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14,100 | QED concludes that the fine-structure constant is an increasing function of energy. It has been shown that at energies of the order of the Z0 boson rest energy, mzc2 ≈ 90 GeV, that: α ≈ 1 129 {\displaystyle \alpha \approx {\frac {1}{129}}} rather than the low-energy α ≈ 1/137. The renormalization procedure of eliminati... | Zero-point energies | 0.81553 |
14,101 | p-groups are fundamental tools in understanding the structure of groups and in the classification of finite simple groups. p-groups arise both as subgroups and as quotient groups. As subgroups, for a given prime p one has the Sylow p-subgroups P (largest p-subgroup not unique but all conjugate) and the p-core O p ( G )... | P-primary group | 0.815529 |
14,102 | The so-called coclass conjectures described the set of all finite p-groups of fixed coclass as perturbations of finitely many pro-p groups. The coclass conjectures were proven in the 1980s using techniques related to Lie algebras and powerful p-groups. The final proofs of the coclass theorems are due to A. Shalev and i... | P-primary group | 0.815529 |
14,103 | Every finite group whose order is divisible by p contains a subgroup which is a non-trivial p-group, namely a cyclic group of order p generated by an element of order p obtained from Cauchy's theorem. In fact, it contains a p-group of maximal possible order: if | G | = n = p k m {\displaystyle |G|=n=p^{k}m} where p doe... | P-primary group | 0.815529 |
14,104 | In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orde... | P-primary group | 0.815529 |
14,105 | Every p-group is periodic since by definition every element has finite order. If p is prime and G is a group of order pk, then G has a normal subgroup of order pm for every 1 ≤ m ≤ k. This follows by induction, using Cauchy's theorem and the Correspondence Theorem for groups. A proof sketch is as follows: because the c... | P-primary group | 0.815529 |
14,106 | Much of the structure of a finite group is carried in the structure of its so-called local subgroups, the normalizers of non-identity p-subgroups.The large elementary abelian subgroups of a finite group exert control over the group that was used in the proof of the Feit–Thompson theorem. Certain central extensions of e... | P-primary group | 0.815529 |
14,107 | Deformation can also be handled by a traditional rigid-body physics engine, modeling the soft-body motion using a network of multiple rigid bodies connected by constraints, and using (for example) matrix-palette skinning to generate a surface mesh for rendering. This is the approach used for deformable objects in Havok... | Soft-body dynamics | 0.815523 |
14,108 | The scope of soft body dynamics is quite broad, including simulation of soft organic materials such as muscle, fat, hair and vegetation, as well as other deformable materials such as clothing and fabric. Generally, these methods only provide visually plausible emulations rather than accurate scientific/engineering simu... | Soft-body dynamics | 0.815523 |
14,109 | The division lattice is an infinite complete bounded distributive lattice whose elements are the natural numbers ordered by divisibility. Its least element is 1, which divides all natural numbers, while its greatest element is 0, which is divisible by all natural numbers. The meet operation is greatest common divisor w... | Division lattice | 0.815521 |
14,110 | It is an important proof technique in set theory, topology and other fields. Proofs by transfinite induction typically distinguish three cases: when n is a minimal element, i.e. there is no element smaller than n; when n has a direct predecessor, i.e. the set of elements which are smaller than n has a largest element; ... | Course of values induction | 0.81551 |
14,111 | P(0) is clearly true: 0 = 0 ( 0 + 1 ) 2 . {\displaystyle 0={\tfrac {0(0+1)}{2}}\,.} Induction step: Show that for every k ≥ 0, if P(k) holds, then P(k + 1) also holds. Assume the induction hypothesis that for a particular k, the single case n = k holds, meaning P(k) is true: It follows that: Algebraically, the right ha... | Course of values induction | 0.81551 |
14,112 | Next-generation sequencing has enabled a genome-wide approach to identify DNA footprints. Open chromatin assays such as DNase-Seq and FAIRE-Seq have proven to provide a robust regulatory landscape for many cell types. However, these assays require some downstream bioinformatics analyses in order to provide genome-wide ... | DNA footprinting | 0.815508 |
14,113 | Plasma electrochemistry is a new field of research where the interaction of plasma with an electrolyte solution is studied. It uses plasma to drive chemical reactions in liquid. == References == | Plasma electrochemistry | 0.815499 |
14,114 | In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line l {\displaystyle l} through a point P {\displaystyle P} not on line R {\displaystyle R} ; however, in the plane, two parallels may be closer to l {\displaystyle l} than all others (one in each direction of R {\... | Limiting parallel | 0.815498 |
14,115 | The prior state of charge is restored when the leaving group (LG) departs with an electron pair. The principal product in this case is R−Nuc. In such reactions, the nucleophile is usually electrically neutral or negatively charged, whereas the substrate is typically neutral or positively charged. An example of nucleoph... | Aromatic substitution | 0.815496 |
14,116 | In organic (and inorganic) chemistry, nucleophilic substitution is a fundamental class of reactions in which a nucleophile selectively bonds with or attacks the positive or partially positive charge on an atom or a group of atoms. As it does so, it replaces a weaker nucleophile, which then becomes a leaving group; the ... | Aromatic substitution | 0.815496 |
14,117 | The Human Protein Atlas program was started in 2003 and funded by the non-profit organization Knut and Alice Wallenberg Foundation (KAW). The main site of the project is the Royal Institute of Technology (KTH), School of Engineering Sciences in Chemistry, Biotechnology and Health (Stockholm, Sweden). Additionally, the ... | Human Protein Atlas | 0.815496 |
14,118 | The Human Protein Atlas consists of twelve sections: The Tissue section of the Human Protein Atlas focuses on the expression profiles in human tissues of genes both on the mRNA and protein level. The protein expression data from 44 normal human tissue types is derived from antibody-based protein profiling using convent... | Human Protein Atlas | 0.815496 |
14,119 | All data has been updated on the approximately 5 million individual web pages. The Human Protein Atlas program has already contributed to several thousands of publications in the field of human biology and disease and was selected by the organization ELIXIR as a European core resource due to its fundamental importance ... | Human Protein Atlas | 0.815496 |
14,120 | The Human Protein Atlas (HPA) is a Swedish-based program started in 2003 with the aim to map all the human proteins in cells, tissues and organs using integration of various omics technologies, including antibody-based imaging, mass spectrometry-based proteomics, transcriptomics and systems biology. All the data in the... | Human Protein Atlas | 0.815496 |
14,121 | The Lie algebra of Killing vector fields of a spherically symmetric static spacetime takes the same form in the isotropic chart as in the Schwarzschild chart. Namely, this algebra is generated by the timelike irrotational Killing vector field ∂ t {\displaystyle \partial _{t}} and three spacelike Killing vector fields ∂... | Isotropic coordinates | 0.815496 |
14,122 | The OGS is a science-based organization that conducts field studies. To facilitate use of geological information by a range of technical and non-technical users, OGS provides many of Ontario's key, regional, geological databases for easy viewing on Google Earth, but using the OGSEarth function. Themes include: bedrock ... | Assessment File Research Imaging | 0.815488 |
14,123 | Its geological survey function is mandated by the Ontario Government. OGS has no regulatory responsibility. Ontario's geology includes: a) the rock (bedrock); b) the deposits of sand, gravel, and till left by the glaciers; c) the mineral resources and potential; d) the energy resource potential within the rocks and soi... | Assessment File Research Imaging | 0.815488 |
14,124 | The Ontario Geological Survey (OGS) is an administrative Branch of the Ontario Ministry of Northern Development, Mines, Natural Resources and Forestry. It is responsible for documenting and communicating the Geology of Ontario, and manages the Abandoned Mines Information System (AMIS), the Ontario Assessment File Datab... | Assessment File Research Imaging | 0.815488 |
14,125 | If we randomly choose coefficients from the set: { − b , − b + 1 , − b + 2 , … , − 2 , − 1 , 0 , 1 , 2 , … , b − 2 , b − 1 , b } {\textstyle \{-b,-b+1,-b+2,\ldots ,-2,-1,0,1,2,\ldots ,b-2,b-1,b\}} the polynomial will be small with respect to the bound ( b {\textstyle b} ). Using discrete Gaussian sampling – For an odd ... | Ring Learning with Errors | 0.815486 |
14,126 | The security of modern cryptography, in particular public-key cryptography, is based on the assumed intractability of solving certain computational problems if the size of the problem is large enough and the instance of the problem to be solved is chosen randomly. The classic example that has been used since the 1970s ... | Ring Learning with Errors | 0.815486 |
14,127 | It is widely believed that solving SVP (and all other lattice problems) in ideal lattices is as hard as in regular lattices." The difficulty of these problems on regular lattices is provably NP-hard. There are, however, a minority of researchers who do not believe that ideal lattices share the same security properties ... | Ring Learning with Errors | 0.815486 |
14,128 | A major advantage that RLWE based cryptography has over the original learning with errors (LWE) based cryptography is found in the size of the public and private keys. RLWE keys are roughly the square root of keys in LWE. For 128 bits of security an RLWE cryptographic algorithm would use public keys around 7000 bits in... | Ring Learning with Errors | 0.815486 |
14,129 | A RLWE version of the classic Feige–Fiat–Shamir Identification protocol was created and converted to a digital signature in 2011 by Lyubashevsky. The details of this signature were extended in 2012 by Gunesyu, Lyubashevsky, and Popplemann in 2012 and published in their paper "Practical Lattice Based Cryptography – A Si... | Ring Learning with Errors | 0.815486 |
14,130 | Homomorphic encryption is a form of encryption that allows computation on ciphertext, such as arithmetic on numeric values stored in an encrypted database. RLWE is more properly called learning with errors over rings and is simply the larger learning with errors (LWE) problem specialized to polynomial rings over finite... | Ring Learning with Errors | 0.815486 |
14,131 | In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography reli... | Ring Learning with Errors | 0.815486 |
14,132 | The Berry mechanism, or Berry pseudorotation mechanism, is a type of vibration causing molecules of certain geometries to isomerize by exchanging the two axial ligands (see Figure at right) for two of the equatorial ones. It is the most widely accepted mechanism for pseudorotation and most commonly occurs in trigonal b... | Berry pseudorotation | 0.815484 |
14,133 | Projects such as ELIXIR (the European life-sciences Infrastructure for biological Information) and GOBLET (Global Organization for Bioinformatics Learning, Education and Training) promote training and support biocuration as a career path.In 2011, biocuration was already recognized as a profession, but there were no for... | Biocuration | 0.815482 |
14,134 | Biocurators commonly employ and take part in the creation and development of shared biomedical ontologies: structured, controlled vocabularies that encompass many biological and medical knowledge domains, such as the Open Biomedical Ontologies. These domains include genomics and proteomics, anatomy, animal and plant de... | Biocuration | 0.815482 |
14,135 | The BioCreAtivE (Critical Assessment of Information Extraction systems in Biology) Challenge is a community-wide effort to develop and evaluate text mining and information extraction systems for the life sciences. The challenge was first launched in 2004 and has since become an important event in the biocuration and bi... | Biocuration | 0.815482 |
14,136 | The divergence theorem gives an equivalent integral definition of a solenoidal field; namely that for any closed surface, the net total flux through the surface must be zero: where d S {\displaystyle d\mathbf {S} } is the outward normal to each surface element. The fundamental theorem of vector calculus states that any... | Solenoidal field | 0.815479 |
14,137 | In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: A common way of expressing this property is to say that the field has no sources or sinks. | Solenoidal field | 0.815479 |
14,138 | Among neural network models, the self-organizing map (SOM) and adaptive resonance theory (ART) are commonly used in unsupervised learning algorithms. The SOM is a topographic organization in which nearby locations in the map represent inputs with similar properties. The ART model allows the number of clusters to vary w... | Unsupervised machine learning | 0.815478 |
14,139 | The classical example of unsupervised learning in the study of neural networks is Donald Hebb's principle, that is, neurons that fire together wire together. In Hebbian learning, the connection is reinforced irrespective of an error, but is exclusively a function of the coincidence between action potentials between the... | Unsupervised machine learning | 0.815478 |
14,140 | Neural network tasks are often categorized as discriminative (recognition) or generative (imagination). Often but not always, discriminative tasks use supervised methods and generative tasks use unsupervised (see Venn diagram); however, the separation is very hazy. For example, object recognition favors supervised lear... | Unsupervised machine learning | 0.815478 |
14,141 | The German word Informatik is usually translated to English as computer science by universities or computer science & engineering by technical universities (German equivalents for institutes of technology). Depending on the context, informatics is also translated into computing, scientific computing or information and ... | Informatics | 0.815477 |
14,142 | Informatics is the study of computational systems. According to the ACM Europe Council and Informatics Europe, informatics is synonymous with computer science and computing as a profession, in which the central notion is transformation of information. In other countries, the term "informatics" is used with a different ... | Informatics | 0.815477 |
14,143 | Former president of Association for Computing Machinery, Peter Denning wrote in 2007: The old definition of computer science - the study of phenomena surrounding computers - is now obsolete. Computing is the study of natural and artificial information processes. The 2008 Research Assessment Exercise, of the UK Funding ... | Informatics | 0.815477 |
14,144 | In the early 1990s, K.K. Kolin proposed an interpretation of informatics as a fundamental science that studies information processes in nature, society, and technical systems.A broad interpretation of informatics, as "the study of the structure, algorithms, behaviour, and interactions of natural and artificial computat... | Informatics | 0.815477 |
14,145 | In some countries, depending on local interpretations, the term "informatics" is used synonymously to mean information systems, information science, information theory, information engineering, information technology, information processing, or other theoretical or practical fields. In Germany, the term informatics alm... | Informatics | 0.815477 |
14,146 | Ancestry was reported to have collected 14 million DNA samples as of November 2018. 23andme's DNA database contained genetic information of over nine million people worldwide by 2019. The company explores selling the "anonymous aggregated genetic data" to other researchers and pharmaceutical companies for research purp... | National DNA database | 0.815473 |
14,147 | In Europe Interpol reported there were 31 national DNA databases and six more planned. The European Network of Forensic Science Institutes (ENFSI) DNA working group made 33 recommendations in 2014 for DNA database management and guidelines for auditing DNA databases. Other countries have adopted privately developed DNA... | National DNA database | 0.815473 |
14,148 | India announced it will launch its genomic database by fall 2019. In the first phase of "Genome India" the genomic data of 10,000 Indians will be catalogued. The Department of Biotechnology (DBT) has initiated the project. The first private DNA bank in India is in Lucknow - the capital of Indian State Uttar Pradesh. Un... | National DNA database | 0.815473 |
14,149 | Stacks entered the computer science literature in 1946, when Alan M. Turing used the terms "bury" and "unbury" as a means of calling and returning from subroutines. Subroutines had already been implemented in Konrad Zuse's Z4 in 1945. Klaus Samelson and Friedrich L. Bauer of Technical University Munich proposed the ide... | Hardware stack | 0.815466 |
14,150 | y=0 ∨ ∃x (Sx = y) Every number is either 0 or the successor of some number. The axiom schema of mathematical induction present in arithmetics stronger than Q turns this axiom into a theorem. x + 0 = x x + Sy = S(x + y) (4) and (5) are the recursive definition of addition. x·0 = 0 x·Sy = (x·y) + x (6) and (7) are the re... | Robinson arithmetic | 0.815463 |
14,151 | Thus the usual proof of the first incompleteness theorem can be used to show that Q is incomplete and undecidable. This indicates that the incompleteness and undecidability of PA cannot be blamed on the only aspect of PA differentiating it from Q, namely the axiom schema of induction. Gödel's theorems do not hold when ... | Robinson arithmetic | 0.815463 |
14,152 | Yet like PA it is incomplete and incompletable in the sense of Gödel's incompleteness theorems, and essentially undecidable. Robinson (1950) derived the Q axioms (1)–(7) above by noting just what PA axioms are required to prove that every computable function is representable in PA.The only use this proof makes of the P... | Robinson arithmetic | 0.815463 |
14,153 | Hence it is often possible to prove in Q every specific instance of a fact about the natural numbers, but not the associated general theorem. For example, 5 + 7 = 7 + 5 is provable in Q, but the general statement x + y = y + x is not. Similarly, one cannot prove that Sx ≠ x. A model of Q that fails many of the standard... | Robinson arithmetic | 0.815463 |
14,154 | However, unlike Peano arithmetic, Tennenbaum's theorem does not apply to Q, and it has computable non-standard models. For instance, there is a computable model of Q consisting of integer-coefficient polynomials with positive leading coefficient, plus the zero polynomial, with their usual arithmetic. A notable characte... | Robinson arithmetic | 0.815463 |
14,155 | To obtain means, variances and other statistics, both quantities and their occurrences are required. The gene effects (above) provide the framework for quantities: and the frequencies of the contrasting alleles in the fertilization gamete-pool provide the information on occurrences. Commonly, the frequency of the allel... | Polygenic trait | 0.815461 |
14,156 | This traditional view of adaptation in quantitative genetics provides a model for how the selected phenotype changes over time, as a function of the selection differential and heritability. However it does not provide insight into (nor does it depend upon) any of the genetic details - in particular, the number of loci ... | Polygenic trait | 0.815461 |
14,157 | The population mean shifts the central reference point from the homozygote midpoint (mp) to the mean of a sexually reproduced population. This is important not only to relocate the focus into the natural world, but also to use a measure of central tendency used by Statistics/Biometrics. In particular, the square of thi... | Polygenic trait | 0.815461 |
14,158 | Tracing various routes according to path analysis rules emulates the algebra of standardized partial regression.The path diagram to the left represents this analysis of sexual reproduction. Of its interesting elements, the important one in the selection context is meiosis. That's where segregation and assortment occur—... | Polygenic trait | 0.815461 |
14,159 | Due to the continuous distribution of phenotypic values, quantitative genetics must employ many other statistical methods (such as the effect size, the mean and the variance) to link phenotypes (attributes) to genotypes. Some phenotypes may be analyzed either as discrete categories or as continuous phenotypes, dependin... | Polygenic trait | 0.815461 |
14,160 | Quantitative genetics deals with quantitative traits, which are phenotypes that vary continuously (such as height or mass)—as opposed to discretely identifiable phenotypes and gene-products (such as eye-colour, or the presence of a particular biochemical). Both branches use the frequencies of different alleles of a gen... | Polygenic trait | 0.815461 |
14,161 | This second derivative is f ″ = 1 N ϕ + 1 1 − ϕ − 2 χ {\displaystyle f''={\frac {1}{N\phi }}+{\frac {1}{1-\phi }}-2\chi } and the solution first becomes unstable when this and the third derivative f ‴ = − 1 / ( N ϕ 2 ) + 1 / ( 1 − ϕ ) 2 {\displaystyle f'''=-1/(N\phi ^{2})+1/(1-\phi )^{2}} are both equal to zero. A litt... | Interaction parameter | 0.815461 |
14,162 | Most issues have articles from several different fields within aerospace engineering, though the journal will occasionally publish special issues that focus on one specific field or development. The latest such issue was published in October 2015, titled Special Issue: DAEDALOS – Dynamics in Aircraft Engineering Design... | Progress in Aerospace Sciences | 0.815456 |
14,163 | The first edition of Progress in Aerospace Sciences was published in 1961, and the journal been published continuously since 1994. For its entire history, it has been published in Oxford, United Kingdom. Until 1972, the journal published articles written in both English and French, while it has been published entirely ... | Progress in Aerospace Sciences | 0.815456 |
14,164 | Progress in Aerospace Sciences is a monthly peer-reviewed scientific journal covering all areas of aerospace and aerospace engineering. It covers all areas of aerospace and aerospace engineering, particularly with respect to new theoretical and experimental developments and their applications in research, industry, and... | Progress in Aerospace Sciences | 0.815456 |
14,165 | The journal publishes articles covering all aspects of theoretical and applied computer science problems. | Computer Science (journal) | 0.815455 |
14,166 | Computer Science is a peer-reviewed scientific journal published by the AGH University of Science and Technology (Kraków Poland) and edited by faculty members of the Departments of Computer Science and Automatics. The journal was established in 1999 and since beginning of 2012 is published quarterly. The editor-in-chie... | Computer Science (journal) | 0.815455 |
14,167 | Scoring assigned by the Polish Ministry of Science and Higher Education, as one of important factors used to evaluate research facilities in Poland, had following values for Computer Science journal: 7.0 (from 2012) 6.0 (2011), 2.0 (2010 and before). | Computer Science (journal) | 0.815455 |
14,168 | E. Sackmann, A.R. Bausch and L. Vonna, Physics of Composite Cell Membrane and Actin Based Cytoskeleton, in Physics of bio-molecules and cells, Edited by H. Flyvbjerg, F. Julicher, P. Ormos And F. David (Springer, Berlin, 2002). G. Lim, M. Wortis, and R. Mukhopadhyay, Stomatocyte–discocyte–echinocyte sequence of the hum... | Elasticity of cell membranes | 0.815453 |
14,169 | Rev. E 48 (1993) 2304-2307. U. Seifert, Vesicles of toroidal topology, Phys. | Elasticity of cell membranes | 0.815453 |
14,170 | Phys. 212 (2006) 757. X. Wang and Q. Du, physics/0605095. | Elasticity of cell membranes | 0.815453 |
14,171 | While epigenetics is of fundamental importance in eukaryotes, especially metazoans, it plays a different role in bacteria. Most importantly, eukaryotes use epigenetic mechanisms primarily to regulate gene expression which bacteria rarely do. However, bacteria make widespread use of postreplicative DNA methylation for t... | Epigenetics | 0.815452 |
14,172 | Gene expression can be controlled through the action of repressor proteins that attach to silencer regions of the DNA. These epigenetic changes may last through cell divisions for the duration of the cell's life, and may also last for multiple generations, even though they do not involve changes in the underlying DNA s... | Epigenetics | 0.815452 |
14,173 | In biology, epigenetics is the study of stable changes in cell function (known as marks) that do not involve alterations in the DNA sequence. The Greek prefix epi- (ἐπι- "over, outside of, around") in epigenetics implies features that are "on top of" or "in addition to" the traditional genetic basis for inheritance. Ep... | Epigenetics | 0.815452 |
14,174 | In 2008, a consensus definition of the epigenetic trait, a "stably heritable phenotype resulting from changes in a chromosome without alterations in the DNA sequence," was made at a Cold Spring Harbor meeting.The similarity of the word to "genetics" has generated many parallel usages. The "epigenome" is a parallel to t... | Epigenetics | 0.815452 |
14,175 | This definition would be inclusive of transient modifications associated with DNA repair or cell-cycle phases as well as stable changes maintained across multiple cell generations, but exclude others such as templating of membrane architecture and prions unless they impinge on chromosome function. Such redefinitions ho... | Epigenetics | 0.815452 |
14,176 | "The term has also been used, however, to describe processes which have not been demonstrated to be heritable, such as some forms of histone modification. Consequently, there are attempts to redefine "epigenetics" in broader terms that would avoid the constraints of requiring heritability. For example, Adrian Bird defi... | Epigenetics | 0.815452 |
14,177 | Robin Holliday defined in 1990 epigenetics as "the study of the mechanisms of temporal and spatial control of gene activity during the development of complex organisms. "More recent usage of the word in biology follows stricter definitions. As defined by Arthur Riggs and colleagues, it is "the study of mitotically and/... | Epigenetics | 0.815452 |
14,178 | This class of algorithms focus on the network graph structures involved where antibodies (or antibody producing cells) represent the nodes and the training algorithm involves growing or pruning edges between the nodes based on affinity (similarity in the problems representation space). Immune network algorithms have be... | Artificial immune systems | 0.815451 |
14,179 | The common techniques are inspired by specific immunological theories that explain the function and behavior of the mammalian adaptive immune system. Clonal selection algorithm: A class of algorithms inspired by the clonal selection theory of acquired immunity that explains how B and T lymphocytes improve their respons... | Artificial immune systems | 0.815451 |
14,180 | In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way ANOVA (regression analysis involving two qualitative factors) to assess whether the factor variables (categorical variables) are additively related to the expected value of the response variable. It can be applied when there... | Tukey's test of additivity | 0.815446 |
14,181 | The Human Genome Diversity Project (HGDP) was started by Stanford University's Morrison Institute in 1990s along with collaboration of scientists around the world. It is the result of many years of work by Luigi Cavalli-Sforza, one of the most cited scientists in the world, who has published extensively in the use of g... | Human Genome Diversity Project | 0.815445 |
14,182 | Work to create a new construction and engineering army began in 2010, and throughout the decade, the Ministry of Defense and the General Staff established six civil engineering units in the 2010s. In October 2019, the Cabinet announced that it would make some amendments to the Law on the Armed Forces on the expansion o... | Construction and Engineering Forces | 0.815439 |
14,183 | 339th Civil Engineering Unit (Bayankhongor Province) 014 Construction Unit | Construction and Engineering Forces | 0.815439 |
14,184 | The Q factor method does not use a metallic enclosure, but the method is based on the assumption that the Q factor of an ideal antenna is known, the ideal antenna being identical to the actual antenna except that the conductors have perfect conductivity and any dielectrics have zero loss. Thus, the Q factor method is o... | Radiation efficiency | 0.815433 |
14,185 | This article developed the Dirac equation using four-vectors and Schrödinger operators. The Dirac equation in the algebra of physical space uses a Clifford algebra over the real numbers, a type of geometric algebra. | Dirac equation | 0.815433 |
14,186 | The Dirac equation was also used (historically) to define a quantum-mechanical theory where ψ ( x ) {\displaystyle \psi (x)} is instead interpreted as a wave-function. The Dirac equation in the form originally proposed by Dirac is: where ψ(x, t) is the wave function for the electron of rest mass m with spacetime coordi... | Dirac equation | 0.815433 |
14,187 | The generator σ μ ν {\displaystyle \sigma _{\mu \nu }} generates a movement from one point in the fiber to another: a movement from x ↦ x ′ {\displaystyle x\mapsto x'} with both x {\displaystyle x} and x ′ {\displaystyle x'} still corresponding to the same spacetime point a . {\displaystyle a.} These perhaps obtuse rem... | Dirac equation | 0.815433 |
14,188 | Its location can be expressed in multiple coordinate systems. In the physics literature, these are written as x {\displaystyle x} and x ′ {\displaystyle x'} , with the understanding that both x {\displaystyle x} and x ′ {\displaystyle x'} describe the same point a {\displaystyle a} , but in different local frames of re... | Dirac equation | 0.815433 |
14,189 | These new gammas will themselves satisfy the Clifford relations, because of the orthogonality of the Lorentz transformation. By the fundamental theorem, one may replace the new set by the old set subject to a unitary transformation. In the new frame, remembering that the rest mass is a relativistic scalar, the Dirac eq... | Dirac equation | 0.815433 |
14,190 | The equation then takes the simple form A fundamental theorem states that if two distinct sets of matrices are given that both satisfy the Clifford relations, then they are connected to each other by a similarity transformation: If in addition the matrices are all unitary, as are the Dirac set, then S itself is unitary... | Dirac equation | 0.815433 |
14,191 | These are the defining relations of a Clifford algebra over a pseudo-orthogonal 4-dimensional space with metric signature (+ − − −). The specific Clifford algebra employed in the Dirac equation is known today as the Dirac algebra. Although not recognized as such by Dirac at the time the equation was formulated, in hind... | Dirac equation | 0.815433 |
14,192 | Thus, the Schrödinger equation may be seen as the far non-relativistic approximation of the Dirac equation when one may neglect spin and work only at low energies and velocities. This also was a great triumph for the new equation, as it traced the mysterious i that appears in it, and the necessity of a complex wave fun... | Dirac equation | 0.815433 |
14,193 | "Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations". Brazilian Journal of Physics. 43 (1–2): 64–77. | Dirac equation | 0.815433 |
14,194 | The latter had been regarded as almost incomprehensible by most of his contemporaries. The appearance of something so seemingly abstract, at such a late date, and in such a direct physical manner, is one of the most remarkable chapters in the history of physics. (Even more so, a validation of the exquisite insight disp... | Dirac equation | 0.815433 |
14,195 | The 4 × 4 matrices αk and β are all Hermitian and are involutory: and they all mutually anticommute: These matrices and the form of the wave function have a deep mathematical significance. The algebraic structure represented by the gamma matrices had been created some 50 years earlier by the English mathematician W. K.... | Dirac equation | 0.815433 |
14,196 | Although Dirac's original intentions were satisfied, his equation had far deeper implications for the structure of matter and introduced new mathematical classes of objects that are now essential elements of fundamental physics. The new elements in this equation are the four 4 × 4 matrices α1, α2, α3 and β, and the fou... | Dirac equation | 0.815433 |
14,197 | Dirac's purpose in casting this equation was to explain the behavior of the relativistically moving electron, and so to allow the atom to be treated in a manner consistent with relativity. His rather modest hope was that the corrections introduced this way might have a bearing on the problem of atomic spectra. Up until... | Dirac equation | 0.815433 |
14,198 | The various representations of the Dirac matrices employed will bring into focus particular aspects of the physical content in the Dirac wave function. The representation shown here is known as the standard representation – in it, the wave function's upper two components go over into Pauli's 2 spinor wave function in t... | Dirac equation | 0.815432 |
14,199 | A conserved current of the theory is Another approach to derive this expression is by variational methods, applying Noether's theorem for the global U ( 1 ) {\displaystyle {\text{U}}(1)} symmetry to derive the conserved current J μ . {\displaystyle J^{\mu }.} | Dirac equation | 0.815432 |
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