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89,300 | In statistics, the Fano factor, like the coefficient of variation, is a measure of the dispersion of a counting process. It was originally used to measure the Fano noise in ion detectors. It is named after Ugo Fano, an Italian American physicist. | Fano factor | 0.781367 |
89,301 | Some of the products included in the Windows Server System product branding are designed specifically for interaction with Microsoft Office. These include: BizTalk Server: Business process design and integration tools Exchange Server: E-mail and collaboration server Host Integration Server: Data and management connecto... | Microsoft Servers | 0.781367 |
89,302 | The Fano factor is used in neuroscience to describe variability in neural spiking. In this context, the events are the neural spiking events and the holding times are the Inter-Spike Intervals (ISI). Often, the limit definition of the Fano factor is used, for which, F = lim t → ∞ Var ( N t ) E = Var ( I S I ) ( ... | Fano factor | 0.781367 |
89,303 | A doughnut chart (also spelled donut) is a variant of the pie chart, with a blank center allowing for additional information about the data as a whole to be included. Doughnut charts are similar to pie charts in that their aim is to illustrate proportions. This type of circular graph can support multiple statistics at ... | Doughnut chart | 0.781367 |
89,304 | The PoDFA method provides information on the composition and concentration of the inclusions in molten aluminum. PoDFA is widely used for process characterization and optimization, as well as product improvement. It allows to quickly and accurately assess the effects of various operating practices on metal cleanliness ... | Aluminium alloy inclusions | 0.781367 |
89,305 | From around the late-Noachian/early-Hesperian to sometime around 3.5 billion years ago, the layered sediments deposited in the earlier Noachian epoch were transformed. This transformation probably included a significant additional deposition of high-sulfur-content material of volcanic origin. The change certainly inclu... | Martian spherules | 0.781367 |
89,306 | In 2021, neuroscientist Rhawn Gabriel Joseph and others, including Rudolph Schild, co-authored a paper accepted by the predatory journal Advances in Microbiology which highlighted a series of Opportunity photos of spherules which appeared to show the objects "expand in size, or conversely, change shape, move to new loc... | Martian spherules | 0.781367 |
89,307 | Martian blueberries are either embedded or loose. That is, Martian blueberries are either embedded in the large body of sediments of Meridiani Planum, or they are loose blueberries that lie directly on outcrops of the sediments or lie on top soils spread over the Meridiani sediments. The size of these spherules varies ... | Martian spherules | 0.781367 |
89,308 | Rosenfeld's law is an axiom relating physics to economics, that states that the amount of energy required to produce one dollar of GDP has decreased by about one percent per year since 1845. The original quote by Arthur H. Rosenfeld is: From 1845 to the present, the amount of energy required to produce the same amount ... | Rosenfeld's law | 0.781366 |
89,309 | In some versions of Gaia philosophy, all lifeforms are considered part of one single living planetary being called Gaia. In this view, the atmosphere, the seas and the terrestrial crust would be results of interventions carried out by Gaia through the coevolving diversity of living organisms. The Gaia paradigm was an i... | Gaia Hypothesis | 0.781365 |
89,310 | In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor—albeit an exceedingly common and often unrecognized metaphor—one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as autopoiet... | Gaia Hypothesis | 0.781365 |
89,311 | The Gaia theorem states that the Earth's atmospheric composition is kept at a dynamically steady state by the presence of life. The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than noble gases present in the atmosphere are either made by organis... | Gaia Hypothesis | 0.781365 |
89,312 | The Gaia hypothesis posits that the Earth is a self-regulating complex system involving the biosphere, the atmosphere, the hydrospheres and the pedosphere, tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for conte... | Gaia Hypothesis | 0.781365 |
89,313 | This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovel... | Gaia Hypothesis | 0.781365 |
89,314 | In 2006, the Geological Society of London awarded Lovelock the Wollaston Medal in part for his work on the Gaia hypothesis.Topics related to the hypothesis include how the biosphere and the evolution of organisms affect the stability of global temperature, salinity of seawater, atmospheric oxygen levels, the maintenanc... | Gaia Hypothesis | 0.781365 |
89,315 | The Mediterranean Sea as being Gaia's kidney is found (here) by Kenneth J. Hsu, a correspondence author in 2001. Hsu suggests the "desiccation" of the Mediterranean is evidence of a functioning Gaia "kidney". In this and earlier suggested cases, it is plate movements and physics, not biology, which performs the regulat... | Gaia Hypothesis | 0.781365 |
89,316 | Another influence for the Gaia hypothesis and the environmental movement in general came as a side effect of the Space Race between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph Earthrise taken by astronaut Willia... | Gaia Hypothesis | 0.781365 |
89,317 | It is at least not impossible to regard the earth's parts—soil, mountains, rivers, atmosphere etc,—as organs or parts of organs of a coordinated whole, each part with its definite function. And if we could see this whole, as a whole, through a great period of time, we might perceive not only organs with coordinated fun... | Gaia Hypothesis | 0.781365 |
89,318 | In the twentieth century, Vladimir Vernadsky formulated a theory of Earth's development that is now one of the foundations of ecology. Vernadsky was a Ukrainian geochemist and was one of the first scientists to recognize that the oxygen, nitrogen, and carbon dioxide in the Earth's atmosphere result from biological proc... | Gaia Hypothesis | 0.781365 |
89,319 | Golding later made reference to Gaia in his Nobel prize acceptance speech. In the eighteenth century, as geology consolidated as a modern science, James Hutton maintained that geological and biological processes are interlinked. Later, the naturalist and explorer Alexander von Humboldt recognized the coevolution of liv... | Gaia Hypothesis | 0.781365 |
89,320 | The idea of the Earth as an integrated whole, a living being, has a long tradition. The mythical Gaia was the primal Greek goddess personifying the Earth, the Greek version of "Mother Nature" (from Ge = Earth, and Aia = PIE grandmother), or the Earth Mother. James Lovelock gave this name to his hypothesis after a sugge... | Gaia Hypothesis | 0.781365 |
89,321 | The Pseudomon-groES RNA motif is a conserved RNA structure identified in certain bacteria using bioinformatics. It is found in most species within the family Pseudomonadaceae, and is consistently located in the 5' untranslated regions (5' UTRs) of operons that contain groES genes. RNA transcripts of the groES genes in ... | Pseudomon-groES RNA motif | 0.781364 |
89,322 | An unschooled child may utilize texts or classroom instruction, but these are not considered central to education. Holt asserted that there is no specific body of knowledge that is, or should be, required of a child.Both unschooling and natural learning advocates believe that children learn best by doing; a child may l... | Home schooling | 0.781364 |
89,323 | 2,2,4,4-Tetramethyl-1,3-cyclobutanediol (CBDO) is an aliphatic diol. This diol is produced as a mixture of cis- and trans-isomers, depending on the relative stereochemistry of the hydroxyl groups. It is used as a monomer for the synthesis of polymeric materials, usually as an alternative to bisphenol A (BPA). CBDO is u... | 2,2,4,4-Tetramethyl-1,3-cyclobutanediol | 0.781363 |
89,324 | Other types of bifurcations are also important in dynamical systems, but the saddle-node bifurcation tends to be most important in biology. Real biological systems are subject to small stochastic variations that introduce error terms into the dynamical equations, and this usually leads to more complex bifurcations simp... | Biological applications of bifurcation theory | 0.781362 |
89,325 | Networks with bifurcation in their dynamics control many important transitions in the cell cycle. The G1/S, G2/M, and Metaphase–Anaphase transitions all act as biochemical switches in the cell cycle. For instance, egg extracts of Xenopus laevis are driven in and out of mitosis irreversibly by positive feedback in the p... | Biological applications of bifurcation theory | 0.781362 |
89,326 | The principle of intrusive relationships concerns crosscutting intrusions. In geology, when an igneous intrusion cuts across a formation of sedimentary rock, it can be determined that the igneous intrusion is younger than the sedimentary rock. There are a number of different types of intrusions, including stocks, lacco... | Relative dating | 0.781362 |
89,327 | The principle of Uniformitarianism states that the geologic processes observed in operation that modify the Earth's crust at present have worked in much the same way over geologic time. A fundamental principle of geology advanced by the 18th century Scottish physician and geologist James Hutton, is that "the present is... | Relative dating | 0.781362 |
89,328 | Methods for relative dating were developed when geology first emerged as a natural science in the 18th century. Geologists still use the following principles today as a means to provide information about geologic history and the timing of geologic events. | Relative dating | 0.781362 |
89,329 | The law of included fragments is a method of relative dating in geology. Essentially, this law states that clasts in a rock are older than the rock itself. One example of this is a xenolith, which is a fragment of country rock that fell into passing magma as a result of stoping. Another example is a derived fossil, whi... | Relative dating | 0.781361 |
89,330 | Relative dating methods in archaeology are similar to some of those applied in geology. The principles of typology can be compared to the biostratigraphic approach in geology. | Relative dating | 0.781361 |
89,331 | Relative dating is the science of determining the relative order of past events (i.e., the age of an object in comparison to another), without necessarily determining their absolute age (i.e., estimated age). In geology, rock or superficial deposits, fossils and lithologies can be used to correlate one stratigraphic co... | Relative dating | 0.781361 |
89,332 | X-rays from the storage ring are directed to beamlines, where research experiments are performed. BASEMA (Beamline for Absorption Spectroscopy for Environmental and Material Applications ), a beamline for X-ray absorption fine structure (XAFS) and X-ray fluorescence (XRF) spectroscopy, the 'day-one' beamline to be read... | Synchrotron-Light for Experimental Science and Applications in the Middle East | 0.781361 |
89,333 | The project cost around $98 million, with $5 million donated each by Jordan, Israel, Turkey, Iran and the European Union. The rest was donated by CERN from existing equipment. Jordan became the greatest contributor to the project by donating land and building construction costs, and by pledging to build a $7 million so... | Synchrotron-Light for Experimental Science and Applications in the Middle East | 0.781361 |
89,334 | The need for a large-scale scientific project to bring the Middle-East back into the scientific community as well as promote peace and foster international collaboration has been recognised for almost 40 years. In his speech at the 1979 Nobel Prize banquet, Pakistani physicist Mohammad Abdus Salam stated that we should... | Synchrotron-Light for Experimental Science and Applications in the Middle East | 0.781361 |
89,335 | The rest was donated by CERN from existing equipment. Jordan became the greatest contributor to the project by donating land and building construction costs, and by pledging to build a $7 million solar power plant, which will make SESAME the first accelerator in the world to be powered by renewable energy. The annual o... | Synchrotron-Light for Experimental Science and Applications in the Middle East | 0.781361 |
89,336 | Synchrotron light (also referred to as synchrotron radiation) is radiation that is emitted when charged particles moving at speeds near the speed of light are forced to change direction by a magnetic field. It is the brightest artificial source of X-rays, allowing for the detailed study of molecular structures. When sy... | Synchrotron-Light for Experimental Science and Applications in the Middle East | 0.781361 |
89,337 | When an electromagnetic wave enters a dielectric medium, it excites (resonates) the material's electrons whether they are free or bound, setting them into a vibratory state with the same frequency as the wave. These electrons will in turn radiate their own electromagnetic fields as a result of their oscillation (EM fie... | Ewald–Oseen extinction theorem | 0.781361 |
89,338 | Additionally, the light emitted by the atoms has a component which looks like a wave traveling at the slower speed of light in glass. Altogether, the only wave in the glass is the slow wave, consistent with what we expect from basic optics. A more complete description can be found in Classical Optics and its Applicatio... | Ewald–Oseen extinction theorem | 0.781361 |
89,339 | Individually, each of these waves travels at the speed of light in vacuum, not at the (slower) speed of light in glass. Yet when the waves are added up, they surprisingly create only a wave that travels at the slower speed. The Ewald–Oseen extinction theorem says that the light emitted by the atoms has a component trav... | Ewald–Oseen extinction theorem | 0.781361 |
89,340 | An important part of optical physics theory is starting with microscopic physics—the behavior of atoms and electrons—and using it to derive the familiar, macroscopic, laws of optics. In particular, there is a derivation of how the refractive index works and where it comes from, starting from microscopic physics. The Ew... | Ewald–Oseen extinction theorem | 0.781361 |
89,341 | In optics, the Ewald–Oseen extinction theorem, sometimes referred to as just the extinction theorem, is a theorem that underlies the common understanding of scattering (as well as refraction, reflection, and diffraction). It is named after Paul Peter Ewald and Carl Wilhelm Oseen, who proved the theorem in crystalline a... | Ewald–Oseen extinction theorem | 0.781361 |
89,342 | To verify the planar variant of the divergence theorem for a region R {\displaystyle R}: R = { ( x , y ) ∈ R 2: x 2 + y 2 ≤ 1 } , {\displaystyle R=\left\{(x,y)\in \mathbb {R} ^{2}\ :\ x^{2}+y^{2}\leq 1\right\},} and the vector field: F ( x , y ) = 2 y i + 5 x j . {\displaystyle \mathbf {F} (x,y)=2y\mathbf {i} +5x\mathb... | Gauss' divergence theorem | 0.781358 |
89,343 | Let's say we wanted to evaluate the flux of the following vector field defined by F = 2 x 2 i + 2 y 2 j + 2 z 2 k {\displaystyle \mathbf {F} =2x^{2}{\textbf {i}}+2y^{2}{\textbf {j}}+2z^{2}{\textbf {k}}} bounded by the following inequalities: { 0 ≤ x ≤ 3 } { − 2 ≤ y ≤ 2 } { 0 ≤ z ≤ 2 π } {\displaystyle \left\{0\leq x\le... | Gauss' divergence theorem | 0.781358 |
89,344 | He proved additional special cases in 1833 and 1839. But it was Mikhail Ostrogradsky, who gave the first proof of the general theorem, in 1826, as part of his investigation of heat flow. Special cases were proven by George Green in 1828 in An Essay on the Application of Mathematical Analysis to the Theories of Electric... | Gauss' divergence theorem | 0.781358 |
89,345 | Joseph-Louis Lagrange introduced the notion of surface integrals in 1760 and again in more general terms in 1811, in the second edition of his Mécanique Analytique. Lagrange employed surface integrals in his work on fluid mechanics. He discovered the divergence theorem in 1762.Carl Friedrich Gauss was also using surfac... | Gauss' divergence theorem | 0.781358 |
89,346 | The theory of abelian integrals originated with a paper by Abel published in 1841. This paper was written during his stay in Paris in 1826 and presented to Augustin-Louis Cauchy in October of the same year. This theory, later fully developed by others, was one of the crowning achievements of nineteenth century mathemat... | Abelian integral | 0.781356 |
89,347 | This is a natural step in the theory of integration to the case of integrals involving algebraic functions A {\displaystyle {\sqrt {A}}} , where A {\displaystyle A} is a polynomial of degree > 4 {\displaystyle >4} . The first major insights of the theory were given by Abel; it was later formulated in terms of the Jacob... | Abelian integral | 0.781356 |
89,348 | On 15 September 2013, it was revealed that the NSA was a client of Vupen and had a subscription to its exploit service. On 9 November 2014, the German magazine Der Spiegel reported that the German information security agency BSI, tasked with the protection of federal government networks, was also a client of Vupen. On ... | Vupen | 0.781355 |
89,349 | On 23 July 2015, Vupen's founders launched their new cybersecurity company Zerodium in the US. The company has a different business model as it acquires zero-day capabilities from independent researchers and reports them, along with protective measures and security recommendations, to its government clients. == Referen... | Vupen | 0.781355 |
89,350 | A fixed orbit is the concept, in atomic physics, where an electron is considered to remain in a specific orbit, at a fixed distance from an atom's nucleus, for a particular energy level. The concept was promoted by quantum physicist Niels Bohr c. 1913. The idea of the fixed orbit is considered a major component of the ... | Fixed orbit | 0.781352 |
89,351 | In mathematics, the Castelnuovo–de Franchis theorem is a classical result on complex algebraic surfaces. Let X be such a surface, projective and non-singular, and let ω1 and ω2be two differentials of the first kind on X which are linearly independent but with wedge product 0. Then this data can be represented as a pull... | Castelnuovo–de Franchis theorem | 0.781351 |
89,352 | Many cities and districts have developed traffic control systems to help monitor the movement and flow of vehicles around the road network. This had typically involved looking at historical data, estimates, observations and statistics, such as: Car park usage Pedestrian crossing usage Number of vehicles along a road Ar... | License plate reader | 0.781351 |
89,353 | The Norwegian Mathematical Society (Norwegian: Norsk matematisk forening, NMF) is a professional society for mathematicians. It was formed in 1918, with Carl Størmer elected as its first president. It organizes mathematical contests and the annual Abel symposium and also awards the Viggo Brun Prize to young Norwegian m... | Norwegian Mathematical Society | 0.78135 |
89,354 | In molecular biology, a chromatosome is a result of histone H1 binding to a nucleosome, which contains a histone octamer and DNA. The chromatosome contains 166 base pairs of DNA. 146 base pairs are from the DNA wrapped around the histone core of the nucleosome. The remaining 20 base pairs are from the DNA of histone H1... | Chromatosome | 0.78135 |
89,355 | The complement of a knot itself (as a topological space) is known to be a "complete invariant" of the knot by the Gordon–Luecke theorem in the sense that it distinguishes the given knot from all other knots up to ambient isotopy and mirror image. Some invariants associated with the knot complement include the knot grou... | Link invariant | 0.781349 |
89,356 | An old result in this direction is the Fáry–Milnor theorem states that if the total curvature of a knot K in R 3 {\displaystyle \mathbb {R} ^{3}} satisfies ∮ K κ d s ≤ 4 π , {\displaystyle \oint _{K}\kappa \,ds\leq 4\pi ,} where κ(p) is the curvature at p, then K is an unknot. Therefore, for knotted curves, ∮ K κ d s >... | Link invariant | 0.781349 |
89,357 | In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some invariants are indeed numbers (algebraic), but invariants can range from the... | Link invariant | 0.781349 |
89,358 | In the language of spectral geometry, the three versions of the Wirtinger inequality above can be rephrased as theorems about the first eigenvalue and corresponding eigenfunctions of the Laplace–Beltrami operator on various one-dimensional Riemannian manifolds: the first eigenvalue of the Laplace–Beltrami operator on t... | Wirtinger's inequality for functions | 0.781348 |
89,359 | In the first form given above, the Wirtinger inequality can be used to prove the isoperimetric inequality for curves in the plane, as found by Adolf Hurwitz in 1901. Let (x, y) be a differentiable embedding of the circle in the plane. Parametrizing the circle by so that (x, y) has constant speed, the length L of the c... | Wirtinger's inequality for functions | 0.781348 |
89,360 | {\displaystyle \int _{0}^{L}y(x)^{2}\,\mathrm {d} x\leq {\frac {L^{2}}{\pi ^{2}}}\int _{0}^{L}y'(x)^{2}\,\mathrm {d} x.} and equality holds if and only if y(x) = c cos πx/L for some number c.Despite their differences, these are closely related to one another, as can be seen from the account given below in terms of spec... | Wirtinger's inequality for functions | 0.781348 |
89,361 | The three versions of the Wirtinger inequality can all be proved by various means. This is illustrated in the following by a different kind of proof for each of the three Wirtinger inequalities given above. In each case, by a linear change of variables in the integrals involved, there is no loss of generality in only p... | Wirtinger's inequality for functions | 0.781348 |
89,362 | {\displaystyle \int _{0}^{1}y_{n}(x)^{2}\,\mathrm {d} x\leq {\frac {1}{\pi ^{2}}}\int _{0}^{1}y_{n}'(x)^{2}\,\mathrm {d} x.} It is possible to replace yn by y, and thereby prove the Wirtinger inequality, as soon as it is verified that yn converges in L2 to y. This is verified in a standard way, by writing y ( x ) − y n... | Wirtinger's inequality for functions | 0.781348 |
89,363 | Consider the third Wirtinger inequality given above. Take L to be 1. Given a continuous function f on of average value zero, let Tf) denote the function u on which is of average value zero, and with u′′ + f = 0 and u′(0) = u′(1) = 0. From basic analysis of ordinary differential equations with constant coefficients, t... | Wirtinger's inequality for functions | 0.781348 |
89,364 | This is resolved as follows. It follows from the Hölder inequality and y(0) = 0 that | y ( x ) | = | ∫ 0 x y ′ ( x ) d x | ≤ ∫ 0 x | y ′ ( x ) | d x ≤ x ( ∫ 0 x y ′ ( x ) 2 d x ) 1 / 2 , {\displaystyle |y(x)|=\left|\int _{0}^{x}y'(x)\,\mathrm {d} x\right|\leq \int _{0}^{x}|y'(x)|\,\mathrm {d} x\leq {\sqrt {x}}\left(\in... | Wirtinger's inequality for functions | 0.781348 |
89,365 | {\displaystyle \int _{0}^{\pi }y(x)^{2}\,\mathrm {d} x+\int _{0}^{\pi }{\big (}y'(x)-y(x)\cot x{\big )}^{2}\,\mathrm {d} x=\int _{0}^{\pi }y'(x)^{2}\,\mathrm {d} x.} This proves the Wirtinger inequality, since the second integral is clearly nonnegative. Furthermore, equality in the Wirtinger inequality is seen to be eq... | Wirtinger's inequality for functions | 0.781348 |
89,366 | Consider the second Wirtinger inequality given above. Take L to be π. Any differentiable function y(x) satisfies the identity y ( x ) 2 + ( y ′ ( x ) − y ( x ) cot x ) 2 = y ′ ( x ) 2 − d d x ( y ( x ) 2 cot x ) . {\displaystyle y(x)^{2}+{\big (}y'(x)-y(x)\cot x{\big )}^{2}=y'(x)^{2}-{\frac {d}{dx}}{\big (}y(x)^{2}... | Wirtinger's inequality for functions | 0.781348 |
89,367 | In physics, droplet-shaped waves are casual localized solutions of the wave equation closely related to the X-shaped waves, but, in contrast, possessing a finite support. A family of the droplet-shaped waves was obtained by extension of the "toy model" of X-wave generation by a superluminal point electric charge (tachy... | Droplet-shaped wave | 0.781346 |
89,368 | Statistics Canada releases regular quarter annual intercensal estimates for provinces and territories in Canada. Japan releases regular annual intercensal estimates for all prefectures and cities, every October. National estimates are released monthly. | Intercensal estimate | 0.781346 |
89,369 | Statistics Indonesia (BPS) releases province by province annual estimates for all provinces, regencies, and kota in Indonesia, with some provinces more up to date than others. A survey in conducted every 10 years, 5 years post census. China 1% Survey (全国1％人口抽样调查) 5 years after each census samples 1% of the population t... | Intercensal estimate | 0.781346 |
89,370 | Also shown is optical momentum p, tangent to a light ray and perpendicular to the wavefront. Vector field p = ∇ S {\displaystyle \mathbf {p} =\nabla S} is conservative vector field. The gradient theorem can then be applied to the optical path length (as given above) resulting in and the optical path length S calculated... | Hamiltonian optics | 0.781343 |
89,371 | Liouville’s theorem is essentially statistical in nature, and it refers to the evolution in time of an ensemble of mechanical systems of identical properties but with different initial conditions. Each system is represented by a single point in phase space, and the theorem states that the average density of points in p... | Hamiltonian optics | 0.781343 |
89,372 | The volume occupied by a set of rays in phase space is called etendue, which is conserved as light rays progress in the optical system along direction x3. This corresponds to Liouville's theorem, which also applies to Hamiltonian mechanics. However, the meaning of Liouville’s theorem in mechanics is rather different fr... | Hamiltonian optics | 0.781343 |
89,373 | In phase space a light ray is identified by a point ( x 1 , x 2 , p 1 , p 2 ) {\displaystyle (x_{1},x_{2},p_{1},p_{2})} which moves with a "velocity" v = ( x ˙ 1 , x ˙ 2 , p ˙ 1 , p ˙ 2 ) {\displaystyle \mathbf {v} =({\dot {x}}_{1},{\dot {x}}_{2},{\dot {p}}_{1},{\dot {p}}_{2})} where the dot represents a derivative rel... | Hamiltonian optics | 0.781343 |
89,374 | Figure "volume variation" shows a volume V bound by an area A. Over time, if the boundary A moves, the volume of V may vary. In particular, an infinitesimal area dA with outward pointing unit normal n moves with a velocity v. This leads to a volume variation d V = d A ( v ⋅ n ) d t {\displaystyle dV=dA(\mathbf {v} \cdo... | Hamiltonian optics | 0.781343 |
89,375 | (A ray parallel to x1 would not be between the two rays, since the momentum is not in-between the two rays) In three-dimensional geometry the optical momentum is given by p = ( p 1 , p 2 , p 3 ) {\displaystyle \mathbf {p} =(p_{1},p_{2},p_{3})} with p 1 2 + p 2 2 + p 3 2 = n 2 {\displaystyle p_{1}^{2}+p_{2}^{2}+p_{3}^{2... | Hamiltonian optics | 0.781343 |
89,376 | The EPS Statistical and Nonlinear Physics Prize is a biannual award by the European Physical Society (EPS) given since 2017. Its aim is to recognize outstanding research contributions in the area of statistical physics, nonlinear physics, complex systems, and complex networks. | EPS Statistical and Nonlinear Physics Prize | 0.781343 |
89,377 | In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonym... | Cipher | 0.781343 |
89,378 | Modern encryption methods can be divided by two criteria: by type of key used, and by type of input data. By type of key used ciphers are divided into: symmetric key algorithms (Private-key cryptography), where one same key is used for encryption and decryption, and asymmetric key algorithms (Public-key cryptography), ... | Cipher | 0.781343 |
89,379 | Since the p1 and p2 components of the momentum are constant, only p3 changes from p3A to p3B. Figure "refraction" shows the geometry of this refraction from which d = ‖ p A ‖ sin θ A = ‖ p B ‖ sin θ B {\displaystyle d=\|\mathbf {p} _{A}\|\sin \theta _{A}=\|\mathbf {p} _{B}\|\sin \theta _{B}} . Since ‖ p A ‖ = n A {... | Hamiltonian optics | 0.781343 |
89,380 | In physics, Hamilton's principle states that the evolution of a system ( q 1 ( σ ) , … , q N ( σ ) ) {\displaystyle \left(q_{1}{\left(\sigma \right)},\dots ,q_{N}{\left(\sigma \right)}\right)} described by N {\displaystyle N} generalized coordinates between two specified states at two specified parameters σA and σB is ... | Hamiltonian optics | 0.781343 |
89,381 | Neodymium nitrate is a chemical compound with the formula Nd(NO3)3. It is typically encountered as the hexahydrate, Nd(NO3)3·6H2O, which is more accurately formulated as .2H2O to reflect the crystal structure. It decomposes to NdONO3 at elevated temperature. This water-soluble salt finds use in fabrication of perovskit... | Neodymium(III) nitrate | 0.781343 |
89,382 | In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation F ( x , y , y ′ , … , y ( n − 1 ) ) = y ( n ) x ∈ [ 0 , + ∞ ) {\displaystyle F(x,y,y',\ \dots ,\ y^{(n-1)})=y^{(n)}\quad x\in [0,+\infty )} is called oscillating if it has an infinite number of ro... | Oscillation theory | 0.781341 |
89,383 | Jim Davies studied mathematics at New College, Oxford, joining the Oxford University Computing Laboratory (now the Oxford University Department of Computer Science) in 1986 for a Masters' and Doctorate. After working as a researcher and lecturer in computer science, at Oxford, Reading, and Royal Holloway, University of... | Jim Davies (computer scientist) | 0.781339 |
89,384 | Jim Davies is Professor of Software Engineering and current Director of the Software Engineering Programme at the University of Oxford, England. | Jim Davies (computer scientist) | 0.781339 |
89,385 | Smith received a BSc and PhD in chemistry at University of Canterbury in Christchurch, New Zealand before postdoctoral work at University of California, Berkeley (1991-1993) and the University of Göttingen (Humboldt Fellow 1989–1991).In 1993 he started work at the University of Queensland, eventually heading up the Com... | Sean Smith (chemist) | 0.781335 |
89,386 | Sean Smith is the director of NCI Australia with a conjoint position of professor of computational nanomaterials science and technology at the Australian National University (ANU). | Sean Smith (chemist) | 0.781335 |
89,387 | The EMBO Gold Medal is an annual award of the European Molecular Biology Organization (EMBO) given to young scientists for outstanding contributions to the life sciences in Europe. Laureates receive a medal and €10,000 and are invited to receive the award and present their research at the annual EMBO Meeting and to wri... | EMBO Gold Medal | 0.781335 |
89,388 | The compound is also used to harden iron and steel, in electroplating, dyeing wool, as a laboratory reagent, and as a mild oxidizing agent in organic chemistry. | Potassium hexacyanoferrate(III) | 0.781334 |
89,389 | Let A and B be finitely generated groups and let A∗B be the free product of A and B. Then rank(A∗B) = rank(A) + rank(B).It is obvious that rank(A∗B) ≤ rank(A) + rank(B) since if X is a finite generating set of A and Y is a finite generating set of B then X∪Y is a generating set for A∗B and that |X ∪ Y| ≤ |X| + |Y|. The... | Grushko's theorem | 0.781333 |
89,390 | In the mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality of a generating set) of a free product of two groups is equal to the sum of the ranks of the two free factors. The theorem was first obtained in a 1940 ar... | Grushko's theorem | 0.781333 |
89,391 | The following is a sketch of the proof of Grushko's theorem based on the use of foldings techniques for groups acting on trees (see for complete proofs using this argument). Let S={g1,....,gn} be a finite generating set for G=A∗B of size |S|=n=rank(G). Realize G as the fundamental group of a graph of groups Y which is ... | Grushko's theorem | 0.781333 |
89,392 | Every Stonean space is a Stone space, but not vice versa. In the duality between Stone spaces and Boolean algebras, the Stonean spaces correspond to the complete Boolean algebras. An extremally disconnected first-countable collectionwise Hausdorff space must be discrete. In particular, for metric spaces, the property o... | Extremally disconnected space | 0.781333 |
89,393 | Ocean Power Technologies Australasia Pty Ltd (OPTA) is an Australian company, a subsidiary of Ocean Power Technologies Inc (OPT) of the United States, a renewable energy company, providing power generation devices, services and related equipment for the extraction of energy from ocean waves. In 2009 OPTA was part of Vi... | Ocean Power Technologies Australasia | 0.781332 |
89,394 | The Cr2(OAc)4(H2O)2 molecule contains two atoms of chromium, two ligated molecules of water, and four acetate bridging ligands. The coordination environment around each chromium atom consists of four oxygen atoms (one from each acetate ligand) in a square, one water molecule (in an axial position), and the other chromi... | Chromium(II) acetate | 0.781331 |
89,395 | The incomplete gamma functions are available in various of the computer algebra systems. Even if unavailable directly, however, incomplete function values can be calculated using functions commonly included in spreadsheets (and computer algebra packages). In Excel, for example, these can be calculated using the gamma f... | Upper incomplete gamma function | 0.781331 |
89,396 | Repeated application of the recurrence relation for the lower incomplete gamma function leads to the power series expansion: Given the rapid growth in absolute value of Γ(z + k) when k → ∞, and the fact that the reciprocal of Γ(z) is an entire function, the coefficients in the rightmost sum are well-defined, and locall... | Upper incomplete gamma function | 0.781331 |
89,397 | The Journal of Organic Chemistry. 48 (21): 3833–3835. doi:10.1021/jo00169a053. | Methyl bromoacetate | 0.78133 |
89,398 | The Journal of Organic Chemistry. 59 (12): 3243–3245. doi:10.1021/jo00091a001. | Methyl bromoacetate | 0.78133 |
89,399 | "Biosynthesis of Gibberellins". Journal of Biological Chemistry. 242 (14): 3285–3292. | Methyl bromoacetate | 0.78133 |
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