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6,100 | Why? Because after a rotation of 120 degrees, the sector that was previously the most valuable is now less valuable, and another sector is now the most valuable. Hence, by the intermediate value theorem, there must be a position in the rotation when partner B views two sectors as tied for largest. At this point, partne... | Fair pie-cutting | 0.829708 |
6,101 | A finite semigroup is aperiodic if and only if it contains no nontrivial subgroups, so a synonym used (only?) in such contexts is group-free semigroup. In terms of Green's relations, a finite semigroup is aperiodic if and only if its H-relation is trivial. These two characterizations extend to group-bound semigroups.A ... | Aperiodic semigroup | 0.829707 |
6,102 | This follows from the Chinese remainder theorem and the fact that a ring of the form Z / k Z {\displaystyle \mathbb {Z} /k\mathbb {Z} } is a field if and only if k {\displaystyle k} is prime. For every positive integer n {\displaystyle n} , the set of all positive divisors of n {\displaystyle n} becomes a partially ord... | Square-free integer | 0.829706 |
6,103 | Jane Richardson learned the necessary technical skills and scientific background in biochemistry and biophysics through work at the lab as she worked alongside her husband, whom she still works with today. Richardson later began drawing her eponymous diagrams as a method of interpreting the structures of protein molecu... | Jane S. Richardson | 0.829704 |
6,104 | The monomorphisms in Grp are precisely the injective homomorphisms, the epimorphisms are precisely the surjective homomorphisms, and the isomorphisms are precisely the bijective homomorphisms. The category Grp is both complete and co-complete. The category-theoretical product in Grp is just the direct product of groups... | Grp (category theory) | 0.829703 |
6,105 | 38 (1): 19–40. doi:10.3233/ICG-2015-38104. Arimaa challenge - comparission study of MCTS versus alpha-beta methodsthesis by Thomas Jakl (Charles University, Prague) Oct 2011 Move Ranking and Evaluation in the Game of Arimaathesis by David Jian Wu (Harvard College, Cambridge, Massachusetts, USA) May 2011 Arimaa, a New C... | Computer Arimaa | 0.829703 |
6,106 | In physics, a vector typically arises as the outcome of a measurement or series of measurements, and is represented as a list (or tuple) of numbers such as ( v 1 , v 2 , v 3 ) . {\displaystyle (v_{1},v_{2},v_{3}).} The numbers in the list depend on the choice of coordinate system. For instance, if the vector represents... | Contravariant vector | 0.829703 |
6,107 | The convex hull of any finite set of points on the moment curve is a cyclic polytope. Cyclic polytopes have the largest possible number of faces for a given number of vertices, and in dimensions four or more have the property that their edges form a complete graph. More strongly, they are neighborly polytopes, meaning ... | Moment curve | 0.8297 |
6,108 | Suspension array technology (or SAT) is a high throughput, large-scale, and multiplexed screening platform used in molecular biology. SAT has been widely applied to genomic and proteomic research, such as single nucleotide polymorphism (SNP) genotyping, genetic disease screening, gene expression profiling, screening dr... | Suspension array technology | 0.829699 |
6,109 | In 499 CE Aryabhata, used this illustrated method in the Aryabhatiya (section 2.6).Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side, but rel... | Area of a triangle | 0.829694 |
6,110 | Mechanical Engineering — includes engineering of total systems where mechanical science principles apply to objects in motion including transportation, energy, buildings, aerospace and machine design. Explores the applications of the theoretical fields of Mechanics, kinematics, thermodynamics, materials science, struct... | Bachelor of Engineering | 0.829693 |
6,111 | Season 4 is focused on geometry, specifically shape, space, and problem solving using those ideas. | Maths Mansion | 0.829692 |
6,112 | In mathematics, a real plane curve is usually a real algebraic curve defined in the real projective plane. | Real plane curve | 0.829689 |
6,113 | In chemistry (and may also be for other scientific branches), uncertainty may be implied by the last significant figure if it is not explicitly expressed. The implied uncertainty is ± the half of the minimum scale at the last significant figure position. For example, if the volume of water in a bottle is reported as 3.... | Decimal place | 0.829689 |
6,114 | Apache Mahout, a library of scalable machine learning algorithms. Deeplearning4j, an open-source, distributed deep learning framework written for the JVM. Keras, a high level open-source software library for machine learning (works on top of other libraries). Microsoft Cognitive Toolkit (previously known as CNTK), an o... | List of artificial intelligence projects | 0.829688 |
6,115 | Furthermore, every complemented distributive lattice forms a Boolean algebra, and conversely every Boolean algebra forms a complemented distributive lattice. This provides an alternative definition of a Boolean algebra, namely as any complemented distributive lattice. Each of these three properties can be axiomatized w... | Boolean algebras canonically defined | 0.829688 |
6,116 | In machine learning, multiple-instance learning (MIL) is a type of supervised learning. Instead of receiving a set of instances which are individually labeled, the learner receives a set of labeled bags, each containing many instances. In the simple case of multiple-instance binary classification, a bag may be labeled ... | Multiple instance learning | 0.829685 |
6,117 | Source: bioinformatics.org 2002 - Michael B. Eisen 2003 - Jim Kent 2004 - Lincoln D. Stein 2005 - Ewan Birney 2006 - Michael Ashburner 2007 - Sean Eddy 2008 - Robert Gentleman 2009 - Philip E. Bourne 2010 - Alex Bateman 2011 - Jonathan Eisen 2012 - Heng Li 2013 - Steven Salzberg 2014 - Helen M. Berman 2015 - Owen White... | Benjamin Franklin Award (Bioinformatics) | 0.829684 |
6,118 | Instead, in an approach borrowed from chemical engineering,: 81 geochemists average the concentration over regions of the Earth called geochemical reservoirs. The choice of reservoir depends on the problem; for example, the ocean may be a single reservoir or be split into multiple reservoirs. In a type of model called ... | Geochemical research | 0.829681 |
6,119 | Therefore, a single recursive call locates the desired element in the correct partition, and we build upon this for quickselect: // Returns the k-th smallest element of list within left..right inclusive // (i.e. left <= k <= right). function select(list, left, right, k) is if left = right then // If the list contains o... | Quickselect | 0.82968 |
6,120 | PSIM has various add on modules, the full list and their descriptions can be found on the Powersim website. There are modules that enable motor drive simulation, digital control, and the calculation of thermal losses due to switching and conduction. There is a renewable energy module which allows for the simulation of ... | PSIM Software | 0.82968 |
6,121 | Moreover, one may ask for the largest m {\displaystyle m} -dimensional hypercube that may be drawn within an n {\displaystyle n} -dimensional unit hypercube. The answer is always an algebraic number. For instance, the problem for ( m , n ) = ( 3 , 4 ) {\displaystyle (m,n)=(3,4)} asks for the largest (three-dimensional)... | Prince Rupert's cube | 0.829676 |
6,122 | That is, does every finite lattice occur as the congruence lattice of a finite algebra? In 1980, Pálfy and Pudlák proved that this problem is equivalent to the problem of deciding whether every finite lattice occurs as an interval in the subgroup lattice of a finite group. For an overview of the group theoretic approac... | Finite lattice representation problem | 0.829676 |
6,123 | ⊢ If Γ ⊢ A, then Γ ⇒ A.It is clear by these theorems that the sequent calculus does not change the notion of truth, because the same collection of propositions remain true. Thus, one can use the same proof objects as before in sequent calculus derivations. As an example, consider the conjunctions. | Introduction rule | 0.829675 |
6,124 | Phoenix read biochemistry at the University of Liverpool followed by completion of a doctorate on amphiphilic membrane protein anchors. He studied part-time to obtain a degree in mathematics from the Open University and moved into the field of molecular engineering. He has published widely on the structure-function rel... | David Phoenix | 0.829674 |
6,125 | The problem appears to come down to the ability of the compiler to correctly optimize the device; it may also interfere with pipelining and branch prediction on some architectures. When numerous instances of Duff's device were removed from the XFree86 Server in version 4.0, there was an improvement in performance and a... | Duff's device | 0.829673 |
6,126 | The fungus does not have any specific nutritional requirements for growth. The teleomorphic features of the microsporum on colonial and microscopic features are often done on Takashio's Medium. However, distinguishing is best done by mating (+/–) or by genetics. | Microsporum gypseum | 0.829672 |
6,127 | 1960 - Myoglobin was the very first high-resolution crystal structure of a protein molecule. Myoglobin cradles an iron-containing heme group that reversibly binds oxygen for use in powering muscle fibers, and those first crystals were of myoglobin from the sperm whale, whose muscles need copious oxygen storage for deep... | List of biophysically important macromolecular crystal structures | 0.829672 |
6,128 | Narendra Karmarkar (PhD 1983) is known for the interior point method, a polynomial algorithm for linear programming known as Karmarkar's algorithm. National Medal of Science laureate Chien-Shiung Wu (PhD 1940), often known as the "Chinese Madame Curie", disproved the Law of Conservation of Parity for which she was awar... | Discoveries and innovation by the University of California, Berkeley | 0.82967 |
6,129 | {\displaystyle X\times Y.} A binary relation is called a homogeneous relation when X = Y. A binary relation is also called a heterogeneous relation when it is not necessary that X = Y. Since relations are sets, they can be manipulated using set operations, including union, intersection, and complementation, and satisfy... | Left-unique relation | 0.829669 |
6,130 | In computer science, a memory map is a structure of data (which usually resides in memory itself) that indicates how memory is laid out. The term "memory map" has different meanings in different contexts. It is the fastest and most flexible cache organization that uses an associative memory. The associative memory stor... | Memory map | 0.829669 |
6,131 | Molecular cohesion and gravity are shown to be contributing factors in the operation of a siphon; the presence of a positive atmospheric pressure is not required".Writing in Physics Today in 2011, J. Dooley from Millersville University stated that both a pressure differential within the siphon tube and the tensile stre... | Inverted siphon | 0.829667 |
6,132 | The ancient Egyptians were the first civilization to develop and solve second-degree (quadratic) equations. This information is found in the Berlin Papyrus fragment. Additionally, the Egyptians solve first-degree algebraic equations found in Rhind Mathematical Papyrus. | Numeration by Hieroglyphics | 0.829667 |
6,133 | Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games—for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group ... | Frank Harary | 0.829664 |
6,134 | A parametric equation for a curve expresses the coordinates of the points of the curve as functions of a variable, called a parameter. For example, x = cos t y = sin t {\displaystyle {\begin{aligned}x&=\cos t\\y&=\sin t\end{aligned}}} are parametric equations for the unit circle, where t is the parameter. Together,... | Mathematical equations | 0.82966 |
6,135 | Methanol, methyl tetrahydrofolate, mono-, di-, and trimethylamine, methanethiol, methyltetrahydromethanopterin, and chloromethane are all methyl donors found in biology as methyl group donors, typically in enzymatic reactions using the cofactor vitamin B12. These substrates contribute to methyl transfer pathways includ... | Methyl transferase | 0.829657 |
6,136 | Some transcendental systems of high-order equations can be solved by “separation” of the unknowns, reducing them to algebraic equations. The following can also be used when solving transcendental equations/inequalities: If x 0 {\displaystyle x_{0}} is a solution to the equation f ( x ) = g ( x ) {\displaystyle f(x)=g(x... | Transcendental equation | 0.829655 |
6,137 | Astro microbiology: the study of microorganisms in outer space Biological agent: the study of those microorganisms which are being used in weapon industries. Nano microbiology: the study of those microscopic organisms on nano level. Predictive microbiology: the quantification of relations between controlling factors in... | Branches of microbiology | 0.829654 |
6,138 | Existential monadic second-order logic (EMSO) is the fragment of MSO in which all quantifiers over sets must be existential quantifiers, outside of any other part of the formula. The first-order quantifiers are not restricted. By analogy to Fagin's theorem, according to which existential (non-monadic) second-order logi... | Monadic second-order | 0.829654 |
6,139 | Basic techniques – Milgrom and Shannon (1994)., Milgrom (1994), Shannon (1995), Topkis (1998), Edlin and Shannon (1998), Athey (2002), Quah (2007), Quah and Strulovici (2009, 2012), Kukushkin (2013); Production complementarities and their implications – Milgrom and Roberts (1990a, 1995); Topkis (1995); Games with strat... | Monotone comparative statics | 0.829651 |
6,140 | In the context of a single isolated region of DNA, denaturing gradient gels and temperature gradient gels can be used to detect the presence of small mismatches between two sequences, a process known as temperature gradient gel electrophoresis.Methods of DNA analysis based on melting temperature have the disadvantage o... | Melting of DNA | 0.82965 |
6,141 | Amino acids with similar polarity are usually attracted to each other, while nonpolar and polar side chains usually repel each other. Nonpolar/polar interactions can still play an important part in stabilizing the secondary structure due to the relatively large amount of them occurring throughout the protein. Spatial p... | Side chains | 0.82965 |
6,142 | 3. In topology, denotes the wedge sum of two pointed spaces. ∧ 1. | Mathematical symbol | 0.829649 |
6,143 | These special bacteria have produced many insights into the chemistry and biology of microbial life. Blue holes have a great diversity of microbes. They create biogeochemical pathways creating a unique and diverse environment within the blue holes. | Blue hole | 0.829643 |
6,144 | As AI technology democratizes, it may become easier to engineer more contagious and lethal pathogens. This could enable individuals with limited skills in synthetic biology to engage in bioterrorism. Dual-use technology that is useful for medicine could be repurposed to create weapons.For example, in 2022, scientists m... | Existential risk from artificial general intelligence | 0.829643 |
6,145 | Many theorems about finite groups can be readily generalised to profinite groups; examples are Lagrange's theorem and the Sylow theorems.To construct a profinite group one needs a system of finite groups and group homomorphisms between them. Without loss of generality, these homomorphisms can be assumed to be surjectiv... | Profinite groups | 0.829642 |
6,146 | The molecules that an organism uses as its carbon source for generating biomass are referred to as "carbon sources" in biology. It is possible for organic or inorganic sources of carbon. Heterotrophs must use organic molecules as both are a source of carbon and energy, in contrast to autotrophs, which can use inorganic... | Carbon source (biology) | 0.829639 |
6,147 | The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms (PID controllers, state space representation, neural networks, fuzzy control, genetic algorithms, etc.). Variations on this problem include multiple links, allowing the motion of th... | Inverted pendulum | 0.829635 |
6,148 | In the era of microsatellites, it was possible to establish that participants shared certain markers and segments of the genome not by chance but by descent. With the advent in the mid-2000s of genotyping chips, which could measure hundreds of thousands of single-letter variations (SNPs) across the genome, deCODE stati... | DeCODE genetics | 0.829633 |
6,149 | Second (MP2), third (MP3), and fourth (MP4) order Møller–Plesset calculations are standard levels used in calculating small systems and are implemented in many computational chemistry codes. Higher level MP calculations, generally only MP5, are possible in some codes. However, they are rarely used because of their cost... | Møller–Plesset perturbation theory | 0.829631 |
6,150 | Biochemistry is the science of the chemical processes which takes place within living organisms. Living organisms need essential elements to survive, among which are carbon, hydrogen, nitrogen, oxygen, calcium, and phosphorus. These elements make up the four macromolecules that living organisms need to survive: carbohy... | Biomedicine | 0.829631 |
6,151 | Modern rear wheel drive cars with independent rear suspension typically use CV joints at the ends of the rear axle halfshafts and increasingly use them on the drive shafts. Constraint – Continuum mechanics – is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rathe... | Glossary of mechanical engineering | 0.82963 |
6,152 | The A-form geometry results in a very deep and narrow major groove and a shallow and wide minor groove. A second consequence of the presence of the 2'-hydroxyl group is that in conformationally flexible regions of an RNA molecule (that is, not involved in formation of a double helix), it can chemically attack the adjac... | RNA | 0.829629 |
6,153 | Electrical and magnetic phenomena have been observed since ancient times, but it was only in the 19th century James Clerk Maxwell discovered that electricity and magnetism are two aspects of the same fundamental interaction. By 1864, Maxwell's equations had rigorously quantified this unified interaction. Maxwell's theo... | Fundamental forces | 0.829626 |
6,154 | Most algebraic structures are examples of universal algebras. Rings, semigroups, quasigroups, groupoids, magmas, loops, and others. Vector spaces over a fixed field and modules over a fixed ring are universal algebras. These have a binary addition and a family of unary scalar multiplication operators, one for each elem... | Equational reasoning | 0.829626 |
6,155 | Relational algebra operates on homogeneous sets of tuples S = { ( s j 1 , s j 2 , . . . | Relational logic | 0.829626 |
6,156 | The five ways formula is to increase leads, conversation rates, average dollar sales, the average number of sales, and average product profit. Profits can be increased by up to 1,000 percent, this is important for sole traders and small businesses let alone big businesses but none the less all profit maximization is a ... | Profit maximization | 0.829625 |
6,157 | In contrast, a smaller length scale corresponds to a microscopic or particle point of view. Macroscopically, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). For example, Robert Boyle studied pneumatic chemistry for... | Atomic gases | 0.829622 |
6,158 | A typical game that has been solved this way is Hex. A related field of study, drawing from computational complexity theory, is game complexity, which is concerned with estimating the computational difficulty of finding optimal strategies.Research in artificial intelligence has addressed both perfect and imperfect info... | Game Theory | 0.829621 |
6,159 | The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory. A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see bel... | Homomorphism | 0.829619 |
6,160 | Algebraic data analysis Bayesian analysis Cluster analysis Combinatorial data analysis Formal concept analysis Functional data analysis Geometric data analysis Regression analysis Shape analysis Topological data analysis Tree structured data analysis | Structured data analysis (statistics) | 0.829618 |
6,161 | A special focus is made on the development of soft skills in order to develop potential in bioinformatics and computational biology students around the world. The ISCB-SC is composed of Regional Student Groups (RSGs) which are located in various regions across the globe. Since its foundation, the ISCB-SC has gained rep... | International Society for Computational Biology Student Council | 0.829617 |
6,162 | Another important approach to partial models consideration that becomes more and more popular is a combinatorial search that is either limited or full. This approach has some advantages against Polynomial Neural Networks, but requires considerable computational power and thus is not effective for objects with a large n... | Group method of data handling | 0.829616 |
6,163 | Finally, the angles CME and FMA are the same. Hence, AFM is an isosceles triangle, and thus the sides AF and FM are equal. The proof that FD = FM goes similarly: the angles FDM, BCM, BME and DMF are all equal, so DFM is an isosceles triangle, so FD = FM. It follows that AF = FD, as the theorem claims. | Brahmagupta theorem | 0.829615 |
6,164 | He obtained his Ph.D. in 1978 at UCSD in the Biology Department working with Bruno H. Zimm, studying the biophysical properties of DNA molecules. Towards the end of his doctoral research, he had become interested in the mechanics of protein folding, specifically the way that the RNA-degrading enzyme Ribonuclease, folds... | Ken A. Dill | 0.829615 |
6,165 | At the base of classical genetics is the concept of a gene, the hereditary factor tied to a particular simple feature (or character).The set of genes for one or more characters possessed by an individual is the genotype. A diploid individual often has two alleles for the determination of a character. | Classical genetics | 0.829613 |
6,166 | Some forms of chemical biology attempt to answer biological questions by studying biological systems at the chemical level. In contrast to research using biochemistry, genetics, or molecular biology, where mutagenesis can provide a new version of the organism, cell, or biomolecule of interest, chemical biology probes s... | Chemical Biology | 0.829612 |
6,167 | / M.Tech. in disciplines of Applied Physics and Mathematics, as listed below. | Joint Entrance Screening Test | 0.829611 |
6,168 | The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Joseph Louis Lagrange, Niels Henrik Abel and Évariste Galois were early res... | History of group theory | 0.82961 |
6,169 | Prior to 1927, Boolean algebra had been considered a calculus of logical values with logical operations of conjunction, disjunction, negation, and so on. Zhegalkin showed that all Boolean operations could be written as ordinary numeric polynomials, representing the false and true values as 0 and 1, the integers mod 2. ... | Boolean polynomial | 0.829609 |
6,170 | This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarised, but also reorient so that their symmetry axes align to the field.The study of dielectric properties concerns storage and... | Debye equation | 0.829608 |
6,171 | ms2 has been frequently used for predicting thermophysical properties of fluids for chemical engineering applications as well as for scientific computing and soft matter physics. It has been used for modelling both model fluids as well as real substances. A large number interaction potentials are implemented in ms2, e.... | Ms2 (software) | 0.829606 |
6,172 | It combines this with a softmax operator and a projection matrix. Transformers have increasingly become the model of choice for natural language processing. Many modern large language models such as ChatGPT, GPT-4, and BERT use it. | Artificial Neural Networks | 0.829603 |
6,173 | If k is close, but not equal, to one, the second orbit resembles the first, but revolves gradually about the center of force; this is known as orbital precession (Figure 3). If k is greater than one, the orbit precesses in the same direction as the orbit (Figure 3); if k is less than one, the orbit precesses in the opp... | Newton's theorem of revolving orbits | 0.829602 |
6,174 | Many probability text books and articles in the field of probability theory derive the conditional probability solution through a formal application of Bayes' theorem; among them books by Gill and Henze. Use of the odds form of Bayes' theorem, often called Bayes' rule, makes such a derivation more transparent.Initially... | Monty Hall problem | 0.829601 |
6,175 | The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equat... | Positive charge | 0.829601 |
6,176 | SolveSpace is a free and open-source 2D/3D constraint-based parametric computer-aided design (CAD) software that supports basic 2D and 3D constructive solid geometry modeling. It is a constraint-based parametric modeler with simple mechanical simulation capabilities. Version 2.1 and onward runs on Windows, Linux and ma... | SolveSpace | 0.829601 |
6,177 | Groups can be axiomatized by the same diagrams (equivalently, operations) as a Hopf algebra, where G is taken to be a set instead of a module. In this case: the field K is replaced by the 1-point set there is a natural counit (map to 1 point) there is a natural comultiplication (the diagonal map) the unit is the identi... | Hopf algebra | 0.8296 |
6,178 | noisy-channel coding theoremA theorem that establishes the limits of the error-free data transmission in a noisy communication channel nominal impedanceThe rated impedance of an element of a circuit. nonlinear controlThe class of control problems relating to the control of systems that are nonlinear. nonodeAny electron... | Glossary of electrical and electronics engineering | 0.829596 |
6,179 | Top cross (or "topcross") hybrids result from the crossing of a top quality or pure-bred male and a lower quality female, intended to improve the quality of the offspring, on average. Population hybrids result from the crossing of plants or animals in one population with those of another population. These include inter... | Hybrid plant | 0.829596 |
6,180 | For beginners, and for writing larger programs in the Bio domain, especially those to be shared and supported by others, Python’s clarity and brevity make it very attractive. For those who might be leaning towards a career in bioinformatics and who want to learn only one language, Java has the widest general programmin... | BioJava | 0.829591 |
6,181 | The discipline emerged after 2010 following the development of genome editing technology including TALENS and CRISPR. In 2015, one project created T cells that became active only in the presence of a specific drug, allowing them to be turned on and off in situ. Another example is a T cell that targets only cells that d... | Synthetic immunology | 0.829591 |
6,182 | Most modern deep learning models are based on multi-layered artificial neural networks such as convolutional neural networks and transformers, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltz... | Deep neural network | 0.82959 |
6,183 | Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of frequencies from 0.3 to 3 terahertz (THz), although the upper boundary is somewhat arbitrary and i... | Terahertz band | 0.829589 |
6,184 | )In particular, the algebraic formulation of constructible numbers leads to a proof of the impossibility of the following construction problems: Doubling the cube The problem of doubling the unit square is solved by the construction of another square on the diagonal of the first one, with side length 2 {\displaystyle {... | Constructible number | 0.829588 |
6,185 | Elementary algebra is the most basic form of algebra. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In algebra, numbers are often represented by symbols ca... | Algebra | 0.829588 |
6,186 | In his work Arithmetica, the Greek mathematician Diophantus (circa 250 AD) solved quadratic equations with a method more recognizably algebraic than the geometric algebra of Euclid. : 39 His solution gives only one root, even when both roots are positive.The Indian mathematician Brahmagupta (597–668 AD) explicitly desc... | Quadratic formula | 0.829587 |
6,187 | Another possibility is to include a highly charged nucleus which itself produces a strong electric field.By electromagnetic duality, the same mechanism in a magnetic field should produce magnetic monopoles, if they exist. A search conducted using the Large Hadron Collider failed to detect monopoles, and analysis indica... | Schwinger pair production | 0.829582 |
6,188 | For example, in the line geometry case, we can identify H as a 12-dimensional subgroup of the 16-dimensional general linear group, GL(4), defined by conditions on the matrix entries h13 = h14 = h23 = h24 = 0,by looking for the stabilizer of the subspace spanned by the first two standard basis vectors. That shows that X... | Inhomogeneous space | 0.829581 |
6,189 | Some important corollaries of the theorem include: PSPACE = NPSPACE That is, the languages that can be recognized by deterministic polynomial-space Turing machines and nondeterministic polynomial-space Turing machines are the same. This follows directly from the fact that the square of a polynomial function is still a ... | Savitch's theorem | 0.82958 |
6,190 | Genetics is the study of how genetic differences affect organisms. Genetics attempts to predict how mutations, individual genes and genetic interactions can affect the expression of a phenotypeWhile researchers practice techniques specific to molecular biology, it is common to combine these with methods from genetics a... | Molecular Microbiology | 0.829579 |
6,191 | The basic stress analysis problem can be formulated by Euler's equations of motion for continuous bodies (which are consequences of Newton's laws for conservation of linear momentum and angular momentum) and the Euler-Cauchy stress principle, together with the appropriate constitutive equations. Thus one obtains a syst... | Physical stress | 0.829578 |
6,192 | As matrices, it may be realized as the subset in which the product of the nonzero entries is an (m/p)th root of unity (rather than just an mth root). Algebraically, G(m, p, n) is a semidirect product of an abelian group of order mn/p by the symmetric group Sym(n); the elements of the abelian group are of the form (θa1,... | Complex reflection group | 0.829577 |
6,193 | Atomic and Molecular Physics (AMP) High Energy Astrophysics (HEA) Optical and Infrared Astronomy (OIR) Radio and Geoastronomy (RG) Solar, Stellar, and Planetary Sciences (SSP) Theoretical Astrophysics (TA) | Harvard–Smithsonian Center for Astrophysics | 0.829573 |
6,194 | In discrete and computational geometry, a set of points in the Euclidean plane or a higher-dimensional Euclidean space is said to be in convex position or convex independent if none of the points can be represented as a convex combination of the others. A finite set of points is in convex position if all of the points ... | Convex position | 0.829573 |
6,195 | A two-dimensional system of linear differential equations can be written in the form: d x d t = A x + B y d y d t = C x + D y {\displaystyle {\begin{aligned}{\frac {dx}{dt}}&=Ax+By\\{\frac {dy}{dt}}&=Cx+Dy\end{aligned}}} which can be organized into a matrix equation: d d t = d v d t = A v . {\displaystyle {\begin{al... | Phase plane | 0.829572 |
6,196 | Some polynomials, such as x2 + 1, do not have any roots among the real numbers. If, however, the set of accepted solutions is expanded to the complex numbers, every non-constant polynomial has at least one root; this is the fundamental theorem of algebra. By successively dividing out factors x − a, one sees that any po... | Integer polynomial | 0.829572 |
6,197 | Springer, Lecture Notes in Computer Science, Volume 2272. ISBN 978-3540431664 Bert, D.; Bowen, J.P. ; King, S.; Walden, M., eds. | Z User Group | 0.82957 |
6,198 | In current application, a quantum dot such as a small sphere confines in three dimensions, a quantum wire confines in two dimensions, and a quantum well confines only in one dimension. These are also known as zero-, one- and two-dimensional potential wells, respectively. In these cases they refer to the number of dimen... | Quantum confinement | 0.829567 |
6,199 | In order to gain further optimizations, byte order may be swapped in certain data, simple data structures and function libraries may be linked inline, and empty class objects may be short-circuited, for example. Being optimized for low memory requirements, Dalvik has some specific characteristics that differentiate it ... | Dalvik virtual machine | 0.829565 |
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