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13,600 | (Doctor of Sciences) degrees in the Academy of Sciences of the Soviet Union, respectively, in 1979 and 1986. Between 1972 and 1992, his major interests include the physics of semiconductors, plasma and solid state physics. During this time, Boris Kerner together with V.V. | Kerner’s breakdown minimization principle | 0.815983 |
13,601 | The six lines of a complete quadrangle meet in pairs to form three additional points called the diagonal points of the quadrangle. Similarly, among the six points of a complete quadrilateral there are three pairs of points that are not already connected by lines; the line segments connecting these pairs are called diag... | Complete quadrilateral | 0.81598 |
13,602 | The four points on the line deriving from the sides and diagonals of the quadrangle are called a harmonic range. Through perspectivity and projectivity, the harmonic property is stable. Developments of modern geometry and algebra note the influence of von Staudt on Mario Pieri and Felix Klein . | Complete quadrilateral | 0.81598 |
13,603 | In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points. Dually, a complete quadrilateral is ... | Complete quadrilateral | 0.81598 |
13,604 | In mathematics, a partial group algebra is an associative algebra related to the partial representations of a group. | Partial group algebra | 0.815979 |
13,605 | The partial group algebra C par ( Z 4 ) {\displaystyle \mathbb {C} _{\text{par}}\left(\mathbb {Z} _{4}\right)} is isomorphic to the direct sum: C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ C ⊕ M 2 ( C ) ⊕ M 3 ( C ) {\displaystyle \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \oplus \mathbb {C} \opl... | Partial group algebra | 0.815979 |
13,606 | Around 2011, a good ILSVRC classification top-5 error rate was 25%. In 2012, a deep convolutional neural net called AlexNet achieved 16%; in the next couple of years, top-5 error rates fell to a few percent. While the 2012 breakthrough "combined pieces that were all there before", the dramatic quantitative improvement ... | ImageNet | 0.815974 |
13,607 | There are 3 real forms: a compact one, a split one, and a third one. They are the isometry groups of the three real Albert algebras. The F4 Lie algebra may be constructed by adding 16 generators transforming as a spinor to the 36-dimensional Lie algebra so(9), in analogy with the construction of E8. In older books and ... | F4 (mathematics) | 0.815965 |
13,608 | In mathematics, F4 is the name of a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The compact form is simply connected and its outer automorphism group is the trivial group. | F4 (mathematics) | 0.815965 |
13,609 | An ion trap is a combination of electric and/or magnetic fields used to capture charged particles — known as ions — often in a system isolated from an external environment. Atomic and molecular ion traps have a number of applications in physics and chemistry such as precision mass spectrometry, improved atomic frequenc... | Ion traps | 0.815964 |
13,610 | A standard configuration for a Penning trap consists of a ring electrode and two end caps. A static voltage differential between the ring and end caps confines ions along the axial direction (between end caps). However, as expected from Earnshaw's theorem, the static electric potential is not sufficient to trap an ion ... | Ion traps | 0.815964 |
13,611 | A charged particle, such as an ion, feels a force from an electric field. As a consequence of Earnshaw's theorem, it is not possible to confine an ion in an electrostatic field. However, physicists have various ways of working around this theorem by using combinations of static magnetic and electric fields (as in a Pen... | Ion traps | 0.815964 |
13,612 | In organic chemistry, an amide, also known as an organic amide or a carboxamide, is a compound with the general formula R−C(=O)−NR′R″, where R, R', and R″ represent any group, typically organyl groups or hydrogen atoms. The amide group is called a peptide bond when it is part of the main chain of a protein, and an isop... | Amide bond | 0.815959 |
13,613 | Some organisms have adapted to lower levels of light through increasing its cellular chlorophyll amounts, and others have adapted by migrating vertically with varying nutrient and light levels. The DCM species composition vary with water chemistry, location, seasonality, and depth. Not only is there a difference in DCM... | Deep chlorophyll maximum | 0.815957 |
13,614 | A drawing meant to depict the physical arrangement of the wires and the components they connect is called artwork or layout, physical design, or wiring diagram. Circuit diagrams are used for the design (circuit design), construction (such as PCB layout), and maintenance of electrical and electronic equipment. In comput... | Circuit diagram | 0.815955 |
13,615 | Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, ... | Multivariate Analysis | 0.815948 |
13,616 | Algorithm for instance selection should identify a subset of the total available data to achieve the original purpose of the data mining (or machine learning) application as if the whole data had been used. Considering this, the optimal outcome of IS would be the minimum data subset that can accomplish the same task wi... | Instance selection | 0.815948 |
13,617 | Instance selection (or dataset reduction, or dataset condensation) is an important data pre-processing step that can be applied in many machine learning (or data mining) tasks. Approaches for instance selection can be applied for reducing the original dataset to a manageable volume, leading to a reduction of the comput... | Instance selection | 0.815948 |
13,618 | Physical schema is a term used in data management to describe how data is to be represented and stored (files, indices, et al.) in secondary storage using a particular database management system (DBMS) (e.g., Oracle RDBMS, Sybase SQL Server, etc.). In the ANSI/SPARC Architecture three schema approach, the internal sche... | Physical data model | 0.815929 |
13,619 | Software studies is an emerging interdisciplinary research field, which studies software systems and their social and cultural effects. The implementation and use of software has been studied in recent fields such as cyberculture, Internet studies, new media studies, and digital culture, yet prior to software studies, ... | Software studies | 0.815929 |
13,620 | As said in the introduction, the stretched exponential was introduced by the German physicist Rudolf Kohlrausch in 1854 to describe the discharge of a capacitor (Leyden jar) that used glass as dielectric medium. The next documented usage is by Friedrich Kohlrausch, son of Rudolf, to describe torsional relaxation. A. We... | Stretched exponential | 0.815926 |
13,621 | In physics, attempts have been made to explain stretched exponential behaviour as a linear superposition of simple exponential decays. This requires a nontrivial distribution of relaxation times, ρ(u), which is implicitly defined by Alternatively, a distribution is used. ρ can be computed from the series expansion: For... | Stretched exponential | 0.815926 |
13,622 | Bayes' theorem states a rule for updating a probability conditioned on other information. In 1967, Ian Hacking argued that in a static form, Bayes' theorem only connects probabilities that are held simultaneously; it does not tell the learner how to update probabilities when new evidence becomes available over time, co... | Radical probabilism | 0.815925 |
13,623 | Radical probabilism is a hypothesis in philosophy, in particular epistemology, and probability theory that holds that no facts are known for certain. That view holds profound implications for statistical inference. The philosophy is particularly associated with Richard Jeffrey who wittily characterised it with the dict... | Radical probabilism | 0.815925 |
13,624 | Which of the possible chair conformations predominate in cyclohexanes bearing one or more substituents depends on the substituents, and where they are located on the ring; generally, "bulky" substituents—those groups with large volumes, or groups that are otherwise repulsive in their interactions—prefer to occupy an eq... | Cyclic compound | 0.815925 |
13,625 | A cyclic compound or ring compound is a compound in which at least some its atoms are connected to form a ring. Rings vary in size from three to many tens or even hundreds of atoms. Examples of ring compounds readily include cases where: all the atoms are carbon (i.e., are carbocycles), none of the atoms are carbon (in... | Cyclic compound | 0.815925 |
13,626 | This can be proven by imitating the usual proofs of Urysohn's lemma, using the last property of proximal neighborhoods to create the infinite increasing chain used in proving the lemma. Given a compact Hausdorff space, there is a unique proximity whose corresponding topology is the given topology: A {\displaystyle A} i... | Proximity space | 0.815924 |
13,627 | Given a proximity space, one can define a topology by letting A ↦ { x: { x } δ A } {\displaystyle A\mapsto \left\{x:\{x\}\;\delta \;A\right\}} be a Kuratowski closure operator. If the proximity space is separated, the resulting topology is Hausdorff. Proximity maps will be continuous between the induced topologies. The... | Proximity space | 0.815924 |
13,628 | In topology, a proximity space, also called a nearness space, is an axiomatization of the intuitive notion of "nearness" that hold set-to-set, as opposed to the better known point-to-set notion that characterize topological spaces. The concept was described by Frigyes Riesz (1909) but ignored at the time. It was redisc... | Proximity space | 0.815924 |
13,629 | In the first year of data recorded by the Wilkinson Microwave Anisotropy Probe (WMAP), a region of sky in the constellation Eridanus was found to be cooler than the surrounding area. Subsequently, using the data gathered by WMAP over 3 years, the statistical significance of such a large, cool region was estimated. The ... | CMB cold spot | 0.815922 |
13,630 | In mathematics and theoretical physics, fusion rules are rules that determine the exact decomposition of the tensor product of two representations of a group into a direct sum of irreducible representations. The term is often used in the context of two-dimensional conformal field theory where the relevant group is gene... | Fusion rules | 0.815922 |
13,631 | The key concepts of physical chemistry are the ways in which pure physics is applied to chemical problems. One of the key concepts in classical chemistry is that all chemical compounds can be described as groups of atoms bonded together and chemical reactions can be described as the making and breaking of those bonds. ... | Physical chemist | 0.815921 |
13,632 | Some journals that deal with physical chemistry include Zeitschrift für Physikalische Chemie (1887) Journal of Physical Chemistry A (from 1896 as Journal of Physical Chemistry, renamed in 1997) Physical Chemistry Chemical Physics (from 1999, formerly Faraday Transactions with a history dating back to 1905) Macromolecul... | Physical chemist | 0.815921 |
13,633 | For example, it is common in universal quantification to make statements over an infinite set such as the set of all natural numbers. Such statements are perfectly reasonable and even required in mathematical proofs but when included in an automated theorem prover executing on a computer may cause the computer to fall ... | Inference engine | 0.815921 |
13,634 | For example, general statements that included universal quantification (for all X some statement is true) and existential quantification (there exists some X such that some statement is true). What researchers discovered is that the power of these theorem-proving environments was also their drawback. Back in 1965, it w... | Inference engine | 0.815921 |
13,635 | The logic that an inference engine uses is typically represented as IF-THEN rules. The general format of such rules is IF THEN . Prior to the development of expert systems and inference engines, artificial intelligence researchers focused on more powerful theorem prover environments that offered much fuller implementat... | Inference engine | 0.815921 |
13,636 | Another very popular technology that was developed was the Prolog logic programming language. Prolog focused primarily on backward chaining and also featured various commercial versions and optimizations for efficiency and robustness.As Expert Systems prompted significant interest from the business world various compan... | Inference engine | 0.815921 |
13,637 | In this context, an 'inference engine' could refer to the specific part of the system, or even the hardware, that executes these operations. This type of inference plays a crucial role in various applications, including (but not limited to) image recognition, natural language processing, and autonomous vehicles. The in... | Inference engine | 0.815921 |
13,638 | Forward chaining starts with the known facts and asserts new facts. Backward chaining starts with goals, and works backward to determine what facts must be asserted so that the goals can be achieved.Additionally, the concept of 'inference' has expanded to include the process through which trained neural networks genera... | Inference engine | 0.815921 |
13,639 | In the field of artificial intelligence, an inference engine is a component of the system that applies logical rules to the knowledge base to deduce new information. The first inference engines were components of expert systems. The typical expert system consisted of a knowledge base and an inference engine. The knowle... | Inference engine | 0.815921 |
13,640 | Application drivers range from smartphones to AI to data centers.IEEE began a road-mapping initiative in 2016, "Rebooting Computing", named the International Roadmap for Devices and Systems (IRDS).Most forecasters, including Gordon Moore, expect Moore's law will end by around 2025. Although Moore's Law will reach a phy... | Computational power | 0.815919 |
13,641 | Other approaches are being investigated, which do not rely on physical scaling. These include the spin state of electron spintronics, tunnel junctions, and advanced confinement of channel materials via nano-wire geometry. Spin-based logic and memory options are being developed actively in labs. | Computational power | 0.815919 |
13,642 | Moore's law is the observation that the number of transistors in an integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empirical relationship linked to gains from experience in production. The observation is n... | Computational power | 0.815919 |
13,643 | The Erdős–Tenenbaum–Ford constant is a mathematical constant that appears in number theory. Named after mathematicians Paul Erdős, Gérald Tenenbaum, and Kevin Ford, it is defined as δ := 1 − 1 + log log 2 log 2 = 0.0860713320 … {\displaystyle \delta :=1-{\frac {1+\log \log 2}{\log 2}}=0.0860713320\dots } where lo... | Erdős–Tenenbaum–Ford constant | 0.815915 |
13,644 | If G is a group and R is a ring, the group ring of G over R is a free module over R having G as basis. Multiplication is defined by the rules that the elements of G commute with the elements of R and multiply together as they do in the group G. The ring of differential operators (depending on the context). In fact, man... | Associative ring | 0.815911 |
13,645 | Every module over a division ring is a free module (has a basis); consequently, much of linear algebra can be carried out over a division ring instead of a field. The study of conjugacy classes figures prominently in the classical theory of division rings; see, for example, the Cartan–Brauer–Hua theorem. A cyclic algeb... | Associative ring | 0.815911 |
13,646 | In particular, the center of a division ring is a field. It turned out that every finite domain (in particular finite division ring) is a field; in particular commutative (the Wedderburn's little theorem). | Associative ring | 0.815911 |
13,647 | The third annual Empowering Women in Organic Chemistry Conference was held virtually on Thursday, June 24, and Friday, June 25, 2021. 2021 Career Panel featured Kay Brummond (Univ of Pittsburgh), Martha A. Sarpong (GlaxoSmithKline), Emma Radoux (Royal Society of Chemistry), Callie Bryan (Janssen), Kimberly Steward (Car... | Empowering Women in Organic Chemistry | 0.81591 |
13,648 | The volunteer-run EWOC conferences allow women leaders to present their scientific research and also allows the participants to hear career stories of how eminent women in the field of organic chemistry have developed their careers and the challenges they have faced – and overcome – along the way. The meeting consists ... | Empowering Women in Organic Chemistry | 0.81591 |
13,649 | The number of female scientists in the organic chemistry community, industry and academics, remains low (<20%). Advancement of women in the chemical sciences is a challenge due to the so-called “leaky pipeline,” wherein growing numbers of women enter academics and industry to study science opt out to pursue alternative... | Empowering Women in Organic Chemistry | 0.81591 |
13,650 | The fourth annual Empowering Women in Organic Chemistry Conference was a hybrid meeting on Thursday, June 23, and Friday, June 24, 2022. == References == | Empowering Women in Organic Chemistry | 0.81591 |
13,651 | The second annual Empowering Women in Organic Chemistry Conference was held virtually on Thursday, August 13, 2020, and Friday, August 14, 2020. 2020 Career Panel featured Shanina Sanders Johnson (Spelman College), Davita Watkins (Univ of Mississippi), Niki Patel (Merck), Stacy Fosu (Abbvie), Beth Lorsbach (Corteva Agr... | Empowering Women in Organic Chemistry | 0.81591 |
13,652 | The first Empowering Women in Organic Chemistry Conference took place on Friday, June 28, 2019, at the University of Pennsylvania, Philadelphia, PA. 2019 Career Panel featured Sarah Wengryniuk (Temple University), Emily McLaughlin (Bard College), Nikki Goodwin (GlaxoSmithKline), Jamie McCabe Dunn (Merck), Zhenzhen Dong... | Empowering Women in Organic Chemistry | 0.81591 |
13,653 | Empowering Women in Organic Chemistry (EWOC) is a scientific conference designed to bring the research and career interests of women in organic chemistry to the forefront and seeks to empower all marginalized individuals by promoting equity, justice, diversity, and inclusion across all chemistry fields. EWOC is the wor... | Empowering Women in Organic Chemistry | 0.81591 |
13,654 | The EWOC Conference structure consists of a combination of scientific presentations, workshops, topical networking sessions, career panel and also includes a poster session. Examples of Workshops have included Cultivate Belonging in the Workplace for Yourself and Others; How to Create, Build and Leverage Networks for S... | Empowering Women in Organic Chemistry | 0.81591 |
13,655 | Consider a Radon space Ω {\displaystyle \Omega } (that is a probability measure defined on a Radon space endowed with the Borel sigma-algebra) and a real-valued random variable T. As discussed above, in this case there exists a regular conditional probability with respect to T. Moreover, we can alternatively define the... | Regular conditional probability | 0.815909 |
13,656 | Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} be a probability space, and let T: Ω → E {\displaystyle T:\Omega \rightarrow E} be a random variable, defined as a Borel-measurable function from Ω {\displaystyle \Omega } to its state space ( E , E ) {\displaystyle (E,{\mathcal {E}})} . One should think of T... | Regular conditional probability | 0.815909 |
13,657 | {\displaystyle \kappa _{Y|X}(x,A)=e_{Y\in A}(x).} As with conditional expectation, this can be further generalized to conditioning on a sigma algebra F {\displaystyle {\mathcal {F}}} . In that case the conditional distribution is a function Ω × B ( R ) → {\displaystyle \Omega \times {\mathcal {B}}(\mathbb {R} )\to }: ... | Regular conditional probability | 0.815909 |
13,658 | In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability distribution is a parametrized family of probability measures called a Markov kernel. | Regular conditional probability | 0.815909 |
13,659 | This makes them useful as biomarkers for geologists to verify the age, origin and degradation processes of different rocks.Biogenic substances have been studied as part of marine biochemistry since the 1960s, which has involved investigating their production, transport, and transformation in the water, and how they may... | Biogenic substance | 0.815908 |
13,660 | Additionally, the transformation and exchange of biogenic substances can by modelled in the environment, particularly their transport in waterways.The observation and measurement of biogenic substances is notably important in the fields of geology and biochemistry. A large proportion of isoprenoids and fatty acids in g... | Biogenic substance | 0.815908 |
13,661 | A biogenic substance is a product made by or of life forms. While the term originally was specific to metabolite compounds that had toxic effects on other organisms, it has developed to encompass any constituents, secretions, and metabolites of plants or animals. In context of molecular biology, biogenic substances are... | Biogenic substance | 0.815908 |
13,662 | There are two main evaluation methods involved: measuring per unit water volume (mg/m3 year) and measuring substances per entire water volume of layer (t of element/year). The former is mostly used to observe biogenic substance dynamics and individual pathways for flux and transformations, and is useful when comparing ... | Biogenic substance | 0.815908 |
13,663 | Current research also aims to produce these biogenic substances on a commercial level using metabolic engineering techniques. By pairing these techniques with biochemical engineering design, algae and their biogenic substances can be produced on a large scale using photobioreactors. Different system types can be used t... | Biogenic substance | 0.815908 |
13,664 | This was facilitated by the development of more advanced analytical methods, and led to greater collaboration between geologists and organic chemists in order to research the biogenic compounds in sediments.Researchers additionally began to investigate the production of compounds by microorganisms in the marine environ... | Biogenic substance | 0.815908 |
13,665 | During a meeting of the New York Academy of Sciences' Section of Geology and Mineralogy in 1903, geologist Amadeus William Grabau proposed a new rock classification system in his paper 'Discussion of and Suggestions Regarding a New Classification of Rocks'. Within the primary subdivision of "Endogenetic rocks" – rocks ... | Biogenic substance | 0.815908 |
13,666 | Definitions in KL-ONE can be directly mapped to set theory and the predicate calculus. This allows specialized theorem provers called classifiers to analyze the various declarations between sets, subsets, and relations in a given model. In this way the model can be validated and any inconsistent definitions flagged. | Logic in computer science | 0.815907 |
13,667 | Rather than arbitrary formulas with the full range of logical operators the starting point is simply what logicians refer to as modus ponens. As a result, rule-based systems can support high-performance computation, especially if they take advantage of optimization algorithms and compilation.Another major area of resea... | Logic in computer science | 0.815907 |
13,668 | There has always been a strong influence from mathematical logic on the field of artificial intelligence (AI). From the beginning of the field it was realized that technology to automate logical inferences could have great potential to solve problems and draw conclusions from facts. Ron Brachman has described first-ord... | Logic in computer science | 0.815907 |
13,669 | In actual logical systems the statements can be numerous and complex. It was realized early on that this kind of analysis could be significantly aided by the use of computers. The Logic Theorist validated the theoretical work of Bertrand Russell and Alfred North Whitehead in their influential work on mathematical logic... | Logic in computer science | 0.815907 |
13,670 | One of the first applications to use the term artificial intelligence was the Logic Theorist system developed by Allen Newell, J. C. Shaw, and Herbert Simon in 1956. One of the things that a logician does is to take a set of statements in logic and deduce the conclusions (additional statements) that must be true by the... | Logic in computer science | 0.815907 |
13,671 | In particular it showed that terms in the simply-typed lambda-calculus correspond to proofs of intuitionistic propositional logic. Category theory represents a view of mathematics that emphasizes the relations between structures. It is intimately tied to many aspects of computer science: type systems for programming la... | Logic in computer science | 0.815907 |
13,672 | The frame problem is a basic problem that must be overcome when using first-order logic to represent the goals and state of an artificial intelligence agent. The Curry–Howard correspondence is a relation between logical systems and software. This theory established a precise correspondence between proofs and programs. | Logic in computer science | 0.815907 |
13,673 | Turing gave the first compelling analysis of what can be called a mechanical procedure and Kurt Gödel asserted that he found Turing's analysis "perfect." In addition some other major areas of theoretical overlap between logic and computer science are: Gödel's incompleteness theorem proves that any logical system powerf... | Logic in computer science | 0.815907 |
13,674 | Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church ... | Logic in computer science | 0.815907 |
13,675 | Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas: Theoretical foundations and analysis Use of computer technology to aid logicians Use of concepts from logic for computer applications | Logic in computer science | 0.815907 |
13,676 | Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. Application areas include system identification and control (vehicle control, trajectory prediction, process control, natural resource management), quantum chemistry, general game... | Parameter (machine learning) | 0.815902 |
13,677 | The multilayer perceptron is a universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters. A specific recurrent architecture with rational-valued weights... | Parameter (machine learning) | 0.815902 |
13,678 | Research is underway on ANN systems designed for penetration testing, for detecting botnets, credit cards frauds and network intrusions. ANNs have been proposed as a tool to solve partial differential equations in physics and simulate the properties of many-body open quantum systems. In brain research ANNs have studied... | Parameter (machine learning) | 0.815902 |
13,679 | ANNs have also been used for building black-box models in geoscience: hydrology, ocean modelling and coastal engineering, and geomorphology. ANNs have been employed in cybersecurity, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for clas... | Parameter (machine learning) | 0.815902 |
13,680 | Analyzing what has been learned by an ANN is much easier than analyzing what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, lo... | Parameter (machine learning) | 0.815902 |
13,681 | Advocates of hybrid models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind. | Parameter (machine learning) | 0.815902 |
13,682 | Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named crossbar adaptive array (CAA). It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the e... | Parameter (machine learning) | 0.815902 |
13,683 | In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is: where F d {\displaystyle F_{\rm {d}}} is the drag force, which is by definition the force component in the direction of the flow velocity, ρ {\... | Drag equation | 0.815898 |
13,684 | These two properties determine the speed of sound in the gas at its given temperature. The Buckingham pi theorem then leads to a third dimensionless group, the ratio of the relative velocity to the speed of sound, which is known as the Mach number. Consequently when a body is moving relative to a gas, the drag coeffici... | Drag equation | 0.815898 |
13,685 | Here, fa is some (as-yet-unknown) function that takes five arguments. Now the right-hand side is zero in any system of units; so it should be possible to express the relationship described by fa in terms of only dimensionless groups. There are many ways of combining the five arguments of fa to form dimensionless groups... | Drag equation | 0.815898 |
13,686 | The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object. Suppose that the fluid is a liquid, and the variables involved – under some conditions – are the: speed u, fluid density ρ, kinematic viscosity ... | Drag equation | 0.815898 |
13,687 | In number theory, Niven's constant, named after Ivan Niven, is the largest exponent appearing in the prime factorization of any natural number n "on average". More precisely, if we define H(1) = 1 and H(n) = the largest exponent appearing in the unique prime factorization of a natural number n > 1, then Niven's constan... | Niven's constant | 0.815893 |
13,688 | There are many variants of the maximum principle. We give a simple one. Theorem. (Weak maximum principle.) | Elliptic boundary value problem | 0.815891 |
13,689 | A regularity theorem for a linear elliptic boundary value problem of the second order takes the form Theorem If (some condition), then the solution u {\displaystyle u} is in H 2 ( Ω ) {\displaystyle H^{2}(\Omega )} , the space of "twice differentiable" functions whose second derivatives are square integrable. There is ... | Elliptic boundary value problem | 0.815891 |
13,690 | The discussion in details of Sobolev spaces is beyond the scope of this article, but we will quote required results as they arise. Unless otherwise noted, all derivatives in this article are to be interpreted in the weak, Sobolev sense. We use the term "strong derivative" to refer to the classical derivative of calculu... | Elliptic boundary value problem | 0.815891 |
13,691 | One may show, via the Lax–Milgram lemma, that whenever A ( u , φ ) {\displaystyle A(u,\varphi )} is coercive and F ( φ ) {\displaystyle F(\varphi )} is continuous, then there exists a unique solution u ∈ H 0 1 ( Ω ) {\displaystyle u\in H_{0}^{1}(\Omega )} to the weak problem (*). If further A ( u , φ ) {\displaystyle A... | Elliptic boundary value problem | 0.815891 |
13,692 | One may further prove that if the boundary of Ω ⊂ R n {\displaystyle \Omega \subset \mathbb {R} ^{n}} is a smooth manifold and f {\displaystyle f} is infinitely differentiable in the strong sense, then u {\displaystyle u} is also infinitely differentiable in the strong sense. In this case, L u = f {\displaystyle Lu=f} ... | Elliptic boundary value problem | 0.815891 |
13,693 | This is necessary because each category must be analyzed using different techniques. The present article deals with the category of boundary value problems known as linear elliptic problems. Boundary value problems and partial differential equations specify relations between two or more quantities. | Elliptic boundary value problem | 0.815891 |
13,694 | In mathematics, an elliptic boundary value problem is a special kind of boundary value problem which can be thought of as the stable state of an evolution problem. For example, the Dirichlet problem for the Laplacian gives the eventual distribution of heat in a room several hours after the heating is turned on. Differe... | Elliptic boundary value problem | 0.815891 |
13,695 | Another Sobolev imbedding theorem states that the inclusion H 1 ⊂ L 2 {\displaystyle H^{1}\subset L^{2}} is a compact linear map. Equipped with the spectral theorem for compact linear operators, one obtains the following result. Theorem Assume that A ( u , φ ) {\displaystyle A(u,\varphi )} is coercive, continuous and s... | Elliptic boundary value problem | 0.815891 |
13,696 | Interleukin 6 (acronym: IL-6) is a cytokine that is important for many aspects of cellular biology including immune responses, cell survival, apoptosis, as well as proliferation. Several studies have outlined the importance of autocrine IL-6 signaling in lung and breast cancers. For example, one group found a positive ... | Autocrine signaling | 0.815889 |
13,697 | The ability of viruses to cause devastating epidemics in human societies has led to the concern that viruses could be weaponised for biological warfare. Further concern was raised by the successful recreation of the infamous 1918 influenza virus in a laboratory. The smallpox virus devastated numerous societies througho... | Novel virus | 0.815886 |
13,698 | Some jokes use a mathematical term with a second non-technical meaning as the punchline of a joke. Occasionally, multiple mathematical puns appear in the same jest: When Noah sends his animals to go forth and multiply, a pair of snakes replies "We can't multiply, we're adders" – so Noah builds them a log table. This in... | Mathematical joke | 0.815883 |
13,699 | A mathematical limerick is an expression which, when read aloud, matches the form of a limerick. The following example is attributed to Leigh Mercer: This is read as follows: Another example using calculus is: which may be read: The limerick is true if log {\displaystyle \log } is interpreted as the natural logarithm. | Mathematical joke | 0.815883 |
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