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6,900 | Organic & Biomolecular Chemistry is a weekly peer-reviewed scientific journal covering all aspects of organic chemistry, including organic aspects of chemical biology, medicinal chemistry, natural product chemistry, supramolecular chemistry, macromolecular chemistry, theoretical chemistry, and catalysis. It is publishe... | Organic and Biomolecular Chemistry | 0.823449 |
6,901 | A matroid that can be generated in this way is called an algebraic matroid. No good characterization of algebraic matroids is known, but certain matroids are known to be non-algebraic; the smallest is the Vámos matroid.Many finite matroids may be represented by a matrix over a field K {\displaystyle K} , in which the m... | Algebraic independence | 0.823437 |
6,902 | Given a field extension L / K {\displaystyle L/K} which is not algebraic, Zorn's lemma can be used to show that there always exists a maximal algebraically independent subset of L {\displaystyle L} over K {\displaystyle K} . Further, all the maximal algebraically independent subsets have the same cardinality, known as ... | Algebraic independence | 0.823437 |
6,903 | The Lindemann–Weierstrass theorem can often be used to prove that some sets are algebraically independent over Q {\displaystyle \mathbb {Q} } . It states that whenever α 1 , … , α n {\displaystyle \alpha _{1},\ldots ,\alpha _{n}} are algebraic numbers that are linearly independent over Q {\displaystyle \mathbb {Q} } , ... | Algebraic independence | 0.823437 |
6,904 | The physics of the zero-temperature phase behavior of jellium is driven by competition between the kinetic energy of the electrons and the electron-electron interaction energy. The kinetic-energy operator in the Hamiltonian scales as 1 / r s 2 {\displaystyle 1/r_{\rm {s}}^{2}} , where r s {\displaystyle r_{\rm {s}}} is... | Homogeneous electron gas | 0.823434 |
6,905 | Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges (i.e. atomic nuclei) are assumed to be uniformly distributed in space; the electron density is a uniform quantity as well in space. This m... | Homogeneous electron gas | 0.823434 |
6,906 | In East Asia, a similar role to Latin and Greek has been played by Chinese, with non-Chinese languages both borrowing a significant number of words from Chinese and using morphemes borrowed from Chinese to coin new words, particularly in formal or technical language. See Sino-Japanese vocabulary, Sino-Korean vocabulary... | Classical compound | 0.823424 |
6,907 | They are often referred to as affixes because some come first and some come last. But if they were affixes proper, a word like biography would have no base whatever. While affixes are grammatical (like prepositions), classical combining forms are lexical (like nouns, adjectives, and verbs): for example, bio- translates... | Classical compound | 0.823424 |
6,908 | In the older sciences, classical combining forms are generally used to form such strictly classical and usually Greek compounds as anthocyanin, astrobleme, chemotherapy, chronobiology, cytokinesis, glossolalia, lalophobia, narcolepsy, osteoporosis, Pliohippus, sympathomimetic. | Classical compound | 0.823424 |
6,909 | Apart from electromagnetics and network theory, other items in the syllabus are particular to electronics engineering course. Electrical engineering courses have other specializations such as machines, power generation and distribution. Note that the following list does not include the large quantity of mathematics (ma... | Education and training of electrical and electronics engineers | 0.823424 |
6,910 | The degree generally includes units covering physics, mathematics, project management and specific topics in electrical and electronics engineering. Initially such topics cover most, if not all, of the sub fields of electrical engineering. Students then choose to specialize in one or more sub fields towards the end of ... | Education and training of electrical and electronics engineers | 0.823424 |
6,911 | Linear constant coefficient differential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits. 2-port network parameters: driving point and transfer functions. State equations. | Education and training of electrical and electronics engineers | 0.823424 |
6,912 | Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta transformation. Steady state sinusoidal analysis using phasors. | Education and training of electrical and electronics engineers | 0.823424 |
6,913 | Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; pulse excitation. Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Antennas: Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, anten... | Education and training of electrical and electronics engineers | 0.823424 |
6,914 | Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems, Maxwell's equations: differential and integral forms. Wave equation, Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth. | Education and training of electrical and electronics engineers | 0.823424 |
6,915 | Function generators and wave-shaping circuits. Power supplies. Digital circuits: Boolean algebra, minimization of Boolean functions; logic gates digital IC families (DTL, TTL, ECL, MOS, CMOS). | Education and training of electrical and electronics engineers | 0.823424 |
6,916 | Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, z-transform. Sampling theorems. Linear Time-Invariant Systems: definitions and properties; casualty, stability, impulse response, convolution, poles and zeros frequency... | Education and training of electrical and electronics engineers | 0.823424 |
6,917 | In cases where an engineer's work fails he or she may be subject to the tort of negligence and, in extreme cases, the charge of criminal negligence. An engineer's work must also comply with numerous other rules and regulations such as building codes and legislation pertaining to environmental law. Significant professio... | Education and training of electrical and electronics engineers | 0.823424 |
6,918 | The first difficulty reflects a crucial problem: Our observations do not contain enough information and additional data are required. Additional data can come from physical prior information on the parameter values, on their spatial distribution or, more generally, on their mutual dependence. It can also come from othe... | Inverse problem | 0.823421 |
6,919 | This area has been studied as a branch of mathematical physics since the 1970s. Nonlinear inverse problems are also currently studied in many fields of applied science (acoustics, mechanics, quantum mechanics, electromagnetic scattering - in particular radar soundings, seismic soundings, and nearly all imaging modaliti... | Inverse problem | 0.823421 |
6,920 | This phenomenon is governed by special nonlinear partial differential evolution equations, for example the Korteweg–de Vries equation. If the spectrum of the operator is reduced to one single eigenvalue, its corresponding motion is that of a single bump that propagates at constant velocity and without deformation, a so... | Inverse problem | 0.823421 |
6,921 | The goal is to recover the wave-speeds (P and S waves) and the density distributions from seismograms. Such inverse problems are of prime interest in seismology and exploration geophysics. We can basically consider two mathematical models: The acoustic wave equation (in which S waves are ignored when the space dimensio... | Inverse problem | 0.82342 |
6,922 | As a result, the optimization problem becomes more difficult. In particular, when the L 1 {\displaystyle L^{1}} norm is used for quantifying the data misfit the objective function is no longer differentiable: its gradient does not make sense any longer. Dedicated methods (see for instance Lemaréchal) from non different... | Inverse problem | 0.82342 |
6,923 | In all cases, computing the gradient of the objective function often is a key element for the solution of the optimization problem. As mentioned above, information about the spatial distribution of a distributed parameter can be introduced through the parametrization. One can also think of adapting this parametrization... | Inverse problem | 0.82342 |
6,924 | The numerical method to be used for solving the optimization problem depends in particular on the cost required for computing the solution F p {\displaystyle Fp} of the forward problem. Once chosen the appropriate algorithm for solving the forward problem (a straightforward matrix-vector multiplication may be not adequ... | Inverse problem | 0.82342 |
6,925 | But this a very specific situation. In general, the solution of an inverse problem requires sophisticated optimization algorithms. When the model is described by a large number of parameters (the number of unknowns involved in some diffraction tomography applications can reach one billion), solving the linear system as... | Inverse problem | 0.82342 |
6,926 | Some inverse problems have a very simple solution, for instance, when one has a set of unisolvent functions, meaning a set of n {\displaystyle n} functions such that evaluating them at n {\displaystyle n} distinct points yields a set of linearly independent vectors. This means that given a linear combination of these f... | Inverse problem | 0.82342 |
6,927 | This problem is tomography like: the measured arrival times are the integral along the ray-path of the slowness. But this tomography like problem is nonlinear, mainly because the unknown ray-path geometry depends upon the velocity (or slowness) distribution. In spite of its nonlinear character, travel-time tomography t... | Inverse problem | 0.82342 |
6,928 | Realizing how difficult is the inverse problem in the wave equation, seismologists investigated a simplified approach making use of geometrical optics. In particular they aimed at inverting for the propagation velocity distribution, knowing the arrival times of wave-fronts observed on seismograms. These wave-fronts can... | Inverse problem | 0.82342 |
6,929 | A master mix is a mixture containing precursors and enzymes used as an ingredient in RT-PCR techniques in molecular biology. Such mixtures contain a mixture dNTPs (required as a substrate for the building of new DNA strands), MgCl2, Taq polymerase (an enzyme required to building new DNA strands), a pH buffer and come m... | Master mix (PCR) | 0.823418 |
6,930 | Contemporary numerical tools include also hybrid multiscale approaches allowing concurrent or sequential utilization of the atomistic scale methods (usually, MD) with the continuum (macro) scale methods (usually, field emission microscopy) within a single mathematical model. Development of these complex methods is a se... | Nanomechanics | 0.823414 |
6,931 | Often, nanomechanics is viewed as a branch of nanotechnology, i.e., an applied area with a focus on the mechanical properties of engineered nanostructures and nanosystems (systems with nanoscale components of importance). Examples of the latter include nanomachines, nanoparticles, nanopowders, nanowires, nanorods, nano... | Nanomechanics | 0.823414 |
6,932 | Nanomechanics is a branch of nanoscience studying fundamental mechanical (elastic, thermal and kinetic) properties of physical systems at the nanometer scale. Nanomechanics has emerged on the crossroads of biophysics, classical mechanics, solid-state physics, statistical mechanics, materials science, and quantum chemis... | Nanomechanics | 0.823414 |
6,933 | {\displaystyle (a+x)(b+y)=ab+ay+bx.} The notion is sometimes called the algebra of dual numbers. A quasi-free algebra, introduced by Cuntz and Quillen, is a sort of generalization of a free algebra and a semisimple algebra over an algebraically closed field. | Unital associative algebra | 0.823409 |
6,934 | The additive identity is 1 and the multiplicative identity is 1 + t {\displaystyle 1+t} . Then A {\displaystyle A} has a canonical structure of a G ( A ) {\displaystyle G(A)} -algebra given by the ring homomorphism On the other hand, if A is a λ-ring, then there is a ring homomorphism giving G ( A ) {\displaystyle G(A)... | Unital associative algebra | 0.823409 |
6,935 | Categorically speaking, the functor that maps an R-module to its tensor algebra is left adjoint to the functor that sends an R-algebra to its underlying R-module (forgetting the multiplicative structure). The following ring is used in the theory of λ-rings. Given a commutative ring A, let G ( A ) = 1 + t A ] , {\displ... | Unital associative algebra | 0.823409 |
6,936 | The free R-algebra on a set E is an algebra of "polynomials" with coefficients in R and noncommuting indeterminates taken from the set E. The tensor algebra of an R-module is naturally an associative R-algebra. The same is true for quotients such as the exterior and symmetric algebras. | Unital associative algebra | 0.823409 |
6,937 | The quaternions form a 4-dimensional associative algebra over the reals (but not an algebra over the complex numbers, since the complex numbers are not in the center of the quaternions). Every polynomial ring R is a commutative R-algebra. In fact, this is the free commutative R-algebra on the set {x1, ..., xn}. | Unital associative algebra | 0.823409 |
6,938 | Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication. This coincides with the previous example when M is a finitely-generated, free R-module. In particular, the square n-by-n matrices with entries from the field K form an associative algebra over K. ... | Unital associative algebra | 0.823409 |
6,939 | Any ring A can be considered as a Z-algebra. The unique ring homomorphism from Z to A is determined by the fact that it must send 1 to the identity in A. Therefore, rings and Z-algebras are equivalent concepts, in the same way that abelian groups and Z-modules are equivalent. Any ring of characteristic n is a (Z/nZ)-al... | Unital associative algebra | 0.823409 |
6,940 | In the commutative case, one can consider the category whose objects are ring homomorphisms R → A; i.e., commutative R-algebras and whose morphisms are ring homomorphisms A → A' that are under R; i.e., R → A → A' is R → A' (i.e., the coslice category of the category of commutative rings under R.) The prime spectrum fun... | Unital associative algebra | 0.823409 |
6,941 | An associative algebra amounts to a ring homomorphism whose image lies in the center. Indeed, starting with a ring A and a ring homomorphism η: R → A {\displaystyle \eta \colon R\to A} whose image lies in the center of A, we can make A an R-algebra by defining r ⋅ x = η ( r ) x {\displaystyle r\cdot x=\eta (r)x} for al... | Unital associative algebra | 0.823409 |
6,942 | A homomorphism between two R-algebras is an R-linear ring homomorphism. Explicitly, φ: A 1 → A 2 {\displaystyle \varphi :A_{1}\to A_{2}} is an associative algebra homomorphism if φ ( r ⋅ x ) = r ⋅ φ ( x ) φ ( x + y ) = φ ( x ) + φ ( y ) φ ( x y ) = φ ( x ) φ ( y ) φ ( 1 ) = 1 {\displaystyle {\begin{aligned}\varphi (r\c... | Unital associative algebra | 0.823409 |
6,943 | The functor which sends A to R ⊗Z A is left adjoint to the functor which sends an R-algebra to its underlying ring (forgetting the module structure). See also: Change of rings. Free algebra A free algebra is an algebra generated by symbols. If one imposes commutativity; i.e., take the quotient by commutators, then one ... | Unital associative algebra | 0.823409 |
6,944 | Tensor products The tensor product of two R-algebras is also an R-algebra in a natural way. See tensor product of algebras for more details. Given a commutative ring R and any ring A the tensor product R ⊗Z A can be given the structure of an R-algebra by defining r · (s ⊗ a) = (rs ⊗ a). | Unital associative algebra | 0.823409 |
6,945 | This becomes an R-algebra with the obvious scalar multiplication. Free products One can form a free product of R-algebras in a manner similar to the free product of groups. The free product is the coproduct in the category of R-algebras. | Unital associative algebra | 0.823409 |
6,946 | Subalgebras A subalgebra of an R-algebra A is a subset of A which is both a subring and a submodule of A. That is, it must be closed under addition, ring multiplication, scalar multiplication, and it must contain the identity element of A. Quotient algebras Let A be an R-algebra. Any ring-theoretic ideal I in A is auto... | Unital associative algebra | 0.823409 |
6,947 | Since a simple Artinian ring is a (full) matrix ring over a division ring, if A is a simple algebra, then A is a (full) matrix algebra over a division algebra D over k; i.e., A = M n ( D ) {\displaystyle A=M_{n}(D)} . More generally, if A is a semisimple algebra, then it is a finite product of matrix algebras (over var... | Unital associative algebra | 0.823409 |
6,948 | In quantum chemistry, size consistency and size extensivity are concepts relating to how the behaviour of quantum chemistry calculations changes with size. Size consistency (or strict separability) is a property that guarantees the consistency of the energy behaviour when interaction between the involved molecular syst... | Size consistency and size extensivity | 0.823399 |
6,949 | (ed.). Probability Theory: The Logic of Science. Cambridge: Cambridge University Press. | Maximum entropy thermodynamics | 0.823394 |
6,950 | The thermodynamic entropy may go "down" as well as up. A more sophisticated analysis is given by the entropy Fluctuation Theorem, which can be established as a consequence of the time-dependent MaxEnt picture. 3. | Maximum entropy thermodynamics | 0.823394 |
6,951 | This may not be the case, for example if the initial description fails to reflect some aspect of the preparation of the system which later becomes relevant. In that case the "failure" of a MaxEnt prediction tells us that there is something more which is relevant that we may have overlooked in the physics of the system.... | Maximum entropy thermodynamics | 0.823394 |
6,952 | In physics, maximum entropy thermodynamics (colloquially, MaxEnt thermodynamics) views equilibrium thermodynamics and statistical mechanics as inference processes. More specifically, MaxEnt applies inference techniques rooted in Shannon information theory, Bayesian probability, and the principle of maximum entropy. The... | Maximum entropy thermodynamics | 0.823394 |
6,953 | The approach also creates a theoretical framework for the study of some very special cases of far-from-equilibrium scenarios, making the derivation of the entropy production fluctuation theorem straightforward. For non-equilibrium processes, as is so for macroscopic descriptions, a general definition of entropy for mic... | Maximum entropy thermodynamics | 0.823394 |
6,954 | (1999). The Concept of Probability in Statistical Physics, Cambridge University Press, Cambridge UK, ISBN 978-0-521-62128-1. Jaynes, E.T. | Maximum entropy thermodynamics | 0.823394 |
6,955 | According to Liouville's theorem for Hamiltonian dynamics, the hyper-volume of a cloud of points in phase space remains constant as the system evolves. Therefore, the information entropy must also remain constant, if we condition on the original information, and then follow each of those microstates forward in time: Δ ... | Maximum entropy thermodynamics | 0.823394 |
6,956 | In principle, maximum entropy thermodynamics does not refer narrowly and only to classical thermodynamic entropy. It is about informational entropy applied to physics, explicitly depending on the data used to formulate the problem at hand. | Maximum entropy thermodynamics | 0.823394 |
6,957 | The Maximum Entropy thermodynamics has some important opposition, in part because of the relative paucity of published results from the MaxEnt school, especially with regard to new testable predictions far-from-equilibrium.The theory has also been criticized in the grounds of internal consistency. For instance, Radu Ba... | Maximum entropy thermodynamics | 0.823394 |
6,958 | The question of how 'rapidly mixing' different properties of the system are then becomes very much of interest. Information about some degrees of freedom of the combined system may become unusable very quickly; information about other properties of the system may go on being relevant for a considerable time. If nothing... | Maximum entropy thermodynamics | 0.823394 |
6,959 | A language model is a probabilistic model of a natural language that can generate probabilities of a series of words, based on text corpora in one or multiple languages it was trained on. Large language models, as their most advanced form, are a combination of feedforward neural networks and transformers. They have sup... | Neural net language model | 0.823393 |
6,960 | In 1637, John Greaves, professor of geometry at Gresham College, made his first of several studies in Egypt and Italy, making numerous measurements of buildings and monuments, including the Great Pyramid. These activities fuelled many centuries of interest in metrology of the ancient cultures by the likes of Isaac Newt... | 366 geometry | 0.823388 |
6,961 | "The first book to ever deal with the possible existence of a 366-degree circle and of a 366-day calendar (rather than speaking of "Megalithic geometry" or "Bronze Age geometry"), The Bronze Age Computer Disc by Alan Butler, has not been commented on either by mainstream scientists or the press. Most scholars and revie... | 366 geometry | 0.823388 |
6,962 | Kendall, Thom's 1955 dataset is unlikely to be the result of chance: "a 1% significance meaning that such a best fit would only occur in 1 in 100 random datasets". A review in The Guardian newspaper of 'Who Built the Moon by Butler and Knight refers to the authors as "an ad man specialising in consumer psychology and a... | 366 geometry | 0.823388 |
6,963 | Publications in pseudoscientific metrology receive little, if any, attention from mainstream scholarship, by nature of being intended for the popular mass market. For French historian Lucien Febvre, Xavier Guichard's work was "time and effort lost based on wordplay".Alexander Thom's theories have been criticized by Ian... | 366 geometry | 0.823388 |
6,964 | In the book Civilization One, Butler and Knight contend that the basic units of volume and mass of the imperial system, the Imperial pint and the avoirdupois pound, are also derived from their Megalithic Yard. Just like the litre is the tenth part of the metre to the cubic power, the tenth part of the Megalithic Yard t... | 366 geometry | 0.823388 |
6,965 | Let V {\displaystyle V} be a real vector space equipped with a nonsingular real antisymmetric bilinear form ( ⋅ , ⋅ ) {\displaystyle (\cdot ,\cdot )} (i.e. a symplectic vector space). The unital *-algebra generated by elements of V {\displaystyle V} subject to the relations f g − g f = i ( f , g ) {\displaystyle fg-gf=... | CAR algebra | 0.823377 |
6,966 | Unlike the axis, its points are not fixed themselves. The axis (where present) and the plane of a rotation are orthogonal.A representation of rotations is a particular formalism, either algebraic or geometric, used to parametrize a rotation map. This meaning is somehow inverse to the meaning in the group theory. | Coordinate rotation | 0.823361 |
6,967 | In spherical geometry, a direct motion of the n-sphere (an example of the elliptic geometry) is the same as a rotation of (n + 1)-dimensional Euclidean space about the origin (SO(n + 1)). For odd n, most of these motions do not have fixed points on the n-sphere and, strictly speaking, are not rotations of the sphere; s... | Coordinate rotation | 0.823361 |
6,968 | As a result, stereoelectronic factors are now commonly considered and exploited in the development of new organic methodology and in the synthesis of complex targets. The scrutiny of stereoelectronic effects has also entered the realms of biochemistry and pharmaceutical chemistry in recent years. A stereoelectronic eff... | Stereoelectronic effect | 0.823355 |
6,969 | It is important to note that stereoelectronic effects should not be misunderstood as a simple combination of steric effects and electronic effects. Founded on a few general principles that govern how orbitals interact, the stereoelectronic effect, along with the steric effect, inductive effect, solvent effect, mesomeri... | Stereoelectronic effect | 0.823355 |
6,970 | In chemistry, primarily organic and computational chemistry, a stereoelectronic effect is an effect on molecular geometry, reactivity, or physical properties due to spatial relationships in the molecules' electronic structure, in particular the interaction between atomic and/or molecular orbitals. Phrased differently, ... | Stereoelectronic effect | 0.823355 |
6,971 | In anisole, the methyl group prefers to be coplanar with the phenyl group, while (trifluoromethoxy)benzene favors a geometry in which the dihedral angle is around 90°. In other words, the O–CF3 bond is perpendicular to the plane of the phenyl group. Further studies illustrate that even for only one or two hydrogen ato... | Stereoelectronic effect | 0.823355 |
6,972 | One structural consequence of acyclic systems due to the stereoelectronic effect is the gauche effect. In 1,2-difluoroethane, despite the steric clash, the preferred conformation is the gauche one because σ(C–H) is a good donor and σ*(C–F) is a good acceptor and the stereoelectronic effect (σ(C–H) → σ*(C–F)) requires t... | Stereoelectronic effect | 0.823355 |
6,973 | Logic: The Laws of Truth is a 2012 book by Nicholas J. Smith, in which the author provides an introduction to classical logic. It covers the formal tools and techniques of logic and their underlying rationales and broader philosophical significance. The book also presents various forms of proof: proof trees, major vari... | Logic: The Laws of Truth | 0.823352 |
6,974 | This equation is different from the standard uncertainty principle, because time is not an operator in quantum mechanics. Corresponding commutator relations also hold for momentum p and position q, which are conjugate variables of each other, along with a corresponding uncertainty principle in momentum and position, si... | Time in physics | 0.823335 |
6,975 | {\displaystyle {\frac {d}{dt}}A=(i\hbar )^{-1}+\left({\frac {\partial A}{\partial t}}\right)_{\mathrm {classical} }.} This equation denotes an uncertainty relation in quantum physics. For example, with time (the observable A), the energy E (from the Hamiltonian H) gives: Δ E Δ T ≥ ℏ 2 {\displaystyle \Delta E\Delta T\ge... | Time in physics | 0.823335 |
6,976 | There is a time parameter in the equations of quantum mechanics. The Schrödinger equation is H ( t ) | ψ ( t ) ⟩ = i ℏ ∂ ∂ t | ψ ( t ) ⟩ {\displaystyle H(t)\left|\psi (t)\right\rangle =i\hbar {\partial \over \partial t}\left|\psi (t)\right\rangle } One solution can be | ψ e ( t ) ⟩ = e − i H t / ℏ | ψ e ( 0 ) ⟩ {\displ... | Time in physics | 0.823335 |
6,977 | His simple and elegant theory shows that time is relative to an inertial frame. In an inertial frame, Newton's first law holds; it has its own local geometry, and therefore its own measurements of space and time; there is no 'universal clock'. An act of synchronization must be performed between two systems, at the leas... | Time in physics | 0.823335 |
6,978 | According to Einstein's general theory of relativity, a freely moving particle traces a history in spacetime that maximises its proper time. This phenomenon is also referred to as the principle of maximal aging, and was described by Taylor and Wheeler as: "Principle of Extremal Aging: The path a free object takes betwe... | Time in physics | 0.823335 |
6,979 | In order to measure time, one can record the number of occurrences (events) of some periodic phenomenon. The regular recurrences of the seasons, the motions of the sun, moon and stars were noted and tabulated for millennia, before the laws of physics were formulated. The sun was the arbiter of the flow of time, but tim... | Time in physics | 0.823335 |
6,980 | At the fifth Solvay conference, that year, Einstein brushed him off with "Vos calculs sont corrects, mais votre physique est abominable." (“Your math is correct, but your physics is abominable”). | Time in physics | 0.823335 |
6,981 | Ilya Prigogine's reprise is "Time precedes existence". In contrast to the views of Newton, of Einstein, and of quantum physics, which offer a symmetric view of time (as discussed above), Prigogine points out that statistical and thermodynamic physics can explain irreversible phenomena, as well as the arrow of time and ... | Time in physics | 0.823335 |
6,982 | Naively applying them to other situations gives rise to such paradoxes as the twin paradox. That paradox can be resolved using for instance Einstein's General theory of relativity, which uses Riemannian geometry, geometry in accelerated, noninertial reference frames. Employing the metric tensor which describes Minkowsk... | Time in physics | 0.823335 |
6,983 | The speed of light c can be seen as just a conversion factor needed because we measure the dimensions of spacetime in different units; since the metre is currently defined in terms of the second, it has the exact value of 299 792 458 m/s. We would need a similar factor in Euclidean space if, for example, we measured wi... | Time in physics | 0.823335 |
6,984 | In physics, time is defined by its measurement: time is what a clock reads. In classical, non-relativistic physics, it is a scalar quantity (often denoted by the symbol t {\displaystyle t} ) and, like length, mass, and charge, is usually described as a fundamental quantity. Time can be combined mathematically with othe... | Time in physics | 0.823335 |
6,985 | See dynamical systems and chaos theory, dissipative structures One could say that time is a parameterization of a dynamical system that allows the geometry of the system to be manifested and operated on. It has been asserted that time is an implicit consequence of chaos (i.e. nonlinearity/irreversibility): the characte... | Time in physics | 0.823335 |
6,986 | In or around 1665, when Isaac Newton (1643–1727) derived the motion of objects falling under gravity, the first clear formulation for mathematical physics of a treatment of time began: linear time, conceived as a universal clock. Absolute, true, and mathematical time, of itself, and from its own nature flows equably wi... | Time in physics | 0.823335 |
6,987 | The variation of refractive index with frequency causes the arrival times of pulses from pulsars and Fast radio bursts to be delayed at lower frequencies (dispersion). The amount of delay is proportional to the column density of free electrons (Dispersion measure, DM), which is useful for both mapping the distribution ... | Warm Ionised Medium | 0.823334 |
6,988 | From the point of view of robust statistics, pivotal quantities are robust to changes in the parameters – indeed, independent of the parameters – but not in general robust to changes in the model, such as violations of the assumption of normality. This is fundamental to the robust critique of non-robust statistics, oft... | Pivotal quantity | 0.823329 |
6,989 | One of the simplest pivotal quantities is the z-score; given a normal distribution with mean μ {\displaystyle \mu } and variance σ 2 {\displaystyle \sigma ^{2}} , and an observation x, the z-score: z = x − μ σ , {\displaystyle z={\frac {x-\mu }{\sigma }},} has distribution N ( 0 , 1 ) {\displaystyle N(0,1)} – a normal ... | Pivotal quantity | 0.823329 |
6,990 | It is relatively easy to construct pivots for location and scale parameters: for the former we form differences so that location cancels, for the latter ratios so that scale cancels. Pivotal quantities are fundamental to the construction of test statistics, as they allow the statistic to not depend on parameters – for ... | Pivotal quantity | 0.823329 |
6,991 | In statistics, a pivotal quantity or pivot is a function of observations and unobservable parameters such that the function's probability distribution does not depend on the unknown parameters (including nuisance parameters). A pivot quantity need not be a statistic—the function and its value can depend on the paramete... | Pivotal quantity | 0.823329 |
6,992 | Inductive reasoning is inherently uncertain. It only deals with the extent to which, given the premises, the conclusion is credible according to some theory of evidence. Examples include a many-valued logic, Dempster–Shafer theory, or probability theory with rules for inference such as Bayes' rule. | Logical induction | 0.823327 |
6,993 | In particular, authors have been encouraged to report their sampling design, reproducibility of molecular data, and details on the spatial data set and spatial analyses utilized. Because the effects of landscape on gene flow are not universal, sweeping generalities cannot be made, and species-specific studies are neces... | Landscape genetics | 0.823321 |
6,994 | As a new and fast growing interdisciplinary field with no explicitly identified best practices, it has been subject to a number of flaws in both study design and interpretation. A 2016 publication identified four common pitfalls of landscape genetics research that should be targeted for correction. These include assumi... | Landscape genetics | 0.823321 |
6,995 | A study published in 2012 analyzed the landscape genetics of white tail deer in Wisconsin and Illinois. They extracted DNA from the lymph nodes of 2,069 harvested deer across 64 townships. Fifteen microsatellite markers were used for genotyping. A Bayesian population assignment test found no distinct subpopulations bas... | Landscape genetics | 0.823321 |
6,996 | There are several ways to collect genetic information. Popular methods in seascape genetics have been single nucleotide polymorphisms (SNPs), mitochondrial DNA, random amplified polymorphic DNAs, microsatellites, allozymes, and full genomes. | Landscape genetics | 0.823321 |
6,997 | A large population will have greater influence from selection than drift, thus marine organisms are more likely to have greater levels of local adaptation. In seascape analyses, genetic data allows for greater species understanding and tracking when the full life history is unknown or unable to be studied with ecology.... | Landscape genetics | 0.823321 |
6,998 | Seascape genetics is a sub discipline of landscape genomics that scientists started to use in 2006. The emergence of this field proceeded landscape genetics, advances in genetic laboratory technology, and higher resolution marine environmental data. Like landscape genetics, seascape genetics is a multidisciplinary fiel... | Landscape genetics | 0.823321 |
6,999 | Landscape genomics also correlates genetic data with landscape data, but the genetic data comes from multiple loci (locations on a chromosome) across the genome of the organism, as in population genomics. Landscape genetics typically measures less than a dozen different microsatellites in an organism, while landscape g... | Landscape genetics | 0.823321 |
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