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19,700 | If F {\displaystyle F} is an isomorphism of the Lindenbaum-Tarski algebra of sentences of L {\displaystyle L} supported by some permutation μ {\displaystyle \mu } of T L {\displaystyle {\cal {T}}L} in the sense that for sentences θ , ϕ {\displaystyle \theta ,\phi } , F ( ) = {\displaystyle F()=~} just when M ⊨ θ ⟺ μ ... | Pure inductive logic | 0.811367 |
19,701 | Pure inductive logic (PIL) is the area of mathematical logic concerned with the philosophical and mathematical foundations of probabilistic inductive reasoning. It combines classical predicate logic and probability theory (Bayesian inference). Probability values are assigned to sentences of a first-order relational lan... | Pure inductive logic | 0.811367 |
19,702 | In the unary case (where L {\displaystyle L} is a language containing q {\displaystyle q} unary predicates), the representation theorem for Ex is equivalent to: Every probability function w {\displaystyle w} for L {\displaystyle L} satisfying Ex can be represented as w = ∫ D w x → d μ ( x → ) . {\displaystyle w=\int _{... | Pure inductive logic | 0.811366 |
19,703 | Representation Theorem for Li with Sx. Every probability function w {\displaystyle w} for L {\displaystyle L} satisfying Li with Sx can be represented as w = ∫ B u p ¯ d μ ( p ¯ ) {\displaystyle w=\int _{\mathbb {B} }\,u^{\overline {p}}\,d\mu ({\overline {p}})} where B {\displaystyle {\mathbb {B} }} is the set of seque... | Pure inductive logic | 0.811366 |
19,704 | Representation Theorem for Ex (employing non-standard analysis and Loeb Integration Theory). Every probability function w {\displaystyle w} for L {\displaystyle L} satisfying Ex can be represented as w = ∫ A ∘ ( ω Ψ ) d μ ( Ψ ) {\displaystyle w=\int _{A}\,^{\circ }\! (\omega ^{\Psi })\,d\mu (\Psi )} where A {\displayst... | Pure inductive logic | 0.811366 |
19,705 | A representation theorem for a class of probability functions provides means of expressing every probability function in the class in terms of generic, relatively simple probability functions from the same class. Representation Theorem for all probability functions. Every probability function w {\displaystyle w} for L ... | Pure inductive logic | 0.811366 |
19,706 | In physics, multivalued functions play an increasingly important role. They form the mathematical basis for Dirac's magnetic monopoles, for the theory of defects in crystals and the resulting plasticity of materials, for vortices in superfluids and superconductors, and for phase transitions in these systems, for instan... | Multiple valued function | 0.811365 |
19,707 | The law of non-contradiction (which states that contradictory statements cannot both at the same time be true) is still valid. For instance, in Heyting arithmetic, one can prove that for any proposition p that does not contain quantifiers, ∀ x , y , z , … ∈ N: p ∨ ¬ p {\displaystyle \forall x,y,z,\ldots \in \mathbb {N}... | Constructive mathematics | 0.811363 |
19,708 | In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and i... | S5 (modal logic) | 0.811362 |
19,709 | Alvin Plantinga has argued that this feature of S5 is not, in fact, counter-intuitive. To justify, he reasons that if X is possibly necessary, it is necessary in at least one possible world; hence it is necessary in all possible worlds and thus is true in all possible worlds. Such reasoning underpins 'modal' formulatio... | S5 (modal logic) | 0.811362 |
19,710 | Schema are generally defined as mental information networks that represent some aspect of collected world knowledge. Frederic Bartlett was one of the first psychologists to propose Schematic theory, suggesting that the individual's understanding of the world is influenced by elaborate neural networks that organize abst... | Reconstructive memory | 0.811361 |
19,711 | Indeed, the semisimple rings are precisely the Noetherian von Neumann regular rings. The ring of affiliated operators of a finite von Neumann algebra is von Neumann regular. A Boolean ring is a ring in which every element satisfies a2 = a. Every Boolean ring is von Neumann regular. | Von Neumann regular element | 0.81136 |
19,712 | Von Neumann regular rings should not be confused with the unrelated regular rings and regular local rings of commutative algebra. An element a of a ring is called a von Neumann regular element if there exists an x such that a = axa. An ideal i {\displaystyle {\mathfrak {i}}} is called a (von Neumann) regular ideal if f... | Von Neumann regular element | 0.81136 |
19,713 | In mathematics, a von Neumann regular ring is a ring R (associative, with 1, not necessarily commutative) such that for every element a in R there exists an x in R with a = axa. One may think of x as a "weak inverse" of the element a; in general x is not uniquely determined by a. Von Neumann regular rings are also call... | Von Neumann regular element | 0.81136 |
19,714 | A Z-source inverter is a type of power inverter, a circuit that converts direct current to alternating current. The circuit functions as a buck-boost inverter without making use of DC-DC converter bridge due to its topology. Impedance (Z) source networks efficiently convert power between source and load from DC to DC, ... | Z-source inverter | 0.811356 |
19,715 | Renewable energy sources Electric vehicles Motor drives == References == | Z-source inverter | 0.811356 |
19,716 | (Note this is an isomorphism of F-linear spaces, but not of rings or F-algebras.) This gives isomorphism of F {\displaystyle F} -modules K ≅ F {\displaystyle K\cong F} that we talked about above, and under it the basis { 1 , X , X 2 , … , X n − 1 } {\displaystyle \{1,X,X^{2},\ldots ,X^{n-1}\}} on the right side corre... | Normal basis theorem | 0.811353 |
19,717 | In the first case dim F M = ∑ i = 1 k deg f i {\textstyle \dim _{F}M=\sum _{i=1}^{k}\deg f_{i}} , in the second case dim F M = ∞ {\displaystyle \dim _{F}M=\infty } . In our case of cyclic G of size n generated by Φ {\displaystyle \Phi } we have an F-algebra isomorphism F ≅ F ( X n − 1 ) {\textstyle F\cong {\fra... | Normal basis theorem | 0.811353 |
19,718 | In case the Galois group is cyclic as above, generated by Φ {\displaystyle \Phi } with Φ n = 1 , {\displaystyle \Phi ^{n}=1,} the normal basis theorem follows from two basic facts. The first is the linear independence of characters: a multiplicative character is a mapping χ from a group H to a field K satisfying χ ( h ... | Normal basis theorem | 0.811353 |
19,719 | A field extension K / F with Galois group G can be naturally viewed as a representation of the group G over the field F in which each automorphism is represented by itself. Representations of G over the field F can be viewed as left modules for the group algebra F. Every homomorphism of left F-modules ϕ: F → K {\displ... | Normal basis theorem | 0.811353 |
19,720 | Let F ⊂ K {\displaystyle F\subset K} be a Galois extension with Galois group G {\displaystyle G} . The classical normal basis theorem states that there is an element β ∈ K {\displaystyle \beta \in K} such that { g ( β ): g ∈ G } {\displaystyle \{g(\beta ):g\in G\}} forms a basis of K, considered as a vector space over ... | Normal basis theorem | 0.811353 |
19,721 | Macromolecular crowding is an important effect in biochemistry and cell biology. For example, the increase in the strength of interactions between proteins and DNA produced by crowding may be of key importance in processes such as transcription and DNA replication. Crowding has also been suggested to be involved in pro... | Macromolecular crowding | 0.811351 |
19,722 | In materials science, fast ion conductors are solid conductors with highly mobile ions. These materials are important in the area of solid state ionics, and are also known as solid electrolytes and superionic conductors. These materials are useful in batteries and various sensors. | Fast ion conductor | 0.81135 |
19,723 | For this reason the partition function under investigation might be well approximated by, Along same lines, the partition function for the b = α Z / 2 {\displaystyle b=\alpha Z/2} parametrization corresponding to the Hydrogen atom on S 3 {\displaystyle S^{3}} has been calculated in, where a more sophisticated approxima... | Trigonometric Rosen–Morse potential | 0.811349 |
19,724 | This Green function to Δ S 3 ( τ , χ , θ , φ ) {\displaystyle \Delta _{S^{3}}(\tau ,\chi ,\theta ,\varphi )} has been calculated for example in.Its values at the respective South and North poles, in turn denoted by G π ( χ ) {\displaystyle {\mathcal {G}}_{\pi }(\chi )} , and G 0 ( χ ) {\displaystyle {\mathcal {G}}_{0}(... | Trigonometric Rosen–Morse potential | 0.811349 |
19,725 | Changing in (10) variables as one observes that the ψ K ℓ ( χ ) {\displaystyle \psi _{K\ell }(\chi )} function satisfies the one-dimensional Schrödinger equation with the csc 2 χ {\displaystyle \csc ^{2}\chi } potential according to The one-dimensional potential in the latter equation, in coinciding with the Rosen–Mo... | Trigonometric Rosen–Morse potential | 0.811349 |
19,726 | In dimensionless units and modulo additive constants, it is defined as where r {\displaystyle r} is a relative distance, λ {\displaystyle \lambda } is an angle rescaling parameter, and R {\displaystyle R} is so far a matching length parameter. Another parametrization of same potential is which is the trigonometric vers... | Trigonometric Rosen–Morse potential | 0.811349 |
19,727 | Within such a picture, a meson is constituted by a quark ( q ) {\displaystyle (q)} -anti-quark ( q ¯ ) {\displaystyle ({\bar {q}})} color dipole in quantum motion on an S 3 {\displaystyle S^{3}} geometry, and gets perturbed by the dipole potential in (39), generated by and other color dipole, such as a gluon ( g ) {\di... | Trigonometric Rosen–Morse potential | 0.811349 |
19,728 | The confining nature of the cotangent potential in (28) finds an application in a phenomenon known from the physics of strong interaction which refers to the non-observability of free quarks, the constituents of the hadrons. Quarks are considered to possess three fundamental internal degree of freedom, conditionally te... | Trigonometric Rosen–Morse potential | 0.811349 |
19,729 | https://westpa.github.io/westpa/ and https://github.com/ADicksonLab/wepy are packages for Weighted Ensemble. PyVisA, An analysis and Visualization software for path sampling outputs with the integration of machine learning based algorithms. == References == | Rare-event sampling | 0.811348 |
19,730 | She follows permanent directors Jeff Neaton (2013-2019), Omar Yaghi (2012-2013), and Carolyn Bertozzi (2006-2010). Users of the Molecular Foundry are provided with free access to instruments, techniques and collaborators for nanoscience research that is in the public domain and intended for open publication. Proposals ... | Molecular Foundry | 0.811346 |
19,731 | New materials based on the self-assembly of biopolymers and bio-inspired polymers, new probes for bio-imaging and synthetic biology techniques to re-engineer organisms and create hybrid biomolecules to interface with devices. Organic and Macromolecular Synthesis, led by Facility Director Yi Liu and was founded by Jean ... | Molecular Foundry | 0.811346 |
19,732 | The National Centers for Biomedical Computing (NCBCs) are part of the U.S. National Institutes of Health plan to develop and implement the core of a universal computing infrastructure that is urgently needed to speed progress in biomedical research. Their mission is to create innovative software programs and other tool... | National Centers for Biomedical Computing | 0.811345 |
19,733 | Center for Computational Biology National Center for Biomedical Ontology Simbios: Physics-based Simulation of Biological Structures, Stanford University National Center for Integrative Biomedical Informatics National Center for Multi-Scale Study of Cellular Networks National Alliance for Medical Imaging Computing | National Centers for Biomedical Computing | 0.811345 |
19,734 | A right-quasigroup (Q, ∗, /) is a type (2, 2) algebra that satisfy both identities: y = (y / x) ∗ x; y = (y ∗ x) / x.A left-quasigroup (Q, ∗, \) is a type (2, 2) algebra that satisfy both identities: y = x ∗ (x \ y); y = x \ (x ∗ y).A quasigroup (Q, ∗, \, /) is a type (2, 2, 2) algebra (i.e., equipped with three binary... | Loop (algebra) | 0.811344 |
19,735 | Given some algebraic structure, an identity is an equation in which all variables are tacitly universally quantified, and in which all operations are among the primitive operations proper to the structure. Algebraic structures that satisfy axioms that are given solely by identities are called a variety. Many standard r... | Loop (algebra) | 0.811344 |
19,736 | For a countably infinite quasigroup Q, it is possible to imagine an infinite array in which every row and every column corresponds to some element q of Q, and where the element a ∗ b is in the row corresponding to a and the column responding to b. In this situation too, the Latin square property says that each row and ... | Loop (algebra) | 0.811344 |
19,737 | If a loop is isotopic to a group, then it is isomorphic to that group and thus is itself a group. However, a quasigroup that is isotopic to a group need not be a group. For example, the quasigroup on R with multiplication given by (x + y)/2 is isotopic to the additive group (R, +), but is not itself a group as it has n... | Loop (algebra) | 0.811344 |
19,738 | Using the language of Lie algebra cohomology, the central extension can be described using a 2-cocycle on the loop algebra. This is the map satisfying Then the extra term added to the bracket is φ ( X ⊗ t m , Y ⊗ t n ) k ^ . {\displaystyle \varphi (X\otimes t^{m},Y\otimes t^{n}){\hat {k}}.} | Loop algebra | 0.811344 |
19,739 | There is a natural derivation on the loop algebra, conventionally denoted d {\displaystyle d} acting as and so can be thought of formally as d = t d d t {\displaystyle d=t{\frac {d}{dt}}} . It is required to define affine Lie algebras, which are used in physics, particularly conformal field theory. | Loop algebra | 0.811344 |
19,740 | If g {\displaystyle {\mathfrak {g}}} is a semisimple Lie algebra, then a nontrivial central extension of its loop algebra L g {\displaystyle L{\mathfrak {g}}} gives rise to an affine Lie algebra. Furthermore this central extension is unique.The central extension is given by adjoining a central element k ^ {\displaystyl... | Loop algebra | 0.811344 |
19,741 | If g {\displaystyle {\mathfrak {g}}} is a Lie algebra, the tensor product of g {\displaystyle {\mathfrak {g}}} with C∞(S1), the algebra of (complex) smooth functions over the circle manifold S1 (equivalently, smooth complex-valued periodic functions of a given period), is an infinite-dimensional Lie algebra with the Li... | Loop algebra | 0.811344 |
19,742 | For a Lie algebra g {\displaystyle {\mathfrak {g}}} over a field K {\displaystyle K} , if K {\displaystyle K} is the space of Laurent polynomials, then with the inherited bracket | Loop algebra | 0.811344 |
19,743 | Similarly, a set of all smooth maps from S1 to a Lie group G forms an infinite-dimensional Lie group (Lie group in the sense we can define functional derivatives over it) called the loop group. The Lie algebra of a loop group is the corresponding loop algebra. | Loop algebra | 0.811344 |
19,744 | In physics, the central extension L g ⊕ C k ^ {\displaystyle L{\mathfrak {g}}\oplus \mathbb {C} {\hat {k}}} is sometimes referred to as the affine Lie algebra. In mathematics, this is insufficient, and the full affine Lie algebra is the vector space where d {\displaystyle d} is the derivation defined above. On this spa... | Loop algebra | 0.811344 |
19,745 | In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics. | Loop algebra | 0.811344 |
19,746 | A Penning trap stores charged particles using a strong homogeneous axial magnetic field to confine particles radially and a quadrupole electric field to confine the particles axially. Penning traps are well suited for measurements of the properties of ions and stable charged subatomic particles. Precision studies of th... | Ion Trap | 0.811338 |
19,747 | In structural biology, resolution can be broken down into 4 groups: (1) sub-atomic, individual elements are distinguishable and quantum effects can be studied, (2) atomic, individual atoms are visible and an accurate three-dimensional model can be constructed, (3) helical, secondary structure, such as alpha helices and... | Resolution (electron density) | 0.811337 |
19,748 | The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered. It turns out that the general language for describing these coverings is that of a Grothendieck topo... | Stack (mathematics) | 0.811337 |
19,749 | In molecular biology, the Hsp17 thermometer is an RNA element (RNA thermometer) found in the 5' UTR of Hsp17 mRNA. Hsp17 is a cyanobacterial heat shock protein belonging to the Hsp20 family.At physiological temperature (28 degrees Celsius) the Hsp17 thermometer forms a hairpin structure, preventing translation of Hsp17... | Hsp17 thermometer | 0.811337 |
19,750 | In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-½ particles, which takes into account the interaction of the particle's spin with an external electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used where... | Pauli equation | 0.811336 |
19,751 | The term in B {\textstyle \mathbf {B} } , is of the form − μ ⋅ B {\textstyle -{\boldsymbol {\mu }}\cdot \mathbf {B} } which is the usual interaction between a magnetic moment μ {\textstyle {\boldsymbol {\mu }}} and a magnetic field, like in the Zeeman effect. For an electron of charge − e {\textstyle -e} in an isotropi... | Pauli equation | 0.811336 |
19,752 | Pauli's equation is derived by requiring minimal coupling, which provides a g-factor g=2. Most elementary particles have anomalous g-factors, different from 2. In the domain of relativistic quantum field theory, one defines a non-minimal coupling, sometimes called Pauli coupling, in order to add an anomalous factor γ μ... | Pauli equation | 0.811336 |
19,753 | Burkey at Kodak in 1984. In 1987, the PPD began to be incorporated into most CCD devices, becoming a fixture in consumer electronic video cameras and then digital still cameras. Since then, the PPD has been used in nearly all CCD sensors and then CMOS sensors.In January 2006, Boyle and Smith were awarded the National A... | Charged couple device | 0.811334 |
19,754 | This was the first experimental application of the CCD in image sensor technology, and used a depleted MOS structure as the photodetector. The first patent (U.S. Patent 4,085,456) on the application of CCDs to imaging was assigned to Tompsett, who filed the application in 1971.The first working CCD made with integrated... | Charged couple device | 0.811334 |
19,755 | In the mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n – 2 edges.The ladder graph can be obtained as the Cartesian product of two path graphs, one of which has only one edge: Ln,1 = Pn × P2. | Ladder graph | 0.811333 |
19,756 | In physics and materials science, the Curie temperature (TC), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism was lost at a ... | Néel temperature | 0.81133 |
19,757 | In theoretical computer science a simulation is a relation between state transition systems associating systems that behave in the same way in the sense that one system simulates the other. Intuitively, a system simulates another system if it can match all of its moves. The basic definition relates states within one tr... | Simulation (computer science) | 0.811329 |
19,758 | If the degree is higher than one, the graph does not have any asymptote. It has two parabolic branches with vertical direction (one branch for positive x and one for negative x). Polynomial graphs are analyzed in calculus using intercepts, slopes, concavity, and end behavior. | Polynomial multiplication | 0.811329 |
19,759 | If R is commutative, then one can associate with every polynomial P in R a polynomial function f with domain and range equal to R. (More generally, one can take domain and range to be any same unital associative algebra over R.) One obtains the value f(r) by substitution of the value r for the symbol x in P. One reason... | Polynomial multiplication | 0.811329 |
19,760 | A polynomial f over a commutative ring R is a polynomial all of whose coefficients belong to R. It is straightforward to verify that the polynomials in a given set of indeterminates over R form a commutative ring, called the polynomial ring in these indeterminates, denoted R {\displaystyle R} in the univariate case an... | Polynomial multiplication | 0.811329 |
19,761 | Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemist... | Polynomial multiplication | 0.811329 |
19,762 | Besides, animal biochemistry contains many small molecule intermediates which assist in energy production through the Krebs cycle, and produces isoprene, the most common hydrocarbon in animals. Isoprenes in animals form the important steroid structural (cholesterol) and steroid hormone compounds; and in plants form ter... | Synthetic organic chemistry | 0.811327 |
19,763 | Biomolecular chemistry is a major category within organic chemistry which is frequently studied by biochemists. Many complex multi-functional group molecules are important in living organisms. Some are long-chain biopolymers, and these include peptides, DNA, RNA and the polysaccharides such as starches in animals and c... | Synthetic organic chemistry | 0.811327 |
19,764 | Converting individual petroleum compounds into types of compounds by various chemical processes led to organic reactions enabling a broad range of industrial and commercial products including, among (many) others: plastics, synthetic rubber, organic adhesives, and various property-modifying petroleum additives and cata... | Synthetic organic chemistry | 0.811327 |
19,765 | For example, cholesterol-related compounds have opened ways to synthesize complex human hormones and their modified derivatives. Since the start of the 20th century, complexity of total syntheses has been increased to include molecules of high complexity such as lysergic acid and vitamin B12. The discovery of petroleum... | Synthetic organic chemistry | 0.811327 |
19,766 | Although Wöhler himself was cautious about claiming he had disproved vitalism, this was the first time a substance thought to be organic was synthesized in the laboratory without biological (organic) starting materials. The event is now generally accepted as indeed disproving the doctrine of vitalism.In 1856, William H... | Synthetic organic chemistry | 0.811327 |
19,767 | Crystallography can be useful for determining molecular geometry when a single crystal of the material is available. Highly efficient hardware and software allows a structure to be determined within hours of obtaining a suitable crystal.Traditional spectroscopic methods such as infrared spectroscopy, optical rotation, ... | Synthetic organic chemistry | 0.811327 |
19,768 | The aliphatic hydrocarbons are subdivided into three groups of homologous series according to their state of saturation: alkanes (paraffins): aliphatic hydrocarbons without any double or triple bonds, i.e. just C-C, C-H single bonds alkenes (olefins): aliphatic hydrocarbons that contain one or more double bonds, i.e. d... | Synthetic organic chemistry | 0.811327 |
19,769 | The principal constituent atoms of organic chemistry – hydrogen and carbon – exist naturally with NMR-responsive isotopes, respectively 1H and 13C. Elemental analysis: A destructive method used to determine the elemental composition of a molecule. See also mass spectrometry, below. | Synthetic organic chemistry | 0.811327 |
19,770 | Since organic compounds often exist as mixtures, a variety of techniques have also been developed to assess purity; chromatography techniques are especially important for this application, and include HPLC and gas chromatography. Traditional methods of separation include distillation, crystallization, evaporation, magn... | Synthetic organic chemistry | 0.811327 |
19,771 | We shall consider not an arbitrary one, but a convenient one for the observable Q in question. A convenient configuration space X is such that each point x produces some unique value of Q. For discrete X it means that all elements of the standard basis are eigenvectors of Q. In other words, Q shall be diagonal in that ... | Transition amplitude | 0.811327 |
19,772 | In a formal setup, any system in quantum mechanics is described by a state, which is a vector |Ψ⟩, residing in an abstract complex vector space, called a Hilbert space. It may be either infinite- or finite-dimensional. A usual presentation of that Hilbert space is a special function space, called L2(X), on certain set ... | Transition amplitude | 0.811327 |
19,773 | In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding, ... | Transition amplitude | 0.811327 |
19,774 | In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density. Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system... | Transition amplitude | 0.811327 |
19,775 | A feedforward neural network (FNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. Its flow is uni-directional, meaning that the information in the model flows in only one direction—forward—from the input nodes, through the hidden nod... | Feedforward neural networks | 0.811325 |
19,776 | The question of determining whether a given rational number is a congruent number is called the congruent number problem. This problem has not (as of 2019) been brought to a successful resolution. Tunnell's theorem provides an easily testable criterion for determining whether a number is congruent; but his result relie... | Congruent number | 0.811324 |
19,777 | In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition includes all positive rational numbers with this property.The sequence of (integer) congruent numbers starts with 5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29, 3... | Congruent number | 0.811324 |
19,778 | In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic graph. Such sets and functions are mainly studied in real algebraic geometry... | Semi-algebraic sets | 0.811323 |
19,779 | Sports biomechanics is a quantitative based study and analysis of professional athletes and sports activities in general. It can simply be described as the physics of sports. In this subfield of biomechanics the laws of mechanics are applied in order to gain a greater understanding of athletic performance through mathe... | Sports biomechanics | 0.811323 |
19,780 | Examples of quantitative forecasting methods are last period demand, simple and weighted N-Period moving averages, simple exponential smoothing, Poisson process model based forecasting and multiplicative seasonal indexes. Previous research shows that different methods may lead to different level of forecasting accuracy... | Rolling forecast | 0.811323 |
19,781 | This is because "predictors are part of the social context about which they are trying to make a prediction and may influence that context in the process". For example, a forecast that a large percentage of a population will become HIV infected based on existing trends may cause more people to avoid risky behavior and ... | Rolling forecast | 0.811323 |
19,782 | For example, the statement "there is an integer n such that if there is a sequence of rooted trees T1, T2, ..., Tn such that Tk has at most k+10 vertices, then some tree can be homeomorphically embedded in a later one"is provable in Peano arithmetic, but the shortest proof has length at least A(1000), where A(0)=1 and ... | Gödel's speed-up theorem | 0.811319 |
19,783 | The statement has a short proof in a more powerful system: in fact the proof given in the previous paragraph is a proof in the system of Peano arithmetic plus the statement "Peano arithmetic is consistent" (which, per the incompleteness theorem, cannot be proved in Peano arithmetic). In this argument, Peano arithmetic ... | Gödel's speed-up theorem | 0.811319 |
19,784 | In mathematics, Gödel's speed-up theorem, proved by Gödel (1936), shows that there are theorems whose proofs can be drastically shortened by working in more powerful axiomatic systems. Kurt Gödel showed how to find explicit examples of statements in formal systems that are provable in that system but whose shortest pro... | Gödel's speed-up theorem | 0.811319 |
19,785 | Disciplines in which one might use the word formulation in the abstract sense include logic, mathematics, linguistics, legal theory, and computer science. For details, see the related articles. | Formulation | 0.811316 |
19,786 | In more material senses the concept of formulation appears in the physical sciences, such as physics, chemistry, and biology. It also is ubiquitous in industry, engineering and medicine, especially pharmaceutics. | Formulation | 0.811316 |
19,787 | On July 22, 2020, Autodesk announced that it would acquire Pype, a Bengaluru-based provider of cloud-based solutions for automating construction project management workflows. In November 2020, Autodesk announced that it would acquire Spacemaker, a cloud-based platform that uses artificial intelligence (AI) and generati... | Autodesk Dynamo | 0.811314 |
19,788 | On May 7, 2008, Autodesk announced that it completed the acquisition of Kynogon SA, the privately held maker of Kynapse artificial intelligence middleware. Paris-based Kynogon specialized in video game middleware and simulation. On May 7, 2008, Autodesk also announced the acquisition of REALVIZ S.A. | Autodesk Dynamo | 0.811314 |
19,789 | With the purchase of Softdesk in 1997, Autodesk started to develop specialty versions of AutoCAD, targeted to broad industry segments, including architecture, civil engineering, and manufacturing. Since the late 1990s, the company has added several significant non-AutoCAD-based products, including Revit, a parametric b... | Autodesk Dynamo | 0.811314 |
19,790 | Sketchbook designer has been discontinued as of November 1, 2012 Softimage was discontinued after the release of Softimage 2015 on April 14, 2014. Face Robot Lagoa Multiphysics Autodesk Stitcher Unlimited Autodesk ImageModeler Autodesk Movimento (formerly Realviz Movimento) Autodesk Combustion Discreet Effect (formerly... | Autodesk Dynamo | 0.811314 |
19,791 | Online map-based application: Interactive maps allow visualisation of global solar resource data at approx 250 m grid resolution, covering global horizontal irradiation (GHI), direct normal irradiation (DNI), diffuse horizontal irradiation (DIF), and also PV power potential (PVOUT) and air temperature (TEMP) data at ap... | Global Solar Atlas | 0.811313 |
19,792 | Several independent comparisons of solar radiation databases have been performed in recent years. Solargis has been repeatedly identified as the best performing database.A PV power simulator is also operated by Solargis, and it calculates the conversion of the solar resource to electric power considering also the impac... | Global Solar Atlas | 0.811313 |
19,793 | The Global Solar Atlas website serves over 23,000 users per month according to data from Google Analytics (June 2020). Data from GSA has been used in the number of scientific studies and R&D programmes. Only in 2019, Google Scholar noticed more than 200 individual scholarly literature, referring to GSA sources. It is r... | Global Solar Atlas | 0.811313 |
19,794 | The GSA also features a rich download section, organized on the level of countries or regions. It involves the popular solar resource maps in multiple languages, country fact-sheets and spatial data in a standard GIS formats.The Global Solar Atlas was launched by the World Bank and ESMAP in January 2017 in partnership ... | Global Solar Atlas | 0.811313 |
19,795 | The Global Solar Atlas (GSA) is a free, online, map-based application that provides information on solar resource and photovoltaic power potential globally. It features the online interactive map tools, simplified photovoltaic (PV) power calculator, reporting tools and the extensive download section. It is intended to ... | Global Solar Atlas | 0.811313 |
19,796 | Natural impervious areas, depending on their nature and antecedent conditions, may produce stormflow from infiltration excess overland flow, saturation overland flow, or direct precipitation. The effects of natural impervious areas on runoff generation are expected to be more important in areas with low TIA than highly... | Impermeable surfaces | 0.811312 |
19,797 | For any triad of spaces ( X ; A , B ) {\displaystyle (X;A,B)} (i.e., a space X and subspaces A, B) and integer k > 2 {\displaystyle k>2} there exists a homomorphism h ∗: π k ( X ; A , B ) → H k ( X ; A , B ) {\displaystyle h_{*}\colon \pi _{k}(X;A,B)\to H_{k}(X;A,B)} from triad homotopy groups to triad homology groups.... | Hurewicz homomorphism | 0.811312 |
19,798 | For any path-connected space X and positive integer n there exists a group homomorphism h ∗: π n ( X ) → H n ( X ) , {\displaystyle h_{*}\colon \pi _{n}(X)\to H_{n}(X),} called the Hurewicz homomorphism, from the n-th homotopy group to the n-th homology group (with integer coefficients). It is given in the following wa... | Hurewicz homomorphism | 0.811312 |
19,799 | For any pair of spaces ( X , A ) {\displaystyle (X,A)} and integer k > 1 {\displaystyle k>1} there exists a homomorphism h ∗: π k ( X , A ) → H k ( X , A ) {\displaystyle h_{*}\colon \pi _{k}(X,A)\to H_{k}(X,A)} from relative homotopy groups to relative homology groups. The Relative Hurewicz Theorem states that if both... | Hurewicz homomorphism | 0.811312 |
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