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30,100 | PSI's membership is around 1000 statisticians from across the Pharmaceutical Industry and academia. About 80% of these are UK based. PSI hosts an annual three day conference for its members, as well as several one-day meetings and training courses. It publishes a quarterly newsletter "SPIN" and sponsors the internation... | Statisticians in the Pharmaceutical Industry | 0.805116 |
30,101 | Statisticians in the Pharmaceutical Industry, abbreviated to PSI, is an organisation for the promotion of statistical thinking in order to improve the quality of research and development in the pharmaceutical industry. PSI is a non-profit organisation formed in 1977 which was later converted to a company limited by gua... | Statisticians in the Pharmaceutical Industry | 0.805116 |
30,102 | In number theory, the optic equation is an equation that requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c: 1 a + 1 b = 1 c . {\displaystyle {\frac {1}{a}}+{\frac {1}{b}}={\frac {1}{c}}.} Multiplying both sides by abc shows that the optic equation... | Optic equation | 0.805114 |
30,103 | The optic equation, permitting but not requiring integer solutions, appears in several contexts in geometry. In a bicentric quadrilateral, the inradius r, the circumradius R, and the distance x between the incenter and the circumcenter are related by Fuss' theorem according to 1 ( R − x ) 2 + 1 ( R + x ) 2 = 1 r 2 , {\... | Optic equation | 0.805114 |
30,104 | Fermat's Last Theorem states that the sum of two integers each raised to the same integer power n cannot equal another integer raised to the power n if n > 2. This implies that no solutions to the optic equation have all three integers equal to perfect powers with the same power n > 2. For if 1 x n + 1 y n = 1 z n , {\... | Optic equation | 0.805114 |
30,105 | If the torque is defined as the z-component of this cross product, then the torque is simply rFperp where Fperp is the force perpendicular to the radius vector, or tangential to the instantaneous velocity of the blade (See figure below) From the figure above, it can be seen that the torque, T, due to gravitational forc... | Rotational sampling in wind turbines | 0.805114 |
30,106 | The set of all affines on M {\displaystyle M} forms a Lie subalgebra of P ( M ) {\displaystyle P(M)} denoted by A ( M ) {\displaystyle A(M)} (the affine algebra) and satisfies for connected M, dim A ( M ) ≤ n ( n + 1 ) {\displaystyle \dim A(M)\leq n(n+1)} . An affine vector is uniquely determined by specifying the va... | Projective vector field | 0.805113 |
30,107 | Several important special cases of projective vector fields can occur and they form Lie subalgebras of P ( M ) {\displaystyle P(M)} . These subalgebras are useful, for example, in classifying spacetimes in general relativity. | Projective vector field | 0.805113 |
30,108 | Killing vector fields (Killings) preserve the metric, i.e. h = L X g = 0 {\displaystyle h={\mathcal {L}}_{X}g=0} . Taking c = 0 {\displaystyle c=0} in the defining property of a homothety, it is seen that every Killing is a homothety (and hence an affine) and the set of all Killing vector fields on M {\displaystyle M} ... | Projective vector field | 0.805113 |
30,109 | Systems science, also referred to as systems research, or, simply, systems, is a transdisciplinary field concerned with understanding systems—from simple to complex—in nature, society, cognition, engineering, technology and science itself. The field is diverse, spanning the formal, natural, social, and applied sciences... | Systems sciences | 0.805111 |
30,110 | Systems engineering (SE) is an interdisciplinary field of engineering, that focuses on the development and organization of complex systems. It is the "art and science of creating whole solutions to complex problems", for example: signal processing systems, control systems and communication system, or other forms of hig... | Systems sciences | 0.805111 |
30,111 | This became known as the "Buscaino Reaction. "In the 1950s, neurochemistry became a recognized scientific research discipline. The founding of neurochemistry as a discipline traces its origins to a series of "International Neurochemical Symposia", of which the first symposium volume published in 1954 was titled Biochem... | Neurochemistry | 0.805109 |
30,112 | He had also established the first department that was solely devoted to the study of neurochemistry in 1928 at the Munich Kaiser Wilhelm Institute for Psychiatry.Back in the 1930s, neurochemistry was mostly referred to as "brain chemistry" and was mostly devoted to finding different chemical species without directly pr... | Neurochemistry | 0.805109 |
30,113 | Neurochemistry is the study of the different types, structures, and functions of neurons and their chemical components. Chemical signaling between neurons is mediated by neurotransmitters, neuropeptides, hormones, neuromodulators, and many other types of signaling molecules. Many neurological diseases arise due to an i... | Neurochemistry | 0.805109 |
30,114 | Neurochemistry is the study of chemicals, including neurotransmitters and other molecules such as psychopharmaceuticals and neuropeptides, that control and influence the physiology of the nervous system. This particular field within neuroscience examines how neurochemicals influence the operation of neurons, synapses, ... | Neurochemistry | 0.805109 |
30,115 | These meetings led to the formation of the International Society for Neurochemistry and the American Society for Neurochemistry. These early gatherings discussed the tentative nature of possible neurotransmitter substances such as acetylcholine, histamine, substance P, and serotonin. | Neurochemistry | 0.805109 |
30,116 | The first large leap forward in the study of neurochemistry came from Johann Ludwig Wilhelm Thudichum, who is one of the pioneers in the field of "brain chemistry." He was one of the first to hypothesize that many neurological illnesses could be attributed to an imbalance of chemicals in the brain. He was also one of t... | Neurochemistry | 0.805109 |
30,117 | While neurochemistry as a recognized science is relatively new, the idea behind neurochemistry has been around since the 18th century. Originally, the brain had been thought to be a separate entity apart from the peripheral nervous system. Beginning in 1856, there was a string of research that refuted that idea. The ch... | Neurochemistry | 0.805109 |
30,118 | The most important aspect of neurochemistry is the neurotransmitters and neuropeptides that comprise the chemical activity in the nervous system. There are many neurochemicals that are integral for proper neural functioning. The neuropeptide oxytocin, synthesized in magnocellular neurosecretory cells, plays an importan... | Neurochemistry | 0.805109 |
30,119 | One of the major areas of research within neurochemistry is looking at how post-traumatic stress disorder alters the brain. Neurotransmitter level fluctuations can dictate whether a PTSD episode occurs and how long the episode lasts. Dopamine has less of an effect than norepinephrine. | Neurochemistry | 0.805109 |
30,120 | In set theory, there is a more general notion of an enumeration than the characterization requiring the domain of the listing function to be an initial segment of the Natural numbers where the domain of the enumerating function can assume any ordinal. Under this definition, an enumeration of a set S is any surjection f... | Enumeration | 0.805104 |
30,121 | An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to... | Enumeration | 0.805104 |
30,122 | While many plants have been used for food, a small number of staple crops including wheat, rice, and maize provide most of the food in the world today. In turn, animals provide much of the meat eaten by the human population, whether farmed or hunted, and until the arrival of mechanised transport, terrestrial mammals pr... | Human uses of living things | 0.805102 |
30,123 | Fungi and microbes may also be given short shrift in archaeology because they are more difficult to study ... perhaps only ... their physical traces ... Yet they are huge determining factors that cannot be overlooked. So too we might include proteins and DNA in our summary of what might be defined as multispecies archa... | Human uses of living things | 0.805102 |
30,124 | Scholars of human culture have traditionally divided uses of living things into two categories: practical use for food and other resources; and symbolic use such as in art and religion. More recently, scholars have added a third type of interaction, where living things, whether animals, plants, fungi or microbes functi... | Human uses of living things | 0.805102 |
30,125 | In genetics, the breeding of pea plants allowed Gregor Mendel to derive the basic laws governing inheritance, and examination of chromosomes in maize allowed Barbara McClintock to demonstrate their connection to inherited traits. The plant Arabidopsis thaliana is used in laboratories as a model organism to understand h... | Human uses of living things | 0.805102 |
30,126 | Biology studies the whole range of living things. Animals such as the fruit fly Drosophila melanogaster, the zebrafish, the chicken and the house mouse, serve a major role in science as experimental models, both in fundamental biological research, such as in genetics, and in the development of new medicines, which must... | Human uses of living things | 0.805102 |
30,127 | In mathematics, the pseudoisotopy theorem is a theorem of Jean Cerf's which refers to the connectivity of a group of diffeomorphisms of a manifold. | Pseudoisotopy theorem | 0.805101 |
30,128 | In molecular biology, glycoside hydrolase family 62 is a family of glycoside hydrolases. Glycoside hydrolases EC 3.2.1. are a widespread group of enzymes that hydrolyse the glycosidic bond between two or more carbohydrates, or between a carbohydrate and a non-carbohydrate moiety. A classification system for glycoside h... | Glycoside hydrolase family 62 | 0.805101 |
30,129 | Given a differentiable manifold M (with or without boundary), a pseudo-isotopy diffeomorphism of M is a diffeomorphism of M × which restricts to the identity on M × { 0 } ∪ ∂ M × {\displaystyle M\times \{0\}\cup \partial M\times } . Given f: M × → M × {\displaystyle f:M\times \to M\times } a pseudo-isotopy diffeomo... | Pseudoisotopy theorem | 0.805101 |
30,130 | Peroxide fusion is used to prepare samples for inductively coupled plasma (ICP), atomic absorption (AA) analysis and wet chemistry. Sodium peroxide (Na2O2) is used to oxidize the sample that becomes soluble in a diluted acid solution. This method allows complete dissolution of numerous refractory compounds like chromit... | Peroxide fusion | 0.805101 |
30,131 | In medicinal chemistry and pharmacology, a binding coefficient is a quantity representing the extent to which a chemical compound will bind to a macromolecule. The preferential binding coefficient can be derived from the Kirkwood-Buff solution theory of solutions. Preferential binding is defined as a thermodynamic expr... | Binding coefficient | 0.805099 |
30,132 | There is a similar definition for Nisnevich sheaf with transfers, where the Etale topology is switched with the Nisnevich topology. | Sheaves with transfers | 0.805098 |
30,133 | In algebraic geometry, a presheaf with transfers is, roughly, a presheaf that, like cohomology theory, comes with pushforwards, “transfer” maps. Precisely, it is, by definition, a contravariant additive functor from the category of finite correspondences (defined below) to the category of abelian groups (in category th... | Sheaves with transfers | 0.805098 |
30,134 | The basic notion underlying all of the different theories are presheaves with transfers. These are contravariant additive functors F: Cor k → Ab {\displaystyle F:{\text{Cor}}_{k}\to {\text{Ab}}} and their associated category is typically denoted P S T ( k ) {\displaystyle \mathbf {PST} (k)} , or just P S T {\displaysty... | Sheaves with transfers | 0.805098 |
30,135 | In studies of molecular and cellular biology it is often desirable to artificially induce fusion. Although this can be accomplished with the addition of calcium as discussed earlier, this procedure is often not feasible because calcium regulates many other biochemical processes and its addition would be a strong confou... | Membrane fusion | 0.805096 |
30,136 | The bacterial colony optimization algorithm is an optimization algorithm which is based on a lifecycle model that simulates some typical behaviors of E. coli bacteria during their whole lifecycle, including chemotaxis, communication, elimination, reproduction, and migration. The bacterial foraging algorithm (BFA) is a ... | Bacterial Colony Optimization | 0.805096 |
30,137 | Castigliano's second theorem (for displacements) Betti's reciprocal theorem Müller-Breslau's principle | Energy principles in structural mechanics | 0.805096 |
30,138 | Energy principles in structural mechanics express the relationships between stresses, strains or deformations, displacements, material properties, and external effects in the form of energy or work done by internal and external forces. Since energy is a scalar quantity, these relationships provide convenient and altern... | Energy principles in structural mechanics | 0.805096 |
30,139 | Minimum total potential energy principle Principle of stationary total complementary potential energy Castigliano's first theorem (for forces) | Energy principles in structural mechanics | 0.805096 |
30,140 | ii) In the Model Forest of Risaralda, the Colombia 'proyecto de Ciencia Abierta y Colaborativa' promotes citizen participation in research related to how the local environment is adapting to climate change. The first meeting took place in the Flora and Fauna Sanctuary Otún Quimbaya. iii) The Citizen Network Environment... | Community science | 0.805094 |
30,141 | i) AppEAR has been developed at the Institute of Limnology and was launched in May 2016. Joaquín Cochero is a researcher who developed an "application that appeals to the collaboration of users of mobile devices in collecting data that allow the study of aquatic ecosystems" (translation). Cochero stated: "Not much of c... | Community science | 0.805094 |
30,142 | An example is using volunteer-classified images to train machine learning algorithms to identify species. While global participation and global databases are found on online platforms, not all locations always have the same amount of data from contributors. Concerns over potential data quality issues, such as measureme... | Community science | 0.805094 |
30,143 | For some projects, participants are instructed to collect and enter data, such as what species they observed, into large digital global databases. For other projects, participants help classify data on digital platforms. Citizen science data is also being used to develop machine learning algorithms. | Community science | 0.805094 |
30,144 | Citizen science (similar to community science, crowd science, crowd-sourced science, civic science, participatory monitoring, or volunteer monitoring) is scientific research conducted with participation from the general public (who are sometimes referred to as amateur/nonprofessional scientists). There are variations i... | Community science | 0.805094 |
30,145 | Resources for computer science and scientific crowdsourcing projects concerning COVID-19 can be found on the internet or as apps. Some such projects are listed below: The distributed computing project Folding@home launched a program to assist researchers around the world who are working on finding a cure and learning m... | Community science | 0.805094 |
30,146 | Reef Life Survey is a marine life monitoring programme based in Hobart, Tasmania. The project uses recreational divers that have been trained to make fish and invertebrate counts, using an approximate 50m constant depth transect of tropical and temperate reefs, which might include coral reefs. Reef Life Survey is inter... | Community science | 0.805094 |
30,147 | Let CG be the complex group algebra over G. Then the center of CG, denoted Z(CG), is defined by Z ( C G ) = { f ∈ C G ∣ ∀ g ∈ C G , f g = g f } {\displaystyle \operatorname {Z} (\mathbf {C} G)=\{f\in \mathbf {C} G\mid \forall g\in \mathbf {C} G,fg=gf\}} .This is equal to the set of all class functions (functions whic... | Conjugacy class sum | 0.805094 |
30,148 | In abstract algebra, a conjugacy class sum, or simply class sum, is a function defined for each conjugacy class of a finite group G as the sum of the elements in that conjugacy class. The class sums of a group form a basis for the center of the associated group algebra. | Conjugacy class sum | 0.805094 |
30,149 | Regular element may refer to: In ring theory, a nonzero element of a ring that is neither a left nor a right zero divisor In ring theory, a von Neumann regular element of a ring A regular element of a Lie algebra or Lie group | Regular element | 0.805093 |
30,150 | An instantaneous response would correspond to a Dirac delta function susceptibility χ(Δt) = χδ(Δt). It is convenient to take the Fourier transform with respect to time and write this relationship as a function of frequency. Because of the convolution theorem, the integral becomes a simple product, P ( ω ) = ε 0 χ ( ω )... | Complex permittivity | 0.805092 |
30,151 | In the case of a lossy medium, i.e. when the conduction current is not negligible, the total current density flowing is: J tot = J c + J d = σ E + i ω ε ′ E = i ω ε ^ E {\displaystyle J_{\text{tot}}=J_{\mathrm {c} }+J_{\mathrm {d} }=\sigma E+i\omega \varepsilon 'E=i\omega {\hat {\varepsilon }}E} where σ is the conducti... | Complex permittivity | 0.805092 |
30,152 | In quantum mechanics, a spin-exchange interaction preserves total angular momentum of the system but may allow other aspects of the system to change. When two spin-polarized atoms in their ground state experience a spin-exchange collision, the total spin of the atoms is preserved yet the orientation of the individual s... | Spin-exchange interaction | 0.805091 |
30,153 | For instance, because pharmacomicrobiomics very broadly denotes the association between xenobiotics and the microbiome, the extent to which studies profile the genetics of the microbiome can vary significantly. Studies aiming to characterize organism identity, but not gene identity or copy number may elect to use 16S s... | Pharmacomicrobiomics | 0.80509 |
30,154 | The same patient can respond properly to a drug on a given day, then—as the patient's microbiome dramatically varies after an infection, antimicrobial therapy, or radiation therapy (for example), the drug response can surprisingly be much different. Sequencing technologies such as 16S rRNA shotgun metagenomic sequencin... | Pharmacomicrobiomics | 0.80509 |
30,155 | This includes cultured organisms and metagenomic DNA samples. Examine ethical, legal, and social implications of HMP research.The primary means of characterization is through 16S rRNA sequencing and shotgun metagenomic sequencing. | Pharmacomicrobiomics | 0.80509 |
30,156 | Personalized medicine in the context of pharmacomicrobiomics refers to the ability to predict an individual’s response to a xenobiotic based on the composition of their gut microbiome. However, current omics approaches investigating microbiome composition using metagenomic sequencing after xenobiotic treatment are spar... | Pharmacomicrobiomics | 0.80509 |
30,157 | In mathematics, trace diagrams are a graphical means of performing computations in linear and multilinear algebra. They can be represented as (slightly modified) graphs in which some edges are labeled by matrices. The simplest trace diagrams represent the trace and determinant of a matrix. Several results in linear alg... | Trace diagram | 0.80509 |
30,158 | Let G be the group of n×n matrices. If a closed trace diagram is labeled by k different matrices, it may be interpreted as a function from G k {\displaystyle G^{k}} to an algebra of multilinear functions. This function is invariant under simultaneous conjugation, that is, the function corresponding to ( g 1 , … , g k )... | Trace diagram | 0.80509 |
30,159 | In statistics, a varimax rotation is used to simplify the expression of a particular sub-space in terms of just a few major items each. The actual coordinate system is unchanged, it is the orthogonal basis that is being rotated to align with those coordinates. The sub-space found with principal component analysis or fa... | Varimax rotation | 0.805088 |
30,160 | George H. Miley is a professor of nuclear engineering and a cold fusion researcher who claims to have replicated the Patterson power cell. During the 2011 World Green Energy Symposium, Miley stated that his device continuously produces several hundred watts of power. Earlier results by Miley have not convinced mainstre... | Patterson Power Cell | 0.805085 |
30,161 | "Patterson has carefully distanced himself from the work of Fleischmann and Pons and from the label of "cold fusion", due to the negative connotations associated to them since 1989. Ultimately, this effort was unsuccessful, and not only did it inherit the label of pathological science, but it managed to make cold fusio... | Patterson Power Cell | 0.805085 |
30,162 | In numerical linear algebra, the Cuthill–McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth. The reverse Cuthill–McKee algorithm (RCM) due to Alan George and Joseph Liu is th... | Cuthill–McKee algorithm | 0.805083 |
30,163 | In the case of the cosmological arrow, most physicists believe that entropy would continue to increase even if the universe began to contract (although the physicist Thomas Gold once proposed a model in which the thermodynamic arrow would reverse in this phase). In the case of the violations of time-symmetry in particl... | Loschmidt's paradox | 0.805081 |
30,164 | Any process that happens regularly in the forward direction of time but rarely or never in the opposite direction, such as entropy increasing in an isolated system, defines what physicists call an arrow of time in nature. This term only refers to an observation of an asymmetry in time; it is not meant to suggest an exp... | Loschmidt's paradox | 0.805081 |
30,165 | The fluctuation theorem considers the probability density for all of the trajectories that are initially in an infinitesimally small region of phase space. This leads directly to the probability of finding a trajectory, in either the forward or the reverse trajectory sets, depending upon the initial probability distrib... | Loschmidt's paradox | 0.805081 |
30,166 | This theorem is applicable for transient systems, which may initially be in equilibrium and then driven away (as was the case for the first experiment by Sevick et al.) or some other arbitrary initial state, including relaxation towards equilibrium. There is also an asymptotic result for systems which are in a nonequil... | Loschmidt's paradox | 0.805081 |
30,167 | One approach to handling Loschmidt's paradox is the fluctuation theorem, derived heuristically by Denis Evans and Debra Searles, which gives a numerical estimate of the probability that a system away from equilibrium will have a certain value for the dissipation function (often an entropy like property) over a certain ... | Loschmidt's paradox | 0.805081 |
30,168 | Rene Descartes (1596–1650), father of analytical geometry, in his La Geometrie published in 1637, set apart a section of about 15 pages to discuss what he had called bifocal ellipses. A bifocal oval was defined there as the locus of a point P which moves in a plane such that A P + λ B P = c {\displaystyle AP+\lambda BP... | Generalized conic | 0.805081 |
30,169 | In rectangular Cartesian coordinates, the equation y = x2 represents a parabola. The generalized equation y = x r, for r ≠ 0 and r ≠ 1, can be treated as defining a generalized parabola. The idea of generalized conic has found applications in approximation theory and optimization theory.Among the several possible ways ... | Generalized conic | 0.805081 |
30,170 | In mathematics, a generalized conic is a geometrical object defined by a property which is a generalization of some defining property of the classical conic. For example, in elementary geometry, an ellipse can be defined as the locus of a point which moves in a plane such that the sum of its distances from two fixed po... | Generalized conic | 0.805081 |
30,171 | Software archaeology or source code archeology is the study of poorly documented or undocumented legacy software implementations, as part of software maintenance. Software archaeology, named by analogy with archaeology, includes the reverse engineering of software modules, and the application of a variety of tools and ... | Software archaeology | 0.805081 |
30,172 | See also hydrogen anionHydrocarbon In organic chemistry, a hydrocarbon (HC) is an organic compound consisting entirely of hydrogen and carbon.Hydrocarbon dew point The hydrocarbon dew point (HDP) or (HCDP) is the temperature (at a given pressure) at which the hydrocarbon components of any hydrocarbon-rich gas mixture, ... | Glossary of fuel cell terms | 0.805081 |
30,173 | Half-reaction A half reaction is either the oxidation or reduction reaction component of a redox reaction.Heat exchanger A heat exchanger is a device built for efficient heat transfer from one medium to another, whether the media are separated by a solid wall so that they never mix, or the media are in direct contact.H... | Glossary of fuel cell terms | 0.805081 |
30,174 | Effluent Effluent is an outflowing of water from a natural body of water, or from a man-made structure.Electrical Balance of Plant Electrical Balance of Plant (EBOP), the user interface panel, control equipment, and converting the fuel cell DC power to AC power.Electricity Electricity is any phenomenon resulting from t... | Glossary of fuel cell terms | 0.805081 |
30,175 | Nafion Nafion is a sulfonated tetrafluoroethylene copolymerNano iron powder Nano iron powder is an iron powder with granules' sizes ranging on the nanoscale.Nanowire A nanowire is a wire of diameter of the order of a nanometer (10−9 meters).Natural gas Natural gas is a gaseous fossil fuel consisting primarily of methan... | Glossary of fuel cell terms | 0.805081 |
30,176 | Individual organisms are ordinarily mortal; they age and die, while the germlines which connect successive generations are potentially immortal. The basis for this difference is a fundamental problem in biology. The Russian biologist and historian Zhores A. Medvedev considered that the accuracy of genome replicative an... | Aging theories based on group selection | 0.80508 |
30,177 | The two key aspects of this topology are that (1), feedback is taken directly from the switching node rather than the filtered output, and (2), the higher order loop provides much higher loop gain at high audio frequencies than would be possible in a conventional single pole amplifier. Financial difficulties caused Tri... | Class-T amplifier | 0.805077 |
30,178 | There is also a Dowling geometry, of rank 3 only, associated with each quasigroup; see Dowling (1973b). This does not generalize in a straightforward way to higher ranks. There is a generalization due to Zaslavsky (2012) that involves n-ary quasigroups. | Dowling geometry | 0.805075 |
30,179 | To define the Dowling geometry, we specify the circuits (minimal dependent sets). The circuits of the matroid are the cycles whose gain is 1, the pairs of cycles with both gains not equal to 1, and which intersect in a single vertex and nothing else, and the theta graphs in which none of the three cycles has gain equal... | Dowling geometry | 0.805075 |
30,180 | A Dowling lattice is the geometric lattice of flats associated with a Dowling geometry. The lattice and the geometry are mathematically equivalent: knowing either one determines the other. Dowling lattices, and by implication Dowling geometries, were introduced by Dowling (1973a,b). A Dowling lattice or geometry of ran... | Dowling geometry | 0.805075 |
30,181 | In combinatorial mathematics, a Dowling geometry, named after Thomas A. Dowling, is a matroid associated with a group. There is a Dowling geometry of each rank for each group. If the rank is at least 3, the Dowling geometry uniquely determines the group. Dowling geometries have a role in matroid theory as universal obj... | Dowling geometry | 0.805075 |
30,182 | In his first paper (1973a) Dowling defined the rank-n Dowling lattice of the multiplicative group of a finite field F. It is the set of all those subspaces of the vector space Fn that are generated by subsets of the set E that consists of vectors with at most two nonzero coordinates. The corresponding Dowling geometry ... | Dowling geometry | 0.805075 |
30,183 | In all of the following theorems we assume some local behavior of the space (usually formulated using curvature assumption) to derive some information about the global structure of the space, including either some information on the topological type of the manifold or on the behavior of points at "sufficiently large" d... | Riemannian Geometry | 0.805075 |
30,184 | Other generalizations of Riemannian geometry include Finsler geometry. There exists a close analogy of differential geometry with the mathematical structure of defects in regular crystals. Dislocations and disclinations produce torsions and curvature.The following articles provide some useful introductory material: Met... | Riemannian Geometry | 0.805075 |
30,185 | Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century. It deals with a broad range of geometries whose metric properties vary from point to point, including the standard types of non-Euclidean geometry. Every smooth manifold admits a Riemannian metric, which often helps to solv... | Riemannian Geometry | 0.805075 |
30,186 | The volume of a metric ball of radius r in a complete n-dimensional Riemannian manifold with positive Ricci curvature has volume at most that of the volume of a ball of the same radius r in Euclidean space. Gromov's compactness theorem. The set of all Riemannian manifolds with positive Ricci curvature and diameter at m... | Riemannian Geometry | 0.805075 |
30,187 | Splitting theorem. If a complete n-dimensional Riemannian manifold has nonnegative Ricci curvature and a straight line (i.e. a geodesic that minimizes distance on each interval) then it is isometric to a direct product of the real line and a complete (n-1)-dimensional Riemannian manifold that has nonnegative Ricci curv... | Riemannian Geometry | 0.805075 |
30,188 | Myers theorem. If a complete Riemannian manifold has positive Ricci curvature then its fundamental group is finite. Bochner's formula. If a compact Riemannian n-manifold has non-negative Ricci curvature, then its first Betti number is at most n, with equality if and only if the Riemannian manifold is a flat torus. | Riemannian Geometry | 0.805075 |
30,189 | A linear model has long been used in health physics to set maximum acceptable radiation exposures. The United States-based National Council on Radiation Protection and Measurements (NCRP), a body commissioned by the United States Congress, recently released a report written by the national experts in the field which st... | LNT model | 0.805073 |
30,190 | In poorly porous intervals, the oil-water, gas-water or gas-oil contacts can similarly be obscured, which makes estimation of hydrocarbon reserves difficult. Descriptions of the well's petrophysics will then often further qualify to delineate a gas-down-to, oil-up-to, oil-down-to and water-up-to line, clearly showing t... | Water contact | 0.805071 |
30,191 | Suppose that Σ {\displaystyle \Sigma } is a closed simple contour in the complex plane dividing the plane into two parts denoted by Σ + {\displaystyle \Sigma _{+}} (the inside) and Σ − {\displaystyle \Sigma _{-}} (the outside), determined by the index of the contour with respect to a point. The classical problem, consi... | Riemann–Hilbert problem | 0.805068 |
30,192 | Furthermore, the distribution of eigenvalues of random matrices in several classical ensembles is reduced to computations involving orthogonal polynomials (see for example Deift (2000)).C. Combinatorial probability The most celebrated example is the theorem of Baik, Deift & Johansson (1999) on the distribution of the l... | Riemann–Hilbert problem | 0.805068 |
30,193 | Riemann–Hilbert problems have applications to several related classes of problems. A. Integrable models The inverse scattering or inverse spectral problem associated to the Cauchy problems for 1+1 dimensional partial differential equations on the line, or to periodic problems, or even to initial-boundary value problems... | Riemann–Hilbert problem | 0.805068 |
30,194 | In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential equations in the complex plane. Several existence theorems for Riemann–Hilbert problems have been produced by Mark Krein, Israel Gohberg and others (see the book by C... | Riemann–Hilbert problem | 0.805068 |
30,195 | Mutualism in microbial ecology is a relationship between microbial species and humans that allow for both sides to benefit. One such example would be syntrophy, also known as cross-feeding, of which 'Methanobacterium omelianskii ' is a classical example. This consortium is formed by an ethanol fermenting organism and a... | Environmental Microbiology | 0.805067 |
30,196 | Amensalism (also commonly known as antagonism) is a type of symbiotic relationship where one species/organism is harmed while the other remains unaffected. One example of such a relationship that takes place in microbial ecology is between the microbial species Lactobacillus casei and Pseudomonas taetrolens. When co-ex... | Environmental Microbiology | 0.805067 |
30,197 | For example, the nitrogen gas which makes up 78% of the earth's atmosphere is unavailable to most organisms, until it is converted to a biologically available form by the microbial process of nitrogen fixation. Differing from the nitrogen and carbon cycles, stable gaseous species are not created in the phosphorus cycle... | Environmental Microbiology | 0.805067 |
30,198 | PWM also works well with digital controls, which, because of their on/off nature, can easily set the needed duty cycle. PWM has also been used in certain communication systems where its duty cycle has been used to convey information over a communications channel. In electronics, many modern microcontrollers (MCUs) inte... | Pulse width modulation | 0.805067 |
30,199 | Stilbene will typically have the chemistry of a diarylethene, a conjugated alkene. Stilbene can undergo photoisomerization under the influence of UV light. Stilbene can undergo stilbene photocyclization, an intramolecular reaction. (Z)-Stilbene can undergo electrocyclic reactions. | (Z)-Stilbene | 0.805067 |
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