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10,300 | Simply typed lambda calculus which is a higher-order logic intuitionistic type theory system F LF is often used to define other type theories calculus of constructions and its derivatives | Propositional equality | 0.819087 |
10,301 | This system represents an XNOR logic gate in absorption and an XOR logic gate in transmittance. In another XOR logic gate system, the chemistry is based on the pseudorotaxane depicted in Figure 11. In organic solution the electron-deficient diazapyrenium salt (rod) and the electron-rich 2,3-dioxynaphthalene units of th... | Molecular logic gate | 0.819086 |
10,302 | They can be used to construct digital architectures with varying degrees of complexity by a cascade of a few to several million logic gates. Logic gates are essentially physical devices that produce a singular binary output after performing logical operations based on Boolean functions on one or more binary inputs. The... | Molecular logic gate | 0.819086 |
10,303 | For example, "the fountain pattern...can be stably performed in two ways...one can perform the fountain with different frequencies for the two hands, but that coordination is difficult because of the tendency of the limbs to synchronize," while "in the cascade...the crossing of the balls between the hands demands that ... | Mathematics of juggling | 0.819075 |
10,304 | The discriminant of a polynomial, which is a fundamental tool in number theory is the quotient by its leading coefficient of the resultant of the polynomial and its derivative. If α {\displaystyle \alpha } and β {\displaystyle \beta } are algebraic numbers such that P ( α ) = Q ( β ) = 0 {\displaystyle P(\alpha )=Q(\be... | Resultant | 0.819073 |
10,305 | Macaulay's resultant, named after Francis Sowerby Macaulay, also called the multivariate resultant, or the multipolynomial resultant, is a generalization of the homogeneous resultant to n homogeneous polynomials in n indeterminates. Macaulay's resultant is a polynomial in the coefficients of these n homogeneous polynom... | Resultant | 0.819073 |
10,306 | The fourth edition appeared in 1955 (with the title changed to Algebra), the fifth in 1960, the sixth in 1964, the seventh in 1966, the eighth in 1971, the ninth in 1993. For volume 2, the first edition was published in 1931, the second in 1940, the third in 1955 (with the title changed to Algebra), the fourth in 1959 ... | Moderne Algebra | 0.819073 |
10,307 | Moderne Algebra has a rather confusing publication history, because it went through many different editions, several of which were extensively rewritten with chapters and major topics added, deleted, or rearranged. In addition the new editions of first and second volumes were issued almost independently and at differen... | Moderne Algebra | 0.819073 |
10,308 | It follows that all solutions of a system of polynomial equations with a finite number of projective zeros can be determined in time d O ( n ) . {\displaystyle d^{O(n)}.} Although this bound is large, it is nearly optimal in the following sense: if all input degrees are equal, then the time complexity of the procedure ... | Resultant | 0.819073 |
10,309 | Again as with the original U-resultant, when this U-resultant is not zero, it factorizes into linear factors over any algebraically closed extension of k. The coefficients of these linear factors are the homogeneous coordinates of the common zeros of P 1 , … , P k , {\displaystyle P_{1},\ldots ,P_{k},} and the multipli... | Resultant | 0.819073 |
10,310 | {\displaystyle u_{1},\ldots ,u_{n}.} The determinant of this matrix is the U-resultant. As with the original U-resultant, it is zero if and only if P 1 , … , P k {\displaystyle P_{1},\ldots ,P_{k}} have infinitely many common projective zeros (that is if the projective algebraic set defined by P 1 , … , P k {\displayst... | Resultant | 0.819073 |
10,311 | van der Waerden, Bartel Leendert (1970). Algebra. Vol 1. | Moderne Algebra | 0.819073 |
10,312 | New York, N. Y.: Frederick Ungar Publishing Co. MR 0029363. van der Waerden, Bartel Leendert (1950). Modern Algebra. | Moderne Algebra | 0.819073 |
10,313 | MR 0002841. van der Waerden, Bartel Leendert (1949). Modern Algebra. Vol I. Translated by Blum, Fred. | Moderne Algebra | 0.819073 |
10,314 | ISBN 978-3-540-56799-8. MR 0009016. van der Waerden, Bartel Leendert (1931). Moderne Algebra. | Moderne Algebra | 0.819073 |
10,315 | van der Waerden, Bartel Leendert (1930). Moderne Algebra. Teil I. Die Grundlehren der mathematischen Wissenschaften (in German). | Moderne Algebra | 0.819073 |
10,316 | The first English edition was published in 1949–1950 and was a translation of the second German edition. There was a second edition in 1953, and a third edition under the new title Algebra in 1970 translated from the 7th German edition of volume 1 and the 5th German edition of volume 2. The three English editions were ... | Moderne Algebra | 0.819073 |
10,317 | The entirety of the original problem statement is as follows: The problem consists in this: To establish rigorously and with an exact determination of the limits of their validity those geometrical numbers which Schubert especially has determined on the basis of the so-called principle of special position, or conservat... | Hilbert's fifteenth problem | 0.819071 |
10,318 | Hilbert's fifteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. The problem is to put Schubert's enumerative calculus on a rigorous foundation. | Hilbert's fifteenth problem | 0.819071 |
10,319 | Schubert calculus is the intersection theory of the 19th century, together with applications to enumerative geometry. Justifying this calculus was the content of Hilbert's 15th problem, and was also the major topic of the 20 century algebraic geometry. In the course of securing the foundations of intersection theory, V... | Hilbert's fifteenth problem | 0.819071 |
10,320 | Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its a... | Hilbert's fifteenth problem | 0.819071 |
10,321 | For titanium, this oxidation state is merely easily oxidised, forming a violet Ti3+ aqua cation in solution. The elements have a significant coordination chemistry: zirconium and hafnium are large enough to readily support the coordination number of 8. All three metals however form weak sigma bonds to carbon and becaus... | Group 4 element | 0.819059 |
10,322 | Titanium, being smaller, is distinct from these two: its oxide is less basic than those of zirconium and hafnium, and its aqueous chemistry is more hydrolyzed. Rutherfordium should have a still more basic oxide than zirconium and hafnium.The chemistry of all three is dominated by the +4 oxidation state, though this is ... | Group 4 element | 0.819059 |
10,323 | The oxides TiO2, ZrO2 and HfO2 are white solids with high melting points and unreactive against most acids.The chemistry of group 4 elements is dominated by the group oxidation state. Zirconium and hafnium are in particular extremely similar, with the most salient differences being physical rather than chemical (meltin... | Group 4 element | 0.819059 |
10,324 | Like other groups, the members of this family show patterns in their electron configurations, especially the outermost shells, resulting in trends in chemical behavior. Most of the chemistry has been observed only for the first three members of the group; chemical properties of rutherfordium are not well-characterized,... | Group 4 element | 0.819059 |
10,325 | Group 4 is the second group of transition metals in the periodic table. It contains the four elements titanium (Ti), zirconium (Zr), hafnium (Hf), and rutherfordium (Rf). The group is also called the titanium group or titanium family after its lightest member. As is typical for early transition metals, zirconium and ha... | Group 4 element | 0.819059 |
10,326 | It also significantly influenced research on computers and the brain. The importance of Syntactic Structures lies in Chomsky’s persuasion for a biological perspective on language at a time when it was unusual, and in the context of formal linguistics where it was unexpected. The book led to Chomsky eventually becoming ... | Syntactic Structures | 0.819057 |
10,327 | They believed that languages should be analysed based on how native speakers feel is right. How to translate this idea into a scientific statement remained a vexing issue in American linguistics for decades. Harris and Rulon Wells justified analyzing the object as part of the verb phrase per 'economy'; but this term, a... | Syntactic Structures | 0.819057 |
10,328 | At the time of its publication, Syntactic Structures presented the state of the art of Zellig Harris's formal model of language analysis which is called transformational generative grammar. It can also be said to present Chomsky's version or Chomsky's theory because there is some original input on a more technical leve... | Syntactic Structures | 0.819057 |
10,329 | It also significantly influenced research on computers and the brain.The importance of Syntactic Structures lies in Chomsky’s persuasion for a biological perspective on language at a time when it was unusual, and in the context of formal linguistics where it was unexpected. The book led to Chomsky eventually becoming r... | Syntactic Structures | 0.819057 |
10,330 | NeuroscienceIn 2011, a group of French neuroscientists conducted research to verify if actual brain mechanisms worked in the way that Chomsky suggested in Syntactic Structures. The results suggested that specific regions of the brain handle syntactic information in an abstract way. These are independent from other brai... | Syntactic Structures | 0.819057 |
10,331 | Computer scienceWith its formal and logical treatment of language, Syntactic Structures also brought linguistics and the new field of computer science closer together. Computer scientist Donald Knuth (winner of the Turing Award) recounted that he read Syntactic Structures in 1961 and was influenced by it. Chomsky's "Th... | Syntactic Structures | 0.819057 |
10,332 | The full range of a mechanism depends on the material and geometry of the structure; due to the nature of flexure joints, no purely compliant mechanism can achieve continuous motion such as found in a normal joint. Also, the forces applied by the mechanism are limited to the loads the structural elements can withstand ... | Compliant mechanism | 0.819056 |
10,333 | Compliant mechanisms can be used to create self-adaptive mechanisms, commonly used for grasping in robotics. Since robots require high accuracy and have limited range, there has been extensive research in compliant robot mechanisms. | Compliant mechanism | 0.819056 |
10,334 | In this method, computational methods are used for topology optimization of the structure. Expected loading and desired motion and force transmission are input and the system is optimized for weight, accuracy, and minimum stresses. More advanced methods first optimize the underlying linkage configuration and then optim... | Compliant mechanism | 0.819056 |
10,335 | In mechanical engineering, a compliant mechanism is a flexible mechanism that achieves force and motion transmission through elastic body deformation. It gains some or all of its motion from the relative flexibility of its members rather than from rigid-body joints alone. These may be monolithic (single-piece) or joint... | Compliant mechanism | 0.819056 |
10,336 | There exist only limited possible states of energy for electrons, atoms and molecules. These are determined by the rules of quantum mechanics, which require quantization of energy of a bound system. The atoms/molecules in a higher energy state are said to be excited. | Modern chemistry | 0.819054 |
10,337 | In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structures, it is invariably accompanied by an increase or decrease of energy of the substances... | Modern chemistry | 0.819054 |
10,338 | In chemistry, matter is defined as anything that has rest mass and volume (it takes up space) and is made up of particles. The particles that make up matter have rest mass as well – not all particles have rest mass, such as the photon. Matter can be a pure chemical substance or a mixture of substances. | Modern chemistry | 0.819054 |
10,339 | The electronic theory of chemical bonds and molecular orbitals was developed by the American scientists Linus Pauling and Gilbert N. Lewis. The year 2011 was declared by the United Nations as the International Year of Chemistry. It was an initiative of the International Union of Pure and Applied Chemistry, and of the U... | Modern chemistry | 0.819054 |
10,340 | Thomson of the University of Cambridge discovered the electron and soon after the French scientist Becquerel as well as the couple Pierre and Marie Curie investigated the phenomenon of radioactivity. In a series of pioneering scattering experiments Ernest Rutherford at the University of Manchester discovered the intern... | Modern chemistry | 0.819054 |
10,341 | The inert gases, later called the noble gases were discovered by William Ramsay in collaboration with Lord Rayleigh at the end of the century, thereby filling in the basic structure of the table. At the turn of the twentieth century the theoretical underpinnings of chemistry were finally understood due to a series of r... | Modern chemistry | 0.819054 |
10,342 | In the following decades, many important discoveries were made, such as the nature of 'air' which was discovered to be composed of many different gases. The Scottish chemist Joseph Black and the Flemish Jan Baptist van Helmont discovered carbon dioxide, or what Black called 'fixed air' in 1754; Henry Cavendish discover... | Modern chemistry | 0.819054 |
10,343 | Interdisciplinary fields include agrochemistry, astrochemistry (and cosmochemistry), atmospheric chemistry, chemical engineering, chemical biology, chemo-informatics, environmental chemistry, geochemistry, green chemistry, immunochemistry, marine chemistry, materials science, mechanochemistry, medicinal chemistry, mole... | Modern chemistry | 0.819054 |
10,344 | The Coulomb operator, named after Charles-Augustin de Coulomb, is a quantum mechanical operator used in the field of quantum chemistry. Specifically, it is a term found in the Fock operator. It is defined as: J ^ j ( 1 ) f i ( 1 ) = f i ( 1 ) ∫ | φ j ( 2 ) | 2 1 r 12 d r 2 {\displaystyle {\widehat {J}}_{j}(1)f_{i}(1)=f... | Coulomb operator | 0.819047 |
10,345 | In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized by the class of topological boolean algebras—that is, boolean algebras with an interior operator. Other modal logics are characterized by various other ... | Algebraic semantics (mathematical logic) | 0.819047 |
10,346 | A complete understanding of experimental risks associated with synthetic biology is helping to enforce the knowledge and effectiveness of biosafety. With the potential future creation of man-made unicellular organisms, some are beginning to consider the effect that these organisms will have on biomass already present. ... | Biological Safety | 0.819046 |
10,347 | They create and monitor the biosafety standards that must be met by labs in order to prevent the accidental release of potentially destructive biological material. (note that in the US, several groups are involved, and efforts are being made to improve processes for government run labs, but there is no unifying regulat... | Biological Safety | 0.819046 |
10,348 | The international Cartagena Protocol on Biosafety deals primarily with the agricultural definition but many advocacy groups seek to expand it to include post-genetic threats: new molecules, artificial life forms, and even robots which may compete directly in the natural food chain. Biosafety in agriculture, chemistry, ... | Biological Safety | 0.819046 |
10,349 | Biosafety is the prevention of large-scale loss of biological integrity, focusing both on ecology and human health. These prevention mechanisms include the conduction of regular reviews of biosafety in laboratory settings, as well as strict guidelines to follow. Biosafety is used to protect from harmful incidents. | Biological Safety | 0.819046 |
10,350 | In the first group of examples u is an unknown function of x, and c and ω are constants that are supposed to be known. Two broad classifications of both ordinary and partial differential equations consist of distinguishing between linear and nonlinear differential equations, and between homogeneous differential equatio... | Order of differential equation | 0.819041 |
10,351 | We can therefore exploit convolutions to construct covariance functions. This method of producing non-separable kernels is known as process convolution. Process convolutions were introduced for multiple outputs in the machine learning community as "dependent Gaussian processes". | Kernel methods for vector output | 0.819039 |
10,352 | Much of the initial research in multitask learning in the machine learning community was algorithmic in nature, and applied to methods such as neural networks, decision trees and k-nearest neighbors in the 1990s. The use of probabilistic models and Gaussian processes was pioneered and largely developed in the context o... | Kernel methods for vector output | 0.819039 |
10,353 | The history of learning vector-valued functions is closely linked to transfer learning- storing knowledge gained while solving one problem and applying it to a different but related problem. The fundamental motivation for transfer learning in the field of machine learning was discussed in a NIPS-95 workshop on “Learnin... | Kernel methods for vector output | 0.819039 |
10,354 | From the regularization perspective, the problem is to learn f ∗ {\displaystyle f_{*}} belonging to a reproducing kernel Hilbert space of vector-valued functions ( H {\displaystyle {\mathcal {H}}} ). This is similar to the scalar case of Tikhonov regularization, with some extra care in the notation. † {\displaystyle ^{... | Kernel methods for vector output | 0.819039 |
10,355 | Kernel methods are a well-established tool to analyze the relationship between input data and the corresponding output of a function. Kernels encapsulate the properties of functions in a computationally efficient way and allow algorithms to easily swap functions of varying complexity. In typical machine learning algori... | Kernel methods for vector output | 0.819039 |
10,356 | In this context, the supervised learning problem is to learn the function f {\displaystyle f} which best predicts vector-valued outputs y i {\displaystyle \mathbf {y_{i}} } given inputs (data) x i {\displaystyle \mathbf {x_{i}} } . f ( x i ) = y i {\displaystyle f(\mathbf {x_{i}} )=\mathbf {y_{i}} } for i = 1 , … , N {... | Kernel methods for vector output | 0.819039 |
10,357 | The geometry of a pseudo-Euclidean space is consistent despite some properties of Euclidean space not applying, most notably that it is not a metric space as explained below. The affine structure is unchanged, and thus also the concepts line, plane and, generally, of an affine subspace (flat), as well as line segments. | Pseudo-Euclidean vector space | 0.819032 |
10,358 | Hence terms norm and distance are avoided in pseudo-Euclidean geometry, which may be replaced with scalar square and interval respectively. Though, for a curve whose tangent vectors all have scalar squares of the same sign, the arc length is defined. It has important applications: see proper time, for example. | Pseudo-Euclidean vector space | 0.819032 |
10,359 | A very important pseudo-Euclidean space is Minkowski space, which is the mathematical setting in which Albert Einstein's theory of special relativity is formulated. For Minkowski space, n = 4 and k = 3 so that q ( x ) = x 1 2 + x 2 2 + x 3 2 − x 4 2 , {\displaystyle q(x)=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{4}^{2},} The ge... | Pseudo-Euclidean vector space | 0.819032 |
10,360 | Like with a Euclidean structure, there are raising and lowering indices operators but, unlike the case with Euclidean tensors, there is no bases where these operations do not change values of components. If there is a vector vβ, the corresponding covariant vector is: v α = q α β v β , {\displaystyle v_{\alpha }=q_{\alp... | Pseudo-Euclidean vector space | 0.819032 |
10,361 | Like Euclidean spaces, every pseudo-Euclidean vector space generates a Clifford algebra. Unlike properties above, where replacement of q to −q changed numbers but not geometry, the sign reversal of the quadratic form results in a distinct Clifford algebra, so for example Cl1,2(R) and Cl2,1(R) are not isomorphic. Just l... | Pseudo-Euclidean vector space | 0.819032 |
10,362 | For any d {\displaystyle d} there is a constant C d {\displaystyle C_{d}} such that for any finite field F q {\displaystyle \mathbb {F} _{q}} , any simple subgroup G ⊂ G L d ( F q ) {\displaystyle G\subset \mathrm {GL} _{d}(\mathbb {F} _{q})} and any K {\displaystyle K} -approximate subgroup A ⊂ G {\displaystyle A\subs... | Approximate group | 0.81903 |
10,363 | The Breuillard–Green–Tao theorem on classification of approximate groups can be used to give a new proof of Gromov's theorem on groups of polynomial growth. The result obtained is actually a bit stronger since it establishes that there exists a "growth gap" between virtually nilpotent groups (of polynomial growth) and ... | Approximate group | 0.81903 |
10,364 | Mechanical engineering technology is the application of engineering principles and technological developments for the creation of useful products and production machinery. | Mechanical engineering technology | 0.819027 |
10,365 | Mechanical engineering technologists are expected to apply current technologies and principles from machine and product design, production and material and manufacturing processes. Expandable specialties may include aerospace, automotive, energy, nuclear, petroleum, manufacturing, product development, and industrial de... | Mechanical engineering technology | 0.819027 |
10,366 | Most courses involve algebra and calculus. Oftentimes, a MET graduate could get hired as an engineer; job titles may include Mechanical Engineer and Manufacturing Engineer. In the U.S. | Mechanical engineering technology | 0.819027 |
10,367 | Mechanical Engineering Technology coursework is less theoretical, and more application based than a mechanical engineering degree. This is evident through the additional laboratory coursework required for a degree. The ability to apply concepts from the chemical engineering and electrical engineering fields is importan... | Mechanical engineering technology | 0.819027 |
10,368 | Further, the scalar potential is the fundamental quantity in quantum mechanics. Not every vector field has a scalar potential. Those that do are called conservative, corresponding to the notion of conservative force in physics. | Scalar Potential | 0.819026 |
10,369 | In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: ... | Scalar Potential | 0.819026 |
10,370 | If F is a conservative vector field (also called irrotational, curl-free, or potential), and its components have continuous partial derivatives, the potential of F with respect to a reference point r0 is defined in terms of the line integral: V ( r ) = − ∫ C F ( r ) ⋅ d r = − ∫ a b F ( r ( t ) ) ⋅ r ′ ( t ) d t , {\dis... | Scalar Potential | 0.819026 |
10,371 | Examples of non-conservative forces include frictional forces, magnetic forces, and in fluid mechanics a solenoidal field velocity field. By the Helmholtz decomposition theorem however, all vector fields can be describable in terms of a scalar potential and corresponding vector potential. In electrodynamics, the electr... | Scalar Potential | 0.819026 |
10,372 | A vector field F that satisfies these conditions is said to be irrotational (conservative). Scalar potentials play a prominent role in many areas of physics and engineering. The gravity potential is the scalar potential associated with the gravity per unit mass, i.e., the acceleration due to the field, as a function of... | Scalar Potential | 0.819026 |
10,373 | {\displaystyle {\nabla }\times {\mathbf {F} }=0.} The first of these conditions represents the fundamental theorem of the gradient and is true for any vector field that is a gradient of a differentiable single valued scalar field P. The second condition is a requirement of F so that it can be expressed as the gradient ... | Scalar Potential | 0.819026 |
10,374 | In fields such as microbiology and chemistry, where there is very little variation between individuals and the group size is easily in the millions, these statistical methods are often bypassed and simply splitting a solution into equal parts is assumed to produce identical sample groups. Once equivalent groups have be... | Scientific experimentation | 0.819023 |
10,375 | This implies that spiral galaxies contain large amounts of dark matter or, alternatively, the existence of exotic physics in action on galactic scales. The additional invisible component becomes progressively more conspicuous in each galaxy at outer radii and among galaxies in the less luminous ones.A popular interpret... | Galaxy rotation problem | 0.819021 |
10,376 | If a greedy algorithm can be proven to yield the global optimum for a given problem class, it typically becomes the method of choice because it is faster than other optimization methods like dynamic programming. Examples of such greedy algorithms are Kruskal's algorithm and Prim's algorithm for finding minimum spanning... | Greedy heuristic | 0.819013 |
10,377 | The activity selection problem is characteristic of this class of problems, where the goal is to pick the maximum number of activities that do not clash with each other. In the Macintosh computer game Crystal Quest the objective is to collect crystals, in a fashion similar to the travelling salesman problem. The game h... | Greedy heuristic | 0.819013 |
10,378 | P. C. Matthews Vector Calculus, Springer 1998, ISBN 3-540-76180-2 H. M. Schey, Div Grad Curl and all that: An informal text on vector calculus, 4th edition (W. W. Norton & Company, 2005) ISBN 0-393-92516-1. | Electromagnetic wave equation | 0.819011 |
10,379 | In his 1865 paper titled A Dynamical Theory of the Electromagnetic Field, James Clerk Maxwell utilized the correction to Ampère's circuital law that he had made in part III of his 1861 paper On Physical Lines of Force. In Part VI of his 1864 paper titled Electromagnetic Theory of Light, Maxwell combined displacement cu... | Electromagnetic wave equation | 0.81901 |
10,380 | ISBN 0-7167-1478-7. David H. Staelin, Ann W. Morgenthaler, and Jin Au Kong, Electromagnetic Waves (Prentice-Hall, 1994) ISBN 0-13-225871-4. Charles F. Stevens, The Six Core Theories of Modern Physics, (MIT Press, 1995) ISBN 0-262-69188-4. Markus Zahn, Electromagnetic Field Theory: a problem solving approach, (John Wile... | Electromagnetic wave equation | 0.81901 |
10,381 | ISBN 0-13-805326-X. Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). | Electromagnetic wave equation | 0.81901 |
10,382 | Because of the linearity of Maxwell's equations in a vacuum, solutions can be decomposed into a superposition of sinusoids. This is the basis for the Fourier transform method for the solution of differential equations. The sinusoidal solution to the electromagnetic wave equation takes the form where t is time (in secon... | Electromagnetic wave equation | 0.81901 |
10,383 | Localized time-varying charge and current densities can act as sources of electromagnetic waves in a vacuum. Maxwell's equations can be written in the form of a wave equation with sources. The addition of sources to the wave equations makes the partial differential equations inhomogeneous. | Electromagnetic wave equation | 0.81901 |
10,384 | ISBN 0-471-30932-X. Landau, L. D., The Classical Theory of Fields (Course of Theoretical Physics: Volume 2), (Butterworth-Heinemann: Oxford, 1987). ISBN 0-08-018176-7. | Electromagnetic wave equation | 0.81901 |
10,385 | In physics, in the theory of general relativity, spacetimes with at least a 1-parameter group of isometries can be classified according to the fixed point-sets of the action. Isolated fixed points are called nuts. The other possibility is that the fixed point set is a metric 2-sphere, called bolt. The number of nuts an... | Nuts and bolts (general relativity) | 0.819005 |
10,386 | Geobiology is a field which studies the effects of the Earth's radiation, such as telluric currents and other electromagnetic fields, on biological life. The term is derived from Ancient Greek gē (ge) meaning ‘earth’ and βίος; (bios) meaning ‘life’. Its findings have not been scientifically proven; thus, it is consider... | Earth radiation | 0.819003 |
10,387 | Within geobiology, distinct patterns of Earth radiation, mainly Hartmann lines (named after Ernst Hartmann) and Curry lines (after Manfred Curry; also called Wittmann lines after Siegfried Wittmann) are posited on occasion to have a negative effect on health and even the viability of biological life. Other similar patt... | Earth radiation | 0.819003 |
10,388 | No solid scientific foundation for these phenomena has been made. A task group of the World Health Organization investigating the effects of extremely low frequency (ELF) electric and magnetic fields on the health of the general public found "no substantive health issues related to ELF electric fields at levels general... | Earth radiation | 0.819003 |
10,389 | Practitioners of geobiology will typically use a dowsing rod, pendulum or their hands to ascertain the location of radiation, and then use this information to make an assessment on its effect on a residential dwelling or workplace and upon localised natural life. Practitioners may also claim be to able to locate and mo... | Earth radiation | 0.819003 |
10,390 | Of the Indian texts, the most relevant is the Sthananga Sutra, which also covers number theory as part of a general study of mathematics. The concept of decimal fractions is closely linked with decimal place-value notation; the two seem to have developed in tandem. For example, it is common for the Jain math sutra to i... | Number systems | 0.818996 |
10,391 | It is likely that the concept of fractional numbers dates to prehistoric times. The Ancient Egyptians used their Egyptian fraction notation for rational numbers in mathematical texts such as the Rhind Mathematical Papyrus and the Kahun Papyrus. Classical Greek and Indian mathematicians made studies of the theory of rat... | Number systems | 0.818996 |
10,392 | The elements of an algebraic function field over a finite field and algebraic numbers have many similar properties (see Function field analogy). Therefore, they are often regarded as numbers by number theorists. The p-adic numbers play an important role in this analogy. | Number systems | 0.818996 |
10,393 | Algebraic numbers are those that are a solution to a polynomial equation with integer coefficients. Real numbers that are not rational numbers are called irrational numbers. Complex numbers which are not algebraic are called transcendental numbers. The algebraic numbers that are solutions of a monic polynomial equation... | Number systems | 0.818996 |
10,394 | Two main topology frameworks have been developed and applied to protein molecules. | Protein topology | 0.818995 |
10,395 | Circuit topology categorises intra-chain contacts based on their arrangements. Circuit topology is a determinant of protein folding kinetics and stability. | Protein topology | 0.818995 |
10,396 | Protein topology is a property of protein molecule that does not change under deformation (without cutting or breaking a bond). | Protein topology | 0.818995 |
10,397 | In biology literature, the term topology is also used to refer to mutual orientation of regular secondary structures, such as alpha-helices and beta strands in protein structure . For example, two adjacent interacting alpha-helices or beta-strands can go in the same or in opposite directions. Topology diagrams of diffe... | Protein topology | 0.818995 |
10,398 | In this model, bodies and signals transferring through the neurons connections represent a physical body, and virtual connections between neurons are representing an astral body. It is proposed to create models of artificial neuron networks on the basis of virtual machine supporting the opportunity for paranormal effec... | Semantic neural network | 0.818995 |
10,399 | Of course, neurons interacting by axons-dendrites should have each other's identifiers. An absolute readdressing can be modulated by using neuron specificity as it was realized for biological neural networks. There’s no description for self-reflectiveness and self-modification abilities into the initial description of ... | Semantic neural network | 0.818995 |
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