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84,200 | Featherstone's algorithm is a technique used for computing the effects of forces applied to a structure of joints and links (an "open kinematic chain") such as a skeleton used in ragdoll physics. The Featherstone's algorithm uses a reduced coordinate representation. This is in contrast to the more popular Lagrange mult... | Featherstone's algorithm | 0.799053 |
84,201 | ACGT is a product of the Southern Education and Research Alliance (SERA) and was established in 2001 as the SERA biotechnology task team. ACGT has since grown into a regional initiative. | African Centre for Gene Technologies | 0.799053 |
84,202 | A preference relation is called continuous if, whenever B is preferred to A, small deviations from B or A will not reverse the ordering between them. Formally, a preference relation on a set X is called continuous if it satisfies one of the following equivalent conditions: For every A ∈ X {\displaystyle A\in X} , the s... | Ordinal preferences | 0.799053 |
84,203 | In this model, matter creates defects in spacetime which generate curvature and all the effects of general relativity.The existence of a shortest length at the Planck level has interesting consequences for quantum physics at ultrahigh energies. For example, the uncertainty relation will be modified. The World Crystal i... | World crystal | 0.799052 |
84,204 | Thus, for each a {\displaystyle a} , p ( E | C ( x ) ) = x a {\displaystyle p(E|C(x))=x_{a}} . The claim of the theorem follows since the left hand side is independent of a {\displaystyle a} . The theorem was proved for two agents but the proof for any number of agents is similar. | Aumann's agreement theorem | 0.799052 |
84,205 | These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution. The prediction interval for any standard score z corresponds numerically to (1 − (1 − Φμ,σ2(z)) · 2). For example, Φ(2) ≈ 0.9772, or Pr(X ≤ μ + 2σ) ≈ 0.9772, corresponding to a prediction interval of (1 −... | Three sigma | 0.799052 |
84,206 | "J. P. McM", reviewing the book in Science in 1917, wrote that "the book is one of the strongest documents in support of the mechanistic view of life that has yet been put forth", contrasting this with "vitalism". The reviewer was interested in the "discussion of the physical factors determining the size of organisms, ... | On Growth and Form | 0.799052 |
84,207 | in Information Systems. Bentley has taught courses such as Systems Analysis and Design Methods; Systems Analysis (using structured analysis-based methods); Systems Analysis (using information engineering-based methods); Systems Design (using RAD design-based methods); Systems Design (using structured design-based metho... | Lonnie D. Bentley | 0.799051 |
84,208 | It uses historical and real-time air data, meteorology, traffic flow, human mobility, road networks, and points of interest, which are fed to artificial neural networks and conditional random fields to be processed. Their model is a significant improvement over previous models of citywide air quality.Chet et al. develo... | Urban computing | 0.799051 |
84,209 | Barnsley's work has been a source of inspiration to graphic artists attempting to imitate nature with mathematical models. The fern code developed by Barnsley is an example of an iterated function system (IFS) to create a fractal. This follows from the collage theorem. | Barnsley fern | 0.799051 |
84,210 | The topology τ {\displaystyle \tau } can also be characterized as the set of all arbitrary unions of finite intersections of elements of B {\displaystyle {\mathcal {B}}} . (See the article about subbase.) Now, if B {\displaystyle {\mathcal {B}}} also satisfies properties (B1) and (B2), the topology generated by B {\dis... | Base (topology) | 0.799051 |
84,211 | To establish a correlation as causal within physics, it is normally understood that the cause and the effect must connect through a local mechanism (cf. for instance the concept of impact) or a nonlocal mechanism (cf. the concept of field), in accordance with known laws of nature. From the point of view of thermodynami... | Causal analysis | 0.799051 |
84,212 | Geminus also wrote extensively on mathematics, including a comprehensive Doctrine, (or Theory) of Mathematics. Although this work has not survived, many extracts are preserved by Proclus, Eutocius, and others. He divided mathematics into two parts: Mental (Greek: νοητά) and Observable (Greek: αἰσθητά), or in other word... | Geminus | 0.79905 |
84,213 | As humans begin venturing into space for a longer time, the nutritional requirements for maintaining crew health is critical. Currently NASA is exploring ways of integrating 3D printing food into space in order to sustain the crew's dietary requirements. The vision is to 3D print powdered food layers that have a shelf ... | 3D food printing | 0.79905 |
84,214 | Researchers at Abbott Laboratories identified three novel series of DPP-4 inhibitors using HTS. After more research and optimization ABT-341 was discovered (Figure 8). It is a potent and selective DPP-4 inhibitor with a 2D-structure very similar to sitagliptin. However, the 3D-structure is quite different. | Discovery and development of dipeptidyl peptidase-4 inhibitors | 0.79905 |
84,215 | The physics of magnetic resonance imaging (MRI) concerns fundamental physical considerations of MRI techniques and technological aspects of MRI devices. MRI is a medical imaging technique mostly used in radiology and nuclear medicine in order to investigate the anatomy and physiology of the body, and to detect patholog... | MRI scanner | 0.799049 |
84,216 | Let μ {\displaystyle \mu } be a set function defined on an algebra of sets A {\displaystyle \scriptstyle {\mathcal {A}}} with values in {\displaystyle } (see the extended real number line). The function μ {\displaystyle \mu } is called additive or finitely additive, if whenever A {\displaystyle A} and B {\displaystyle... | Sigma additive | 0.799049 |
84,217 | There may be epigenetic inheritance of disease risk.Watve and Yajnik suggested that changing insulin resistance mediates two phenotypic transitions: a transition in reproductive strategy from "r" (large number of offspring with smaller investment in each) to "K" (smaller number of offspring with greater investment in e... | Thrifty gene hypothesis | 0.799049 |
84,218 | Here we assume that the reader is familiar with partial differential equations. We will be solving the partial differential equation uxx + uyy = f (**)We impose boundedness at infinity. We decompose the domain R² into two overlapping subdomains H1 = (− ∞,1] × R and H2 = [0,+ ∞) × R. In each subdomain, we will be solvin... | Additive Schwarz method | 0.799049 |
84,219 | In 1992, the commercial amorphous alloy, Vitreloy 1 (41.2% Zr, 13.8% Ti, 12.5% Cu, 10% Ni, and 22.5% Be), was developed at Caltech, as a part of Department of Energy and NASA research of new aerospace materials.By 2000, research in Tohoku University and Caltech yielded multicomponent alloys based on lanthanum, magnesiu... | Bulk metallic glasses | 0.799049 |
84,220 | Boethius provided a place for mathematics in the curriculum in the 6th century when he coined the term quadrivium to describe the study of arithmetic, geometry, astronomy, and music. He wrote De institutione arithmetica, a free translation from the Greek of Nicomachus's Introduction to Arithmetic; De institutione music... | History of mathematical notation | 0.799049 |
84,221 | It was shown that this is due to the fact that these attacks can leak data using transient instructions that never get committed during a very short transient window and so are not visible from architecture layer (software) before leakage, but they are visible in microarchitecture layer (hardware). Additionally, softwa... | Bounds Check Bypass Store | 0.799048 |
84,222 | Two major problems in solving DAEs are index reduction and consistent initial conditions. Most numerical solvers require ordinary differential equations and algebraic equations of the form d x d t = f ( x , y , t ) , 0 = g ( x , y , t ) . {\displaystyle {\begin{aligned}{\frac {dx}{dt}}&=f\left(x,y,t\right),\\0&=g\left(... | Differential-algebraic equation | 0.799048 |
84,223 | This allows us to write the latter as rational functions of t (solutions are given below). The parameter t represents the stereographic projection of the point (cos φ, sin φ) onto the y-axis with the center of projection at (−1, 0). Thus, the tangent half-angle formulae give conversions between the stereographic coordi... | Tangent half-angle formula | 0.799048 |
84,224 | The Brunn–Minkowski inequality can be used to deduce the following inequality V ( K , … , K , L ) n ≥ V ( K ) n − 1 V ( L ) {\textstyle V(K,\ldots ,K,L)^{n}\geq V(K)^{n-1}V(L)} , where the V ( K , … , K , L ) {\textstyle V(K,\ldots ,K,L)} term is a mixed-volume. Equality holds iff K,L are homothetic. (See theorem 3.4.3... | Brunn–Minkowski theorem | 0.799048 |
84,225 | The understanding of GIST biology changed significantly with identification of the molecular basis of GIST,: 1065 particularly c-KIT. Historically, literature reviews prior to the molecular definition of GIST, and for a short time thereafter, asserted that 70-80% of GISTs were benign. The identification of a molecular ... | Gastrointestinal stromal tumor | 0.799047 |
84,226 | The HHK-1 lander may include a small ultraviolet telescope called Lunar Ultraviolet Cosmic Imager (LUCI) that was developed by the Indian Institute of Astrophysics. In June 2016 a letter of intent was signed with the French space agency CNES to carry the Color CMOS Camera for Space Exploration (CASPEX) micro-camera on ... | TeamIndus | 0.799047 |
84,227 | In 1986 she was made a professor of physical chemistry at Pierre-and-Marie-Curie University. Here she focused her research on phenomena involving mixing and on the physics of Interfaces. In 1991 she joined the Curie Institute and began research on biophysics. | Françoise Brochard-Wyart | 0.799047 |
84,228 | The palimpsest contains the only known copy of The Method of Mechanical Theorems. In his other works, Archimedes often proves the equality of two areas or volumes with Eudoxus' method of exhaustion, an ancient Greek counterpart of the modern method of limits. Since the Greeks were aware that some numbers were irrationa... | Archimedes Palimpsest | 0.799047 |
84,229 | Static valves are defined as valves which have fixed geometry without any moving parts. These valves provide flow rectification through addition of energy (active) or inducing desired flow behavior by fluid inertia (passive). Two most common types of static geometry passive valves are Diffuser-Nozzle Elements and Tesla... | Micropump | 0.799047 |
84,230 | The detailed story behind these events, long forgotten, was brought back to life in a sequence of publications by multiple authors in the early and mid 1990s, including Barrow-Green's dissertation, a journal publication based on the dissertation, and this book.The first chapter of Poincaré and the Three-Body Problem in... | Poincaré and the Three-Body Problem | 0.799047 |
84,231 | Between 1958 and 1972, the Riverside Methodist Hospital in Columbus, Ohio became the first hospital in Central Ohio to develop an extensive cobalt therapy program, where the use of cobalt-60 became the dominant radiation source for treating patients with cancer. In 1973, 30-year-old Joel Axt was hired by the hospital a... | Columbus radiotherapy accident | 0.799046 |
84,232 | In addition to the above concrete examples, there are a number of standard linear algebraic constructions that yield vector spaces related to given ones. In addition to the definitions given below, they are also characterized by universal properties, which determine an object X {\displaystyle X} by specifying the linea... | Complex vector space | 0.799046 |
84,233 | Many times special sessions were scheduled within the programme of the Workshop. In the year 2016 there was a session "Integrability and Geometry" financed by National Science Foundation. In the year 2017 there was a session dedicated to the memory and scientific achievements of S. Twareque Ali, long time participant a... | Workshop on Geometric Methods in Physics | 0.799046 |
84,234 | Examples of basketball statistics include: Averages per game are denoted by *PG (e.g. BLKPG or BPG, STPG or SPG, APG, RPG and MPG). Sometime the players statistics are divided by minutes played and multiplied by 48 minutes (had he played the entire game), denoted by * per 48 min. or *48M. | Basketball statistics | 0.799046 |
84,235 | Repovš is the leading Slovenian expert on nonlinear analysis and topology and is one of the best known Slovenian mathematicians. He has published over 450 research papers and has given numerous invited talks at various international conferences and universities around the world. His research interests are in nonlinear ... | Dušan Repovš | 0.799046 |
84,236 | In molecular biology, restriction fragment length polymorphism (RFLP) is a technique that exploits variations in homologous DNA sequences, known as polymorphisms, populations, or species or to pinpoint the locations of genes within a sequence. The term may refer to a polymorphism itself, as detected through the differi... | Restriction Fragment Length Polymorphism | 0.799045 |
84,237 | A number of quantum algorithms for machine learning are based on the idea of amplitude encoding, that is, to associate the amplitudes of a quantum state with the inputs and outputs of computations. Since a state of n {\displaystyle n} qubits is described by 2 n {\displaystyle 2^{n}} complex amplitudes, this information... | Quantum artificial intelligence | 0.799045 |
84,238 | The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), ... The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prim... | Prime factor | 0.799045 |
84,239 | Certain research areas are interdisciplinary, such as biophysics and quantum chemistry, which means that the boundaries of physics are not rigidly defined. In the nineteenth and twentieth centuries physicalism emerged as a major unifying feature of the philosophy of science as physics provides fundamental explanations ... | Scientific discipline | 0.799045 |
84,240 | Among ringed spaces, especially important and prominent is a locally ringed space: a ringed space in which the analogy between the stalk at a point and the ring of germs of functions at a point is valid. Ringed spaces appear in analysis as well as complex algebraic geometry and the scheme theory of algebraic geometry. ... | Structure sheaf | 0.799045 |
84,241 | , β n {\displaystyle \beta _{1},..,\beta _{n}} are irrational algebraic numbers such that the set { 1 , β 1 , . . . , β n } {\displaystyle \{1,\beta _{1},...,\beta _{n}\}} is linearly independent over the rational numbers, then the number α 1 β 1 α 2 β 2 ⋯ α n β n {\displaystyle \alpha _{1}^{\beta _{1}}\alpha _{2}^{\be... | Alan Baker (mathematician) | 0.799045 |
84,242 | The Center for Life Detection (CLD) is a collaboration among scientists and technologists from NASA’s Ames Research Center and Goddard Spaceflight Center, which formed in 2018 to support the planning and implementation of missions that will seek evidence of life beyond Earth. CLD is supported by NASA’s Planetary Scienc... | Center for Life Detection | 0.799044 |
84,243 | In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining thei... | Ginzburg–Landau theory | 0.799044 |
84,244 | Such physical ideas have nothing to do with the mathematical theory on a technical level, but there are examples of indirect involvement (see for example Mark Kac's question Can you hear the shape of a drum?). Hilbert's adoption of the term "spectrum" has been attributed to an 1897 paper of Wilhelm Wirtinger on Hill di... | Spectral theory | 0.799044 |
84,245 | GPS observation processing must also compensate for the Sagnac effect. The GPS time scale is defined in an inertial system but observations are processed in an Earth-centered, Earth-fixed (co-rotating) system. A coordinate transformation is thus applied to convert from the inertial system to the ECEF system. The result... | Error analysis for the Global Positioning System | 0.799044 |
84,246 | In field theory, the independent variable is replaced by an event in spacetime (x, y, z, t), or more generally still by a point s on a Riemannian manifold. The dependent variables are replaced by the value of a field at that point in spacetime φ ( x , y , z , t ) {\displaystyle \varphi (x,y,z,t)} so that the equations ... | Lagrangian (field theory) | 0.799044 |
84,247 | Bhattacharyya, Sayantani; Hubeny, Veronika E.; Minwalla, Shiraz; Rangamani, Mukund (2008). "Nonlinear fluid dynamics from gravity". Journal of High Energy Physics. | Veronika Hubeny | 0.799043 |
84,248 | The combination of high gain, low noise, high frequency response or, equivalently, ultra-fast response, and large area of collection has maintained photomultipliers an essential place in low light level spectroscopy, confocal microscopy, Raman spectroscopy, fluorescence spectroscopy, nuclear and particle physics, astro... | Photomultiplier tubes | 0.799043 |
84,249 | A supporting electrolyte, in electrochemistry, according to an IUPAC definition, is an electrolyte containing chemical species that are not electroactive (within the range of potentials used) and which has an ionic strength and conductivity much larger than those due to the electroactive species added to the electrolyt... | Supporting electrolyte | 0.799042 |
84,250 | The projection of a string is essentially the same as a projection in relational algebra. String projection may be promoted to the projection of a language. Given a formal language L, its projection is given by π Σ ( L ) = { π Σ ( s ) | s ∈ L } {\displaystyle \pi _{\Sigma }(L)=\{\pi _{\Sigma }(s)\ \vert \ s\in L\}} | String substitution | 0.799041 |
84,251 | In mathematics, geometry and topology is an umbrella term for the historically distinct disciplines of geometry and topology, as general frameworks allow both disciplines to be manipulated uniformly, most visibly in local to global theorems in Riemannian geometry, and results like the Gauss–Bonnet theorem and Chern–Wei... | Geometry and topology | 0.799041 |
84,252 | The reciprocity theorem for view factors allows one to calculate F B → A {\displaystyle F_{B\rightarrow A}} if one already knows F A → B {\displaystyle F_{A\rightarrow B}} . Using the areas of the two surfaces A A {\displaystyle A_{A}} and A B {\displaystyle A_{B}} , A A F A → B = A B F B → A {\displaystyle A_{A}F_{A\r... | Form factor (radiative transfer) | 0.799041 |
84,253 | In biology, a biological life cycle (or just life cycle when the biological context is clear) is a series of changes in form that an organism undergoes, returning to the starting state. "The concept is closely related to those of the life history, development and ontogeny, but differs from them in stressing renewal." T... | Parasitic life cycles | 0.799041 |
84,254 | A Java implementation is included in the ELKI data mining framework. A Julia implementation of affinity propagation is contained in Julia Statistics's Clustering.jl package. A Python version is part of the scikit-learn library. An R implementation is available in the "apcluster" package. == References == | Affinity propagation | 0.799041 |
84,255 | In Campi (2015) a non-convex theory of scenario optimization was proposed. This involves measuring the number of support constraints, S {\displaystyle S} , for the Interval Predictor Model after training and hence making predictions about the reliability of the model. This enables non-convex IPMs to be created, such as... | Interval predictor model | 0.79904 |
84,256 | Linguistic educational programmes were broadcast on television, the most famous being Álljunk meg egy szóra! "Let's stop for a word", screened more than 500 occasions between 1987 and 1997, and some of its issues were published in a book.Apart from the Geographical Names Committee and the manual on geographical names m... | Hungarian orthography | 0.79904 |
84,257 | Using stylus and data gloves as input devices, the user can create, modify mesh, and specify boundary conditions. For a simple geometry, real-time color-coded results are obtained by changing loads on the model. Studies have used artificial neural networks (ANN) or approximation methods to achieve real-time interaction... | Presence (virtual reality) | 0.79904 |
84,258 | For instance, curves of this type could be realized algebraically as certain rose curves. However, it is common instead to draw a petal projection using straight line segments across the crossing point, connected at their endpoints by smooth curves to form the petals.In order to specify the above-below relation of the ... | Petal projection | 0.79904 |
84,259 | In physics, particularly kinematics, jerk is defined as the third derivative of the position function of an object. It is, essentially, the rate at which acceleration changes. In mathematical terms: j ( t ) = d 3 r d t 3 {\displaystyle \mathbf {j} (t)={\frac {d^{3}\mathbf {r} }{dt^{3}}}} where j(t) is the jerk function... | Third derivative | 0.79904 |
84,260 | The goals of Europa Clipper are to explore Europa, investigate its habitability and aid in the selection of a landing site for the future Europa Lander. This exploration is focused on understanding the three main requirements for life: liquid water, chemistry, and energy. Specifically, the objectives are to study: Ice ... | Europa Clipper | 0.79904 |
84,261 | Abraham Quintanilla Jr., singer-songwriter; former shipping clerk at Dow's Freeport, Texas facility. Sheldon Roberts, semiconductor pioneer who helped found Silicon Valley; former technical researcher at Dow. Alexander Shulgin, chemist and pharmacologist credited with introducing the drug MDMA ("ecstasy") to psychologi... | Dow Chemical Company | 0.799039 |
84,262 | Because there were few jobs in Baltimore, Theodorsen took a job working the third shift as an oiler at the Sparrows Point electrical generating plant 20 miles from Baltimore. Then Johns Hopkins University advertised for an instructor in mechanical engineering and he obtained the position. He taught at Johns Hopkins for... | Theodore Theodorsen | 0.799039 |
84,263 | He became a Copernican at that time. In a student disputation, he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe. Despite his desire to become a minister, near the end of his studies, Kepler was recommended fo... | Johannes Kepler | 0.799039 |
84,264 | The ISS provides a platform to conduct scientific research, with power, data, cooling, and crew available to support experiments. Small uncrewed spacecraft can also provide platforms for experiments, especially those involving zero gravity and exposure to space, but space stations offer a long-term environment where st... | ISS flare | 0.799038 |
84,265 | The biotic or living elements are all of the local species and local ecosystems - including humans and urban ecologies - that interact with the site. This concept is distinctly different from green building, or sustainable architecture where the goal is to "minimize the negative environmental impact of buildings". Ecol... | Ecological Building | 0.799038 |
84,266 | Oxidation of these complexes yields formaldehyde, and reduction yields methane. Free methylene undergoes the typical chemical reactions of a carbene. Addition reactions are very fast and exothermic.When the methylene molecule is in its state of lowest energy, the unpaired valence electrons are in separate atomic orbita... | Methylene radical | 0.799038 |
84,267 | "The method of killing homotopy groups", due to Cartan and Serre (1952a, 1952b) involves repeatedly using the Hurewicz theorem to compute the first non-trivial homotopy group and then killing (eliminating) it with a fibration involving an Eilenberg–MacLane space. In principle this gives an effective algorithm for compu... | Stable stem | 0.799038 |
84,268 | In physics, if you observe a gas at a fixed temperature and pressure in a uniform gravitational field, the heights of the various molecules also follow an approximate exponential distribution, known as the Barometric formula. This is a consequence of the entropy property mentioned below. In hydrology, the exponential d... | Negative exponential distribution | 0.799038 |
84,269 | Examples of PPE include face masks, face shields, connectors, gowns, and goggles. The most popular forms of 3D printed PPE are face masks, face shields, and connectors.Nowadays, Additive Manufacturing is also employed in the field of pharmaceutical sciences. Different techniques of 3D printing (e.g. FDM, SLS, Inkjet Pr... | Applications of 3D printing | 0.799037 |
84,270 | Nicanor Robles Austriaco, Jr. OP is a Filipino-American molecular biologist and Catholic priest. He is a professor of biology and professor of theology at Providence College, in Providence, Rhode Island, and a research fellow at the Center for Theology, Religious Studies, and Ethics, at the University of Santo Tomas in... | Thomistic evolution | 0.799037 |
84,271 | A metal may be a chemical element such as iron; an alloy such as stainless steel; or a molecular compound such as polymeric sulfur nitride.In physics, a metal is generally regarded as any substance capable of conducting electricity at a temperature of absolute zero. Many elements and compounds that are not normally cla... | Metallic crystal | 0.799037 |
84,272 | The infamous quote "Hilbert space is a big place!" is attributed to Caves in a paper on quantum information.Caves is the author of over 140 scientific papers on these and other topics. His present research is concentrated on quantum metrology, quantum control, and quantum information science. In addition to his interes... | Carlton M. Caves | 0.799036 |
84,273 | Cranmer is active in the discussions of data preservation, open access, reproducibility, machine learning, and e-science in the context of particle physics. Cranmer performed a search for exotic Higgs decays in archived data from the ALEPH experiment ten years after the experiment finalized. He serves on the advisory b... | Kyle Cranmer | 0.799036 |
84,274 | The Combined Array for Research in Millimeter-wave Astronomy (CARMA) was an astronomical instrument comprising 23 radio telescopes, dedicated in 2006. These telescopes formed an astronomical interferometer where all the signals are combined in a purpose-built computer (a correlator) to produce high-resolution astronomi... | Combined Array for Research in Millimeter-wave Astronomy | 0.799036 |
84,275 | This paper recommended the 2-sample variance with T = τ, referring to it as Allan variance (now without the quotes). The choice of such parametrisation allows good handling of some noise forms and getting comparable measurements; it is essentially the least common denominator with the aid of the bias functions B1 and B... | Allan variance | 0.799036 |
84,276 | In molecular biology, BAR domains are highly conserved protein dimerisation domains that occur in many proteins involved in membrane dynamics in a cell. The BAR domain is banana-shaped and binds to membrane via its concave face. It is capable of sensing membrane curvature by binding preferentially to curved membranes. ... | BAR domain | 0.799036 |
84,277 | Using more trigonometry, the law of cosines can be deduced by using the Pythagorean theorem only once. In fact, by using the right triangle on the left hand side of Fig. 6 it can be shown that: using the trigonometric identity This proof needs a slight modification if b < a cos(γ). In this case, the right triangle to w... | Laws of cosines | 0.799036 |
84,278 | In 1958 however, he received a letter from Saul Kripke, who pointed out that this assumption is perhaps unwarranted. In a development that foreshadowed a similar one in computer science, Prior took this under advisement, and developed two theories of branching time, which he called "Ockhamist" and "Peircean". | Tense logic | 0.799035 |
84,279 | André Weil's famous Weil conjectures proposed that certain properties of equations with integral coefficients should be understood as geometric properties of the algebraic variety that they define. His conjectures postulated that there should be a cohomology theory of algebraic varieties that gives number-theoretic inf... | Grothendieck topologies | 0.799035 |
84,280 | The following table summarizes the properties of the various maps mentioned in the definition The image of G under the adjoint representation is denoted by Ad(G). If G is connected, the kernel of the adjoint representation coincides with the kernel of Ψ which is just the center of G. Therefore, the adjoint representati... | Adjoint representation of a Lie group | 0.799035 |
84,281 | In molecular biology, Glycoside hydrolase family 14 is a family of glycoside hydrolases. Glycoside hydrolases EC 3.2.1. are a widespread group of enzymes that hydrolyse the glycosidic bond between two or more carbohydrates, or between a carbohydrate and a non-carbohydrate moiety. A classification system for glycoside h... | Glycoside hydrolase family 14 | 0.799035 |
84,282 | Land Change Modeling should also better integrate positive and normative approaches to explanation and prediction based on evidence-based accounts of land systems. It should also integrate optimization approaches to explore the outcomes that are the most beneficial and the processes that might produce those outcomes. | Land change modeling | 0.799035 |
84,283 | He dedicated his thesis dissertation "To those who could have done a better job than I, but never received the opportunities...may they (one day) receive the opportunities to share their knowledge and their skills in a society w/o prejudices". Following his PhD, Colón-Ramos moved to California in 2004 to pursue a postd... | Daniel Colón-Ramos | 0.799034 |
84,284 | Exact statistics, such as that described in exact test, is a branch of statistics that was developed to provide more accurate results pertaining to statistical testing and interval estimation by eliminating procedures based on asymptotic and approximate statistical methods. The main characteristic of exact methods is t... | Exact Statistics | 0.799034 |
84,285 | To send M 1 {\displaystyle M_{1}} and M 2 {\displaystyle M_{2}} to Alice, Bob may naively encrypt the messages and transmit the resulting ciphertexts C 1 ; C 2 {\displaystyle C_{1};C_{2}} . Eve can easily recover M 1 ; M 2 {\displaystyle M_{1};M_{2}} , given C 1 ; C 2 {\displaystyle C_{1};C_{2}} , by using the followin... | Coppersmith's attack | 0.799034 |
84,286 | Optimization algorithms can be considered self-organizing because they aim to find the optimal solution to a problem. If the solution is considered as a state of the iterative system, the optimal solution is the selected, converged structure of the system. Self-organizing networks include small-world networks self-stab... | Self organisation | 0.799034 |
84,287 | The curve has genus two, and so by Faltings theorem there are only a finite number of rational points on it. These rational points were proven by Nils Bruin using the computer program Kash to be the only ones on C168, and they give only four distinct trinomial polynomials with Galois group PSL(2,7): x7-7x+3 (the Trinks... | Elkies trinomial curves | 0.799034 |
84,288 | In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of o... | Boole's inequality | 0.799034 |
84,289 | In this case, one can take L n = S n , {\displaystyle L_{n}=S_{n},} and L k = 0 {\displaystyle L_{k}=0} (the zero module) for every k > n. This allows restating Hilbert's syzygy theorem: If R = K {\displaystyle R=K} is a polynomial ring in n indeterminates over a field K, then every free resolution is finite of length... | Linear relation | 0.799033 |
84,290 | Its unit of dimension when working with the International System of Units is meters to the fourth power, m4. Arithmetic meanIn mathematics and statistics, the arithmetic mean or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection... | Glossary of engineering: A–L | 0.799033 |
84,291 | In geometry, the rhombicosacron (or midly dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U56. It has 50 vertices, 120 edges, and 60 crossed-quadrilateral faces. | Rhombicosacron | 0.799033 |
84,292 | The statement of the Thomas–Yau conjecture is not completely precise, as the particular stability condition is not yet known. In the work of Thomas and Thomas–Yau, the stability condition was given in terms of the Lagrangian mean curvature flow inside the Hamiltonian isotopy class of the Lagrangian, but Joyce's reinter... | Thomas–Yau conjecture | 0.799033 |
84,293 | Point processes are employed in other mathematical and statistical disciplines, hence the notation may be used in fields such stochastic geometry, spatial statistics or continuum percolation theory, and areas which use the methods and theory from these fields. | Point process notation | 0.799033 |
84,294 | {\displaystyle x^{4}+a^{4}=\left(x^{2}+a{\sqrt {2}}\cdot x+a^{2}\right)\left(x^{2}-a{\sqrt {2}}\cdot x+a^{2}\right).} A first attempt at proving the theorem was made by d'Alembert in 1746, but his proof was incomplete. Among other problems, it assumed implicitly a theorem (now known as Puiseux's theorem), which would n... | Fundamental Theorem of Algebra | 0.799033 |
84,295 | A palynofacies is the complete assemblage of organic matter and palynomorphs in a fossil deposit. The term was introduced by the French geologist André Combaz in 1964. Palynofacies studies are often linked to investigations of the organic geochemistry of sedimentary rocks. | Palynology | 0.799032 |
84,296 | The exceptional yield strength of nanocrystalline metals is due to grain boundary strengthening, as grain boundaries are extremely effective at blocking the motion of dislocations. Yielding occurs when the stress due to dislocation pileup at a grain boundary becomes sufficient to activate slip of dislocations in the ad... | Nanocrystalline material | 0.799032 |
84,297 | In model theory, the notion of a categorical theory is refined with respect to cardinality. A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley (1965) stating that if a first-order theory in a cou... | Categorical (model theory) | 0.799031 |
84,298 | In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds to a new kind of dependency ... | Lambda cube | 0.799031 |
84,299 | Due to the reduction of water leakage on the delivery, the country gets additional water sources; for example, Pakistan got about an additional 75 MAF of flowing rivers. At the same time, the proper riverine fields keep getting the requisite aquifer recharge, and the riparian ecology and biodiversity have been recoveri... | Warabandi system | 0.79903 |
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