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87,100 | 1900 BC). The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction".Plato's influence has been especially strong in mathematics and the sciences. He helped to dist... | History of mathematical notation | 0.798449 |
87,101 | In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. This is one of several commonly used representations of graphs for use in computer... | Adjacency list | 0.798449 |
87,102 | Pyrophosphate copper plating baths possess gentler chemistry compared to the toxic alkaline cyanide baths and the corrosive acid copper baths, operating at mildly alkaline pH and utilizing relatively non-toxic pyrophosphate compounds. While pyrophosphate electrolytes are easier to waste treat than alkaline cyanide and ... | Copper electroplating | 0.798449 |
87,103 | As with the proof by infinite descent, we obtain a 2 = 2 b 2 {\displaystyle a^{2}=2b^{2}} . Being the same quantity, each side has the same prime factorization by the fundamental theorem of arithmetic, and in particular, would have to have the factor 2 occur the same number of times. However, the factor 2 appears an od... | Square root of 2 | 0.798449 |
87,104 | In aqueous solution chemistry and precipitates ageing, the term refers to the growth of larger crystals from those of smaller size which have a higher solubility than the larger ones. In the process, many small crystals formed initially (nuclei) slowly disappear, except for a few that grow larger, at the expense of the... | Ostwald ripening | 0.798448 |
87,105 | Bio-Inspired computing can be distinguished from traditional artificial intelligence by its approach to computer learning. Bio-inspired computing uses an evolutionary approach, while traditional A.I. uses a 'creationist' approach. Bio-inspired computing begins with a set of simple rules and simple organisms which adher... | Bio-inspired computing | 0.798448 |
87,106 | The use of neural network techniques to cluster and visualise failure modes were suggested starting from 2010. An alternative approach is to combine the traditional FMEA table with set of bow-tie diagrams. The diagrams provide a visualisation of the chains of cause and effect, while the FMEA table provides the detailed... | Failure modes and effects analysis | 0.798448 |
87,107 | An ε-approximate consensus halving can be computed by an algorithm based on Tucker's lemma, which is the discrete version of Borsuk-Ulam theorem. An adaptation of this algorithm shows that the problem is in the complexity class PPA. This holds even for arbitrary bounded and non-atomic valuations. However, the run-time ... | Exact division | 0.798448 |
87,108 | A pulse-forming network (PFN) is an electric circuit that accumulates electrical energy over a comparatively long time, and then releases the stored energy in the form of a relatively square pulse of comparatively brief duration for various pulsed power applications. In a PFN, energy storage components such as capacito... | Pulse forming network | 0.798448 |
87,109 | For example, Karl Nickel explored more effective implementations, while improved containment procedures for the solution set of systems of equations were due to Arnold Neumaier among others. In the 1960s, Eldon R. Hansen dealt with interval extensions for linear equations and then provided crucial contributions to glob... | Interval analysis | 0.798448 |
87,110 | The study of finite extensions of F p ( t ) , {\displaystyle \mathbb {F} _{p}(t),} or equivalently smooth projective curves over F p {\displaystyle \mathbb {F} _{p}} is an important branch in algebraic number theory.A smooth projective curve of genus one is called an elliptic curve. As a consequence of the Riemann–Roch... | Projective variety | 0.798448 |
87,111 | Finally, in 2020, Jain, Lin, and Sahai proposed a construction of IO based on the symmetric external Diffie-Helman, learning with errors, and learning plus noise assumptions, as well as the existence of a super-linear stretch pseudorandom generator in the function class NC0. (The existence of pseudorandom generators in... | Indistinguishability obfuscation | 0.798447 |
87,112 | In particular, it seems that Aristotle considers sense-perception only as a vehicle for knowledge through intuition. He restricted his investigations in natural history to their natural settings, such as at the Pyrrha lagoon, now called Kalloni, at Lesbos. Aristotle and Theophrastus together formulated the new science ... | History of scientific method | 0.798447 |
87,113 | Although the original scope of statistics was limited to data useful for governance, the approach was extended to many fields of a scientific or commercial nature during the 19th century. The mathematical foundations for the subject heavily drew on the new probability theory, pioneered in the 16th century by Gerolamo C... | History of statistics | 0.798447 |
87,114 | In graph theory, a mixed graph G = (V, E, A) is a graph consisting of a set of vertices V, a set of (undirected) edges E, and a set of directed edges (or arcs) A. | Mixed graph | 0.798447 |
87,115 | Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis. He wrote extensively on statistical mechanics and on foundations of probability and statistical inference, initiating in 1957 the maximum entropy interpretation of thermody... | Edwin Thompson Jaynes | 0.798447 |
87,116 | However, according to Mahn, this theory may be an example of folk etymology. Assuming an Egyptian origin, chemistry is defined as follows: Chemistry, from the ancient Egyptian word "khēmia" meaning transmutation of earth, is the science of matter at the atomic to molecular scale, dealing primarily with collections of a... | Etymology of chemistry | 0.798447 |
87,117 | In the geometry of hyperbolic 3-space, the order-5-5 pentagonal honeycomb (or 5,5,5 honeycomb) a regular space-filling tessellation (or honeycomb) with Schläfli symbol {5,5,5}. All vertices are ultra-ideal (existing beyond the ideal boundary) with five order-5 pentagonal tilings existing around each edge and with an or... | Order-5-4 square honeycomb | 0.798446 |
87,118 | The authors conclude: "These and other concerns about electron transfer at olfactory receptors, together with our extensive experimental data, argue against the plausibility of the vibration theory." In commenting on this work, Vosshall writes "In PNAS, Block et al.... shift the "shape vs. vibration" debate from olfact... | Shape theory of olfaction | 0.798446 |
87,119 | He attended the Goethe-Gymnasium again for his final three years of secondary schooling, from 1922 to 1924.Having passed his Abitur, Bethe entered the University of Frankfurt in 1924. He decided to major in chemistry. The instruction in physics was poor, and while there were distinguished mathematicians in Frankfurt su... | Hans Bethe | 0.798446 |
87,120 | Because it changes the constrained optimization problem associated with reliability-based optimization into an unconstrained optimization problem, it often leads to computationally more tractable problem formulations. In the marketing field there is a huge literature about optimal design for multiattribute products and... | Multidisciplinary optimization | 0.798446 |
87,121 | The on-site student outreach program brings over 2,000 youth to the facility annually to experience workshops on robotics, rocketry, aviation, and other STEM topics. The ERC also runs numerous student STEM competitions in the fields of robotics and aviation. Starting in 2012 the ERC became the partner for the FIRST LEG... | Independent Verification and Validation Facility | 0.798446 |
87,122 | Lexicographic optimization is sometimes called preemptive optimization, since a small increase in one objective value preempts a much larger increase in less important objective values. As an example, consider a firm which puts safety above all. | Lexicographic optimization | 0.798445 |
87,123 | In fact, given that the geometrization conjecture is now settled, the only case needed to be proven for the virtually fibered conjecture is that of hyperbolic 3-manifolds. The original interest in the virtually fibered conjecture (as well as its weaker cousins, such as the virtually Haken conjecture) stemmed from the f... | Virtually fibered conjecture | 0.798445 |
87,124 | If an application of number theory were to be found, then certainly no one would try to dethrone the "queen of mathematics" because of that. What Gauss meant, according to Hardy, is that the underlying concepts that constitute number theory are deeper and more elegant compared to those of any other branch of mathematic... | A Mathematician's Apology | 0.798445 |
87,125 | 11th century: Alhazen systematically studies optics and refraction, which would later be important in making the connection between geometric (ray) optics and wave theory. 11th century: Shen Kuo discovers atmospheric refraction and provides the correct explanation of rainbow phenomenon c1290 – Eyeglasses are invented i... | Timeline of scientific discoveries | 0.798445 |
87,126 | In statistics, the standard deviation line (or SD line) marks points on a scatter plot that are an equal number of standard deviations away from the average in each dimension. For example, in a 2-dimensional scatter diagram with variables x {\displaystyle x} and y {\displaystyle y} , points that are 1 standard deviatio... | Standard deviation line | 0.798445 |
87,127 | He spent two years in the theory group at Bell Laboratories, and subsequently was a faculty member at University of California, Berkeley (physics), Princeton University (physics), California Institute of Technology (chemistry and biology) and again at Princeton, where he is the Howard A. Prior Professor of Molecular Bi... | John Hopfield | 0.798445 |
87,128 | Proof: The diffeomorphism group Diff ( M ) {\displaystyle \operatorname {Diff} (M)} is a smooth manifold since it is an open subset in C ∞ ( M , M ) {\displaystyle C^{\infty }(M,M)} . Composition is smooth by restriction. Inversion is smooth: If t → f ( t , ) {\displaystyle t\to f(t,\ )} is a smooth curve in Diff (... | Convenient vector space | 0.798445 |
87,129 | Below is a table of the handbooks published by ASM International as of April 2023. These handbooks are recognized as a standard reference in the field of materials science. | ASM International (society) | 0.798444 |
87,130 | The need for the Institute arose out of the significant growth of the field of mathematical biology over the last decade with research becoming more closely linked to observation and experiment. Rather than starting from mathematical abstractions, it is now common for researchers to: 1) Begin with observations; 2) Use ... | National Institute for Mathematical and Biological Synthesis | 0.798444 |
87,131 | Back-formation may be particularly common in English given that many English words are borrowed from Latin, French and Greek, which together provide English a large range of common affixes. Many words with affixes have entered English, such as dismantle and dishevelled, so it may be easy to believe that these are forme... | Back formation | 0.798444 |
87,132 | Material published in the report is in the public domain and may be reprinted without permission. As of 2019, the journal's editor-in-chief is Charlotte Kent.As noted in the sequel, some single reports have evoked media interest also outside health and medical contexts. However, many reports are parts of series, provid... | Morbidity and Mortality Weekly Report | 0.798444 |
87,133 | Shaw is chief scientist of D. E. Shaw Research, which conducts interdisciplinary research in the field of computational biochemistry. According to the Institutional Investor's Alpha magazine's annual ranking for 2014, D. E. Shaw, who made $530 million in 2014, and James H. Simons of Renaissance Technologies who made $1... | David E. Shaw | 0.798444 |
87,134 | The Carnegie Classification of Institutions of Higher Education, or simply the Carnegie Classification, is a framework for classifying colleges and universities in the United States. It was created in 1970 by the Carnegie Foundation for the Advancement of Teaching. It is managed by the American Council on Education. Th... | Carnegie Classification of Institutions of Higher Education | 0.798444 |
87,135 | {\displaystyle \mu \left({\mbox{after-mixing}}(A)\cap B\right)=\mu (A)\mu (B).} This product-of-volumes has more than passing resemblance to Bayes theorem in probabilities; this is not an accident, but rather a consequence that measure theory and probability theory are the same theory: they share the same axioms (the K... | Topologically mixing | 0.798444 |
87,136 | The American Society of Plant Biologists also has partnered with the Society for Experimental Biology, and Wiley to publish an online-only science journal Plant Direct. In 2000, it published the first edition of the textbook Biochemistry & Molecular Biology of Plants.The society has given the Charles Reid Barnes Life M... | American Society of Plant Biologists | 0.798443 |
87,137 | This is skew-symmetric since x × y = − y × x {\displaystyle x\times y=-y\times x} , and instead of associativity it satisfies the Jacobi identity: x × ( y × z ) = ( x × y ) × z + y × ( x × z ) . {\displaystyle x\times (y\times z)\ =\ (x\times y)\times z\ +\ y\times (x\times z).} This is the Lie algebra of the Lie group... | Center of a Lie algebra | 0.798443 |
87,138 | In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear inequality constraints and nonlinear objective functions; there are criss-cross algorithms for linear-fractional programming... | Criss-cross algorithm | 0.798443 |
87,139 | These algebras can be obtained from the N = ( 1 , 1 ) {\displaystyle {\mathcal {N}}=(1,1)} subalgebra by removing Q − 1 {\displaystyle Q_{-}^{1}} resp. Q + 1 {\displaystyle Q_{+}^{1}} from the generators. | Supersymmetry algebras in 1 + 1 dimensions | 0.798443 |
87,140 | ICSP has five major departments working on several branches of astrophysics and related subjects. Optical Astronomy is done at the Sitapur campus where two faculties, namely Dr. Ashish Raj and Dr. Devendra Bisht work. Prof. Sandip Chakrabarti, Dr. Sourav Palit, Dr. Tamal Basak and Engineer Debashish Bhowmick work on th... | Indian Centre for Space Physics | 0.798443 |
87,141 | Technical criticism based upon unclassified calculations suggested that the X-ray laser would be of at best marginal use for missile defense. Such critics often cite the X-ray laser system as being the primary focus of SDI, with its apparent failure being a main reason to oppose the program; however, the laser was neve... | Homing Overlay Experiment | 0.798442 |
87,142 | In chemistry, a metallofullerene is a molecule composed of a metal atom trapped inside a fullerene cage. Simple metallofullerenes consist of a fullerene cage, typically C80, with one or two metal atoms trapped inside. Recently, research has produced metallofullerenes that enclose small clusters of atoms, such as Sc3N@C... | Metallofullerene | 0.798442 |
87,143 | Towards the end of the 1970s, Feyerabend was assigned a position as Professor of Philosophy at the Eidgenössische Technische Hochschule (ETH) in Zurich. There, he ran well attended lectures, including on the Theatetus, Timeaus, and Aristotle's physics as well as public debates and seminars for the non-academic public. ... | Paul Feyerabend | 0.798442 |
87,144 | He was the head of the laboratory of quantum radiophysics at the LPI until his death in 2001.In the early 1950s Basov and Prokhorov developed theoretical grounds for creation of a molecular oscillator and constructed such an oscillator based on ammonia. Later this oscillator became known as maser. | Nikolay Basov | 0.798441 |
87,145 | The term "smart structures" is commonly used for structures which have the ability to adapt to environmental conditions according to the design requirements. As a rule, the adjustments are designed and performed in order to increase the efficiency or safety of the structure. Combining "smart structures" with the "sophi... | Smart intelligent aircraft structure | 0.798441 |
87,146 | In membrane biology, the Hodgkin cycle is a key component of membrane physiology that describes bioelectrical impulses, especially prevalent in neural and muscle tissues. It was identified by British physiologist and biophysicist Sir Alan Lloyd Hodgkin.The Hodgkin cycle represents a positive feedback loop in which an i... | Hodgkin cycle | 0.79844 |
87,147 | Today it is accepted that the neutrinos produced in the Sun are not massless particles as predicted by the Standard Model but rather mixed quantum states made up of defined-mass eigenstates in different (complex) proportions. That allows a neutrino produced as a pure electron neutrino to change during propagation into ... | Solar neutrino problem | 0.79844 |
87,148 | Evaluate product: Product designers do usability testing to get users' feedback for the product at every stage of User-Centered Design.In the next steps, the above procedure is repeated to further finish the product. These phases are general approaches and factors like design goals, team and their timeline, and environ... | User-centered design | 0.79844 |
87,149 | In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, when is there a diffeomorphism ϕ: M → N {\displaystyle \phi... | Theory of equivalence | 0.79844 |
87,150 | Proteasome inhibitors have effective anti-tumor activity in cell culture, inducing apoptosis by disrupting the regulated degradation of pro-growth cell cycle proteins. This approach of selectively inducing apoptosis in tumor cells has proven effective in animal models and human trials. Lactacystin, a natural product sy... | Proteasome | 0.79844 |
87,151 | A vital component of a mini-grid electric system is on-site, reliable source of energy generation. Traditional mini-grid generation for remote areas came from diesel engine alternators, which incurred high running costs, low efficiency and high maintenance. To obtain the reliability of a fossil fuel powered grid with g... | Mini-grid | 0.79844 |
87,152 | In August 2010, the Board on Physics and Astronomy of the National Science Foundation (NSF) recommended the Wide Field Infrared Survey Telescope (WFIRST) mission, a renamed JDEM-Omega proposal which has superseded SNAP, Destiny, and Advanced Dark Energy Physics Telescope (ADEPT), as the highest priority for development... | Joint Dark Energy Mission | 0.798439 |
87,153 | The FEniCS Project is a collection of free and open-source software components with the common goal to enable automated solution of differential equations. The components provide scientific computing tools for working with computational meshes, finite-element variational formulations of ordinary and partial differentia... | FEniCS Project | 0.798439 |
87,154 | On the one hand, he was concerned with how one culture might appropriate, and so alter, the science of another (earlier) culture in order to make that earlier scientific knowledge more accessible to the recipient culture. On the other hand, Pingree was also interested in how scientific texts surviving from a later cult... | David Pingree | 0.798439 |
87,155 | Since the Chinese remainder theorem provides us with a method to uniquely determine a number S modulo k-many relatively prime integers m 1 , m 2 , . . . , m k {\displaystyle m_{1},m_{2},...,m_{k}} , given that S < ∏ i = 1 k m i {\displaystyle S<\prod _{i=1}^{k}m_{i}} , then, the idea is to construct a scheme that will ... | Secret sharing using the Chinese remainder theorem | 0.798438 |
87,156 | Consider the category of pointed finite sets. This category has an object k + = { 0 , 1 , … , k } {\textstyle k_{+}=\{0,1,\ldots ,k\}} for every natural number k, and the morphisms in this category are the functions f: m + → n + {\textstyle f:m_{+}\to n_{+}} which preserve the zero element. A theorem of Barratt, Priddy... | K-theory of a category | 0.798438 |
87,157 | "Wheeler's delayed-choice experiment" refers to a series of thought experiments in quantum physics, the first being proposed by him in 1978. Another prominent version was proposed in 1983. All of these experiments try to get at the same fundamental issues in quantum physics. Many of them are discussed in Wheeler's 1978... | Delayed choice experiment | 0.798438 |
87,158 | Day-ahead operation schedules the generation units that can be called upon to provide the electricity on the next day (unit commitment). The dispatchable generation units can produce electricity on demand and thus can be scheduled with accuracy. The production of the weather-dependent variable renewable energy for the ... | Day-ahead operation | 0.798437 |
87,159 | The classes therefore form a family of ambient cohomology classes restricting to a basis of the cohomology of the fiber. The Leray–Hirsch theorem then states that any class in H ∗ ( P ( E ) ) {\displaystyle H^{*}(\mathbb {P} (E))} can be written uniquely as a linear combination of the 1, a, a2, ..., an−1 with classes o... | Chern roots | 0.798437 |
87,160 | Oppenheimer published more than a dozen papers while in Europe, including many important contributions to the new field of quantum mechanics. He and Born published a famous paper on the Born–Oppenheimer approximation, which separates nuclear motion from electronic motion in the mathematical treatment of molecules, allo... | J. Robert Oppenheimer | 0.798437 |
87,161 | DIDO – MATLAB tool for optimal control named after Dido, the first queen of Carthage. GPOPS-II: General Purpose Optimal Control Software GESOP – Graphical Environment for Simulation and OPtimization OpenOCL – Open Optimal Control Library PROPT – MATLAB Optimal Control Software PSOPT – Open Source Pseudospectral Optimal... | Pseudospectral optimal control | 0.798437 |
87,162 | An algebraic dual of a connected graph G is a graph G* such that G and G* have the same set of edges, any cycle of G is a cut of G*, and any cut of G is a cycle of G*. Every planar graph has an algebraic dual, which is in general not unique (any dual defined by a plane embedding will do). The converse is actually true,... | Planar dual | 0.798437 |
87,163 | She refused to accept that possibility, however, and learned to walk supported by two strong metal canes. She became Canada's first woman graduate in electrical engineering. Following graduation, MacGill took a junior job with a firm in Pontiac, Michigan. | Elsie MacGill | 0.798437 |
87,164 | In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets. A uniform 7-polytope is one whose symmetry group is transitive on vertices and whose facets are uniform 6-polytopes. | Uniform 6-honeycomb | 0.798437 |
87,165 | Number theory dates back to ancient Babylon and probably China. Two prominent early number theorists were Euclid of ancient Greece and Diophantus of Alexandria. The modern study of number theory in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler. | Fields of mathematics | 0.798437 |
87,166 | Grasshopper is primarily used to build generative algorithms, such as for generative art. Many of Grasshopper's components create 3D geometry. Programs may also contain other types of algorithms including numeric, textual, audio-visual and haptic applications.Advanced uses of Grasshopper include parametric modelling fo... | Grasshopper 3D | 0.798437 |
87,167 | 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 | 0.798436 |
87,168 | In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory... | Hom space | 0.798436 |
87,169 | A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. When a paper is cut with scissors, the paper fails in shear. In structural and mechanical engineering, the shear strength of a component is important for designing the dimensions a... | Virtual leak | 0.798436 |
87,170 | 2006 DuPont and Syngenta announce GreenLeaf Genetics LLC, a joint venture to market seed genetics and biotech traits. 2010 DuPont and Syngenta end their joint venture, GreenLeaf Genetics LLC, with Syngenta retaining complete ownership. 2012 Pioneer announces update to business name to be DuPont Pioneer. | Pioneer Hi-Bred | 0.798436 |
87,171 | A Folding@home participant installs a client program on their personal computer. The user interacts with the client, which manages the other software components in the background. Through the client, the user may pause the folding process, open an event log, check the work progress, or view personal statistics. The com... | Folding@home | 0.798436 |
87,172 | Now we can replace all occurrences of Q inside the provable formula ¬ Φ {\displaystyle \neg \Phi } by some other formula dependent on the same variables, and we will still get a provable formula. (This is yet another basic result of first-order predicate calculus. Depending on the particular formalism adopted for the c... | Original proof of Gödel's completeness theorem | 0.798435 |
87,173 | A Mars jar or Mars simulation chamber is a container that simulates the atmosphere of the planet Mars. It is used in astrobiology experiments to determine what kind of life on Mars might be viable. | Mars jar | 0.798435 |
87,174 | Caltech is no stranger to the idea of nanotechnology the ability to manipulate matter at the atomic and molecular level. Over 40 years ago, Caltech's own Richard Feynman asked, "What would happen if we could arrange the atoms one by one the way we want them?" President George W. Bush further increased funding for nanot... | History of nanotechnology | 0.798435 |
87,175 | {\displaystyle {\begin{Bmatrix}x\end{Bmatrix}}={\begin{Bmatrix}X\end{Bmatrix}}e^{i\omega t}.} Note: Using the exponential solution of { X } e i ω t {\displaystyle {\begin{Bmatrix}X\end{Bmatrix}}e^{i\omega t}} is a mathematical trick used to solve linear differential equations. Using Euler's formula and taking only the ... | Mechanical vibration | 0.798435 |
87,176 | Thus the conditions for Cochran's theorem are met. Cochran's theorem then states that Q1 and Q2 are independent, with chi-squared distributions with n − 1 and 1 degree of freedom respectively. This shows that the sample mean and sample variance are independent. This can also be shown by Basu's theorem, and in fact this... | Cochran's theorem | 0.798435 |
87,177 | The analytical solution is allowed for a very limited number of theoretical cases. Vice versa a large variety of instances may be quickly solved in an approximate way via the central limit theorem in terms of confidence interval around a Gaussian distribution – that's the benefit. The drawback is that the central limit... | Algorithmic inference | 0.798434 |
87,178 | This understanding can potentially be used to learn more about how to make better prosthetics, and eventually help patients who have lost the use of a limb. Also, by learning more about how different sensory inputs can combine can have profound effects on new engineering approaches using robotics. The robot's sensory d... | Sensory processing | 0.798434 |
87,179 | Every positive definite matrix is invertible and its inverse is also positive definite. If M ≥ N > 0 {\displaystyle M\geq N>0} then N − 1 ≥ M − 1 > 0 {\displaystyle N^{-1}\geq M^{-1}>0} . Moreover, by the min-max theorem, the kth largest eigenvalue of M {\displaystyle M} is greater than or equal to the kth largest eige... | Positive-semidefinite matrix | 0.798434 |
87,180 | Hypercomplex number is a term for an element of a unital algebra over the field of real numbers. The complex numbers are often symbolised by a boldface C (or blackboard bold C {\displaystyle \mathbb {\mathbb {C} } } , Unicode U+2102 ℂ DOUBLE-STRUCK CAPITAL C), while the set of quaternions is denoted by a boldface H (or... | List of numbers | 0.798434 |
87,181 | A Lie algebra is a vector space g {\displaystyle {\mathfrak {g}}} over a field F {\displaystyle F} with a binary operation (called the Lie bracket or abbr. bracket) , which satisfies the following conditions: ∀ a , b ∈ F , x , y , z ∈ g {\displaystyle \forall a,b\in F,x,y,z\in {\mathfrak {g}}} , = a + b {\displayst... | Glossary of Lie groups and Lie algebras | 0.798433 |
87,182 | This multiplies by all vectors to generate the elements of even subalgebra. All the properties of complex numbers can be derived from bivectors, but two are of particular interest. | Oriented plane segment | 0.798433 |
87,183 | in chemical engineering at University of Wisconsin–Madison. Her 2011 dissertation was titled Catalytic strategies and catalyst design for the conversion of biomass-derived carbohydrates to chemicals. Pagán's doctoral advisor was James Dumesic. | Yomaira Pagán Torres | 0.798433 |
87,184 | In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. | Euclid | 0.798433 |
87,185 | Chartrand, Gary; Lesniak, Linda; Zhang, Ping (2010), Graphs & Digraphs (5th ed. ), CRC Press, p. 139, ISBN 9781439826270. Diestel, Reinhard (2012), "10. Hamiltonian cycles", Graph Theory (PDF) (corrected 4th electronic ed.) | Fleischner's theorem | 0.798432 |
87,186 | Aizik Isaakovich Vol'pert (Russian: Айзик Исаакович Вольперт) (5 June 1923 – January 2006) (the family name is also transliterated as Volpert or Wolpert) was a Soviet and Israeli mathematician and chemical engineer working in partial differential equations, functions of bounded variation and chemical kinetics. | Aizik Volpert | 0.798432 |
87,187 | Shape optimization, as a software process and tool, first appeared as an algorithm in 1995 and as commercial software for the automotive industry by 1998, as noted by F. Muyl. Relative to the age of the automotive and aeronautical companies, this software is very new. The difficulty was not with the science behind the ... | Wing shape optimization | 0.798432 |
87,188 | Sampling theory Scheme theory the study of schemes introduced by Alexander Grothendieck. It allows the use of sheaf theory to study algebraic varieties and is considered the central part of modern algebraic geometry. Secondary calculus Semialgebraic geometry a part of algebraic geometry; more specifically a branch of r... | Glossary of areas of mathematics | 0.798431 |
87,189 | A dimensionless quantity (also known as a bare quantity, pure quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities ar... | Dimensionless ratio | 0.798431 |
87,190 | Pathology is the study of the causes and effects of disease or injury. The word pathology also refers to the study of disease in general, incorporating a wide range of biology research fields and medical practices. However, when used in the context of modern medical treatment, the term is often used in a narrower fashi... | Pathology | 0.798431 |
87,191 | The reaction steps are: hydrogenation of D-glucose to D-sorbitol, an organic reaction with nickel as a catalyst under high temperature and high pressure. Microbial oxidation or fermentation of sorbitol to L-sorbose with acetobacter at pH 4-6 and 30 °C. protection of the 4 hydroxyl groups in sorbose by formation of the ... | Reichstein process | 0.798431 |
87,192 | In theoretical physics, it is usually possible to organize physical phenomena according to the energy scale or distance scale. The theory of renormalization group is based on this paradigm. The short-distance, ultraviolet (UV) physics does not directly affect qualitative features of the long-distance, infrared (IR) phy... | UV/IR mixing | 0.798431 |
87,193 | This technique was reinvented several times and is due to Hans Boltz (1923), who used it for the inversion of geodetic matrices, and Tadeusz Banachiewicz (1937), who generalized it and proved its correctness. The nullity theorem says that the nullity of A equals the nullity of the sub-block in the lower right of the in... | Non-singular matrix | 0.798431 |
87,194 | of Energy official Joseph Romm concluded that renewable energy cannot economically be used to make hydrogen for an FCV fleet "either now or in the future." GreenTech Media's analyst reached similar conclusions in 2014. | Fuel Cell Electric Vehicle | 0.798431 |
87,195 | Engineering Administration (EA) is a branch of engineering that is mainly concerned with the analysis and solution of operational and management problems using scientific and mathematical methods. Engineering Administration is considered to be a subdiscipline of industrial engineering / systems engineering. | Engineering administration | 0.798431 |
87,196 | Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family converge to their theoretical probabilities. Uniform convergence in probability h... | Uniform convergence in probability | 0.798431 |
87,197 | Regular polyhedron Platonic solid: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron Regular spherical polyhedron Dihedron, Hosohedron Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron, Great stellated dodecahedron, Great icosahedron, Great dodecahedron Abstract regular polyhedra (P... | List of polygons, polyhedra and polytopes | 0.798431 |
87,198 | Descriptive inorganic chemistry focuses on the classification of compounds based on their properties. Partly the classification focuses on the position in the periodic table of the heaviest element (the element with the highest atomic weight) in the compound, partly by grouping compounds by their structural similaritie... | Inorganic chemist | 0.79843 |
87,199 | The basic capabilities of Psi are concentrated around the following methods of quantum chemistry: Hartree–Fock method Density functional theory Møller–Plesset perturbation theory Coupled cluster CASSCF multireference configuration interaction methods symmetry-adapted perturbation theorySeveral methods are available for... | PSI (computational chemistry) | 0.79843 |
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