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23,100 | The above example is a special case of the following general theorem:: 274 G is a bipartite graph if-and-only-if MP(G) = FMP(G) if-and-only-if all corners of FMP(G) have only integer coordinates.This theorem can be proved in several ways. | Matching polytope | 0.809 |
23,101 | In univariate statistics, the Student's t-test makes use of Student's t-distribution. Hotelling's T-squared distribution is a distribution that arises in multivariate statistics. The matrix t-distribution is a distribution for random variables arranged in a matrix structure. | Multivariate Student distribution | 0.808998 |
23,102 | Regardless of which method they use, they will conclude that the geometry is well approximated by a certain Riemannian metric, namely the Langevin–Landau–Lifschitz metric. This is in turn very well approximated by the geometry of the hyperbolic plane (with the negative curvatures –3 ω2 and –3 ω2 r2, respectively). But ... | Born coordinates | 0.808998 |
23,103 | But the experience when the observers try to synchronize their clocks along a closed path in space is puzzling: there are always at least two neighboring clocks which have different times. To remedy the situation, the observers agree on an external synchronization procedure (coordinate time t — or for ring-riding obser... | Born coordinates | 0.808998 |
23,104 | In all such cases, however, they will most likely obtain results which are inconsistent with any Riemannian metric. In particular, if they use the simplest notion of distance, radar distance, owing to various effects such as the asymmetry already noted, they will conclude that the "geometry" of the disk is not only non... | Born coordinates | 0.808998 |
23,105 | In relativistic physics, the Born coordinate chart is a coordinate chart for (part of) Minkowski spacetime, the flat spacetime of special relativity. It is often used to analyze the physical experience of observers who ride on a ring or disk rigidly rotating at relativistic speeds, so called Langevin observers. This ch... | Born coordinates | 0.808998 |
23,106 | To this definition fits naturally another global formula (similar to the Kelvin-Stokes theorem) which equates the volume integral of the curl of a vector field to the above surface integral taken over the boundary of the volume. Whereas the above two definitions of the curl are coordinate free, there is another "easy t... | Curl (mathematics) | 0.808994 |
23,107 | The above formula means that the projection of the curl of a vector field along a certain axis is the infinitesimal area density of the circulation of the field projected onto a plane perpendicular to that axis. This formula does not a priori define a legitimate vector field, for the individual circulation densities wi... | Curl (mathematics) | 0.808994 |
23,108 | The geometry and behavior of Gaussian beam in the Fraunhofer region imply that the electromagnetic beams diverge more as the frequencies of the beams decrease and thus the resolution decreases. This implies that terahertz imaging systems have higher resolution than scanning acoustic microscope (SAM) but lower resolutio... | Terahertz wave | 0.808992 |
23,109 | In 2020 the company launched a Smart Waste application. Latest developments relate to blockchain and cybersecurity services for Smart Cities. == References == | Paradox Engineering | 0.808989 |
23,110 | It is also possible to deal with ellipsoids in Cartesian coordinates by using a modified version of the spherical coordinates. Let P be an ellipsoid specified by the level set The modified spherical coordinates of a point in P in the ISO convention (i.e. for physics: radius r, inclination θ, azimuth φ) can be obtained ... | Spherical coordinate | 0.808988 |
23,111 | Since N2O does not absorb light at wavelengths greater than 280 nm, direct photolysis had been discarded as a possible explanation. It was then observed that light would decompose chloromethanes when they were absorbed on silica sand, and this occurred at wavelengths far above the absorption spectra for these compounds... | Photogeochemistry | 0.808987 |
23,112 | One of the pioneer experiments was that of Bach in 1893, who observed the formation of lower uranium oxides upon irradiation of a solution of uranium acetate and carbon dioxide, implying the formation of formaldehyde. Some experiments included reducing agents such as hydrogen gas, and others detected formaldeyhde or ot... | Photogeochemistry | 0.808987 |
23,113 | Any reaction in the domain of photogeochemistry, either observed in the environment or studied in the laboratory, may be broadly classified according to the nature of the materials involved. Reactions among naturally occurring compounds. Photogeochemistry, both observational and exploratory, is concerned with reactions... | Photogeochemistry | 0.808987 |
23,114 | Similarly, photogeochemistry may also include photochemical reactions of naturally occurring materials that are not touched by sunlight, if there is the possibility that these materials may become exposed (e.g. deep soil layers uncovered by mining). Except for several isolated instances, studies that fit the definition... | Photogeochemistry | 0.808987 |
23,115 | For example, many inorganic compounds have been synthesized in the laboratory to study photocatalytic reactions. Although these studies are usually not undertaken in the context of environmental or Earth sciences, the study of such reactions is relevant to photogeochemistry if there is a geochemical implication (i.e. s... | Photogeochemistry | 0.808987 |
23,116 | The reactions comprising photosynthesis in plants and other organisms, for example, are not considered photogeochemistry, since the physiochemical context for these reactions is installed by the organism, and must be maintained in order for these reactions to continue (i.e. the reactions cease if the organism dies). In... | Photogeochemistry | 0.808987 |
23,117 | Photogeochemistry merges photochemistry and geochemistry into the study of light-induced chemical reactions that occur or may occur among natural components of Earth's surface. The first comprehensive review on the subject was published in 2017 by the chemist and soil scientist Timothy A Doane, but the term photogeoche... | Photogeochemistry | 0.808987 |
23,118 | Studies of reactions among materials related to naturally occurring materials may contribute to understanding of natural processes. These complementary studies are relevant to photogeochemistry in that they illustrate reactions that may have a natural counterpart. | Photogeochemistry | 0.808987 |
23,119 | As in many emerging fields, experiments were largely empirical, but the enthusiasm surrounding this early work did lead to significant advances in photochemistry. The simple but challenging principle of transforming solar energy into chemical energy capable of performing a desired reaction remains the basis of applicat... | Photogeochemistry | 0.808987 |
23,120 | {\displaystyle v_{F}({\mathfrak {D}}_{F/K})={1 \over e_{L/F}}\sum _{s\not \in H}i_{G}(s).} If s ∈ G i , t ∈ G j , i , j ≥ 1 {\displaystyle s\in G_{i},t\in G_{j},i,j\geq 1} , then s t s − 1 t − 1 ∈ G i + j + 1 {\displaystyle sts^{-1}t^{-1}\in G_{i+j+1}} . In the terminology of Lazard, this can be understood to mean the ... | Inertia subgroup | 0.808985 |
23,121 | Ramification groups are a refinement of the Galois group G {\displaystyle G} of a finite L / K {\displaystyle L/K} Galois extension of local fields. We shall write w , O L , p {\displaystyle w,{\mathcal {O}}_{L},{\mathfrak {p}}} for the valuation, the ring of integers and its maximal ideal for L {\displaystyle L} . As ... | Inertia subgroup | 0.808985 |
23,122 | Also running on a JOHNNIAC, the Logic Theory Machine constructed proofs from a small set of propositional axioms and three deduction rules: modus ponens, (propositional) variable substitution, and the replacement of formulas by their definition. The system used heuristic guidance, and managed to prove 38 of the first 5... | First-order theorem provers | 0.808985 |
23,123 | The logic is expressive enough to allow the specification of arbitrary problems, often in a reasonably natural and intuitive way. On the other hand, it is still semi-decidable, and a number of sound and complete calculi have been developed, enabling fully automated systems. More expressive logics, such as Higher-order ... | First-order theorem provers | 0.808985 |
23,124 | In the late 1960s agencies funding research in automated deduction began to emphasize the need for practical applications. One of the first fruitful areas was that of program verification whereby first-order theorem provers were applied to the problem of verifying the correctness of computer programs in languages such ... | First-order theorem provers | 0.808985 |
23,125 | If G {\displaystyle G} is a commutative algebraic group defined over an algebraic number field and A {\displaystyle A} is a Lie subgroup of G {\displaystyle G} with Lie algebra defined over the number field then A {\displaystyle A} does not contain any non-zero algebraic point of G {\displaystyle G} unless A {\displays... | Analytic subgroup theorem | 0.808985 |
23,126 | One of the spectacular consequences of the analytic subgroup theorem was the Isogeny Theorem published by Masser and Wüstholz. A direct consequence is the Tate conjecture for abelian varieties which Gerd Faltings had proved with totally different methods which has many applications in modern arithmetic geometry. Using ... | Analytic subgroup theorem | 0.808985 |
23,127 | In mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on linear forms in logarithms. Gisbert Wüstholz proved it in the 1980s. It marked a breakthrough in the theory of transcendental numbers. Many longstanding ... | Analytic subgroup theorem | 0.808985 |
23,128 | This chapter is a self-contained introduction to quantum mechanics. It introduces the EPR paradox and the measurement problem. Bell's Theorem and the GHZ experiment are then introduced in the context of hidden-variables interpretations of quantum mechanics. De Broglie–Bohm theory, the Many-worlds interpretation, the Ma... | Time's Arrow and Archimedes' Point | 0.808983 |
23,129 | Covers the thermodynamics arrow of time, arising from the Second Law of Thermodynamics. Discusses Ludwig Boltzmann and his development of the second law as a statistical law. The chapter also discusses Boltzmann's H-Theorem and Loschmidt's Paradox. Price takes a time-symmetric view and comes to the conclusion that the ... | Time's Arrow and Archimedes' Point | 0.808983 |
23,130 | Price notes that the independence assumption in Bell's Theorem can be relaxed in two ways: the first being that the measurement basis and the state of the quantum system are correlated through a common cause in the past, and the second being what Price calls 'advanced action' - a 'common cause' in the future. He argues... | Time's Arrow and Archimedes' Point | 0.808983 |
23,131 | Time's Arrow and Archimedes' Point was generally well received. Many reviewers found Price's arguments stimulating and praised his explanations of the issues. However, many took issues with some of his specific arguments. Joel Lebowitz gave the book a mixed review for Physics Today where he called Price's arguments reg... | Time's Arrow and Archimedes' Point | 0.808983 |
23,132 | Time's Arrow and Archimedes Point: New Directions for the Physics of Time is a 1996 book by Huw Price, on the physics and philosophy of the Arrow of Time. It explores the problem of the direction of time, looking at issues in thermodynamics, cosmology, electromagnetism, and quantum mechanics. Price argues that it is fr... | Time's Arrow and Archimedes' Point | 0.808983 |
23,133 | Price then introduces the idea of viewing the block universe from an Archimedean Point from outside of time, which is the view that is taken in the rest of the book. Finally, Price introduces two problems regarding the Arrow of Time, which he calls the taxonomy problem and the genealogy problem. The taxonomy problem is... | Time's Arrow and Archimedes' Point | 0.808983 |
23,134 | The Star Thrust Experiment (STX) was a plasma physics experiment at the University of Washington's Redmond Plasma Physics Laboratory which ran from 1999 to 2001. The experiment studied magnetic plasma confinement to support controlled nuclear fusion experiments. Specifically, STX pioneered the possibility of forming a ... | Star Thrust Experiment | 0.808982 |
23,135 | Atomic collisions are "ops." Machine language is the laws of physics. The universe is a quantum computer. | Programming the Universe | 0.808981 |
23,136 | Reviewer Corey S. Powell of The New York Times writes: In the space of 221 dense, frequently thrilling and occasionally exasperating pages, … tackles computer logic, thermodynamics, chaos theory, complexity, quantum mechanics, cosmology, consciousness, sex and the origin of life — throwing in, for good measure, a heart... | Programming the Universe | 0.808981 |
23,137 | Programming the Universe: A Quantum Computer Scientist Takes On the Cosmos is a 2006 popular science book by Seth Lloyd, professor of mechanical engineering at the Massachusetts Institute of Technology. The book proposes that the Universe is a quantum computer (supercomputer), and advances in the understanding of physi... | Programming the Universe | 0.808981 |
23,138 | The equations are Then the complete Oseen solution is given by a splitting theorem due to Horace Lamb. The splitting is unique if conditions at infinity (say u = 0 , p = p ∞ {\displaystyle \mathbf {u} =0,\ p=p_{\infty }} ) are specified. | Oseen equations | 0.808979 |
23,139 | That changed within two years, since the formulation of Schrödinger's equation made the Hilbert-Courant techniques of immediate relevance to the new wave mechanics. There was a second edition (1931/7), wartime edition in the USA (1943), and a third German edition (1968). The English version Methods of Mathematical Phys... | Methoden der mathematischen Physik | 0.808976 |
23,140 | The material of the book was worked up from the content of Hilbert's lectures. While Courant played the major editorial role, many at the University of Göttingen were involved in the writing-up, and in that sense it was a collective production. On its appearance in 1924 it apparently had little direct connection to the... | Methoden der mathematischen Physik | 0.808976 |
23,141 | Methoden der mathematischen Physik (Methods of Mathematical Physics) is a 1924 book, in two volumes totalling around 1000 pages, published under the names of Richard Courant and David Hilbert. It was a comprehensive treatment of the "methods of mathematical physics" of the time. The second volume is devoted to the theo... | Methoden der mathematischen Physik | 0.808976 |
23,142 | In this case, σ may be referred to as the integral cross section or total cross section. The latter term may be confusing in contexts where multiple events are involved, since “total” can also refer to the sum of cross sections over all events. The differential cross section is extremely useful quantity in many fields ... | Differential cross section | 0.808974 |
23,143 | Let us assume that a particle supports only electric and magnetic dipole modes with polarizabilities p = α e E {\textstyle \mathbf {p} =\alpha ^{e}\mathbf {E} } and m = ( μ μ 0 ) − 1 α m H {\textstyle \mathbf {m} =(\mu \mu _{0})^{-1}\alpha ^{m}\mathbf {H} } (here we use the notation of magnetic polarizability in the ma... | Differential cross section | 0.808974 |
23,144 | Single-particle trajectories (SPTs) consist of a collection of successive discrete points causal in time. These trajectories are acquired from images in experimental data. In the context of cell biology, the trajectories are obtained by the transient activation by a laser of small dyes attached to a moving molecule. Mo... | Single-particle trajectory | 0.808971 |
23,145 | Cognitive automation, as a subset of AI, is an emerging genus of automation enabled by cognitive computing. Its primary concern is the automation of clerical tasks and workflows that consist of structuring unstructured data. Cognitive automation relies on multiple disciplines: natural language processing, real-time com... | Automatic control system | 0.808969 |
23,146 | However, two-thirds of books, music, and films are now purchased online. In addition, automation and online shopping could reduce demands for shopping malls, and retail property, which in the USA is currently estimated to account for 31% of all commercial property or around 7 billion square feet (650 million square met... | Automatic control system | 0.808969 |
23,147 | Transmission of electrical energy without wires was observed by many inventors and experimenters, but lack of a coherent theory attributed these phenomena vaguely to electromagnetic induction. A concise explanation of these phenomena would come from the 1860s Maxwell's equations by James Clerk Maxwell, establishing a t... | Contactless energy transfer | 0.808968 |
23,148 | In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables.The coefficient ... | Multiple correlation | 0.808967 |
23,149 | open graph, sequentially closed graph, sequentially open graph) in X × Y if the graph of f, Gr f, is a closed (resp. open, sequentially closed, sequentially open) subset of X × Y when X × Y is endowed with the product topology. If S = X or if X is clear from context then we may omit writing "in X × Y"Observation: If g:... | Closed graph | 0.808964 |
23,150 | We give the more general definition of when a Y-valued function or set-valued function defined on a subset S of X has a closed graph since this generality is needed in the study of closed linear operators that are defined on a dense subspace S of a topological vector space X (and not necessarily defined on all of X). T... | Closed graph | 0.808964 |
23,151 | Definition and notation: When we write f: D(f) ⊆ X → Y then we mean that f is a Y-valued function with domain D(f) where D(f) ⊆ X. If we say that f: D(f) ⊆ X → Y is closed (resp. sequentially closed) or has a closed graph (resp. has a sequentially closed graph) then we mean that the graph of f is closed (resp. sequenti... | Closed graph | 0.808964 |
23,152 | Let X denote the real numbers ℝ with the usual Euclidean topology, let Y denote ℝ with the discrete topology, and let Id: X → Y be the identity map (i.e. Id(x) := x for every x ∈ X). Then Id: X → Y is a linear map whose graph is closed in X × Y but it is clearly not continuous (since singleton sets are open in Y but no... | Closed graph | 0.808964 |
23,153 | Let X and Y both denote the real numbers ℝ with the usual Euclidean topology. Let f: X → Y be defined by f(0) = 0 and f(x) = 1/x for all x ≠ 0. Then f: X → Y has a closed graph (and a sequentially closed graph) in X × Y = ℝ2 but it is not continuous (since it has a discontinuity at x = 0). | Closed graph | 0.808964 |
23,154 | The closed graph theorem states that any closed linear operator f: X → Y between two F-spaces (such as Banach spaces) is continuous, where recall that if X and Y are Banach spaces then f: X → Y being continuous is equivalent to f being bounded. | Closed graph | 0.808964 |
23,155 | Sticking coefficient is the term used in surface physics to describe the ratio of the number of adsorbate atoms (or molecules) that adsorb, or "stick", to a surface to the total number of atoms that impinge upon that surface during the same period of time. Sometimes the symbol Sc is used to denote this coefficient, and... | Sticking coefficient | 0.808963 |
23,156 | {\displaystyle f(x)\approx f(0)+f'(0)(x-0)=1+\alpha x.} By Taylor's theorem, the error in this approximation is equal to α ( α − 1 ) x 2 2 ⋅ ( 1 + ζ ) α − 2 {\textstyle {\frac {\alpha (\alpha -1)x^{2}}{2}}\cdot (1+\zeta )^{\alpha -2}} for some value of ζ {\displaystyle \zeta } that lies between 0 and x. For example, if... | Binomial approximation | 0.808963 |
23,157 | The function f ( x ) = ( 1 + x ) α {\displaystyle f(x)=(1+x)^{\alpha }} is a smooth function for x near 0. Thus, standard linear approximation tools from calculus apply: one has f ′ ( x ) = α ( 1 + x ) α − 1 {\displaystyle f'(x)=\alpha (1+x)^{\alpha -1}} and so f ′ ( 0 ) = α . {\displaystyle f'(0)=\alpha .} Thus f ( x ... | Binomial approximation | 0.808963 |
23,158 | The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that ( 1 + x ) α ≈ 1 + α x . {\displaystyle (1+x)^{\alpha }\approx 1+\alpha x.} It is valid when | x | < 1 {\displaystyle |x|<1} and | α x | ≪ 1 {\displaystyle |\alpha x|\ll 1} where x {\displaystyle x... | Binomial approximation | 0.808963 |
23,159 | Fermat and Lagrange found calculus-based formulae for identifying optima, while Newton and Gauss proposed iterative methods for moving towards an optimum. The term "linear programming" for certain optimization cases was due to George B. Dantzig, although much of the theory had been introduced by Leonid Kantorovich in 1... | Numerical optimization problem | 0.808961 |
23,160 | The choice among "Pareto optimal" solutions to determine the "favorite solution" is delegated to the decision maker. In other words, defining the problem as multi-objective optimization signals that some information is missing: desirable objectives are given but combinations of them are not rated relative to each other... | Numerical optimization problem | 0.808961 |
23,161 | Adding more than one objective to an optimization problem adds complexity. For example, to optimize a structural design, one would desire a design that is both light and rigid. When two objectives conflict, a trade-off must be created. There may be one lightest design, one stiffest design, and an infinite number of des... | Numerical optimization problem | 0.808961 |
23,162 | Optimization techniques are used in many facets of computational systems biology such as model building, optimal experimental design, metabolic engineering, and synthetic biology. Linear programming has been applied to calculate the maximal possible yields of fermentation products, and to infer gene regulatory networks... | Numerical optimization problem | 0.808961 |
23,163 | A widely used technique today is the Piecewise Linear Interface Calculation by Youngs. PLIC is based on the idea that the interface can be represented as a line in R2 or a plane in R3; in the latter case we may describe the interface by: n x + n y + n z = α , {\displaystyle \mathbf {n} _{x}+\mathbf {n} _{y}+\mathbf {n}... | Volume of fluid method | 0.80896 |
23,164 | Line techniques circumvent the problems associated with the discretization of the transport equation by not tracking the interface in a cell explicitly. Instead, the fluid distribution in a cell an interface is obtained by using the volume fraction distribution of neighbouring cells. The Simple Line Interface Calculati... | Volume of fluid method | 0.80896 |
23,165 | Differentiable programming has been applied in areas such as combining deep learning with physics engines in robotics, solving electronic structure problems with differentiable density functional theory, differentiable ray tracing, image processing, and probabilistic programming. | Differentiable programming | 0.808958 |
23,166 | Their dynamic and interactive nature lets most programs be written and reasoned about more easily. However, they lead to interpreter overhead (particularly when composing many small operations), poorer scalability, and reduced benefit from compiler optimization. A package for the Julia programming language – Zygote – w... | Differentiable programming | 0.808958 |
23,167 | Most differentiable programming frameworks work by constructing a graph containing the control flow and data structures in the program. Attempts generally fall into two groups: Static, compiled graph-based approaches such as TensorFlow, Theano, and MXNet. They tend to allow for good compiler optimization and easier sca... | Differentiable programming | 0.808958 |
23,168 | Differentiable programming is a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation. This allows for gradient-based optimization of parameters in the program, often via gradient descent, as well as other learning approaches that are based on higher ord... | Differentiable programming | 0.808958 |
23,169 | In molecular biology, repeat-induced point mutation or RIP is a process by which DNA accumulates G:C to A:T transition mutations. Genomic evidence indicates that RIP occurs or has occurred in a variety of fungi while experimental evidence indicates that RIP is active in Neurospora crassa, Podospora anserina, Magnaporth... | Point mutation | 0.808957 |
23,170 | Many methods have been proposed to predict the effects of missense mutations on proteins. Machine learning algorithms train their models to distinguish known disease-associated from neutral mutations whereas other methods do not explicitly train their models but almost all methods exploit the evolutionary conservation ... | Point mutation | 0.808957 |
23,171 | Weak values have been implemented into quantum computing to get a giant speed up in time complexity. In a paper, Arun Kumar Pati describes a new kind of quantum computer using weak value amplification and post-selection (WVAP), and implements search algorithm which (given a successful post selection) can find the targe... | Weak value | 0.808956 |
23,172 | This final approximation is only valid when As p {\displaystyle p} is the generator of translations, the ancilla's wavefunction is now given by This is the original wavefunction, shifted by an amount γ A w {\displaystyle \gamma A_{w}} . By Busch's theorem the system and meter wavefunctions are necessarily disturbed by ... | Weak value | 0.808956 |
23,173 | In quantum mechanics (and computation), a weak value is a quantity related to a shift of a measuring device's pointer when usually there is pre- and postselection. It should not be confused with a weak measurement, which is often defined in conjunction. The weak value was first defined by Yakir Aharonov, David Albert, ... | Weak value | 0.808956 |
23,174 | In molecular biology, the Cys/Met metabolism PLP-dependent enzyme family is a family of proteins including enzymes involved in cysteine and methionine metabolism which use PLP (pyridoxal-5'-phosphate) as a cofactor. | Cys/Met metabolism PLP-dependent enzyme family | 0.808954 |
23,175 | The above table shows the proportions of energy consumption by source in the U.S. from 2000-2017 using data from the Energy Information Administration. Fossil fuel consumption has declined overall, although natural gas consumption has increased. Both biomass and general renewable energy consumption has increased. | Substitutional fuel | 0.808953 |
23,176 | Substitutional fuel has been gaining popularity along with renewable energy in the United States over the past several decades. The Energy Independence and Security Act of 2007 requires that U.S. transportation fuels contain 36 billion gallons of renewable fuels. "A market failure can arise in the transport fuels marke... | Substitutional fuel | 0.808953 |
23,177 | For example, when a matrix is sparse, an iterative algorithm can skip many of the steps that a direct approach would necessarily follow, even if they are redundant steps given a highly structured matrix. The core of many iterative methods in numerical linear algebra is the projection of a matrix onto a lower dimensiona... | Numerical linear algebra | 0.808953 |
23,178 | There are two reasons that iterative algorithms are an important part of numerical linear algebra. First, many important numerical problems have no direct solution; in order to find the eigenvalues and eigenvectors of an arbitrary matrix, we can only adopt an iterative approach. Second, noniterative algorithms for an a... | Numerical linear algebra | 0.808953 |
23,179 | From the numerical linear algebra perspective, Gaussian elimination is a procedure for factoring a matrix A into its LU factorization, which Gaussian elimination accomplishes by left-multiplying A by a succession of matrices L m − 1 ⋯ L 2 L 1 A = U {\displaystyle L_{m-1}\cdots L_{2}L_{1}A=U} until U is upper triangular... | Numerical linear algebra | 0.808953 |
23,180 | Numerical linear algebra characteristically approaches matrices as a concatenation of columns vectors. In order to solve the linear system x = A − 1 b {\displaystyle x=A^{-1}b} , the traditional algebraic approach is to understand x as the product of A − 1 {\displaystyle A^{-1}} with b. Numerical linear algebra instead... | Numerical linear algebra | 0.808953 |
23,181 | The center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the mean location of a distribution of mass in space. | Centers of gravity | 0.808953 |
23,182 | Real-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines".Real-time responses are often understood... | Realtime computing | 0.808951 |
23,183 | A series of derived terms have been coined to identify several branches of biotechnology, for example: Bioinformatics (also called "gold biotechnology") is an interdisciplinary field that addresses biological problems using computational techniques, and makes the rapid organization as well as analysis of biological dat... | Regulation of biotechnologies | 0.808949 |
23,184 | Biotechnology has applications in four major industrial areas, including health care (medical), crop production and agriculture, non-food (industrial) uses of crops and other products (e.g., biodegradable plastics, vegetable oil, biofuels), and environmental uses. For example, one application of biotechnology is the di... | Regulation of biotechnologies | 0.808949 |
23,185 | Bioengineering is the application of the principles of engineering and natural sciences to tissues, cells, and molecules. This can be considered as the use of knowledge from working with and manipulating biology to achieve a result that can improve functions in plants and animals. Relatedly, biomedical engineering is a... | Regulation of biotechnologies | 0.808949 |
23,186 | Biotechnology is based on the basic biological sciences (e.g., molecular biology, biochemistry, cell biology, embryology, genetics, microbiology) and conversely provides methods to support and perform basic research in biology. Biotechnology is the research and development in the laboratory using bioinformatics for exp... | Regulation of biotechnologies | 0.808949 |
23,187 | The concept of biotechnology encompasses a wide range of procedures for modifying living organisms for human purposes, going back to domestication of animals, cultivation of the plants, and "improvements" to these through breeding programs that employ artificial selection and hybridization. Modern usage also includes g... | Regulation of biotechnologies | 0.808949 |
23,188 | Gray biotechnology is dedicated to environmental applications, and focused on the maintenance of biodiversity and the remotion of pollutants. Brown biotechnology is related to the management of arid lands and deserts. One application is the creation of enhanced seeds that resist extreme environmental conditions of arid... | Regulation of biotechnologies | 0.808949 |
23,189 | "Yellow biotechnology" refers to the use of biotechnology in food production (food industry), for example in making wine (winemaking), cheese (cheesemaking), and beer (brewing) by fermentation. It has also been used to refer to biotechnology applied to insects. This includes biotechnology-based approaches for the contr... | Regulation of biotechnologies | 0.808949 |
23,190 | An example is the designing of an organism to produce a useful chemical. Another example is the using of enzymes as industrial catalysts to either produce valuable chemicals or destroy hazardous/polluting chemicals. White biotechnology tends to consume less in resources than traditional processes used to produce indust... | Regulation of biotechnologies | 0.808949 |
23,191 | This branch involves the production of vaccines and antibiotics, regenerative therapies, creation of artificial organs and new diagnostics of diseases. As well as the development of hormones, stem cells, antibodies, siRNA and diagnostic tests. White biotechnology, also known as industrial biotechnology, is biotechnolog... | Regulation of biotechnologies | 0.808949 |
23,192 | It is commonly considered as the next phase of green revolution, which can be seen as a platform to eradicate world hunger by using technologies which enable the production of more fertile and resistant, towards biotic and abiotic stress, plants and ensures application of environmentally friendly fertilizers and the us... | Regulation of biotechnologies | 0.808949 |
23,193 | An example of this is the engineering of a plant to express a pesticide, thereby ending the need of external application of pesticides. An example of this would be Bt corn. Whether or not green biotechnology products such as this are ultimately more environmentally friendly is a topic of considerable debate. | Regulation of biotechnologies | 0.808949 |
23,194 | An example would be the selection and domestication of plants via micropropagation. Another example is the designing of transgenic plants to grow under specific environments in the presence (or absence) of chemicals. One hope is that green biotechnology might produce more environmentally friendly solutions than traditi... | Regulation of biotechnologies | 0.808949 |
23,195 | Blue biotechnology is based on the exploitation of sea resources to create products and industrial applications. This branch of biotechnology is the most used for the industries of refining and combustion principally on the production of bio-oils with photosynthetic micro-algae. Green biotechnology is biotechnology app... | Regulation of biotechnologies | 0.808949 |
23,196 | Jointly biotechnology and synthetic biology play a crucial role in generating cost-effective products with nature-friendly features by using bio-based production instead of fossil-based. Synthetic biology can be used to engineer model microorganisms, such as Escherichia coli, by genome editing tools to enhance their ab... | Regulation of biotechnologies | 0.808949 |
23,197 | Industrial biotechnology (known mainly in Europe as white biotechnology) is the application of biotechnology for industrial purposes, including industrial fermentation. It includes the practice of using cells such as microorganisms, or components of cells like enzymes, to generate industrially useful products in sector... | Regulation of biotechnologies | 0.808949 |
23,198 | After two chapters reviewing the basic notions of algebraic topology, and proving the Borsuk–Ulam theorem, the applications to combinatorics and geometry begin in the third chapter, with topics including the ham sandwich theorem, the necklace splitting problem, Gale's lemma on points in hemispheres, and several results... | Using the Borsuk–Ulam Theorem | 0.808946 |
23,199 | Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry is a graduate-level mathematics textbook in topological combinatorics. It describes the use of results in topology, and in particular the Borsuk–Ulam theorem, to prove theorems in combinatorics and discrete geometry. It was wri... | Using the Borsuk–Ulam Theorem | 0.808946 |
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