Nelson ) During the renaissance, particularly with Bruno, actual infinity transfers from God to the world. The finite world models of contemporary science clearly show how this power of the idea of actual infinity has ceased with classical (modern) physics. Under this aspect, the inclusion of actual infinity into m... | Actual infinite | 0.798656 |
86,089 | These can all be constructed with Clifford algebra using an invertible form 3 e 1234567 ± φ {\displaystyle 3e_{1234567}\pm \varphi } for octonions. For other signed variations of φ {\displaystyle \varphi } , this form has remainders that classify 6 other non-associative algebras that show partial G 2 {\displaystyle G_{... | G2 (mathematics) | 0.798656 |
86,090 | 351, 351 (1976).Flory, Paul J. (1992). Principles of polymer chemistry (15. pr. | List of important publications in physics | 0.798656 |
86,091 | The Human Protein Atlas (HPA) is a Swedish-based program started in 2003 with the aim to map all the human proteins in cells, tissues and organs using integration of various omics technologies, including antibody-based imaging, mass spectrometry-based proteomics, transcriptomics and systems biology. All the data in the... | Human Protein Atlas | 0.798655 |
86,092 | In the United States, high school biology textbooks devote only 15% of their content to plants. In many societies, there is not thought to be a comprehensive understanding among citizens of the complexity behind plants' behaviors, reactions, and movements. The pervasive misunderstanding of evolution as a linear mechani... | Plant blindness | 0.798654 |
86,093 | Suppose V is a subset of R n {\displaystyle \mathbb {R} ^{n}} (in the case of n = 3, V represents a volume in 3D space) which is compact and has a piecewise smooth boundary S (also indicated with ∂V = S ). If F is a continuously differentiable vector field defined on a neighborhood of V, then the divergence theorem say... | Spatial geometry | 0.798654 |
86,094 | In organic chemistry, creation of 2D periodic network structures has been a dream for decades. Another noteworthy approach is "on-surface polymerization" whereby 2DPs with lateral dimensions not exceeding some tens of nanometers were reported. | Two-dimensional polymer | 0.798653 |
86,095 | Difficulty in categorisation of nano-weapons, and their intended purposes (defensive or offensive) compromises the balance of stability and trust in the global environment. "A lack of transparency about an emerging technology not only negatively effects public perception but also negatively impacts the perceived balanc... | Nanotechnology in warfare | 0.798653 |
86,096 | Gauss, Bolyai and Lobachevsky independently discovered them 100 years later. Their research uncovered two types of spaces whose geometric structures differ from that of classical Euclidean space; these gave rise to hyperbolic geometry and elliptic geometry. In the modern theory of manifolds, these notions correspond to... | Boundary of a manifold | 0.798653 |
86,097 | Hans-Joachim Nastold (13 July 1929 – 26 January 2004) was a German mathematician, who made notable contributions to algebra and number theory. Born in Stuttgart, Nastold earned his Abitur in Göppingen. He attended the University of Heidelberg, earning his doctorate in 1957, under supervision of Friedrich Karl Schmidt. | Hans-Joachim Nastold | 0.798653 |
86,098 | The chemistry of concrete degradation is quite complex and only the chemistry relating to calcium carbonate deposition is considered in . Calcium is also part of other hydration products in concrete, such as calcium aluminium hydrates and calcium aluminium iron hydrate. | Calthemite | 0.798653 |
86,099 | The basic result is that (over an algebraically closed field), the commuting matrices A , B {\displaystyle A,B} or more generally A 1 , … , A k {\displaystyle A_{1},\ldots ,A_{k}} are simultaneously triangularizable. This can be proven by first showing that commuting matrices have a common eigenvector, and then inducti... | Triangular matrix | 0.798652 |
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