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25,800 | Every body of constant width is a convex set, its boundary crossed at most twice by any line, and if the line crosses perpendicularly it does so at both crossings, separated by the width. By Barbier's theorem, the body's perimeter is exactly π times its width, but its area depends on its shape, with the Reuleaux triang... | Curve of constant width | 0.80745 |
25,801 | In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform, the name given to these shapes by Leonhard Euler. Standard e... | Curve of constant width | 0.80745 |
25,802 | However, there are other shapes of constant width. A standard example is the Reuleaux triangle, the intersection of three circles, each centered where the other two circles cross. Its boundary curve consists of three arcs of these circles, meeting at 120° angles, so it is not smooth, and in fact these angles are the sh... | Curve of constant width | 0.80745 |
25,803 | For a curve of constant width, each vertex of locally minimum curvature is paired with a vertex of locally maximum curvature, opposite it on a diameter of the curve, and there must be at least six vertices. This stands in contrast to the four-vertex theorem, according to which every simple closed smooth curve in the pl... | Curve of constant width | 0.80745 |
25,804 | By the isoperimetric inequality and Barbier's theorem, the circle has the maximum area of any curve of given constant width. The Blaschke–Lebesgue theorem says that the Reuleaux triangle has the least area of any convex curve of given constant width. Every proper superset of a body of constant width has strictly greate... | Curve of constant width | 0.80745 |
25,805 | Curves of constant width are examples of self-parallel or auto-parallel curves, curves traced by both endpoints of a line segment that moves in such a way that both endpoints move perpendicularly to the line segment. However, there exist other self-parallel curves, such as the infinite spiral formed by the involute of ... | Curve of constant width | 0.80745 |
25,806 | The curves of constant width can be generalized to certain non-convex curves, the curves that have two tangent lines in each direction, with the same separation between these two lines regardless of their direction. As a limiting case, the projective hedgehogs (curves with one tangent line in each direction) have also ... | Curve of constant width | 0.80745 |
25,807 | There are four departments with a number of research groups and laboratories: Astrophysics (José Ramón Valdés Parra) Visible Astronomical Instrumentation Laboratory and of High Energies (Esperanza Carrasco-Licea) Millimeter Wavelength Instrumentation Laboratory Fourier Spectroscopy Laboratory (Fabián Rosales) Photograp... | National Institute of Astrophysics, Optics and Electronics | 0.807449 |
25,808 | The National Institute of Astrophysics, Optics and Electronics (in Spanish: Instituto Nacional de Astrofísica, Óptica y Electrónica, INAOE) is a Mexican science research institute located in Tonantzintla, Puebla. Founded by presidential decree on November 12, 1971, it has over 100 researchers in Astrophysics, Optics, E... | National Institute of Astrophysics, Optics and Electronics | 0.807449 |
25,809 | The theory allows the construction of embedded minimal hypersurfaces through variational methods.In his PhD thesis Almgren proved that the m-th homotopy group of the space of flat k-dimensional cycles on a closed Riemannian manifold is isomorphic to the (m+k)-th dimensional homology group of M. This result is a general... | Almgren–Pitts min-max theory | 0.807447 |
25,810 | In mathematics, the Almgren–Pitts min-max theory (named after Frederick J. Almgren, Jr. and his student Jon T. Pitts) is an analogue of Morse theory for hypersurfaces. The theory started with the efforts for generalizing George David Birkhoff's method for the construction of simple closed geodesics on the sphere, to al... | Almgren–Pitts min-max theory | 0.807447 |
25,811 | Spectral data acquired by satellite sensors are influenced by a number of factors, such as atmospheric absorption, scattering, sensor-target-illumination geometry, sensor calibration, and image data processing procedures, which tend to change through time. Targets in multi-date scenes are extremely variable and have be... | Radiometric calibration | 0.807447 |
25,812 | Kirchhoff's law of thermal radiation is another special case of the Onsager reciprocal relations applied to the wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium. For his discovery of these reciprocal relations, Lars Onsager was awarded the 1968 Nobel Prize in Chemist... | Onsager reciprocal relations | 0.807446 |
25,813 | The Campus Biotech is a Swiss institution hosting research institutes and biotechnology companies. The Campus Biotech is located in the former Merck Serono building, in Geneva (Switzerland).The Campus Biotech is a part of the Swiss Innovation Park. | Campus Biotech | 0.807445 |
25,814 | Note too that the broadly sinusoidal relative motion of our observers is fully consistent with the behavior of the expansion tensor (concerning the frame field corresponding to our family of observers) which was noted above. It is worth noting that these somewhat tricky points confused no less a figure than Albert Eins... | Monochromatic electromagnetic plane wave | 0.807444 |
25,815 | Our spacetime is modeled by a Lorentzian manifold which has some remarkable symmetries. Namely, our spacetime admits a six-dimensional Lie group of self-isometries. This group is generated by a six-dimensional Lie algebra of Killing vector fields. | Monochromatic electromagnetic plane wave | 0.807444 |
25,816 | The head/tail domain of GEP genes (both normal and homeotic) is the basic building block of all GEP algorithms. However, gene expression programming also explores other chromosomal organizations that are more complex than the head/tail structure. Essentially these complex structures consist of functional units or genes... | Gene expression programming | 0.807444 |
25,817 | In logic there is no model structure (as defined above for classification and logistic regression) to explore: the domain and range of logical functions comprises only 0's and 1's or false and true. So, the fitness functions available for Boolean algebra can only be based on the hits or on the confusion matrix as expla... | Gene expression programming | 0.807444 |
25,818 | Fitness functions and selection environments (called training datasets in machine learning) are the two facets of fitness and are therefore intricately connected. Indeed, the fitness of a program depends not only on the cost function used to measure its performance but also on the training data chosen to evaluate fitne... | Gene expression programming | 0.807444 |
25,819 | This genotype/phenotype system is multigenic, thus encoding multiple parse trees in each chromosome. This means that the computer programs created by GEP are composed of multiple parse trees. Because these parse trees are the result of gene expression, in GEP they are called expression trees. Masood Nekoei, et al. util... | Gene expression programming | 0.807444 |
25,820 | Evolutionary algorithms use populations of individuals, select individuals according to fitness, and introduce genetic variation using one or more genetic operators. Their use in artificial computational systems dates back to the 1950s where they were used to solve optimization problems (e.g. Box 1957 and Friedman 1959... | Gene expression programming | 0.807444 |
25,821 | Broadly speaking, there are essentially three different kinds of problems based on the kind of prediction being made: Problems involving numeric (continuous) predictions; Problems involving categorical or nominal predictions, both binomial and multinomial; Problems involving binary or Boolean predictions.The first type... | Gene expression programming | 0.807444 |
25,822 | As a more concrete example, below is shown a neural net gene for the exclusive-or problem. It has a head size of 3 and Dw size of 6: 0123456789012 DDDabab393257Its expression results in the following neural network: which, for the set of weights: W = {−1.978, 0.514, −0.465, 1.22, −1.686, −1.797, 0.197, 1.606, 0, 1.753}... | Gene expression programming | 0.807444 |
25,823 | For example, below is shown a neural network with two input units (i1 and i2), two hidden units (h1 and h2), and one output unit (o1). It has a total of six connections with six corresponding weights represented by the numerals 1–6 (for simplicity, the thresholds are all equal to 1 and are omitted): This representation... | Gene expression programming | 0.807444 |
25,824 | Structurally, the Dw comes after the tail and its length dw depends on the head size h and maximum arity nmax and is evaluated by the formula: d w = h n max {\displaystyle d_{w}=hn_{\max }} The Dt comes after Dw and has a length dt equal to t. Both domains are composed of symbols representing the weights and thresholds... | Gene expression programming | 0.807444 |
25,825 | The head contains special functions/neurons that activate the hidden and output units (in the GEP context, all these units are more appropriately called functional units) and terminals that represent the input units. The tail, as usual, contains only terminals/input units. Besides the head and the tail, these neural ne... | Gene expression programming | 0.807444 |
25,826 | In summary, the basic components of a neural network are the units, the connections between the units, the weights, and the thresholds. So, in order to fully simulate an artificial neural network one must somehow encode these components in a linear chromosome and then be able to express them in a meaningful way. In GEP... | Gene expression programming | 0.807444 |
25,827 | An artificial neural network (ANN or NN) is a computational device that consists of many simple connected units or neurons. The connections between the units are usually weighted by real-valued weights. These weights are the primary means of learning in neural networks and a learning algorithm is usually used to adjust... | Gene expression programming | 0.807444 |
25,828 | For instance, for the following 10 element array of RNCs: C = {0.611, 1.184, 2.449, 2.98, 0.496, 2.286, 0.93, 2.305, 2.737, 0.755}the expression tree above gives: This elegant structure for handling random numerical constants is at the heart of different GEP systems, such as GEP neural networks and GEP decision trees. ... | Gene expression programming | 0.807444 |
25,829 | Inversion is an interesting operator, especially powerful for combinatorial optimization. It consists of inverting a small sequence within a chromosome. In gene expression programming it can be easily implemented in all gene domains and, in all cases, the offspring produced is always syntactically correct. For any gene... | Gene expression programming | 0.807444 |
25,830 | In nuclear physics, separation energy is the energy needed to remove one nucleon (or other specified particle or particles) from an atomic nucleus. The separation energy is different for each nuclide and particle to be removed. Values are stated as "neutron separation energy", "two-neutron separation energy", "proton s... | Separation energy | 0.80744 |
25,831 | On Conoids and Spheroids (Ancient Greek: Περὶ κωνοειδέων καὶ σφαιροειδέων) is a surviving work by the Greek mathematician and engineer Archimedes (c. 287 BC – c. 212 BC). Consisting of 32 propositions, the work explores properties of and theorems related to the solids generated by revolution of conic sections about the... | On Conoids and Spheroids | 0.807435 |
25,832 | If sufficiently strong nonlinear terms are present in the energy function, energy may be transferred between the normal modes, leading to ergodicity and rendering the law of equipartition valid. However, the Kolmogorov–Arnold–Moser theorem states that energy will not be exchanged unless the nonlinear perturbations are ... | Equipartition principle | 0.807435 |
25,833 | Such a degree of freedom is said to be "frozen out" when the thermal energy is much smaller than this spacing. For example, the heat capacity of a solid decreases at low temperatures as various types of motion become frozen out, rather than remaining constant as predicted by equipartition. Such decreases in heat capaci... | Equipartition principle | 0.807435 |
25,834 | The equipartition theorem can also be used to predict the properties of stars, even white dwarfs and neutron stars, since it holds even when relativistic effects are considered. Although the equipartition theorem makes accurate predictions in certain conditions, it is inaccurate when quantum effects are significant, su... | Equipartition principle | 0.807435 |
25,835 | Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle ... | Equipartition principle | 0.807435 |
25,836 | In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is... | Equipartition principle | 0.807435 |
25,837 | In an ideal gas the particles are assumed to interact only through collisions. The equipartition theorem may also be used to derive the energy and pressure of "non-ideal gases" in which the particles also interact with one another through conservative forces whose potential U(r) depends only on the distance r between t... | Equipartition principle | 0.807435 |
25,838 | A similar example is provided by a rotating molecule with principal moments of inertia I1, I2 and I3. According to classical mechanics, the rotational energy of such a molecule is given by H r o t = 1 2 ( I 1 ω 1 2 + I 2 ω 2 2 + I 3 ω 3 2 ) , {\displaystyle H_{\mathrm {rot} }={\tfrac {1}{2}}(I_{1}\omega _{1}^{2}+I_{2}\... | Equipartition principle | 0.807435 |
25,839 | In that case, the equipartition theorem for the canonical ensemble follows immediately N ∫ e − β H ( p , q ) x k ∂ H ∂ x k d Γ = ⟨ x k ∂ H ∂ x k ⟩ = 1 β = k B T . {\displaystyle {\mathcal {N}}\int e^{-\beta H(p,q)}x_{k}{\frac {\partial H}{\partial x_{k}}}\,d\Gamma =\left\langle x_{k}{\frac {\partial H}{\partial x_{k}}}... | Equipartition principle | 0.807435 |
25,840 | The case of a two-variable signal which is i1D appears frequently in computer vision and image processing and captures the idea of local image regions which contain lines or edges. The analysis of such regions has a long history, but it was not until a more formal and theoretical treatment of such operations began that... | Intrinsic dimension | 0.807435 |
25,841 | Additional classes include the Monoblepharidomycetes, with two orders, and the Hyaloraphidiomycetes with a single order.Molecular phylogenetics, and other techniques such as ultrastructure analysis, has greatly increased the understanding of chytrid phylogeny, and led to the formation of several new zoosporic fungal ph... | Chytrids | 0.807434 |
25,842 | As with sodium channels, the potassium channels have their own toxins that block channel protein action. An example of such a toxin is the large cation, tetraethylammonium (TEA), but it is notable that the toxin does not have the same mechanism of action on all potassium channels, given the variety of channel types acr... | Molecular Neuroscience | 0.807432 |
25,843 | Metabotropic receptors, are slow response receptors in postsynaptic cells. Typically these slow responses are characterized by more elaborate intracellular changes in biochemistry. Responses of neurotransmitter uptake by metabotropic receptors can result in the activation of intracellualar enzymes and cascades involvin... | Molecular Neuroscience | 0.807432 |
25,844 | This can give rise to formaldehyde-induced fluorescence when exposed to ultraviolet light. Dopamine, a catecholamine, was identified in the nematode C. elegans by using this technique.Immunocytochemistry, which involves raising antibodies against targeted chemical or biological entities, includes a few other techniques... | Molecular Neuroscience | 0.807432 |
25,845 | In molecular biology, communication between neurons typically occurs by chemical transmission across gaps between the cells called synapses. The transmitted chemicals, known as neurotransmitters, regulate a significant fraction of vital body functions. It is possible to anatomically locate neurotransmitters by labeling... | Molecular Neuroscience | 0.807432 |
25,846 | Molecular neuroscience is a branch of neuroscience that observes concepts in molecular biology applied to the nervous systems of animals. The scope of this subject covers topics such as molecular neuroanatomy, mechanisms of molecular signaling in the nervous system, the effects of genetics and epigenetics on neuronal d... | Molecular Neuroscience | 0.807432 |
25,847 | MIPS is a modular architecture supporting up to four coprocessors (CP0/1/2/3). In MIPS terminology, CP0 is the System Control Coprocessor (an essential part of the processor that is implementation-defined in MIPS I–V), CP1 is an optional floating-point unit (FPU) and CP2/3 are optional implementation-defined coprocesso... | MIPS V | 0.807424 |
25,848 | A passed ball may be scored when a base runner reaches the next base on a bobble or missed catch by the catcher, or when the batter–runner reaches first base on an uncaught strike three (see also Strikeout).A closely related statistic is the wild pitch. As with many baseball statistics, whether a pitch that gets away f... | Passed ball | 0.807424 |
25,849 | A run scored due to a passed ball is not recorded as an earned run. However, a run scored due to a wild pitch is recorded as an earned run.Passed balls and wild pitches are considered to be part of the act of pitching rather than fielding. Thus they are kept as separate statistics and are not recorded as errors.There t... | Passed ball | 0.807424 |
25,850 | Indeed, before x-ray structural determination methods were made available in the early 20th century all organic structures were entirely conjectural: tetrahedral carbon, for example, was only confirmed by the crystal structure of diamond, and the delocalized structure of benzene was confirmed by the crystal structure o... | Physical organic chemistry | 0.807421 |
25,851 | Unlike spectroscopic methods, X-ray crystallography always allows for unambiguous structure determination and provides precise bond angles and lengths totally unavailable through spectroscopy. It is often used in physical organic chemistry to provide an absolute molecular configuration and is an important tool in impro... | Physical organic chemistry | 0.807421 |
25,852 | The term physical organic chemistry was itself coined by Louis Hammett in 1940 when he used the phrase as a title for his textbook. | Physical organic chemistry | 0.807421 |
25,853 | Hammond, George S. (1997). "Physical organic chemistry after 50 years: It has changed, but is it still there?" (PDF). | Physical organic chemistry | 0.807421 |
25,854 | Chemists use the study of intramolecular and intermolecular non-covalent bonding/interactions in molecules to evaluate reactivity. Such interactions include, but are not limited to, hydrogen bonding, electrostatic interactions between charged molecules, dipole-dipole interactions, polar-π and cation-π interactions, π-s... | Physical organic chemistry | 0.807421 |
25,855 | Physical organic chemists use the mathematical foundation of chemical kinetics to study the rates of reactions and reaction mechanisms. Unlike thermodynamics, which is concerned with the relative stabilities of the products and reactants (ΔG°) and their equilibrium concentrations, the study of kinetics focuses on the f... | Physical organic chemistry | 0.807421 |
25,856 | Quantum chemistry can also provide insight into the mechanism of an organic transformation without the collection of any experimental data. Because wavefunctions provide the total energy of a given molecular state, guessed molecular geometries can be optimized to give relaxed molecular structures very similar to those ... | Physical organic chemistry | 0.807421 |
25,857 | Due to complex interactions which arise from electron-electron repulsion, algebraic solutions of the Schrödinger equation are only possible for systems with one electron such as the hydrogen atom, H2+, H32+, etc.; however, from these simple models arise all the familiar atomic (s,p,d,f) and bonding (σ,π) orbitals. In s... | Physical organic chemistry | 0.807421 |
25,858 | The energy associated with a particular wavefunction, perhaps the most important information contained in a wavefunction, can be extracted by solving the Schrödinger equation (above, Ψ is the wavefunction, E is the energy, and Ĥ is the Hamiltonian operator) in which an appropriate Hamiltonian operator is applied. In th... | Physical organic chemistry | 0.807421 |
25,859 | Many aspects of the structure-reactivity relationship in organic chemistry can be rationalized through resonance, electron pushing, induction, the eight electron rule, and s-p hybridization, but these are only helpful formalisms and do not represent physical reality. Due to these limitations, a true understanding of ph... | Physical organic chemistry | 0.807421 |
25,860 | Real world equipment may not perfectly follow these models, especially at extremes of loading (both high and low), but for most purposes, they suffice. The two models of non-ideal generators are interchangeable; either can be used for any given generator. Thévenin's theorem allows a non-ideal current source model to be... | Generator (circuit theory) | 0.807421 |
25,861 | In computer science, a circular buffer, circular queue, cyclic buffer or ring buffer is a data structure that uses a single, fixed-size buffer as if it were connected end-to-end. This structure lends itself easily to buffering data streams. There were early circular buffer implementations in hardware. | Circular buffer | 0.807419 |
25,862 | Perhaps the most common version of the circular buffer uses 8-bit bytes as elements. Some implementations of the circular buffer use fixed-length elements that are bigger than 8-bit bytes—16-bit integers for audio buffers, 53-byte ATM cells for telecom buffers, etc. Each item is contiguous and has the correct data alig... | Circular buffer | 0.807419 |
25,863 | Magnetic translations are naturally defined operators acting on wave function on a two-dimensional particle in a magnetic field. The motion of an electron in a magnetic field on a plane is described by the following four variables: guiding center coordinates ( X , Y ) {\displaystyle (X,Y)} and the relative coordinates ... | Magnetic translation | 0.807412 |
25,864 | Greg worked on the core infrastructure of the FlashMob run time environment. John Witchel (Stuyvesant High School '86) was a USF graduate student in computer science during the spring of 2004. | Flash mob computing | 0.807412 |
25,865 | Pat Miller was a research scientist at a national lab and adjunct professor at USF. His class on Do-It-Yourself Supercomputers evolved into FlashMob I from the original idea of every student bringing a commodity CPU or an Xbox to class to make an evanescent cluster at each meeting. Pat worked on all aspects of the Flas... | Flash mob computing | 0.807412 |
25,866 | One of the fundamental themes in differential geometry is a trichotomy between the Riemannian manifolds of positive, zero, and negative curvature K. It manifests itself in many diverse situations and on several levels. In the context of compact Riemann surfaces X, via the Riemann uniformization theorem, this can be see... | Hurwitz's automorphisms theorem | 0.807411 |
25,867 | The theorem is named after Adolf Hurwitz, who proved it in (Hurwitz 1893). Hurwitz's bound also holds for algebraic curves over a field of characteristic 0, and over fields of positive characteristic p>0 for groups whose order is coprime to p, but can fail over fields of positive characteristic p>0 when p divides the g... | Hurwitz's automorphisms theorem | 0.807411 |
25,868 | In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g − 1). A group for which the maximum is achieved is called a Hurwitz... | Hurwitz's automorphisms theorem | 0.807411 |
25,869 | In fact, we will prove h {\displaystyle h} is injective. Assume φ ∈ G {\displaystyle \varphi \in G} acts as the identity on V {\displaystyle V} . If fix ( φ ) {\displaystyle \operatorname {fix} (\varphi )} is finite, then by the Lefschetz fixed-point theorem, This is a contradiction, and so fix ( φ ) {\displaystyle... | Hurwitz's automorphisms theorem | 0.807411 |
25,870 | Theorem: Let X {\displaystyle X} be a smooth connected Riemann surface of genus g ≥ 2 {\displaystyle g\geq 2} . Then its automorphism group Aut ( X ) {\displaystyle \operatorname {Aut} (X)} has size at most 84 ( g − 1 ) {\displaystyle 84(g-1)} . Proof: Assume for now that G = Aut ( X ) {\displaystyle G=\operatornam... | Hurwitz's automorphisms theorem | 0.807411 |
25,871 | If g 1 {\displaystyle {\mathfrak {g}}_{1}} is the Levi component of a parabolic subalgebra of g {\displaystyle {\mathfrak {g}}} with weight lattice P1 ⊃ {\displaystyle \supset } P then L ( λ ) | g 1 = ⨁ σ L g 1 ( σ ( 1 ) ) , {\displaystyle L(\lambda )|_{{\mathfrak {g}}_{1}}=\bigoplus _{\sigma }L_{{\mathfrak {g}}_{1}}(\... | Path model | 0.80741 |
25,872 | In mathematics, the Littelmann path model is a combinatorial device due to Peter Littelmann for computing multiplicities without overcounting in the representation theory of symmetrisable Kac–Moody algebras. Its most important application is to complex semisimple Lie algebras or equivalently compact semisimple Lie grou... | Path model | 0.80741 |
25,873 | In 1971 John O'Keefe and Jonathon Dostrovsky reported the discovery of place cells in the rat hippocampus—cells that fire action potentials when an animal passes through a specific small region of space, which is called the place field of the cell. This discovery, although controversial at first, led to a series of inv... | Grid cells | 0.807409 |
25,874 | A grid cell is a type of neuron within the entorhinal cortex that fires at regular intervals as an animal navigates an open area, allowing it to understand its position in space by storing and integrating information about location, distance, and direction. Grid cells have been found in many animals, including rats, mi... | Grid cells | 0.807409 |
25,875 | Many species of mammals can keep track of spatial location even in the absence of visual, auditory, olfactory, or tactile cues, by integrating their movements—the ability to do this is referred to in the literature as path integration. A number of theoretical models have explored mechanisms by which path integration co... | Grid cells | 0.807409 |
25,876 | The FACS group, inaugurated on 16 March 1978, organizes meetings for its members and others on formal methods and related computer science topics. There is an associated journal, Formal Aspects of Computing, published by Springer, and a more informal FACS FACTS newsletter.The group celebrated its 20th anniversary with ... | FACS FACTS | 0.807409 |
25,877 | The Birmingham Solar Oscillations Network (BiSON) consists of a network of six remote solar observatories monitoring low-degree solar oscillation modes. It is operated by the High Resolution Optical Spectroscopy group of the School of Physics and Astronomy at the University of Birmingham, UK, in collaboration with Shef... | Birmingham Solar Oscillations Network | 0.807409 |
25,878 | Astrophysics and Space Science. Springer. 179 (2): 275–283. | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,879 | "Conditions for the appearance of gravitational ultrarelativistic spin-orbital interaction". Soviet Physics Journal. Springer. | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,880 | R. Plyatsko (2011). "Can Mathisson-Papapetrou equations give clue to some problems in astrophysics?". arXiv:1110.2386 . | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,881 | Soviet Physics Journal. Springer. 28 (7): 601–604. | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,882 | "An analytic perturbation approach for classical spinning particle dynamics". International Journal of Theoretical Physics. General Relativity and Gravitation. | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,883 | "Spinning Particles in Spacetimes with Torsion". International Journal of Theoretical Physics. General Relativity and Gravitation. | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,884 | C. Chicone; B. Mashhoon; B. Punsly (2005). "Relativistic motion of spinning particles in a gravitational field". Physics Letters A. 343 (1–3): 1–7. | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,885 | In physics, specifically general relativity, the Mathisson–Papapetrou–Dixon equations describe the motion of a massive spinning body moving in a gravitational field. Other equations with similar names and mathematical forms are the Mathisson–Papapetrou equations and Papapetrou–Dixon equations. All three sets of equatio... | Mathisson–Papapetrou–Dixon equations | 0.807408 |
25,886 | A large application is vector quantization, commonly used in data compression. In geometry, Voronoi diagrams can be used to find the largest empty circle amid a set of points, and in an enclosing polygon; e.g. to build a new supermarket as far as possible from all the existing ones, lying in a certain city. Voronoi dia... | Voronoi cell | 0.807405 |
25,887 | Also the probability of each class p ( l a b e l | θ ) {\displaystyle p({\rm {label}}|{\boldsymbol {\theta }})} is estimated from the collected dataset. Note that the usage of 'Bayes rule' in a pattern classifier does not make the classification approach Bayesian. Bayesian statistics has its origin in Greek philosophy ... | Pattern detection | 0.807405 |
25,888 | Parametric: Linear discriminant analysis Quadratic discriminant analysis Maximum entropy classifier (aka logistic regression, multinomial logistic regression): Note that logistic regression is an algorithm for classification, despite its name. (The name comes from the fact that logistic regression uses an extension of ... | Pattern detection | 0.807405 |
25,889 | Feature selection algorithms attempt to directly prune out redundant or irrelevant features. A general introduction to feature selection which summarizes approaches and challenges, has been given. The complexity of feature-selection is, because of its non-monotonous character, an optimization problem where given a tota... | Pattern detection | 0.807404 |
25,890 | In principle, some of the sites can intersect and even coincide (an application is described below for sites representing shops), but usually they are assumed to be disjoint. In addition, infinitely many sites are allowed in the definition (this setting has applications in geometry of numbers and crystallography), but ... | Voronoi cell | 0.807404 |
25,891 | In particular, Lee Ellis' evolutionary neuroandrogenic theory posits that sexual selection has led to increased exposure to testosterone in males, causing greater competitive behavior which could lead to criminality.Despite the difficulty of interpreting them, crime statistics may provide a way to investigate such a re... | Sex differences in humans | 0.807404 |
25,892 | Statistics have been consistent in reporting that men commit more criminal acts than women. Self-reported delinquent acts are also higher for men than women across many different actions. Many professionals have offered explanations for this sex difference. Some differing explanations include men's evolutionary tendenc... | Sex differences in humans | 0.807404 |
25,893 | Sex differences in suicide have been shown to be significant; there are highly asymmetric rates of suicide and suicide attempts between males and females. The gap, also called the gender paradox of suicidal behavior, can vary significantly between different countries. Statistics demonstrate that males die much more oft... | Sex differences in humans | 0.807404 |
25,894 | In an isothermal titration calorimeter, the heat of reaction is used to follow a titration experiment. This permits determination of the midpoint (stoichiometry) (N) of a reaction as well as its enthalpy (delta H), entropy (delta S) and of primary concern the binding affinity (Ka) The technique is gaining in importance... | Constant-volume calorimeter | 0.807404 |
25,895 | A calorimeter is an object used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal micro calorimeters, titration calorimeters and accelerated rate calorimeters are among the most common types. A simple ... | Constant-volume calorimeter | 0.807404 |
25,896 | Many mapping spaces are ANRs. In particular, let Y be an ANR with a closed subspace A that is an ANR, and let X be any compact metrizable space with a closed subspace B. Then the space ( Y , A ) ( X , B ) {\textstyle \left(Y,A\right)^{\left(X,B\right)}} of maps of pairs ( X , B ) → ( Y , A ) {\textstyle \left(X,B\right... | Deformation retraction | 0.807404 |
25,897 | For example, the Whitehead theorem holds for ANRs: a map of ANRs that induces an isomorphism on homotopy groups (for all choices of base point) is a homotopy equivalence. Since ANRs include topological manifolds, Hilbert cube manifolds, Banach manifolds, and so on, these results apply to a large class of spaces. | Deformation retraction | 0.807404 |
25,898 | In infinite dimensions, Hanner's theorem implies that every Hilbert cube manifold as well as the (rather different, for example not locally compact) Hilbert manifolds and Banach manifolds are ANRs. Every locally finite CW complex is an ANR. An arbitrary CW complex need not be metrizable, but every CW complex has the ho... | Deformation retraction | 0.807404 |
25,899 | (By Dugundji's theorem above, V {\textstyle V} cannot be locally convex.) Since V {\textstyle V} is contractible and not an AR, it is also not an ANR. By Cauty's theorem above, V {\textstyle V} has an open subset U {\textstyle U} that is not homotopy equivalent to a CW complex. Thus there is a metrizable space U {\text... | Deformation retraction | 0.807404 |
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