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9,000 | The magnetic monopole in the quantum theory of magnetic charge started with a paper by the physicist Paul A.M. Dirac in 1931. The detection of magnetic monopoles is an open problem in experimental physics. | History of electromagnetic theory | 0.820773 |
9,001 | Meitner, and her nephew Otto Robert Frisch, correctly interpreted these results as being nuclear fission. Frisch confirmed this experimentally on 13 January 1939. In 1944, Hahn received the Nobel Prize in Chemistry for the discovery of nuclear fission. | History of electromagnetic theory | 0.820773 |
9,002 | At higher orders in the series infinities emerged, making such computations meaningless and casting serious doubts on the internal consistency of the theory itself. With no solution for this problem known at the time, it appeared that a fundamental incompatibility existed between special relativity and quantum mechanic... | History of electromagnetic theory | 0.820773 |
9,003 | (Einstein 1905b) His paper on the electrodynamics of moving bodies introduced the radical theory of special relativity, which showed that the observed independence of the speed of light on the observer's state of motion required fundamental changes to the notion of simultaneity. Consequences of this include the time-sp... | History of electromagnetic theory | 0.820773 |
9,004 | In 1864 James Clerk Maxwell of Edinburgh announced his electromagnetic theory of light, which was perhaps the greatest single step in the world's knowledge of electricity. Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/6 when On Faraday's lines of force was read to the Camb... | History of electromagnetic theory | 0.820773 |
9,005 | George Green wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism in 1828. The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what... | History of electromagnetic theory | 0.820773 |
9,006 | When the heat of a lamp is applied to the junction of the copper and bismuth an electric current is set up which deflects the needle.Around this time, Siméon Denis Poisson attacked the difficult problem of induced magnetization, and his results, though differently expressed, are still the theory, as a most important fi... | History of electromagnetic theory | 0.820773 |
9,007 | These experiments were the beginning of electrochemistry, the investigation of which Faraday took up, and concerning which in 1833 he announced his important law of electrochemical equivalents, viz.: "The same quantity of electricity — that is, the same electric current — decomposes chemically equivalent quantities of ... | History of electromagnetic theory | 0.820773 |
9,008 | A Grand Unified Theory (GUT) is a model in particle physics in which, at high energy, the electromagnetic force is merged with the other two gauge interactions of the Standard Model, the weak and strong nuclear forces. Many candidates have been proposed, but none is directly supported by experimental evidence. GUTs are... | History of electromagnetic theory | 0.820773 |
9,009 | Main purpose of the COSINE ETN is the development of ab-initio research tools to study optical properties and excited electronic states, which are dominated by electron correlation. This tools are developed for the investigation of organic photochemistry with the aim of accurate simulation of spectroscopic experiments ... | Computational Spectroscopy In Natural Sciences and Engineering | 0.820767 |
9,010 | COmputational Spectroscopy In Natural Sciences and Engineering (COSINE) is a Marie Skłodowska-Curie Innovative Training Network. in the field of theoretical and computational chemistry, focused on Computational Spectroscopy. The developing of theoretical tools is the main goal of the projects: computational codes based... | Computational Spectroscopy In Natural Sciences and Engineering | 0.820767 |
9,011 | In order to formalize patterns I utilized everything from linguistics to holography ... The models that constitute NLP are all formal models based on mathematical, logical principles such as predicate calculus and the mathematical equations underlying holography." However, there is no mention of the mathematics of holo... | Neuro-linguistic programming | 0.82076 |
9,012 | "Surveys in the academic community have shown NLP to be widely discredited among scientists. Among the reasons for considering NLP a pseudoscience are that evidence in favor of it is limited to anecdotes and personal testimony, that it is not informed by scientific understanding of neuroscience and linguistics, and tha... | Neuro-linguistic programming | 0.82076 |
9,013 | Macromonomers incorporating HEMA can be effective in the dispersion of pigments in the paints. The chemistry is very effective under emulsion polymerisation conditions and has been used in the printing industry since 2000. The vinylic end group acts as an addition fragmentation agent and has been utilised to make multi... | Catalytic Chain Transfer | 0.820757 |
9,014 | For a less trivial example of the point made by Example 2, consider a Venn diagram formed by n closed curves partitioning the diagram into 2n regions, and let X be the (infinite) set of all points in the plane not on any curve but somewhere within the diagram. The interior of each region is thus an infinite subset of X... | Logic operation | 0.820748 |
9,015 | Example 2. The empty set and X. This two-element algebra shows that a concrete Boolean algebra can be finite even when it consists of subsets of an infinite set. It can be seen that every field of subsets of X must contain the empty set and X. Hence no smaller example is possible, other than the degenerate algebra obta... | Logic operation | 0.820748 |
9,016 | Hence modern authors allow the degenerate Boolean algebra and let X be empty.) Example 1. The power set 2X of X, consisting of all subsets of X. Here X may be any set: empty, finite, infinite, or even uncountable. | Logic operation | 0.820748 |
9,017 | A concrete Boolean algebra or field of sets is any nonempty set of subsets of a given set X closed under the set operations of union, intersection, and complement relative to X. (As an aside, historically X itself was required to be nonempty as well to exclude the degenerate or one-element Boolean algebra, which is the... | Logic operation | 0.820748 |
9,018 | In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition A is logically equivalent to not (not-A), or by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence an... | Double negation introduction | 0.820748 |
9,019 | The complement operation is defined by the following two laws. Complementation 1 x ∧ ¬ x = 0 Complementation 2 x ∨ ¬ x = 1 {\displaystyle {\begin{aligned}&{\text{Complementation 1}}&x\wedge \neg x&=0\\&{\text{Complementation 2}}&x\vee \neg x&=1\end{aligned}}} All properties of negation including the laws below follow f... | Logic operation | 0.820748 |
9,020 | The 256-element free Boolean algebra on three generators is deployed in computer displays based on raster graphics, which use bit blit to manipulate whole regions consisting of pixels, relying on Boolean operations to specify how the source region should be combined with the destination, typically with the help of a th... | Logic operation | 0.820748 |
9,021 | The dividend puzzle is a concept in finance in which companies that pay dividends are rewarded by investors with higher valuations, even though, according to many economists, it should not matter to investors whether a firm pays dividends or not. The reasoning goes that dividends, from the investor’s point of view, sho... | Dividend puzzle | 0.820744 |
9,022 | It comes with many predefined styles, but installing a new style can be somewhat complicated.The developer of Scientific WorkPlace, MacKichan Software, Inc., announced on June 30, 2021 that it had ceased business and would no longer sell licenses to its software. Existing licenses would remain valid, but new installs w... | Scientific WorkPlace | 0.820738 |
9,023 | Scientific WorkPlace (often abbreviated to SWP) is a software package for scientific word processing on Microsoft Windows and OS X. Although advertised as a WYSIWYG LaTeX-based word processor, it is actually a graphical user interface for editing LaTeX source files with the same ease-of-use of a word processor, while m... | Scientific WorkPlace | 0.820738 |
9,024 | Natural-language understanding (NLU) or natural-language interpretation (NLI) is a subtopic of natural-language processing in artificial intelligence that deals with machine reading comprehension. Natural-language understanding is considered an AI-hard problem.There is considerable commercial interest in the field beca... | Natural language understanding | 0.820737 |
9,025 | In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them. A related notion is the circuit complexity of a recursive language that is decided by a uniform family of... | Circuit class | 0.820734 |
9,026 | This work has excited great interest because it might enable experimental verification of the basic concept of Hawking radiation, which is widely regarded as one of the most revolutionary proposals in twentieth century physics, but which in its gravitational incarnation seems to be impossible to verify in experiments i... | Polarizable vacuum | 0.820731 |
9,027 | According to mainstream physics, their claims rest upon incorrect computations using quantum field theory. Recent work, motivated in large part by the discoveries of the Unruh effect, Hawking radiation, and black hole thermodynamics, to work out a complete theory of physical analogues such as optical black holes. This ... | Polarizable vacuum | 0.820731 |
9,028 | The 1967 proposal of Andrei Sakharov that gravitation might arise from underlying quantum field theory effects, in a manner somewhat analogous to the way that the (simple) classical theory of elasticity arises from (complicated) particle physics. This work is generally regarded as mainstream and not entirely implausibl... | Polarizable vacuum | 0.820731 |
9,029 | Puthoff himself has apparently offered various characterizations of his proposal, which has been variously characterized as an attempt to reformulate general relativity in terms of a purely formal analogy with the propagation of light through an optical medium, an attempt to replace general relativity with a scalar the... | Polarizable vacuum | 0.820731 |
9,030 | In theoretical physics, particularly fringe physics, polarizable vacuum (PV) and its associated theory refers to proposals by Harold Puthoff, Robert H. Dicke, and others to develop an analogue of general relativity to describe gravity and its relationship to electromagnetism. | Polarizable vacuum | 0.820731 |
9,031 | In two-player zero-sum games, the minimax solution is the same as the Nash equilibrium. In the context of zero-sum games, the minimax theorem is equivalent to: For every two-person, zero-sum game with finitely many strategies, there exists a value V and a mixed strategy for each player, such that (a) Given Player 2's s... | Minimax solution | 0.820718 |
9,032 | Explicitly, with ( α , β , u ) {\displaystyle ({\boldsymbol {\alpha }},{\boldsymbol {\beta }},\mathbf {u} )} a right-handed orthonormal basis, R u ( θ ) α = cos ( θ ) α + sin ( θ ) β , R u ( θ ) β = − sin ( θ ) α + cos ( θ ) β , R u ( θ ) u = u . {\displaystyle R_{\mathbf {u} }(\theta ){\boldsymbol {\alpha }}=\... | Rotation matrix | 0.820709 |
9,033 | The matrices in the Lie algebra are not themselves rotations; the skew-symmetric matrices are derivatives, proportional differences of rotations. An actual "differential rotation", or infinitesimal rotation matrix has the form I + A d θ , {\displaystyle I+A\,d\theta ,} where dθ is vanishingly small and A ∈ so(n), for i... | Rotation matrix | 0.820709 |
9,034 | In Euclidean geometry, a rotation is an example of an isometry, a transformation that moves points without changing the distances between them. Rotations are distinguished from other isometries by two additional properties: they leave (at least) one point fixed, and they leave "handedness" unchanged. In contrast, a tra... | Rotation matrix | 0.820709 |
9,035 | Connecting the Lie algebra to the Lie group is the exponential map, which is defined using the standard matrix exponential series for eA For any skew-symmetric matrix A, exp(A) is always a rotation matrix.An important practical example is the 3 × 3 case. In rotation group SO(3), it is shown that one can identify every ... | Rotation matrix | 0.820709 |
9,036 | A prime example – in mathematics and physics – would be the theory of spherical harmonics. Their role in the group theory of the rotation groups is that of being a representation space for the entire set of finite-dimensional irreducible representations of the rotation group SO(3). For this topic, see Rotation group SO... | Rotation matrix | 0.820709 |
9,037 | Below follow some basic facts about the role of the collection of all rotation matrices of a fixed dimension (here mostly 3) in mathematics and particularly in physics where rotational symmetry is a requirement of every truly fundamental law (due to the assumption of isotropy of space), and where the same symmetry, whe... | Rotation matrix | 0.820709 |
9,038 | Despite the small dimension, we actually have considerable freedom in the sequence of axis pairs we use; and we also have some freedom in the choice of angles. Thus we find many different conventions employed when three-dimensional rotations are parameterized for physics, or medicine, or chemistry, or other disciplines... | Rotation matrix | 0.820709 |
9,039 | The Lie algebra so(n) of SO(n) is given by s o ( n ) = o ( n ) = { X ∈ M n ( R ) ∣ X = − X T } , {\displaystyle {\mathfrak {so}}(n)={\mathfrak {o}}(n)=\left\{X\in M_{n}(\mathbb {R} )\mid X=-X^{\mathsf {T}}\right\},} and is the space of skew-symmetric matrices of dimension n, see classical group, where o(n) is the Lie a... | Rotation matrix | 0.820709 |
9,040 | It is compact and connected, but not simply connected. It is also a semi-simple group, in fact a simple group with the exception SO(4). The relevance of this is that all theorems and all machinery from the theory of analytic manifolds (analytic manifolds are in particular smooth manifolds) apply and the well-developed ... | Rotation matrix | 0.820709 |
9,041 | The n × n rotation matrices for each n form a group, the special orthogonal group, SO(n). This algebraic structure is coupled with a topological structure inherited from GL n ( R ) {\displaystyle \operatorname {GL} _{n}(\mathbb {R} )} in such a way that the operations of multiplication and taking the inverse are anal... | Rotation matrix | 0.820709 |
9,042 | Since matrix multiplication has no effect on the zero vector (the coordinates of the origin), rotation matrices describe rotations about the origin. Rotation matrices provide an algebraic description of such rotations, and are used extensively for computations in geometry, physics, and computer graphics. In some litera... | Rotation matrix | 0.820709 |
9,043 | In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = {\displaystyle R={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}} rotates points in the xy plane countercloc... | Rotation matrix | 0.820709 |
9,044 | In general, we obtain the equation 0 = 2 ( Q − M ) + 2 Q Y , {\displaystyle 0=2(Q-M)+2QY,} so that M = Q ( I + Y ) = Q S , {\displaystyle M=Q(I+Y)=QS,} where Q is orthogonal and S is symmetric. To ensure a minimum, the Y matrix (and hence S) must be positive definite. Linear algebra calls QS the polar decomposition of ... | Rotation matrix | 0.820709 |
9,045 | If the n × n matrix M is nonsingular, its columns are linearly independent vectors; thus the Gram–Schmidt process can adjust them to be an orthonormal basis. Stated in terms of numerical linear algebra, we convert M to an orthogonal matrix, Q, using QR decomposition. However, we often prefer a Q closest to M, which thi... | Rotation matrix | 0.820709 |
9,046 | Complexity of conversion escalates with Euler angles (used here in the broad sense). The first difficulty is to establish which of the twenty-four variations of Cartesian axis order we will use. Suppose the three angles are θ1, θ2, θ3; physics and chemistry may interpret these as Q ( θ 1 , θ 2 , θ 3 ) = Q z ( θ 1 ) Q y... | Rotation matrix | 0.820709 |
9,047 | More importantly in applications to physics, the corresponding spin representation of the Lie algebra sits inside the Clifford algebra. It can be exponentiated in the usual way to give rise to a 2-valued representation, also known as projective representation of the rotation group. This is the case with SO(3) and SU(2)... | Rotation matrix | 0.820709 |
9,048 | The coverings are all two-to-one, with SO(n), n > 2, having fundamental group Z2. The natural setting for these groups is within a Clifford algebra. One type of action of the rotations is produced by a kind of "sandwich", denoted by qvq∗. | Rotation matrix | 0.820709 |
9,049 | Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle — the amount of rotation about that axis (Euler rotation theorem). There are several methods to compute the axis and angle from a rotation matrix (see also axis–angle representation). Here, w... | Rotation matrix | 0.820709 |
9,050 | Sets and proper classes. These include Von Neumann–Bernays–Gödel set theory, which has the same strength as ZFC for theorems about sets alone, and Morse–Kelley set theory and Tarski–Grothendieck set theory, both of which are stronger than ZFC.The above systems can be modified to allow urelements, objects that can be me... | Transfinite set theory | 0.820705 |
9,051 | The work of Zermelo in 1908 and the work of Abraham Fraenkel and Thoralf Skolem in 1922 resulted in the set of axioms ZFC, which became the most commonly used set of axioms for set theory. The work of analysts, such as that of Henri Lebesgue, demonstrated the great mathematical utility of set theory, which has since be... | Transfinite set theory | 0.820705 |
9,052 | Mathematical topics typically emerge and evolve through interactions among many researchers. Set theory, however, was founded by a single paper in 1874 by Georg Cantor: "On a Property of the Collection of All Real Algebraic Numbers".Since the 5th century BC, beginning with Greek mathematician Zeno of Elea in the West a... | Transfinite set theory | 0.820705 |
9,053 | For example, properties of the natural and real numbers can be derived within set theory, as each number system can be identified with a set of equivalence classes under a suitable equivalence relation whose field is some infinite set.Set theory as a foundation for mathematical analysis, topology, abstract algebra, and... | Transfinite set theory | 0.820705 |
9,054 | Many mathematical concepts can be defined precisely using only set theoretic concepts. For example, mathematical structures as diverse as graphs, manifolds, rings, vector spaces, and relational algebras can all be defined as sets satisfying various (axiomatic) properties. Equivalence and order relations are ubiquitous ... | Transfinite set theory | 0.820705 |
9,055 | Besides its foundational role, set theory also provides the framework to develop a mathematical theory of infinity, and has various applications in computer science (such as in the theory of relational algebra), philosophy and formal semantics. Its foundational appeal, together with its paradoxes, its implications for ... | Transfinite set theory | 0.820705 |
9,056 | Pharmacogenetics play an increasingly important role in antineoplastic treatment. Rapid sequencing technologies can identify genetic markers for treatment sensitivity and potential resistance. Certain markers are more representative and more likely to be used clinically.When BRCA1 and BRCA2 are missing, as in 5 percent... | Antineoplastic resistance | 0.820698 |
9,057 | There are always vacuum fluctuations of the electromagnetic field, according to quantum mechanics. Due to such fluctuations degeneracy between states of the same j but different l is lifted, giving them slightly different energies. This has been demonstrated in the famous Lamb–Retherford experiment and was the starting... | Hydrogen atom | 0.820696 |
9,058 | Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers. According to the usual rules of quantum mechanics, the actual state of the electron may be any superposition of these states. This explains also why the choice of z {\displaystyle z} -axis for the directional quan... | Hydrogen atom | 0.820696 |
9,059 | Further, by applying special relativity to the elliptic orbits, Sommerfeld succeeded in deriving the correct expression for the fine structure of hydrogen spectra (which happens to be exactly the same as in the most elaborate Dirac theory). However, some observed phenomena, such as the anomalous Zeeman effect, remained... | Hydrogen atom | 0.820696 |
9,060 | For n = 1 {\displaystyle n=1} , the value is called the Rydberg unit of energy. It is related to the Rydberg constant R ∞ {\displaystyle R_{\infty }} of atomic physics by 1 Ry ≡ h c R ∞ . {\displaystyle 1\,{\text{Ry}}\equiv hcR_{\infty }.} | Hydrogen atom | 0.820696 |
9,061 | It also yields two other quantum numbers and the shape of the electron's wave function ("orbital") for the various possible quantum-mechanical states, thus explaining the anisotropic character of atomic bonds. The Schrödinger equation also applies to more complicated atoms and molecules. When there is more than one ele... | Hydrogen atom | 0.820696 |
9,062 | Attempts have also been made in the area of artificial intelligence research to create smaller, explicit, new proofs of mathematical theorems from the bottom up using automated reasoning techniques such as heuristic search. Such automated theorem provers have proved a number of new results and found new proofs for know... | Computer assisted proof | 0.820685 |
9,063 | A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof th... | Computer assisted proof | 0.820685 |
9,064 | It has been argued the term fundamental physical constant should be restricted to the dimensionless universal physical constants that currently cannot be derived from any other source; this stricter definition is followed here. However, the term fundamental physical constant has also been used occasionally to refer to ... | Dimensionless physical constant | 0.820681 |
9,065 | In the 1920s and 1930s, Arthur Eddington embarked upon extensive mathematical investigation into the relations between the fundamental quantities in basic physical theories, later used as part of his effort to construct an overarching theory unifying quantum mechanics and cosmological physics. For example, he speculate... | Dimensionless physical constant | 0.820681 |
9,066 | The original standard model of particle physics from the 1970s contained 19 fundamental dimensionless constants describing the masses of the particles and the strengths of the electroweak and strong forces. In the 1990s, neutrinos were discovered to have nonzero mass, and a quantity called the vacuum angle was found to... | Dimensionless physical constant | 0.820681 |
9,067 | Others denote this ratio by Ω Λ {\displaystyle \Omega _{\Lambda }} ; Q ≈ 10−5: The energy required to break up and disperse an instance of the largest known structures in the universe, namely a galactic cluster or supercluster, expressed as a fraction of the energy equivalent to the rest mass m of that structure, namel... | Dimensionless physical constant | 0.820681 |
9,068 | In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.The concept should not be confused with dimensionless numbers, that are not universally constan... | Dimensionless physical constant | 0.820681 |
9,069 | Then the fork of c {\displaystyle c} and d {\displaystyle d} is given by Another form of composition of relations, which applies to general n {\displaystyle n} -place relations for n ≥ 2 , {\displaystyle n\geq 2,} is the join operation of relational algebra. The usual composition of two binary relations as defined here... | Composition of relations | 0.820674 |
9,070 | In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R; S from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication, and its result is called a relative product. : 40 Function composition ... | Composition of relations | 0.820674 |
9,071 | In particular the forgetful functor from complete Boolean algebras to sets has no left adjoint, even though it is continuous and the category of Boolean algebras is small-complete. This shows that the "solution set condition" in Freyd's adjoint functor theorem is necessary. Given a set X, one can form the free Boolean ... | Complete Boolean algebra | 0.820673 |
9,072 | Unless the Axiom of Choice is relaxed, free complete boolean algebras generated by a set do not exist (unless the set is finite). More precisely, for any cardinal κ, there is a complete Boolean algebra of cardinality 2κ greater than κ that is generated as a complete Boolean algebra by a countable subset; for example th... | Complete Boolean algebra | 0.820673 |
9,073 | In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion, which is a complete Boolea... | Complete Boolean algebra | 0.820673 |
9,074 | Every subset of a complete Boolean algebra has a supremum, by definition; it follows that every subset also has an infimum (greatest lower bound). For a complete boolean algebra, both infinite distributive laws hold if and only if it is isomorphic to the powerset of some set. For a complete boolean algebra infinite de-... | Complete Boolean algebra | 0.820673 |
9,075 | The corresponding regular open algebra can be used to form Boolean-valued models which are then equivalent to generic extensions by the given forcing poset. The algebra of all measurable subsets of a σ-finite measure space, modulo null sets, is a complete Boolean algebra. When the measure space is the unit interval wit... | Complete Boolean algebra | 0.820673 |
9,076 | Every finite Boolean algebra is complete. The algebra of subsets of a given set is a complete Boolean algebra. The regular open sets of any topological space form a complete Boolean algebra. This example is of particular importance because every forcing poset can be considered as a topological space (a base for the top... | Complete Boolean algebra | 0.820673 |
9,077 | The completion of a Boolean algebra can be defined in several equivalent ways: The completion of A is (up to isomorphism) the unique complete Boolean algebra B containing A such that A is dense in B; this means that for every nonzero element of B there is a smaller non-zero element of A. The completion of A is (up to i... | Complete Boolean algebra | 0.820673 |
9,078 | The algebra of all subsets of an infinite set that are finite or have finite complement is a Boolean algebra but is not complete. The algebra of all measurable subsets of a measure space is a ℵ1-complete Boolean algebra, but is not usually complete. Another example of a Boolean algebra that is not complete is the Boole... | Complete Boolean algebra | 0.820673 |
9,079 | Psychometrics addresses human abilities, attitudes, traits, and educational evolution. Notably, the study of behavior, mental processes, and abilities of non-human animals is usually addressed by comparative psychology, or with a continuum between non-human animals and the rest of animals by evolutionary psychology. No... | Psychometrics | 0.820672 |
9,080 | The origin of psychometrics also has connections to the related field of psychophysics. Around the same time that Darwin, Galton, and Cattell were making their discoveries, Herbart was also interested in "unlocking the mysteries of human consciousness" through the scientific method. Herbart was responsible for creating... | Psychometrics | 0.820672 |
9,081 | The committee's report highlighted the importance of the definition of measurement. While Stevens's response was to propose a new definition, which has had considerable influence in the field, this was by no means the only response to the report. Another, notably different, response was to accept the classical definiti... | Psychometrics | 0.820672 |
9,082 | The classic applications of bipolar coordinates are in solving partial differential equations, e.g., Laplace's equation or the Helmholtz equation, for which bipolar coordinates allow a separation of variables (in 2D). A typical example would be the electric field surrounding two parallel cylindrical conductors. | Bipolar cylindrical coordinates | 0.820671 |
9,083 | Plant hormones play an important part in the process, with the gibberellins having a particularly important role.There are many signals that regulate the molecular biology of the process. The following three genes in Arabidopsis thaliana possess both common and independent functions in floral transition: FLOWERING LOCU... | ABC model of flower development | 0.820668 |
9,084 | Soltis, DE; Soltis, PS; Leebens-Mack, J, eds. (2006). Advances in botanical research: Developmental genetics of the flower. New York, NY: Academic Press. | ABC model of flower development | 0.820668 |
9,085 | Project Physics course work was broken into six main subject areas, organized into separate books each called a "Project Physics Text and Handbook" or "Student Guide": Concepts of Motion Motion in the Heavens The Triumph of Mechanics Light and Electromagnetism Models of the Atom The NucleusThe books presented the mater... | Harvard Project Physics | 0.820668 |
9,086 | The project was active from 1962 to 1972, and produced the Project Physics series of texts, which were used in physics classrooms in the 1970s and 1980s. The project was centered at Harvard University, but drew from schools and educators from across the country. The directors of this project were: F. James Rutherford, ... | Harvard Project Physics | 0.820668 |
9,087 | Harvard Project Physics, also called Project Physics, was a national curriculum development project to create a secondary school physics education program in the United States during the Cold War era. | Harvard Project Physics | 0.820668 |
9,088 | Harvard Project Physics publications and reports, 1962-1982, Niels Bohr Library & Archives | Harvard Project Physics | 0.820668 |
9,089 | The course readers allowed students to further explore a topic, and lab exercises enabled students to verify that their understanding was confirmed by experimental outcomes. Special lab equipment, brief film loops, films, and a teacher's guide were also developed. The texts and all other aids are now available for free... | Harvard Project Physics | 0.820668 |
9,090 | Project Physics course work was broken into six main subject areas, organized into separate books each called a "Project Physics Text and Handbook" or "Student Guide": Concepts of Motion Motion in the Heavens The Triumph of Mechanics Light and Electromagnetism Models of the Atom The NucleusThe books presented the mater... | Harvard Project Physics | 0.820668 |
9,091 | The National Institutes of Health and pharmaceutical companies collectively contribute $26.4 billion and $27 billion, which constitute 28% and 29% of the total, respectively. Other significant contributors include biotechnology companies ($17.9 billion, 19% of total), medical device companies ($9.2 billion, 10% of tota... | Biomedical research | 0.820667 |
9,092 | As personalised medicine is practiced more widely, a number of challenges arise. The current approaches to intellectual property rights, reimbursement policies, patient privacy, data biases and confidentiality as well as regulatory oversight will have to be redefined and restructured to accommodate the changes personal... | Personalized Medicine | 0.820666 |
9,093 | It does not literally mean the creation of drugs or medical devices that are unique to a patient, but rather the ability to classify individuals into subpopulations that differ in their susceptibility to a particular disease, in the biology or prognosis of those diseases they may develop, or in their response to a spec... | Personalized Medicine | 0.820666 |
9,094 | That is, a homomorphism f: A → B {\displaystyle f\colon A\to B} is a split epimorphism if there exists a homomorphism g: B → A {\displaystyle g\colon B\to A} such that f ∘ g = Id B . {\displaystyle f\circ g=\operatorname {Id} _{B}.} A split epimorphism is always an epimorphism, for both meanings of epimorphism. For set... | Surjective homomorphism | 0.820662 |
9,095 | Every localization is a ring epimorphism, which is not, in general, surjective. As localizations are fundamental in commutative algebra and algebraic geometry, this may explain why in these areas, the definition of epimorphisms as right cancelable homomorphisms is generally preferred. A split epimorphism is a homomorph... | Surjective homomorphism | 0.820662 |
9,096 | Algebraic structures for which there exist non-surjective epimorphisms include semigroups and rings. The most basic example is the inclusion of integers into rational numbers, which is a homomorphism of rings and of multiplicative semigroups. For both structures it is a monomorphism and a non-surjective epimorphism, bu... | Surjective homomorphism | 0.820662 |
9,097 | A surjective homomorphism is always right cancelable, but the converse is not always true for algebraic structures. However, the two definitions of epimorphism are equivalent for sets, vector spaces, abelian groups, modules (see below for a proof), and groups. The importance of these structures in all mathematics, espe... | Surjective homomorphism | 0.820662 |
9,098 | In algebra, epimorphisms are often defined as surjective homomorphisms. : 134: 43 On the other hand, in category theory, epimorphisms are defined as right cancelable morphisms. This means that a (homo)morphism f: A → B {\displaystyle f:A\to B} is an epimorphism if, for any pair g {\displaystyle g} , h {\displaystyle h}... | Surjective homomorphism | 0.820662 |
9,099 | That is, a homomorphism f: A → B {\displaystyle f\colon A\to B} is a split monomorphism if there exists a homomorphism g: B → A {\displaystyle g\colon B\to A} such that g ∘ f = Id A . {\displaystyle g\circ f=\operatorname {Id} _{A}.} A split monomorphism is always a monomorphism, for both meanings of monomorphism. For ... | Surjective homomorphism | 0.820662 |
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