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In geophysics, admittance is a term for a transfer function, that measures the response (can be amplitude, force) to the applied change (force, pressure) in function of variable of interest (frequency, wave number) applied to the physical body, such as the atmosphere or the Earth's crust. In seismology or geodesy it de...
Admittance (geophysics)
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The original context for the formulation of the group in question was the question of the Galois representation on the Tate module of an abelian variety A. Conjecturally, the image of such a Galois representation, which is an l-adic Lie group for a given prime number l, is determined by the corresponding Mumford–Tate g...
Mumford–Tate group
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There are many different ways to measure the relationships of nodes when analyzing a network. In many cases, the measure used to find nodes that share similarity within a network is specific to the application it is being used. One of the types of measures that biologists utilize is correlation which specifically cente...
Network biology
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It follows that the invertible elements in any octonion algebra form a Moufang loop, as do the elements of unit norm. The construction of general octonion algebras over an arbitrary field k was described by Leonard Dickson in his book Algebren und ihre Zahlentheorie (1927) (Seite 264) and repeated by Max Zorn. The prod...
Cayley algebra
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Three-coordinate compounds of boron typically exhibit trigonal planar geometry, therefore the boroxine ring is locked in a planar geometry as well. These compounds are isoelectronic to benzene. With the vacant p-orbital on the boron atoms, they may possess some aromatic character. Boron single-bonds on boroxine compoun...
Boroxine
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In 1958, Blackman and Tukey cited Nyquist's 1928 article as a reference for the sampling theorem of information theory, even though that article does not treat sampling and reconstruction of continuous signals as others did. Their glossary of terms includes these entries: Sampling theorem (of information theory) Nyquis...
Sampling theorem
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Weil function A Weil function on an algebraic variety is a real-valued function defined off some Cartier divisor which generalises the concept of Green's function in Arakelov theory. They are used in the construction of the local components of the Néron–Tate height. Weil height machine The Weil height machine is an eff...
Arakelov divisor
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Around 1735, Leonhard Euler discovered the formula V − E + F = 2 {\displaystyle V-E+F=2} relating the number of vertices, edges and faces of a convex polyhedron, and hence of a planar graph. The study and generalization of this formula, specifically by Cauchy (1789-1857) and L'Huilier (1750-1840), boosted the study of ...
Topological spaces
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doi:10.5038/2375-0901.5.2.1. Across Latitudes and Cultures Bus Rapid Transit An international Centre of Excellence for BRT development Transit Capacity and Quality of Service Manual Transportation Research Board BRT Technologies: Assisting Drivers Operating Buses on Road Shoulders. University of Minnesota Center for Tr...
Bus rapid transit
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Ovarian follicles are the basic units of female reproductive biology. Each of them contains a single oocyte (immature ovum or egg cell). These structures are periodically initiated to grow and develop, culminating in ovulation of usually a single competent oocyte in humans. They also consist of granulosa cells and thec...
Ovarian follicles
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As of 2013, he had published over 250 peer-reviewed articles, one of which has over 1800 citations. His works have appeared in such journals as the Journal of Vibration and Control and various Journal of Physics journals. == References ==
Rudolf Gorenflo
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This is usually done by calculating the acceptance rate, which is the fraction of proposed samples that is accepted in a window of the last N {\displaystyle N} samples. The desired acceptance rate depends on the target distribution, however it has been shown theoretically that the ideal acceptance rate for a one-dimens...
Metropolis-Hastings algorithm
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In geometry, the biaugmented triangular prism is one of the Johnson solids (J50). As the name suggests, it can be constructed by augmenting a triangular prism by attaching square pyramids (J1) to two of its equatorial faces. A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon face...
Biaugmented triangular prism
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Paper engineering is a branch of engineering that deals with the usage of physical science (e.g. chemistry and physics) and life sciences (e.g. biology and biochemistry) in conjunction with mathematics as applied to the converting of raw materials into useful paper products and co-products. The field applies various pr...
Paper engineering
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The database service is recommended in the authors' instructions of more than 10 biochemistry journals, including Nature, The Journal of Biological Chemistry, eLife, and PLoS. It has been referred as a standard tool for the validation and storage of enzyme kinetics data in multifold publications A recent study examinin...
Standards for Reporting Enzymology Data
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In polymer chemistry, the equivalent weight of a reactive polymer is the mass of polymer which has one equivalent of reactivity (often, the mass of polymer which corresponds to one mole of reactive side-chain groups). It is widely used to indicate the reactivity of polyol, isocyanate, or epoxy thermoset resins which wo...
Equivalent mass
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The first reference about Artificial Chemistries come from a Technical paper written by John McCaskill .Walter Fontana working with Leo Buss then took up the work developing the AlChemy model . The model was presented at the second International Conference of Artificial Life. In his first papers he presented the concep...
Artificial chemistry
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However, there is also a specific "biquad" topology. It is also sometimes called the 'ring of 3' circuit.Biquad filters are typically active and implemented with a single-amplifier biquad (SAB) or two-integrator-loop topology. The SAB topology uses feedback to generate complex poles and possibly complex zeros.
Ladder topology
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A linear combination of such functions can be represented as a linear combination of phasors (known as phasor arithmetic or phasor algebra: 53 ) and the time/frequency dependent factor that they all have in common. The origin of the term phasor rightfully suggests that a (diagrammatic) calculus somewhat similar to that...
Complex-valued amplitude
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The term "variance structure" refers to the algebraic form of the covariance matrix between outcomes, Y, in the sample. Examples of variance structure specifications include independence, exchangeable, autoregressive, stationary m-dependent, and unstructured.
Generalized estimating equation
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A re-optimization, or "melt re-comp", can then be performed on the lens design using measured index of refraction data where available. When manufactured, the resulting lens performance will more closely match the desired requirements than if average glass catalog values for index of refraction were assumed. Delivery s...
Lens design
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Kushite sundials applied mathematics in the form of advanced trigonometry.The earliest practical water-powered machines, the water wheel and watermill, first appeared in the Persian Empire, in what are now Iraq and Iran, by the early 4th century BC. In ancient Greece, the works of Archimedes (287–212 BC) influenced mec...
Mechanical design
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Bram van Leer was a doctoral student in astrophysics at Leiden Observatory (1966–1970) when he got interested in Computational Fluid Dynamics (CFD) for the sake of solving cosmic flow problems. His first major result in CFD was the formulation of the upwind numerical flux function for a hyperbolic system of conservatio...
Bram van Leer
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There appeared numerous renowned researchers within the field of lichenology such as Henry Nicollon des Abbayes, William Alfred Weber, Antonina Georgievna Borissova, Irwin M. Brodo, and George Albert Llano. Lichenology has found applications beyond biology itself in the field of geology in a technique known as lichenom...
Lichenology
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( t + d − 1 ) ! {\displaystyle \displaystyle \mathrm {Tr} \left=\sum _{j,k}\left|\langle \phi _{j}|\phi _{k}\rangle \right|^{2t}={\frac {n^{2}t!(d-1)!}{(t+d-1)!}}} It then immediately follows that every SIC-POVM is a 2-design, since T r ( S 2 2 ) = ∑ j , k | ⟨ ϕ j | ϕ k ⟩ | 4 = 2 d 3 d + 1 {\displaystyle \mathrm {Tr} (...
Zauner's conjecture
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Any topology or rooting error can be misinterpreted and cause systematic bias. For instance, in DL reconciliations, errors on the lower tree bias the reconciliation toward more duplication events closer to the root and more losses closer to the leaves.On the other hand, reconciliation, as a macro evolutionary model, ca...
Phylogenetic reconciliation
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Process engineering is the understanding and application of the fundamental principles and laws of nature that allow humans to transform raw material and energy into products that are useful to society, at an industrial level. By taking advantage of the driving forces of nature such as pressure, temperature and concent...
Process Engineer
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The platform allows visualization of critical brain networks and helps neurosurgeons make more informed decisions, reduce surgical uncertainty, and have better patient conversations about surgical outcomes. In 2021, Quicktome received regulatory clearance from the FDA, Health Canada, and the Therapeutic Goods Administr...
Connectomics
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An ideal Q of a ring is said to be primary if Q is proper and whenever xy ∈ Q, either x ∈ Q or yn ∈ Q for some positive integer n. In Z, the primary ideals are precisely the ideals of the form (pe) where p is prime and e is a positive integer. Thus, a primary decomposition of (n) corresponds to representing (n) as the ...
Commutative ring theory
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The growing acceptance of design-based research methodology as a means for study is often viewed as a significant factor that distinguishes LS from many of the fields that contribute to it. By including design-based research within its methodological toolkit, learning sciences qualifies as a "design science", sharing c...
Learning Sciences
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In mathematics, the Brauer–Nesbitt theorem can refer to several different theorems proved by Richard Brauer and Cecil J. Nesbitt in the representation theory of finite groups. In modular representation theory, the Brauer–Nesbitt theorem on blocks of defect zero states that a character whose order is divisible by the hi...
Brauer–Nesbitt theorem
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Messenger RNA contained in microvesicles secreted from glioblastomal cells were shown to generate a functional protein in recipient (human brain microvascular endothelial) cells in vitro. In another study of extracellular mRNAs, mRNAs transported by microvesicles from endothelial progenitor cells (EPCs) to human microv...
Extracellular RNA
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In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. It is the two-dimensional special case of Stokes' theorem.
Green’s theorem
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Topic: the domains in which GIS is applied largely fall into those concerned with the human world (e.g., economics, politics, transportation, education, landscape architecture, archaeology, urban planning, real estate, public health, crime mapping, national defense), and those concerned with the natural world (e.g., ge...
Geographic Information System
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Language Computer Corporation (LCC) is a natural language processing research company based in Richardson, Texas. The company develops a variety of natural language processing products, including software for question answering, information extraction, and automatic summarization.Since its founding in 1995, the low-pro...
Language Computer Corporation
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In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices. Geodetic graphs were introduced in 1962 by Øystein Ore, who observed that they generalize a property of trees (in which there exists a unique path between each two vertices rega...
Geodetic graph
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Critics of neuroethology might consider it a branch of neuroscience concerned with 'animal trivia'. Though neuroethological subjects tend not to be traditional neurobiological model systems (i.e. Drosophila, C. elegans, or Danio rerio), neuroethological approaches emphasizing comparative methods have uncovered many con...
Species-specific behavior
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The first-order theory of algebraically closed fields of a given characteristic, established by Tarski in 1949. The first-order theory of real-closed ordered fields, established by Tarski in 1949 (see also Tarski's exponential function problem). The first-order theory of Euclidean geometry, established by Tarski in 194...
Decidability (logic)
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A curious feature of this book on projective geometry is the opening on abstract algebra including laws of composition, group theory, ring theory, fields, finite fields, vector spaces and linear mapping. These seven introductory sections on algebraic structures provide an enhanced vocabulary for the treatment of 15 cla...
Luis Santaló
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Traversable wormholes via a double trace deformation. Journal of High Energy Physics. 2017 Dec;2017(12):1-25.
Aron Wall
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doi:10.1086/498868. S2CID 11685964. Michaud, Peter; Heyer, Inge; Leggett, Sandy K.; and Adamson, Andy; "Discovery Narrows the Gap Between Planets and Brown Dwarfs", Gemini and Joint Astronomy Centre, 2007 Deacon, Niall R.; and Hambly, Nigel C.; "Y-Spectral class for Ultra-Cool Dwarfs", 2006
Brown dwarfs
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Anaerobic exercise is a type of exercise that breaks down glucose in the body without using oxygen; anaerobic means "without oxygen". In practical terms, this means that anaerobic exercise is more intense, but shorter in duration than aerobic exercise. The biochemistry of anaerobic exercise involves a process called gl...
Anaerobic exercise
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(He then argued, though inconclusively, that this is the usual main reason why the same distant sound, e.g. foghorn, can be heard stronger or fainter on different days or at different times of day. )An index of 19th-century scientific research journals has John Tyndall as the author of more than 147 papers in science r...
John Tyndall
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However the probability is interpreted, each state in the ensemble evolves over time according to the equation of motion. Thus, the ensemble itself (the probability distribution over states) also evolves, as the virtual systems in the ensemble continually leave one state and enter another. The ensemble evolution is giv...
Non-equilibrium statistical mechanics
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Advanced Quantum Mechanics: A Practical Guide. Cambridge University Press. ISBN 978-0-521-76150-5.
Relativistic quantum mechanics
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Brunswik's concept of "ecological validity" is tied to his concept of "representative design." In a "representative design", the variances and correlations of some dependent variable Y and independent variables X1, X2, and X3 match their values in some specific real world ecology. Quoting Hammond (1998), "Generalizabil...
Ecological validity (perception)
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In geometry, a trapezoid () in USA and Canadian English, or trapezium () in British and other forms of English, is a quadrilateral that has at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parall...
Trapezoid
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The adjugate can be viewed in abstract terms using exterior algebras. Let V be an n-dimensional vector space. The exterior product defines a bilinear pairing V × ∧ n − 1 V → ∧ n V . {\displaystyle V\times \wedge ^{n-1}V\to \wedge ^{n}V.}
Adjugate matrix
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In 1913 he became an instructor in meteorology at the Central Flying School, and was at the Royal Aircraft Establishment, Farnborough, from 1916 to 1918. In 1921 he was appointed lecturer in meteorology at the University of Oxford, becoming reader in meteorology in 1927, a position he held until 1950, when he became un...
G. M. B. Dobson
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With this metric H1(n)R is a Riemannian manifold. It is one of the model spaces of Riemannian geometry, the hyperboloid model of hyperbolic space. It is a space of constant negative curvature −1/R2. The 1 in the upper index refers to an enumeration of the different model spaces of hyperbolic geometry, and the n for its...
Minkowski inner product
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Several papers also concluded that Bitcoin mining loads would reduce curtailment, hedge electricity price risk, stabilize the grid, increase the profitability of renewable energy power stations and therefore accelerate transition to sustainable energy. But others argue that Bitcoin mining can never be sustainable.Insta...
Intermittent power sources
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Many phenomena tend to be attributed to the wrong causes when regression to the mean is not taken into account. An extreme example is Horace Secrist's 1933 book The Triumph of Mediocrity in Business, in which the statistics professor collected mountains of data to prove that the profit rates of competitive businesses t...
Regression to the mean
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In numerical linear algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner.
Incomplete LU factorization
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In 1996, he obtained a master's degree in semiconductor physics engineering from Grenoble Institute of Technology. The following year, El-Ouazzane graduated in economics and finance from the Grenoble Institute of Political Studies. In 2004, he graduated from Harvard Business School’s General Management (GMP) program. E...
Remi El-Ouazzane
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A large error in the initial estimate can contribute to non-convergence of the algorithm. To overcome this problem one can often linearize the function that is being optimized using calculus, logs, differentials, or even using evolutionary algorithms, such as the stochastic tunneling. Good initial estimates lie close t...
Newton iteration
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In particular, for the exceptional Lie algebras, the maximal compact subalgebras are as follows: A non-symmetric version of the magic square can also be obtained by combining the split algebras with the usual division algebras. According to Barton and Sudbery, the resulting table of Lie algebras is as follows. The real...
Octooctonionic projective plane
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Geometry & Physics, Barut, Asim O., 1989, ISBN 8870882241, American Institute of Physics (A I P Press). Dynamical Groups & Spectrum Generating Algebra, Barut, Asim O.; Bohm, A.; Ne'Eman, Yuval, 1988, ISBN 0318420643, World Scientific Publishing Company. Dynamical Groups & Spectrum Generating Algebra, Barut, Asim O.; Bo...
Asım Orhan Barut
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These ecological ideas are still current, and research on the details continues. In assessing the geology of the reef, Darwin showed his remarkable ability to collect facts and find patterns to reconstruct geological history on the basis of the very limited evidence available. He gave attention to the smallest detail.
The Structure and Distribution of Coral Reefs
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Dynamics is the branch of classical mechanics that is concerned with the study of forces and their effects on motion. Isaac Newton was the first to formulate the fundamental physical laws that govern dynamics in classical non-relativistic physics, especially his second law of motion.
Dynamics (mechanics)
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The American Institute of Aeronautics and Astronautics (AIAA) is a professional society for the field of aerospace engineering. The AIAA is the U.S. representative on the International Astronautical Federation and the International Council of the Aeronautical Sciences. In 2015, it had more than 30,000 members among aer...
American Institute of Aeronautics and Astronautics
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It is on the ultimate success of such a quest that Gödel's theorem casts the shadow of judicious doubt. It seems on the strength of Gödel's theorem that the ultimate foundations of the bold symbolic constructions of mathematical physics will remain embedded forever in that deeper level of thinking characterized both b...
Stanley Jaki
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In materials science, the concept of the Cottrell atmosphere was introduced by A. H. Cottrell and B. A. Bilby in 1949 to explain how dislocations are pinned in some metals by boron, carbon, or nitrogen interstitials. Cottrell atmospheres occur in body-centered cubic (BCC) and face-centered cubic (FCC) materials, such a...
Cottrell atmosphere
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In engineering and materials science, necking is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material. The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck". Because the local strains in the n...
Necking (engineering)
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Symmetry is important to chemistry because it undergirds essentially all specific interactions between molecules in nature (i.e., via the interaction of natural and human-made chiral molecules with inherently chiral biological systems). The control of the symmetry of molecules produced in modern chemical synthesis cont...
Symmetry transformation
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C-ISAM was first created by Informix Corporation in the 1980s. It provided the underlying file storage mechanism for the popular first generation Informix Relational Database Management System (RDBMS), which allows data manipulation by way of the Structured Query Language (SQL) protocol. This version later became known...
IBM Informix C-ISAM
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Depending on the setting, the process has several equivalent definitions as well as definitions of varying generality owing to its many applications and characterizations. The Poisson point process can be defined, studied and used in one dimension, for example, on the real line, where it can be interpreted as a countin...
Inhomogeneous Poisson process
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Originally, the critical path method considered only logical dependencies between terminal elements. Since then, it has been expanded to allow for the inclusion of resources related to each activity, through processes called activity-based resource assignments and resource optimization techniques such as Resource Level...
Critical Path Method
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Particular cases are obtained by taking φ(t) =C cosh t, C sinh t and C et. The latter case is the classical pseudosphere generated by rotating a tractrix around a central axis. In 1868 Eugenio Beltrami showed that the geometry of the pseudosphere was directly related to that of the hyperbolic plane, discovered independ...
Differentiable surface
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HVAC makes extensive use of tortuosity in evaporator and condenser coils for heat exchangers, whereas Ultra-high vacuum makes use of the inverse of tortuosity, which is conductivity, with short, straight, voluminous paths. Tortuosity has been used in ecology to describe the movement paths of animals. == References ==
Tortuosity
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The localization theorem generalizes the localization theorem for abelian categories. Let C ⊂ D {\displaystyle C\subset D} be exact categories. Then C is said to be cofinal in D if (i) it is closed under extension in D and if (ii) for each object M in D there is an N in D such that M ⊕ N {\displaystyle M\oplus N} is in...
Basic theorems in algebraic K-theory
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Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations are used to establish new results in differential geometry and differential topology.
Global differential geometry
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Photoionisation cross section in the context of condensed matter physics refers to the probability of a particle (usually an electron) being emitted from its electronic state.
Photoionisation cross section
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These principles are motivated by neuroscience insights about learning at the level of nerve cells (synaptic plasticity) and the coupling between cortical systems for language and action in the human brain. Constraint-induced therapy contrasts sharply with traditional therapy by the strong belief that mechanisms to com...
Non-fluent aphasia
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Apart from the CCU, membership of a CC is open to National Metrology Institutes (NMIs) of Member States that are recognized internationally as most expert in the field. NMIs from Member States that are active in the field, but lack the expertise to become Members, are able to attend CC meetings as observers.These commi...
General Conference on Weights and Measures
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Direct quantum chemistry covers a set of quantum chemical methods not using the Born-Oppenheimer representation. Direct quantum chemistry considers the motion of the nuclei and the electrons on the same time scales. The method therefore considers the molecular Hamiltonian as a whole without trying to solve separately t...
Direct quantum chemistry
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Proof of the conformal relation can be easily done when one writes down the first law of thermodynamics (dU=TdS+...) in differential form with a few manipulations. The Weinhold geometry is also considered as a thermodynamic geometry.
Weinhold metric
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Most of the issues concerning the uses of stem cells in the brain are the same as any of the bioethical or purely ethical questions you will find regarding the use and research of stem cells. The field of stem cell research is a very new field that poses many ethical questions concerning the allocation of stem cells as...
Neuroethics
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93,277
The geometry of the still also plays a role in determining how much reflux occurs. In a pot still, if the tube leading from the boiler to the condenser, the lyne arm, is angled upward, more liquid will have a chance to condense and flow back into the boiler leading to increased reflux. Typical results can increase prod...
Reflux
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Soil is the living top layer of mineral and organic dirt that covers the surface of the planet. It is the chief organizing centre of most ecosystem functions, and it is of critical importance in agricultural science and ecology. The decomposition of dead organic matter (for example, leaves on the forest floor), results...
Ecology
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93,279
Serre's formalism of graphs is slightly different from the standard formalism from graph theory. Here a graph A consists of a vertex set V, an edge set E, an edge reversal map E → E , e ↦ e ¯ {\displaystyle E\to E,\ e\mapsto {\overline {e}}} such that e ≠ e and e ¯ ¯ = e {\displaystyle {\overline {\overline {e}}}=e} fo...
Bass–Serre theory
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Edmund Orme Harriss (born 1976 in Worcester, UK) is a British mathematician, writer and artist. Since 2010 he has been at the Fulbright College of Arts & Sciences at The University of Arkansas in Fayetteville, Arkansas where he is an Assistant Professor of Arts & Sciences (ARSC) and Mathematical Sciences (MASC). He doe...
Edmund Harriss
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Domenico Giulini, Algebraic and geometric structures of Special Relativity, A Chapter in "Special Relativity: Will it Survive the Next 100 Years? ", edited by Claus Lämmerzahl, Jürgen Ehlers, Springer, 2006.
Gyrovector space
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An additional "B" was later appended to designate 133 MHz FSB models, resulting in an "EB" suffix. In overall performance, Coppermine had a small advantage over the Advanced Micro Devices (AMD) Athlons it was released against, which was reversed when AMD applied their own die shrink and added an on-die L2 cache to the ...
Coppermine (microprocessor)
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1904 and later ran a successful battery company. Burgess published one of the first texts on the field in 1920. Industrial electrochemistry followed an empirical approach during the first three decades of the 20th century.After the Second World War, interest focused on the fundaments of electrochemical reactions.
Electrochemical engineering
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An Automatic Charging Robot, unveiled on July 27, 2022, is an arm-shaped automatic charging robot, charging an electric vehicle. It has been running a pilot operation at Hyundai Motor Group's headquarters since 2021. VISION AI System based on deep learning technology has been applied.
Autonomous robot
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93,285
Rigid systems, whose geometry is not greatly dependent on oxidation state, therefore experience less vibrational excitation during electron transfer, and have a lower intrinsic barrier. Photocatalysts such as 2+, are held in a rigid arrangement by flat, bidentate ligands arranged in an octahedral geometry around the me...
Photoredox catalysis
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It is soluble in cold water as well as a variety of non-polar and moderately polar solvents.In decaborane, the B10 framework resembles an incomplete octadecahedron. Each boron has one "radial" hydride, and four boron atoms near the open part of the cluster feature extra hydrides. In the language of cluster chemistry, t...
Boron decahydride
0.79717
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Demosthenis Teneketzis (Greek: Δημοσθένης Τενεκετζής) IEEE is a Greek-American electrical engineer specializing in Systems Science and Engineering. He is Professor Emeritus in the Department of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor. His works are in the fields of control, ...
Demosthenis Teneketzis
0.79717
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The pedagogy of digital literacy has begun to move across disciplines. In academia, digital literacy is a part of the computing subject area alongside computer science and information technology. while some literacy scholars have argued for expanding the framing beyond Information Communication Technologies and into li...
Digital Literacy
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93,289
Cryptography is computationally intensive and is used in many different contexts. Software implementations often serve as a bottleneck to information flow or increase network latency. Specialist hardware such as cryptographic accelerators can mitigate the bottleneck problem by introducing parallelism. Certain kinds of ...
OpenBSD Cryptographic Framework
0.79717
93,290
In linear algebra, the identity matrix of size n {\displaystyle n} is the n × n {\displaystyle n\times n} square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transforma...
Unit matrix
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93,291
Conservation of books and paper involves techniques of bookbinding, restoration, paper chemistry, and other material technologies including preservation and archival techniques.Book and paper conservation seeks to prevent and, in some cases, reverse damage due to handling, inherent vice, and the environment. Conservato...
Paper conservation
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93,292
Database-centric Architecture or data-centric architecture has several distinct meanings, generally relating to software architectures in which databases play a crucial role. Often this description is meant to contrast the design to an alternative approach. For example, the characterization of an architecture as "datab...
Database-centric architecture
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93,293
In consequence of this definition the binomial theorem can be stated by saying that the sequence { x n: n = 0 , 1 , 2 , … } {\displaystyle \{x^{n}:n=0,1,2,\ldots \}} is of binomial type. The sequence of "lower factorials" is defined by(In the theory of special functions, this same notation denotes upper factorials, but...
Binomial type
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93,294
Campbell's theorem states that any n-dimensional Riemannian manifold can be embedded locally in an (n + 1)-manifold with a Ricci curvature of R'a b = 0. The theorem also states, in similar form, that an n-dimensional pseudo-Riemannian manifold can be both locally and isometrically embedded in an n(n + 1)/2-pseudo-Eucli...
Campbell's theorem (geometry)
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93,295
In molecular nanotechnology, chemosynthesis is any chemical synthesis where reactions occur due to random thermal motion, a class which encompasses almost all of modern synthetic chemistry. The human-authored processes of chemical engineering are accordingly represented as biomimicry of the natural phenomena above, and...
Chemosynthesis (nanotechnology)
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This section illustrates how basic probabilistic rules may be reformulated as (multi)linear algebraic operations in the kernel embedding framework and is primarily based on the work of Song et al. The following notation is adopted: P ( X , Y ) = {\displaystyle P(X,Y)=} joint distribution over random variables X , Y {\d...
Kernel embedding of distributions
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Hugh MacColl, Gottlob Frege, Giuseppe Peano, and A. N. Whitehead all shared Leibniz's dream of combining symbolic logic, mathematics, and philosophy. Some writings by Leopold Löwenheim and Thoralf Skolem on algebraic logic appeared after the 1910–13 publication of Principia Mathematica, and Tarski revived interest in r...
Algebraic logic
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Archaeometry aims to systematize archaeological measurement. It emphasizes the application of analytical techniques from physics, chemistry, and engineering. It is a field of research that frequently focuses on the definition of the chemical composition of archaeological remains for source analysis. Archaeometry also i...
Archaeology
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In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extens...
Tensor (intrinsic definition)
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