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80,000 | In mathematics, Reeb stability theorem, named after Georges Reeb, asserts that if one leaf of a codimension-one foliation is closed and has finite fundamental group, then all the leaves are closed and have finite fundamental group. | Reeb stability theorem | 0.78511 |
80,001 | An important problem in foliation theory is the study of the influence exerted by a compact leaf upon the global structure of a foliation. For certain classes of foliations, this influence is considerable. Theorem: Let F {\displaystyle F} be a C 1 {\displaystyle C^{1}} , codimension one foliation of a closed manifold M... | Reeb stability theorem | 0.78511 |
80,002 | The concept of relationship extraction was first introduced during the 7th Message Understanding Conference in 1998. Relationship extraction involves the identification of relations between entities and it usually focuses on the extraction of binary relations. Application domains where relationship extraction is useful... | Relationship extraction | 0.785109 |
80,003 | In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic. Morera's theorem states that a continuous, complex-valued function f defined on an open set D in the complex plane that satisfies for every closed piecewi... | Morera's theorem | 0.785109 |
80,004 | There is a relatively elementary proof of the theorem. One constructs an anti-derivative for f explicitly. Without loss of generality, it can be assumed that D is connected. Fix a point z0 in D, and for any z ∈ D {\displaystyle z\in D} , let γ: → D {\displaystyle \gamma :\to D} be a piecewise C1 curve such that γ ( 0 ... | Morera's theorem | 0.785109 |
80,005 | The hypotheses of Morera's theorem can be weakened considerably. In particular, it suffices for the integral to be zero for every closed (solid) triangle T contained in the region D. This in fact characterizes holomorphy, i.e. f is holomorphic on D if and only if the above conditions hold. It also implies the following... | Morera's theorem | 0.785109 |
80,006 | Morera's theorem is a standard tool in complex analysis. It is used in almost any argument that involves a non-algebraic construction of a holomorphic function. | Morera's theorem | 0.785109 |
80,007 | Morera's theorem can also be used in conjunction with Fubini's theorem and the Weierstrass M-test to show the analyticity of functions defined by sums or integrals, such as the Riemann zeta function or the Gamma function Specifically one shows that for a suitable closed curve C, by writing and then using Fubini's theor... | Morera's theorem | 0.785109 |
80,008 | For example, suppose that f1, f2, ... is a sequence of holomorphic functions, converging uniformly to a continuous function f on an open disc. By Cauchy's theorem, we know that for every n, along any closed curve C in the disc. Then the uniform convergence implies that for every closed curve C, and therefore by Morera'... | Morera's theorem | 0.785109 |
80,009 | In linear algebra, a finite-dimensional vector space is isomorphic to its dual space but not canonically isomorphic to it. On the other hand a finite-dimensional vector space V {\displaystyle V} endowed with a non-degenerate bilinear form ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } , is canonically isomorph... | Musical isomorphism | 0.785107 |
80,010 | In the context of exterior algebra, an extension of the musical operators may be defined on ⋀V and its dual ⋀∗V, which with minor abuse of notation may be denoted the same, and are again mutual inverses: defined by In this extension, in which ♭ maps p-vectors to p-covectors and ♯ maps p-covectors to p-vectors, all the ... | Musical isomorphism | 0.785107 |
80,011 | In mathematics—more specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle T M {\displaystyle \mathrm {T} M} and the cotangent bundle T ∗ M {\displaystyle \mathrm {T} ^{*}M} of a pseudo-Riemannian manifold induced by its metric tensor. Ther... | Musical isomorphism | 0.785107 |
80,012 | The Fannes–Audenaert inequality is a mathematical bound on the difference between the von Neumann entropies of two density matrices as a function of their trace distance. It was proved by Koenraad M. R. Audenaert in 2007 as an optimal refinement of Mark Fannes' original inequality, which was published in 1973. Mark Fan... | Fannes–Audenaert inequality | 0.785107 |
80,013 | Lenses can focus a beam, reducing its size in one transverse dimension while increasing its angular spread, but cannot change the total emittance. This is a result of Liouville's theorem. Ways of reducing the beam emittance include radiation damping, stochastic cooling, and electron cooling. | Beam emittance | 0.785105 |
80,014 | As particle momentum along an axis is usually described as an angle relative to that axis, an area on a position-momentum plot will have dimensions of length × angle (for example, millimeters × milliradian). : 78–83 Emittance is important for analysis of particle beams. As long as the beam is only subjected to conserva... | Beam emittance | 0.785105 |
80,015 | In accelerator physics, emittance is a property of a charged particle beam. It refers to the area occupied by the beam in a position-and-momentum phase space.Each particle in a beam can be described by its position and momentum along each of three orthogonal axes, for a total of six position and momentum coordinates. W... | Beam emittance | 0.785105 |
80,016 | Thus, IRI is highly correlated to the overall ride vibration level and to the overall pavement loading vibration level. Although it is not optimized to match any particular vehicle with full fidelity, it is so strongly correlated with ride quality and road loading that most research projects that have tested alternate ... | International roughness index | 0.785105 |
80,017 | A low pitch (also known as the pitch of the missing fundamental or virtual pitch) can sometimes be heard when there is no apparent source or component of that frequency. This perception is due to the brain interpreting repetition patterns that are present.It was once thought that this effect was because the missing fun... | Residue pitch | 0.785103 |
80,018 | A tactic macromolecule in the IUPAC definition is a macromolecule in which essentially all the configurational (repeating) units are identical. Tacticity is particularly significant in vinyl polymers of the type -H2C-CH(R)- where each repeating unit with a substituent R on one side of the polymer backbone is followed b... | Tacticity | 0.785103 |
80,019 | Tacticity (from Greek: τακτικός, romanized: taktikos, "relating to arrangement or order") is the relative stereochemistry of adjacent chiral centers within a macromolecule. The practical significance of tacticity rests on the effects on the physical properties of the polymer. The regularity of the macromolecular struct... | Tacticity | 0.785103 |
80,020 | Larry R. Harris is an American researcher and businessperson. He is best known for his work in artificial intelligence, and is founder of the companies AICorp and EasyAsk, originally known as Linguistic Technology Corporation. | Larry Harris (computer scientist) | 0.785103 |
80,021 | Harris cofounded Artificial Intelligence Corporation (later known as AICorp) in 1975, serving as CEO and chairman, where he developed the mainframe product, INTELLECT, which was available for purchase as of 1981, and became a widely used natural language mainframe interface product in the early 1980s. The system used a... | Larry Harris (computer scientist) | 0.785103 |
80,022 | Strength of the source: How much radiation is being emitted by the seed, expressed as air kerma strength and denoted by S k {\displaystyle S_{k}} . Dose rate of the source: How much dose the seed will deliver to the reference point over a certain period of time, denoted by Λ {\displaystyle \Lambda } . Geometry factor: ... | Dose from radioactive seeds | 0.785102 |
80,023 | The calculation of radiation dose from radioactive seeds is crucial in the planning and administration of brachytherapy treatments. Most modern calculation are done using the formalism published by the American Association of Physicists in Medicine. For the geometry in figure 1, this formalism uses five parameters. | Dose from radioactive seeds | 0.785102 |
80,024 | To see how the binomial theorem relates to the simple construction of Pascal's triangle, consider the problem of calculating the coefficients of the expansion of ( x + y ) n + 1 {\displaystyle (x+y)^{n+1}} in terms of the corresponding coefficients of ( x + 1 ) n {\displaystyle (x+1)^{n}} (setting y = 1 {\displaystyle ... | Pascal's Triangle | 0.785102 |
80,025 | In other words, a k = ( n k ) {\displaystyle a_{k}={n \choose k}} .This is the binomial theorem. The entire right diagonal of Pascal's triangle corresponds to the coefficient of y n {\displaystyle y^{n}} in these binomial expansions, while the next diagonal corresponds to the coefficient of x y n − 1 {\displaystyle xy^... | Pascal's Triangle | 0.785102 |
80,026 | In mathematics, Pascal's triangle is a triangular array of the binomial coefficients arising in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, India, China, G... | Pascal's Triangle | 0.785102 |
80,027 | When divided by 2 n {\displaystyle 2^{n}} , the n {\displaystyle n} th row of Pascal's triangle becomes the binomial distribution in the symmetric case where p = 1 2 {\displaystyle p={\frac {1}{2}}} . By the central limit theorem, this distribution approaches the normal distribution as n {\displaystyle n} increases. Th... | Pascal's Triangle | 0.785102 |
80,028 | Gerolamo Cardano, also, published the triangle as well as the additive and multiplicative rules for constructing it in 1570.Pascal's Traité du triangle arithmétique (Treatise on Arithmetical Triangle) was published posthumously in 1665. In this, Pascal collected several results then known about the triangle, and employ... | Pascal's Triangle | 0.785102 |
80,029 | Petrus Apianus (1495–1552) published the full triangle on the frontispiece of his book on business calculations in 1527. Michael Stifel published a portion of the triangle (from the second to the middle column in each row) in 1544, describing it as a table of figurate numbers. In Italy, Pascal's triangle is referred to... | Pascal's Triangle | 0.785102 |
80,030 | The pattern of numbers that forms Pascal's triangle was known well before Pascal's time. The Persian mathematician Al-Karaji (953–1029) wrote a now-lost book which contained the first formulation of the binomial coefficients and the first description of Pascal's triangle. It was later repeated by Omar Khayyám (1048–113... | Pascal's Triangle | 0.785102 |
80,031 | This is a limit proof by Riemann sums. To begin, we recall the mean value theorem. Stated briefly, if F is continuous on the closed interval and differentiable on the open interval (a, b), then there exists some c in (a, b) such that Let f be (Riemann) integrable on the interval , and let f admit an antiderivative F o... | Fundamental theorem of the calculus | 0.785102 |
80,032 | There are two parts to the theorem. The first part deals with the derivative of an antiderivative, while the second part deals with the relationship between antiderivatives and definite integrals. | Fundamental theorem of the calculus | 0.785102 |
80,033 | The most familiar extensions of the fundamental theorem of calculus in higher dimensions are the divergence theorem and the gradient theorem. One of the most powerful generalizations in this direction is Stokes' theorem (sometimes known as the fundamental theorem of multivariable calculus): Let M be an oriented piecewi... | Fundamental theorem of the calculus | 0.785102 |
80,034 | The difference here is that the integrability of f does not need to be assumed.The version of Taylor's theorem, which expresses the error term as an integral, can be seen as a generalization of the fundamental theorem. There is a version of the theorem for complex functions: suppose U is an open set in C and f: U → C i... | Fundamental theorem of the calculus | 0.785102 |
80,035 | Conversely, if f is any integrable function, then F as given in the first formula will be absolutely continuous with F′ = f almost everywhere. The conditions of this theorem may again be relaxed by considering the integrals involved as Henstock–Kurzweil integrals. Specifically, if a continuous function F(x) admits a de... | Fundamental theorem of the calculus | 0.785102 |
80,036 | Part II of the theorem is true for any Lebesgue integrable function f, which has an antiderivative F (not all integrable functions do, though). In other words, if a real function F on admits a derivative f(x) at every point x of and if this derivative f is Lebesgue integrable on , then This result may fail for contin... | Fundamental theorem of the calculus | 0.785102 |
80,037 | The first fundamental theorem may be interpreted as follows. Given a continuous function y = f(x) whose graph is plotted as a curve, one defines a corresponding "area function" x ↦ A ( x ) {\displaystyle x\mapsto A(x)} such that A(x) is the area beneath the curve between 0 and x. The area A(x) may be not easily computa... | Fundamental theorem of the calculus | 0.785102 |
80,038 | Suppose is to be calculated. Using the first part of the theorem with f ( t ) = t 3 {\displaystyle f(t)=t^{3}} gives This can also be checked using the second part of the theorem. Specifically, F ( t ) = 1 4 t 4 {\textstyle F(t)={\frac {1}{4}}t^{4}} is an antiderivative of f ( t ) {\displaystyle f(t)} , so | Fundamental theorem of the calculus | 0.785102 |
80,039 | Suppose Then f ( x ) {\displaystyle f(x)} is not continuous at zero. Moreover, this is not just a matter of how f {\displaystyle f} is defined at zero, since the limit as x → 0 {\displaystyle x\to 0} of f ( x ) {\displaystyle f(x)} does not exist. Therefore, the corollary cannot be used to compute But consider the func... | Fundamental theorem of the calculus | 0.785102 |
80,040 | Suppose F is an antiderivative of f, with f continuous on . Let By the first part of the theorem, we know G is also an antiderivative of f. Since F′ − G′ = 0 the mean value theorem implies that F − G is a constant function, that is, there is a number c such that G(x) = F(x) + c for all x in . Letting x = a, we have whi... | Fundamental theorem of the calculus | 0.785102 |
80,041 | It is also severely affected from feedback inhibition caused mostly by HPBS and 2-HBP, the products of DszA and DszB respectively, For that reason, it has been targeted for optimization through enzyme engineering. DszA is responsible for the third step of the pathway. It catalyzes the first carbon-sulfur bond cleavage,... | Biodesulfurization | 0.785102 |
80,042 | Also, x i − x i − 1 {\displaystyle x_{i}-x_{i-1}} can be expressed as Δ x {\displaystyle \Delta x} of partition i {\displaystyle i} . We are describing the area of a rectangle, with the width times the height, and we are adding the areas together. Each rectangle, by virtue of the mean value theorem, describes an approx... | Fundamental theorem of the calculus | 0.785102 |
80,043 | Let there be numbers x0, ..., xn such that It follows that Now, we add each F(xi) along with its additive inverse, so that the resulting quantity is equal: The above quantity can be written as the following sum: The function F is differentiable on the interval (a, b) and continuous on the closed interval ; therefore, i... | Fundamental theorem of the calculus | 0.785102 |
80,044 | In that case, we can conclude that the function F is differentiable almost everywhere and F′(x) = f(x) almost everywhere. On the real line this statement is equivalent to Lebesgue's differentiation theorem. These results remain true for the Henstock–Kurzweil integral, which allows a larger class of integrable functions... | Fundamental theorem of the calculus | 0.785102 |
80,045 | The function f does not have to be continuous over the whole interval. Part I of the theorem then says: if f is any Lebesgue integrable function on and x0 is a number in such that f is continuous at x0, then is differentiable for x = x0 with F′(x0) = f(x0). We can relax the conditions on f still further and suppose t... | Fundamental theorem of the calculus | 0.785102 |
80,046 | Therefore, the left-hand side also tends to zero, and: That is, the derivative of the area function A(x) exists and is equal to the original function f(x), so the area function is an antiderivative of the original function. Thus, the derivative of the integral of a function (the area) is the original function, so that ... | Fundamental theorem of the calculus | 0.785102 |
80,047 | In the first stages of the development of the Melomics system, Iamus composed Opus one (on October 15, 2010), arguably the first fragment of professional contemporary classical music ever composed by a computer in its own style, rather than attempting to emulate the style of existing composers. The first full compositi... | Melomics | 0.785101 |
80,048 | Molecular biology findings have provided definitive evidence for two human TP receptor subtypes. The originally cloned TP from placenta (343 amino acids in length) is known as the α isoform and the splice variant cloned from endothelium (with 407 amino acids), termed the β isoform. The first 328 amino acids are the sam... | Thromboxane receptor antagonist | 0.7851 |
80,049 | This concept is known as Gemini. After Assembly complete, the Gemini concept was eliminated in the realignment of the core ISS flight control positions. TITAN (Telemetry, Information Transfer, and Attitude Navigation) is responsible for Communication & Tracking (CATO), Command & Data Handling (ODIN), and Motion Control... | Capsule communicator | 0.785099 |
80,050 | As has been discussed above, although the distinction between a symmetric operator and a self-adjoint (or essentially self-adjoint) operator is a subtle one, it is important since self-adjointness is the hypothesis in the spectral theorem. Here we discuss some concrete examples of the distinction; see the section below... | Selfadjoint operator | 0.785094 |
80,051 | A more subtle example of the distinction between symmetric and (essentially) self-adjoint operators comes from Schrödinger operators in quantum mechanics. If the potential energy is singular—particularly if the potential is unbounded below—the associated Schrödinger operator may fail to be essentially self-adjoint. In ... | Selfadjoint operator | 0.785094 |
80,052 | Of particular importance in quantum physics is the case in which T {\displaystyle T} is the Hamiltonian operator H ^ {\displaystyle {\hat {H}}} and h ( x ) := e − i t x / ℏ {\displaystyle h(x):=e^{-itx/\hbar }} is an exponential. In this case, the functional calculus should allow us to define the operator U ( t ) := h ... | Selfadjoint operator | 0.785094 |
80,053 | One important application of the spectral theorem is to define a "functional calculus." That is to say, if h {\displaystyle h} is a function on the real line and T {\displaystyle T} is a self-adjoint operator, we wish to define the operator h ( T ) {\displaystyle h(T)} . If T {\displaystyle T} has a true orthonormal ba... | Selfadjoint operator | 0.785094 |
80,054 | The School of Cybersecurity and Privacy was founded in 2020 and Richard DeMillo was appointed as the school's founding chair. The creation of the school represented an enlargement and continuation of the vision held by the Institute for Information Security & Privacy (IISP), the former organizing locus of cybersecurity... | Georgia Institute of Technology School of Cybersecurity and Privacy | 0.785094 |
80,055 | The School of Cybersecurity and Privacy offers bachelor's degrees, master's degrees, and doctoral degrees in several fields. These degrees are technically granted by the School's parent organization, the Georgia Tech College of Computing, and often awarded in conjunction with other academic units within Georgia Tech. | Georgia Institute of Technology School of Cybersecurity and Privacy | 0.785094 |
80,056 | The School of Cybersecurity and Privacy (SCP) is an academic unit located within the College of Computing at the Georgia Institute of Technology. This interdisciplinary unit draws its faculty from the College of Computing as well as the College of Engineering, the School of Public Policy, the Sam Nunn School of Interna... | Georgia Institute of Technology School of Cybersecurity and Privacy | 0.785094 |
80,057 | The nanoprobes rewrite the cellular DNA, altering the victim's biochemistry, and eventually form larger, more complicated structures and networks within the body, like electrical pathways, processing and data-storage nodes, and ultimately prosthetic devices that spring forth from the skin. In "Mortal Coil", Seven of Ni... | Borg Cube | 0.785093 |
80,058 | In the graphic novel Star Trek: The Manga, the Borg resulted from an experiment in medical nanotechnology gone wrong. An alien species under threat of extinction by an incurable disease created a repository satellite containing test subjects infused with body parts, organs, and DNA of multiple species along with cybern... | Borg Cube | 0.785093 |
80,059 | With the arrival of computer applications into the legal domain, and especially artificial intelligence applied to it, logic has been used as the major tool to formalize legal reasoning and has been developed in many directions, ranging from deontic logics to formal systems of argumentation. The knowledge base of legal... | Norm (artificial intelligence) | 0.785093 |
80,060 | Norms can be considered from different perspectives in artificial intelligence to create computers and computer software that are capable of intelligent behaviour. In artificial intelligence and law, legal norms are considered in computational tools to automatically reason upon them. In multi-agent systems (MAS), a bra... | Norm (artificial intelligence) | 0.785093 |
80,061 | Morse homology is a particularly easy way to understand the homology of smooth manifolds. It is defined using a generic choice of Morse function and Riemannian metric. The basic theorem is that the resulting homology is an invariant of the manifold (that is, independent of the function and metric) and isomorphic to the... | Morse index | 0.785092 |
80,062 | Synthetic Reaction Updates is a current awareness bibliographic database from the Royal Society of Chemistry that provides alerts of recently published developments in synthetic organic chemistry. It covers primary research in general and organic chemistry published in chemistry journals. Each record contains a reactio... | Catalysts and Catalysed Reactions | 0.785091 |
80,063 | The systems modeling language (SysML) is a general-purpose modeling language for systems engineering applications. It supports the specification, analysis, design, verification and validation of a broad range of systems and systems-of-systems. SysML was originally developed by an open source specification project, and ... | Systems Modeling Language | 0.78509 |
80,064 | As an OMG UML 2.0 profile, SysML models are designed to be exchanged using the XML Metadata Interchange (XMI) standard. In addition, architectural alignment work is underway to support the ISO 10303 (also known as STEP, the Standard for the Exchange of Product model data) AP-233 standard for exchanging and sharing info... | Systems Modeling Language | 0.78509 |
80,065 | The resulting specification, which will incorporate language enhancements from experience applying the language, will include a UML profile, a metamodel, and a mapping between the profile and metamodel. A second RFP for a SysML v2 Application Programming Interface (API) and Services RFP was issued in June 2018. Its aim... | Systems Modeling Language | 0.78509 |
80,066 | The SysML initiative originated in a January 2001 decision by the International Council on Systems Engineering (INCOSE) Model Driven Systems Design workgroup to customize the UML for systems engineering applications. Following this decision, INCOSE and the Object Management Group (OMG), which maintains the UML specific... | Systems Modeling Language | 0.78509 |
80,067 | SysML offers several systems engineering specific improvements over UML, which has been developed as a software modeling language. These improvements include the following: SysML's diagrams express system engineering concepts better due to the removal of UML's software-centric restrictions and adds two new diagram type... | Systems Modeling Language | 0.78509 |
80,068 | PEEK melts at a relatively high temperature (343 °C / 649.4 °F) compared to most other thermoplastics. In the range of its melting temperature it can be processed using injection moulding or extrusion methods. It is technically feasible to process granular PEEK into filament form and 3D printing parts from the filament... | Polyether ether ketone | 0.785089 |
80,069 | Local mean time (LMT) is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude. This measurement of time was used for everyday use during the 19th century before time zones were introduced beginning in the late 19th century; it still has some uses... | Local Mean Time | 0.785089 |
80,070 | Physical Review Letters (Divisional Associate Editor for Biological Physics) Chaos - Interdisciplinary Journal of Nonlinear Science (American Institute of Physics) | Theo Geisel (physicist) | 0.785089 |
80,071 | Theo Geisel is known for fundamental research on nonlinear and stochastic dynamics with applications in a broad range of complex living and non-living systems. He is leading in transferring methods between fields, including randomly appearing motion known in chaos theory to solid state physics, pattern formation theory... | Theo Geisel (physicist) | 0.785089 |
80,072 | Theo Geisel (born 24 August 1948 in Limburg an der Lahn, Hesse) is a German physicist. Geisel is a director at the Max Planck Institute for Dynamics and Self-Organization and professor of theoretical physics at the University of Göttingen. His research is primarily concerned with the behavior of complex systems ranging... | Theo Geisel (physicist) | 0.785089 |
80,073 | During this time, he was awarded the prestigious Gottfried Wilhelm Leibniz Prize. Since 1996, he has been professor for theoretical physics at the University of Göttingen and Director of the Max Planck Institute for Dynamics and Self-Organization. He is chairperson of the Bernstein Center for Computational Neuroscience... | Theo Geisel (physicist) | 0.785089 |
80,074 | Geisel studied physics in Frankfurt and Regensburg. After graduating from the University of Regensburg in 1975, he worked as Post-Doc at the Max Planck Institute for Solid State Research in Stuttgart (1976–77) and at the Xerox Palo Alto Research Center (1978–79). In 1980, he returned to Regensburg as assistant professo... | Theo Geisel (physicist) | 0.785089 |
80,075 | Injury prevention research can be challenging because the usual outcome of interest is deaths or injuries prevented and it is difficult to measure how many people did not get hurt who otherwise would have. Education efforts can be measured by changes in knowledge, attitudes, and beliefs and behaviors before and after a... | Injury prevention | 0.785088 |
80,076 | Geotechnical engineering, also known as geotechnics, is the branch of civil engineering concerned with the engineering behavior of earth materials. It uses the principles of soil mechanics and rock mechanics to solve its engineering problems. It also relies on knowledge of geology, hydrology, geophysics, and other rela... | Observational method (geotechnics) | 0.785087 |
80,077 | Stability analysis is needed for the design of engineered slopes and for estimating the risk of slope failure in natural or designed slopes by determining the conditions under which the topmost mass of soil will slip relative to the base of soil and lead to slope failure. If the interface between the mass and the base ... | Observational method (geotechnics) | 0.785087 |
80,078 | Higher levels of blood or CSF NF-L have been associated with increased mortality, as would be expected as release of this protein reflects ongoing axonal loss. Recent work performed as a collaboration between EnCor Biotechnology Inc. and the University of Florida showed that the NF-L antibodies employed in the most wid... | Neurofilament light polypeptide | 0.785086 |
80,079 | The Denjoy–Carleman theorem, proved by Carleman (1926) after Denjoy (1921) gave some partial results, gives criteria on the sequence M under which CM() is a quasi-analytic class. It states that the following conditions are equivalent: CM() is quasi-analytic. ∑ 1 / L j = ∞ {\displaystyle \sum 1/L_{j}=\infty } where L j ... | Denjoy–Carleman theorem | 0.785086 |
80,080 | Accurate, comprehensive data are needed in any automated medical equipment management system. Data quality initiatives can help to insure the accuracy of clinical/biomedical engineering data. The data needed to establish basic, accurate, maintainable automated records for medical equipment management includes: nomencla... | Medical equipment management | 0.785084 |
80,081 | Longer hours may be required to meet research deadlines, work with patients at times convenient to them, or work on medical equipment that is in use during daytime hours. Duties: Biomedical engineers work closely with life scientists, chemists and medical professionals (physicians, nurses, therapists and technicians) o... | Medical equipment management | 0.785084 |
80,082 | • clinical engineering – applying the latest technology to health care and health care systems in hospitals. • genomics and genetic engineering – mapping, sequencing and analyzing genomes (DNA), and applying molecular biology methods to manipulate the genetic material of cells, viruses and organisms. • medical or biolo... | Medical equipment management | 0.785084 |
80,083 | • bio-nano-engineering – developing novel structures of nanometer dimensions for application to biology, drug delivery, molecular diagnostics, microsystems and nanosystems. • biophotonics – applying and manipulating light, usually laser light, for sensing or imaging properties of biological tissue. • cellular and tissu... | Medical equipment management | 0.785084 |
80,084 | • prepare and present reports for health professionals and the public. • supervise and train technologists and technicians. Biomedical engineers may work primarily in one or a combination of the following fields: • bioinformatics – developing and using computer tools to collect and analyze data. | Medical equipment management | 0.785084 |
80,085 | Medical equipment management (sometimes referred to as clinical engineering, clinical engineering management, clinical technology management, healthcare technology management, biomedical maintenance, biomedical equipment management, and biomedical engineering) is a term for the professionals who manage operations, anal... | Medical equipment management | 0.785084 |
80,086 | Then one says that sin ( π z ) {\displaystyle \sin(\pi z)} is of exponential type π {\displaystyle \pi } , since π {\displaystyle \pi } is the smallest number that bounds the growth of sin ( π z ) {\displaystyle \sin(\pi z)} along the imaginary axis. So, for this example, Carlson's theorem cannot apply, as it requi... | Exponential type | 0.785084 |
80,087 | In complex analysis, a branch of mathematics, a holomorphic function is said to be of exponential type C if its growth is bounded by the exponential function e C | z | {\displaystyle e^{C|z|}} for some real-valued constant C {\displaystyle C} as | z | → ∞ {\displaystyle |z|\to \infty } . When a function is bounded in t... | Exponential type | 0.785084 |
80,088 | An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical... | Instanton bundle | 0.785083 |
80,089 | This is equivalent, via Stokes' theorem, to taking the integral ∫ R 4 Tr . {\displaystyle \int _{\mathbb {R} ^{4}}\operatorname {Tr} .} This is a homotopy invariant and it tells us which homotopy class the instanton belongs to. | Instanton bundle | 0.785083 |
80,090 | Thus a solution to the simpler first order (non-linear) equation ∗ F = ± F {\displaystyle {*F}=\pm F\,} is automatically also a solution of the Yang–Mills equation. This simplification occurs on 4 manifolds with: s = 1 {\displaystyle s=1} so that ∗ 2 = + 1 {\displaystyle *^{2}=+1} on 2-forms. Such solutions usually exi... | Instanton bundle | 0.785083 |
80,091 | The classical Yang–Mills action on a principal bundle with structure group G, base M, connection A, and curvature (Yang–Mills field tensor) F is S Y M = ∫ M | F | 2 d v o l M , {\displaystyle S_{YM}=\int _{M}\left|F\right|^{2}d\mathrm {vol} _{M},} where d v o l M {\displaystyle d\mathrm {vol} _{M}} is the volume form o... | Instanton bundle | 0.785083 |
80,092 | In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance. Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used... | F-test of equality of variances | 0.785083 |
80,093 | In the same year, WorldViz started cooperating with SMI to enable calculation of intersects of gaze vectors with 3D objects and saving the data in one common database for deeper analysis. German Research Center for Artificial Intelligence (DFKI) used the Eye Tracking Glasses to create Talking Places – the prototype of ... | SensoMotoric Instruments | 0.785081 |
80,094 | SensoMotoric Instruments (SMI) was a German provider of dedicated computer vision applications with a major focus on eye tracking technology. SMI was founded in 1991 as a spin-off from academic and medical research at the Free University of Berlin. The company has its headquarters in Teltow near Berlin, Germany, office... | SensoMotoric Instruments | 0.785081 |
80,095 | According to Marcel Berger, Weil, who was a student of Hadamard at the time, was prompted to work on this problem due to "a question asked during or after a Hadamard seminar at the Collège de France" by the probability theorist Paul Lévy. Weil's proof relies on conformal maps and harmonic analysis, Croke's proof is bas... | Cartan–Hadamard conjecture | 0.785081 |
80,096 | In mathematics, the Cartan–Hadamard conjecture is a fundamental problem in Riemannian geometry and Geometric measure theory which states that the classical isoperimetric inequality may be generalized to spaces of nonpositive sectional curvature, known as Cartan–Hadamard manifolds. The conjecture, which is named after F... | Cartan–Hadamard conjecture | 0.785081 |
80,097 | In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space Rn, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are named after the German mathematician Carl Friedrich Gauss. One reason why Gaussian ... | Gaussian measure | 0.785081 |
80,098 | The standard Gaussian measure γn on Rn is a Borel measure (in fact, as remarked above, it is defined on the completion of the Borel sigma algebra, which is a finer structure); is equivalent to Lebesgue measure: λ n ≪ γ n ≪ λ n {\displaystyle \lambda ^{n}\ll \gamma ^{n}\ll \lambda ^{n}} , where ≪ {\displaystyle \ll } st... | Gaussian measure | 0.785081 |
80,099 | Let n ∈ N and let B0(Rn) denote the completion of the Borel σ-algebra on Rn. Let λn: B0(Rn) → denote the usual n-dimensional Lebesgue measure. Then the standard Gaussian measure γn: B0(Rn) → is defined by γ n ( A ) = 1 2 π n ∫ A exp ( − 1 2 ‖ x ‖ R n 2 ) d λ n ( x ) {\displaystyle \gamma ^{n}(A)={\frac {1}{{\sqrt {... | Gaussian measure | 0.785081 |
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