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22,100 | However, not all pointed pseudotriangulations can be formed in this way. Aichholzer et al. (2004) show that a set of n points, h of which belong to the convex hull of the set, must have at least Ch−2×3n−h different pointed pseudotriangulations, where Ci denotes the ith Catalan number. As a consequence, they show that t... | Pointed pseudotriangulation | 0.809701 |
22,101 | Qalculate! supports common mathematical functions and operations, multiple bases, autocompletion, complex numbers, infinite numbers, arrays and matrices, variables, mathematical and physical constants, user-defined functions, symbolic derivation and integration, solving of equations involving unknowns, uncertainty prop... | Qalculate! | 0.80969 |
22,102 | In the study of combinatorial optimization problems, bin packing problems involve an input sequence of items with fractional sizes, which must be placed into bins whose capacity (the total size of items placed into each bin) is one. Research into these problems has included the study of restricted bin packing problems ... | Unit fractions | 0.80969 |
22,103 | Known uses of magnetic levitation include maglev trains, contactless melting, magnetic bearings, and for product display purposes. Moreover, recently magnetic levitation has been approached in the field of microbotics. | Magnetic levitation device | 0.809689 |
22,104 | For successful levitation and control of all 6 axes (degrees of freedom; 3 translational and 3 rotational) a combination of permanent magnets and electromagnets or diamagnets or superconductors as well as attractive and repulsive fields can be used. From Earnshaw's theorem at least one stable axis must be present for t... | Magnetic levitation device | 0.809689 |
22,105 | Axonometry is a graphical procedure belonging to descriptive geometry that generates a planar image of a three-dimensional object. The term "axonometry" means "to measure along axes", and indicates that the dimensions and scaling of the coordinate axes play a crucial role. The result of an axonometric procedure is a un... | Axonometry | 0.809687 |
22,106 | Pohlke's theorem is the basis for the following procedure to construct a scaled parallel projection of a three-dimensional object: Select projections of the coordinate axes, such that all three coordinate axes are not collapsed to a single point or line. Usually the z-axis is vertical. Select for these projections the ... | Axonometry | 0.809687 |
22,107 | Fields can be constructed inside a given bigger container field. Suppose given a field E, and a field F containing E as a subfield. For any element x of F, there is a smallest subfield of F containing E and x, called the subfield of F generated by x and denoted E(x). The passage from E to E(x) is referred to by adjoini... | Field theory (mathematics) | 0.809685 |
22,108 | Differential fields are fields equipped with a derivation, i.e., allow to take derivatives of elements in the field. For example, the field R(X), together with the standard derivative of polynomials forms a differential field. These fields are central to differential Galois theory, a variant of Galois theory dealing wi... | Field theory (mathematics) | 0.809685 |
22,109 | Basic invariants of a field F include the characteristic and the transcendence degree of F over its prime field. The latter is defined as the maximal number of elements in F that are algebraically independent over the prime field. Two algebraically closed fields E and F are isomorphic precisely if these two data agree.... | Field theory (mathematics) | 0.809685 |
22,110 | That is to say, if x is algebraic, all other elements of E(x) are necessarily algebraic as well. Moreover, the degree of the extension E(x) / E, i.e., the dimension of E(x) as an E-vector space, equals the minimal degree n such that there is a polynomial equation involving x, as above. | Field theory (mathematics) | 0.809685 |
22,111 | A pivotal notion in the study of field extensions F / E are algebraic elements. An element x ∈ F {\displaystyle x\in F} is algebraic over E if it is a root of a polynomial with coefficients in E, that is, if it satisfies a polynomial equation en xn + en−1xn−1 + ⋯ + e1x + e0 = 0,with en, ..., e0 in E, and en ≠ 0. For ex... | Field theory (mathematics) | 0.809685 |
22,112 | A commutative ring is a set, equipped with an addition and multiplication operation, satisfying all the axioms of a field, except for the existence of multiplicative inverses a−1. For example, the integers Z form a commutative ring, but not a field: the reciprocal of an integer n is not itself an integer, unless n = ±1... | Field theory (mathematics) | 0.809685 |
22,113 | Let C be an algebraic curve defined over an algebraically closed field K, and let K(C) be the field of rational functions of C. The valuation on K(C) corresponding to a smooth point P ∈ C {\displaystyle P\in C} is defined as ord P ( f / g ) = ord P ( f ) − ord P ( g ) {\displaystyle \operatorname {ord} _{P}(f/g)=... | Local parameter | 0.809684 |
22,114 | In the geometry of complex algebraic curves, a local parameter for a curve C at a smooth point P is a meromorphic function on C that has a simple zero at P. This concept can be generalized to curves defined over fields other than C {\displaystyle \mathbb {C} } (or schemes), because the local ring at a smooth point P of... | Local parameter | 0.809684 |
22,115 | A real-world current source has a very high, but finite output impedance. In the case of transistor current sources, impedance of a few megohms (at low frequencies) is typical. Since no ideal sources of either variety exist (all real-world examples have finite and non-zero source impedance), any current source can be c... | Ideal voltage source | 0.809673 |
22,116 | In other words, any mathematical theorem, or result that holds for a regular random walk, will also hold for both A and B. Consider now a more elaborate example. Assume that A starts from the point (0,0) and B from (10,10). First couple them so that they walk together in the vertical direction, i.e. if A goes up, so do... | Coupling (probability) | 0.809672 |
22,117 | In probability theory, coupling is a proof technique that allows one to compare two unrelated random variables (distributions) X and Y by creating a random vector W whose marginal distributions correspond to X and Y respectively. The choice of W is generally not unique, and the whole idea of "coupling" is about making ... | Coupling (probability) | 0.809672 |
22,118 | Michael A. Jackson originally developed JSP in the 1970s. He documented the system in his 1975 book Principles of Program Design. In a 2001 conference talk, he provided a retrospective analysis of the original driving forces behind the method, and related it to subsequent software engineering developments. Jackson's ai... | Jackson Structured Programming | 0.809671 |
22,119 | Purely by use of this existence theorem I avoided the lengthy and unclear argumentation of Weierstrass and the highly complicated calculations of Dedekind, and in addition, I believe, only my proof uncovers the inner reason for the validity of the assertions adumbrated by Gauss and formulated by Weierstrass and Dedekin... | Brouwer–Hilbert controversy | 0.809669 |
22,120 | In the late 1890s Hilbert successfully axiomatized geometry. Then he went on to successfully (or so Hilbert thought) use the Cantorian-inspired notion of the completed infinity to produce elegant, radically abbreviated proofs in analysis (1896 and afterwards). In his own words of defense Hilbert believed himself quite ... | Brouwer–Hilbert controversy | 0.809669 |
22,121 | Rather, his recursion steps through integers assigned to variable k (cf his (2) on page 602). His skeleton-proof of Theorem V, however, "use(s) induction on the degree of φ", and uses "the induction hypothesis". Without a full proof of this, we are left to assume that his use of the "induction hypothesis" is the intuit... | Brouwer–Hilbert controversy | 0.809669 |
22,122 | The nature of Hilbert's proof of the Hilbert basis theorem from 1888 was controversial. Although Leopold Kronecker, a constructivist, had conceded, Hilbert would later respond to others' similar criticisms that "many different constructions are subsumed under one fundamental idea" — in other words (to quote Reid): "Thr... | Brouwer–Hilbert controversy | 0.809669 |
22,123 | Brouwer's insistence on "constructibility" in the search for a "consistency proof for arithmetic" resulted in sensitivity to the issue as reflected by the work of Finsler and Gödel. Ultimately Gödel would "numeralize" his formulae; Gödel then used primitive recursion (and its instantiation of the intuitive, constructiv... | Brouwer–Hilbert controversy | 0.809669 |
22,124 | Thus for all T, T would be provable by P or not provable by P and under all conditions (i.e. for any assignment of numerical values to T's variables). This is a perfect illustration of the use of the Law of Excluded Middle extended over the infinite, in fact extended twice – first over all theorems (formulas, procedure... | Brouwer–Hilbert controversy | 0.809669 |
22,125 | Brouwer viewed this loss of constructibility as bad, but worse when applied to a generalized "proof of consistency" for all of mathematics. In his 1900 address Hilbert had specified, as the second of his 23 problems for the twentieth century, the quest for a generalized proof of (procedure for determining) the consiste... | Brouwer–Hilbert controversy | 0.809669 |
22,126 | By 1910, he had published a number of important papers, in particular the fixed-point theorem. Hilbert admired Brouwer and helped him receive a regular academic appointment in 1912 at the University of Amsterdam. Then, Brouwer decided to return to intuitionism.In the later 1920s, Brouwer became involved in a public con... | Brouwer–Hilbert controversy | 0.809669 |
22,127 | The background for the controversy was set with David Hilbert's axiomatization of geometry in the late 1890s. In his biography of Kurt Gödel, John W. Dawson, Jr observed that "partisans of three principal philosophical positions took part in the debate" – the logicists (Gottlob Frege and Bertrand Russell), the formalis... | Brouwer–Hilbert controversy | 0.809669 |
22,128 | In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some "bad" topology, but can also be considered an algorithm in its own righ... | Asymptotic Decider | 0.809666 |
22,129 | Among other things, the company manufactures robotics that are used in the production of batteries and electronics. The firm works closely with universities within dual track studies of Mechanical Engineering and Robotic Process Automation. In addition, it provides training in the field of Technical Product Design, Ind... | Tesla Automation | 0.809664 |
22,130 | Now, if the change in lift distribution is known at given lift section, it is possible to predict how that section influences the lift over its neighbors: the vertical induced velocity (upwash or downwash, ω i {\displaystyle \omega _{i}} ) can be quantified using the velocity distribution within a vortex and related to... | Lifting-line theory | 0.809663 |
22,131 | The lifting-line theory applies the concept of circulation and the Kutta–Joukowski theorem, L ~ ( y ) = ρ V Γ ( y ) , {\displaystyle {\tilde {L}}_{(y)}=\rho V\Gamma _{(y)},} so that instead of the lift distribution function, the unknown effectively becomes the distribution of circulation over the span, Γ ( y ) {\displa... | Lifting-line theory | 0.809663 |
22,132 | However, it turns out that this approximation is grossly incorrect: on a real wing, the lift over each wing segment (local lift per unit span, l {\displaystyle l} or L ~ {\displaystyle {\tilde {L}}} ) does not correspond simply to what two-dimensional analysis predicts. In reality, the local amount of lift on each cros... | Lifting-line theory | 0.809663 |
22,133 | It is difficult to predict analytically the overall amount of lift that a wing of given geometry will generate. When analyzing a three-dimensional finite wing, the first approximation to understanding is to consider slicing the wing into cross-sections and analyzing each cross-section independently as a wing in a two-d... | Lifting-line theory | 0.809663 |
22,134 | (Based on.) Nomenclature: Γ {\displaystyle \ \Gamma } is the circulation over the entire wing (m²/s) C L {\displaystyle \ C_{L}} is the 3D lift coefficient (for the entire wing) A R {\displaystyle \ AR} is the aspect ratio α ∞ {\displaystyle \ \alpha _{\infty }} is the freestream angle of attack (rad) V ∞ {\displaystyl... | Lifting-line theory | 0.809663 |
22,135 | The Prandtl lifting-line theory is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing based on its geometry. It is also known as the Lanchester–Prandtl wing theory.The theory was expressed independently by Frederick W. Lanchester in 1907, and by Ludwig Prandtl in 1918–191... | Lifting-line theory | 0.809663 |
22,136 | The maximum power theorem applies to its "upstream" connection to the solar panel, so it emulates a load resistance equal to the solar panel source resistance. However, the maximum power theorem does not apply to its "downstream" connection. That connection is an impedance bridging connection; it emulates a high-voltag... | Impedance mismatch | 0.809663 |
22,137 | Whenever a source of power with a fixed output impedance such as an electric signal source, a radio transmitter or a mechanical sound (e.g., a loudspeaker) operates into a load, the maximum possible power is delivered to the load when the impedance of the load (load impedance or input impedance) is equal to the complex... | Impedance mismatch | 0.809663 |
22,138 | Terminologies have continued to evolve: in 2011, the National Academies updated the definition to include a large variety of dataified objects such as "spectrographic, genomic sequencing, and electron microscopy data; observational data, such as remote sensing, geospatial, and socioeconomic data; and other forms of dat... | Open science data | 0.809662 |
22,139 | Open scientific data or open research data is a type of open data focused on publishing observations and results of scientific activities available for anyone to analyze and reuse. A major purpose of the drive for open data is to allow the verification of scientific claims, by allowing others to look at the reproducibi... | Open science data | 0.809662 |
22,140 | In molecular biology, glycoside hydrolase family 101 is a family of glycoside hydrolases. Glycoside hydrolases EC 3.2.1. are a widespread group of enzymes that hydrolyse the glycosidic bond between two or more carbohydrates, or between a carbohydrate and a non-carbohydrate moiety. A classification system for glycoside ... | Glycoside hydrolase family 101 | 0.809662 |
22,141 | The International Journal of Applied Mathematics and Computer Science is a peer-reviewed quarterly scientific journal published since 1991 by the University of Zielona Góra in partnership with De Gruyter Poland and Lubuskie Scientific Society, under the auspices of the Committee on Automatic Control and Robotics of the... | International Journal of Applied Mathematics and Computer Science | 0.809661 |
22,142 | Therefore, as the capacitor charges or discharges, the voltage changes at a different rate than the galvani potential difference. In these situations, one cannot calculate capacitance merely by looking at the overall geometry and using Gauss's law. One must also take into account the band-filling / band-emptying effect... | Quantum capacitance | 0.809661 |
22,143 | The Galvani potential changes by Δ V galvani = Q / C g e o m {\displaystyle \Delta V_{\text{galvani}}=Q/C_{geom}} . Additionally, the internal chemical potential of electrons in the 2DEG changes by Δ μ internal = N / ρ = Q / ( ρ e ) {\displaystyle \Delta \mu _{\text{internal}}=N/\rho =Q/(\rho e)} , which is equivalent ... | Quantum capacitance | 0.809661 |
22,144 | Automotive engineering, along with aerospace engineering and naval architecture, is a branch of vehicle engineering, incorporating elements of mechanical, electrical, electronic, software, and safety engineering as applied to the design, manufacture and operation of motorcycles, automobiles, and trucks and their respec... | Automotive engineering | 0.809661 |
22,145 | Manufacturing engineers are responsible for ensuring proper production of the automotive components or complete vehicles. While the development engineers are responsible for the function of the vehicle, manufacturing engineers are responsible for the safe and effective production of the vehicle. This group of engineers... | Automotive engineering | 0.809661 |
22,146 | When considering elective genetic testing, it is important to take into account the type and goals of testing. Providers and patients should be familiar with differing testing methodologies the potential results from each test. For many individuals, factors such as test cost, scope, and deliverables, in combination wit... | Elective genetic and genomic testing | 0.80966 |
22,147 | Genetic testing for a variety of disorders has seen many advances starting with cytogenetics to evaluate human chromosomes for aneuploidy and other chromosome abnormalities. The development of molecular cytogenetics involving techniques such as fluorescence in situ hybridization (FISH) followed, permitting the detectio... | Elective genetic and genomic testing | 0.80966 |
22,148 | Due to their advanced training, genetic counselors have a unique set of skills. Their clinical and psychosocial skills are used to help patients understand their genetic risks, determine which tests are most appropriate for their needs, and explain what the possible test results could mean for both the patient and the ... | Elective genetic and genomic testing | 0.80966 |
22,149 | Pharmacogenomic tests (also called pharmacogenetics) provide information that can help predict how an individual will respond to a medication. Changes in certain genes affect drug pharmacodynamics (effects on drug receptors) and pharmacokinetics (drug uptake, distribution, and metabolism). Identifying these changes mak... | Elective genetic and genomic testing | 0.80966 |
22,150 | Mathematical methods developed to some degree of sophistication in ancient Egypt, Babylon, India, and China, apparently without employing the axiomatic method. Euclid of Alexandria authored the earliest extant axiomatic presentation of Euclidean geometry and number theory. His idea begins with five undeniable geometric... | Axiomatic theory | 0.80966 |
22,151 | Quadratic forms over the ring of integers are called integral quadratic forms, whereas the corresponding modules are quadratic lattices (sometimes, simply lattices). They play an important role in number theory and topology. An integral quadratic form has integer coefficients, such as x2 + xy + y2; equivalently, given ... | Signature of a quadratic form | 0.809658 |
22,152 | Using homogeneous coordinates, a non-zero quadratic form in n variables defines an (n−2)-dimensional quadric in the (n−1)-dimensional projective space. This is a basic construction in projective geometry. In this way one may visualize 3-dimensional real quadratic forms as conic sections. An example is given by the thre... | Signature of a quadratic form | 0.809658 |
22,153 | In the arithmetic theory of quadratic forms, the coefficients belong to a fixed commutative ring, frequently the integers Z or the p-adic integers Zp. Binary quadratic forms have been extensively studied in number theory, in particular, in the theory of quadratic fields, continued fractions, and modular forms. The theo... | Signature of a quadratic form | 0.809658 |
22,154 | Quadratic forms are homogeneous quadratic polynomials in n variables. In the cases of one, two, and three variables they are called unary, binary, and ternary and have the following explicit form: where a, ..., f are the coefficients.The theory of quadratic forms and methods used in their study depend in a large measur... | Signature of a quadratic form | 0.809658 |
22,155 | Although their definition involved a choice of basis and consideration of the corresponding real symmetric matrix A, Sylvester's law of inertia means that they are invariants of the quadratic form q. The quadratic form q is positive definite if q(v) > 0 (similarly, negative definite if q(v) < 0) for every nonzero vecto... | Signature of a quadratic form | 0.809658 |
22,156 | This means that A is a symmetric n × n matrix such that where x is the column vector of coordinates of v in the chosen basis. Under a change of basis, the column x is multiplied on the left by an n × n invertible matrix S, and the symmetric square matrix A is transformed into another symmetric square matrix B of the sa... | Signature of a quadratic form | 0.809658 |
22,157 | The particular normalization on the metric depends on the application. In Riemannian geometry, one uses a normalization so that the Fubini–Study metric simply relates to the standard metric on the (2n+1)-sphere. In algebraic geometry, one uses a normalization making CPn a Hodge manifold. | Fubini–Study metric | 0.809656 |
22,158 | The package runs on Unix and Unix-like (Linux) workstations, clusters of workstations, and on Windows in sequential mode. MDynaMix is developed at the Division of Physical Chemistry, Department of Materials and Environmental Chemistry, Stockholm University, Sweden. It is released as open-source software under a GNU Gen... | MDynaMix | 0.809656 |
22,159 | Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis, correspondence analysis (CA) and its derivatives (detrended correspondence analysis, canonical correspondence analysis, and redundancy analysi... | Gradient analysis | 0.809652 |
22,160 | In software engineering, a test case is a specification of the inputs, execution conditions, testing procedure, and expected results that define a single test to be executed to achieve a particular software testing objective, such as to exercise a particular program path or to verify compliance with a specific requirem... | Test case | 0.809652 |
22,161 | In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. | Triangulation | 0.809649 |
22,162 | The Medical Intelligence and Language Engineering Laboratory, also known as MILE lab, is a research laboratory at the Indian Institute of Science, Bangalore under the Department of Electrical Engineering. The lab is known for its work on Image processing, online handwriting recognition, Text-To-Speech and Optical chara... | Medical intelligence and language engineering lab | 0.809646 |
22,163 | The category Mod(T) of models of some first-order theory T with countable signature is ℵ 1 {\displaystyle \aleph _{1}} -accessible. ℵ 1 {\displaystyle \aleph _{1}} -presentable objects are models with a countable number of elements. Further examples of locally presentable categories are finitary algebraic categories (i... | Accessible object | 0.809644 |
22,164 | An emphasis on breadth, together with the inherently mathematical nature of theoretical computer science, means that BCTCS always actively solicits both computer scientists and mathematicians as participants at its annual Conference, and offers an environment within which the two communities can meet and exchange ideas... | British Colloquium for Theoretical Computer Science | 0.809644 |
22,165 | The purpose of BCTCS is: to provide a platform from which the interests and future well-being of British theoretical computer science may be advanced; to offer a forum in which UK-based researchers in all aspects of theoretical computer science can meet, present research findings, and discuss recent developments in the... | British Colloquium for Theoretical Computer Science | 0.809644 |
22,166 | The British Colloquium for Theoretical Computer Science (BCTCS) is an organisation, founded in 1985, that represents the interests of Theoretical Computer Science in the UK, e.g. through representation on academic boards and providing commentary and evidence in response to consultations from public bodies. The BCTCS op... | British Colloquium for Theoretical Computer Science | 0.809644 |
22,167 | Unit Operations of Chemical Engineering, first published in 1956, is one of the oldest chemical engineering textbooks still in widespread use. The current Seventh Edition, published in 2004, continues its successful tradition of being used as a textbook in university undergraduate chemical engineering courses. It is wi... | Unit Operations of Chemical Engineering | 0.809642 |
22,168 | The book starts with an introductory chapter devoted to definitions and principles. It then follows with 28 additional chapters, each covering a principal chemical engineering unit operation. The 28 chapters are grouped into four major sections: Fluid mechanics Heat transfer Mass transfer and equilibrium stages Operati... | Unit Operations of Chemical Engineering | 0.809642 |
22,169 | Sparse activation: For example, in a randomly initialized network, only about 50% of hidden units are activated (have a non-zero output). Better gradient propagation: Fewer vanishing gradient problems compared to sigmoidal activation functions that saturate in both directions. Efficient computation: Only comparison, ad... | Rectifier (neural networks) | 0.809641 |
22,170 | Squareplus is the function squareplus b ( x ) = x + x 2 + b 2 {\displaystyle \operatorname {squareplus} _{b}(x)={\frac {x+{\sqrt {x^{2}+b}}}{2}}} where b ≥ 0 {\displaystyle b\geq 0} is a hyperparameter that determines the "size" of the curved region near x = 0 {\displaystyle x=0} . (For example, letting b = 0 {\displ... | Rectifier (neural networks) | 0.809641 |
22,171 | It was later argued that it has strong biological motivations and mathematical justifications. In 2011 it was found to enable better training of deeper networks, compared to the widely used activation functions prior to 2011, e.g., the logistic sigmoid (which is inspired by probability theory; see logistic regression) ... | Rectifier (neural networks) | 0.809641 |
22,172 | In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the positive part of its argument: where x is the input to a neuron. This is also known as a ramp function and is analogous to half-wave rectification in electrical engine... | Rectifier (neural networks) | 0.809641 |
22,173 | The mirror circuit of Fig. 5 forces the drain current of M1 to equal the input current and the output configuration assures that the output current equals the drain current of M2. Expanding equation (8) in a two-variable Taylor series about i D 1 {\displaystyle \scriptstyle i_{D1}} and truncating after the first linear... | Wilson current mirror | 0.809641 |
22,174 | When the Wilson current mirror is used in CMOS circuits, it is usually in the four transistor form as in Fig. 5. If the transistor pairs M1-M2 and M3-M4 are exactly matched and the input and output potentials are approximately equal, then in principle there is no static error, the input and output currents are equal be... | Wilson current mirror | 0.809641 |
22,175 | Finally, the collector current in a bipolar transistor for low and moderate emitter currents conforms closely to the relation i C = I S C exp ( v B E V T ) {\displaystyle \scriptstyle i_{C}~=~I_{SC}\exp \left({\frac {v_{BE}}{V_{T}}}\right)} where V T = k T q {\displaystyle \scriptstyle V_{T}~=~{\frac {kT}{q}}} is the... | Wilson current mirror | 0.809641 |
22,176 | The zeta potential can be determined through measurement by sedimentation potential, as the concentration, conductivity of the suspension, density of the particle, and potential difference are known. By rotating the column 180 degrees, drift and geometry differences of the column can be ignored. ζ = η λ E s ε r ε 0 ( ρ... | Sedimentation potential | 0.809637 |
22,177 | In software engineering, a plain old CLR object, or plain old class object (POCO) is a simple object created in the .NET Common Language Runtime (CLR) that is unencumbered by inheritance or attributes. This is often used in opposition to the complex or specialized objects that object-relational mapping frameworks often... | Plain Old CLR Object | 0.809637 |
22,178 | While it's possible to estimate P ( Y = 1 | X ) {\displaystyle \mathbf {P} (\mathbf {Y} =1|\mathbf {X} )} using other statistical or machine learning methods, the requirements of simplicity and easy interpretation (and monotonicity per risk factor) make most of these methods difficult to use for scoring in this context... | Risk score | 0.809636 |
22,179 | Risk score (or risk scoring) is the name given to a general practice in applied statistics, bio-statistics, econometrics and other related disciplines, of creating an easily calculated number (the score) that reflects the level of risk in the presence of some risk factors (e.g. risk of mortality or disease in the prese... | Risk score | 0.809636 |
22,180 | Software sizing or software size estimation is an activity in software engineering that is used to determine or estimate the size of a software application or component in order to be able to implement other software project management activities (such as estimating or tracking). Size is an inherent characteristic of a... | Software Sizing | 0.809633 |
22,181 | Several software quality standards mandate the use of a valid sizing method as part of the organization's standard software engineering life cycle. For instance, Capability Maturity Model Integration (CMMI) poses such a requirement. An organization cannot be appraised (certified) as CMMI level 2 or level 3 unless softw... | Software Sizing | 0.809632 |
22,182 | The unreasonable ineffectiveness of mathematics is a phrase that alludes to the article by physicist Eugene Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". This phrase is meant to suggest that mathematical analysis has not proved as valuable in other fields as it has in physics. | Unreasonable ineffectiveness of mathematics | 0.809629 |
22,183 | It occurred in physics about the time of the Renaissance; it began in chemistry after John Dalton developed atomic theory" and by the 1990s was taking place in biology. By the early 1990s, "Biology was no longer the science of things that smelled funny in refrigerators (my view from undergraduate days in the 1960s). Th... | Unreasonable ineffectiveness of mathematics | 0.809629 |
22,184 | I. M. Gelfand, a mathematician who worked in biomathematics and molecular biology, as well as many other fields in applied mathematics, is quoted as stating, Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing whic... | Unreasonable ineffectiveness of mathematics | 0.809629 |
22,185 | Roberto Poli of McGill University delivered a number of lectures entitled The unreasonable ineffectiveness of mathematics in cognitive sciences in 1999. The abstract is: My argument is that it is possible to gain better understanding of the "unreasonable effectiveness" of mathematics in study of the physical world only... | Unreasonable ineffectiveness of mathematics | 0.809629 |
22,186 | Still, our mathematical models offer a valuable design tool to engineer our economic systems. But the mathematics of economics and finance cannot be that of physics. The mathematics of economics and finance is the mathematics of learning and complexity, similar to the mathematics used in studying biological or ecologic... | Unreasonable ineffectiveness of mathematics | 0.809628 |
22,187 | The SSA can be measured by adsorption using the BET isotherm. This has the advantage of measuring the surface of fine structures and deep texture on the particles. However, the results can differ markedly depending on the substance adsorbed. The BET theory has inherent limitations but has the advantage to be simple and... | Specific surface area | 0.809627 |
22,188 | In molecular biology, the 5.8S ribosomal RNA (5.8S rRNA) is a non-coding RNA component of the large subunit of the eukaryotic ribosome and so plays an important role in protein translation. It is transcribed by RNA polymerase I as part of the 45S precursor that also contains 18S and 28S rRNA. Its function is thought to... | 5.8S rRNA | 0.809626 |
22,189 | Alexandru Proca was the first to develop and report the massive vector boson field equations and a theory of the mesonic field of nuclear forces. Proca's equations were known to Wolfgang Pauli who mentioned the equations in his Nobel address, and they were also known to Yukawa, Wentzel, Taketani, Sakata, Kemmer, Heitle... | Nuclear Science | 0.809623 |
22,190 | Ab initio methods try to solve the nuclear many-body problem from the ground up, starting from the nucleons and their interactions.Much of current research in nuclear physics relates to the study of nuclei under extreme conditions such as high spin and excitation energy. Nuclei may also have extreme shapes (similar to ... | Nuclear Science | 0.809623 |
22,191 | This includes nuclear power, nuclear weapons, nuclear medicine and magnetic resonance imaging, industrial and agricultural isotopes, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology. Such applications are studied in the field of nuclear engineering. Particle physics evolved o... | Nuclear Science | 0.809623 |
22,192 | Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons. Discoveries in nuclear physics ha... | Nuclear Science | 0.809623 |
22,193 | The transformed Hamiltonian depends only on the Gi, and hence the equations of motion have the simple form for some function F. There is an entire field focusing on small deviations from integrable systems governed by the KAM theorem. The integrability of Hamiltonian vector fields is an open question. In general, Hamil... | Hamilton's Equations | 0.809621 |
22,194 | A Hamiltonian may have multiple conserved quantities Gi. If the symplectic manifold has dimension 2n and there are n functionally independent conserved quantities Gi which are in involution (i.e., {Gi, Gj} = 0), then the Hamiltonian is Liouville integrable. The Liouville–Arnold theorem says that, locally, any Liouville... | Hamilton's Equations | 0.809621 |
22,195 | If F and G are smooth functions on M then the smooth function ω2(IdG, IdF) is properly defined; it is called a Poisson bracket of functions F and G and is denoted {F, G}. The Poisson bracket has the following properties: bilinearity antisymmetry Leibniz rule: { F 1 ⋅ F 2 , G } = F 1 { F 2 , G } + F 2 { F 1 , G } {\disp... | Hamilton's Equations | 0.809621 |
22,196 | The collection of symplectomorphisms induced by the Hamiltonian flow is commonly called "the Hamiltonian mechanics" of the Hamiltonian system. The symplectic structure induces a Poisson bracket. The Poisson bracket gives the space of functions on the manifold the structure of a Lie algebra. | Hamilton's Equations | 0.809621 |
22,197 | The Hamiltonian vector field induces a Hamiltonian flow on the manifold. This is a one-parameter family of transformations of the manifold (the parameter of the curves is commonly called "the time"); in other words, an isotopy of symplectomorphisms, starting with the identity. By Liouville's theorem, each symplectomorp... | Hamilton's Equations | 0.809621 |
22,198 | Repeating over all x ∈ M , {\displaystyle x\in M,} we end up with an isomorphism J − 1: Vect ( M ) → Ω 1 ( M ) {\displaystyle J^{-1}:{\text{Vect}}(M)\to \Omega ^{1}(M)} between the infinite-dimensional space of smooth vector fields and that of smooth 1-forms. For every f , g ∈ C ∞ ( M , R ) {\displaystyle f,g\in C^{\in... | Hamilton's Equations | 0.809621 |
22,199 | The Hamiltonian can induce a symplectic structure on a smooth even-dimensional manifold M2n in several equivalent ways, the best known being the following:As a closed nondegenerate symplectic 2-form ω. According to the Darboux's theorem, in a small neighbourhood around any point on M there exist suitable local coordina... | Hamilton's Equations | 0.809621 |
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