id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
97,300 | When a user clicks on one of the listings in the search results, they are directed to the corresponding website and data is transferred from the website's server, thus counting the visitors towards the overall flow of traffic to that website. Search engine optimization (SEO), is the ongoing practice of optimizing a web... | Web traffic | 0.777807 |
97,301 | Not all web traffic is welcomed. Some companies offer advertising schemes that, in return for increased web traffic (visitors), pay for screen space on the site. Sites also often aim to increase their web traffic through inclusion on search engines and through search engine optimization. | Web traffic | 0.777807 |
97,302 | The amount of traffic seen by a website is a measure of its popularity. By analyzing the statistics of visitors, it is possible to see shortcomings of the site and look to improve those areas. It is also possible to increase the popularity of a site and the number of people that visit it. | Web traffic | 0.777807 |
97,303 | NMEA OneNet is a latest standard for maritime data networking based on 802.3 Ethernet, and will complement existing onboard NMEA 2000 networks by allowing for high-capacity data transfers.Current maritime data networks have bandwidth capacities of less than 1 Mbit/s. Building on Ethernet, OneNet allows for capacity in ... | NMEA OneNet | 0.777803 |
97,304 | On June 4, 2018, at the Apple Worldwide Developers Conference, Xcode version 10 was announced; a beta version was released the same day. Xcode 10 introduced support for the Dark Mode announced for macOS Mojave, the collaboration platforms Bitbucket and GitLab (in addition to already supported GitHub), training machine ... | Xcode | 0.777802 |
97,305 | In materials science, the sol–gel process is a method for producing solid materials from small molecules. The method is used for the fabrication of metal oxides, especially the oxides of silicon (Si) and titanium (Ti). The process involves conversion of monomers into a colloidal solution (sol) that acts as the precurso... | Sol–gel process | 0.777801 |
97,306 | The containment of a uniformly dispersed assembly of strongly interacting particles in suspension requires total control over particle-particle interactions. Monodisperse colloids provide this potential.Monodisperse powders of colloidal silica, for example, may therefore be stabilized sufficiently to ensure a high degr... | Sol–gel process | 0.777801 |
97,307 | CoDel has been backported to Kernel 3.3. This encapsulates Traffic shaping to ensure fair distribution of bandwidth among multiple users and quality of service (QoS) for simultaneous use of applications such as VoIP, online gaming, and streaming media without experiencing the negative impacts of link saturation. Load b... | LEDE | 0.777799 |
97,308 | Stereochemistry such as E-Z notation or cis-trans alkene geometry is important since some transition metal cross-coupling reactions, such as the Suzuki coupling, can retain olefin geometry. In synthesis, it is useful to introduce vinyl iodide at various positions to be set up for a coupling reaction at the next synthet... | Vinyl iodide functional group | 0.777799 |
97,309 | Vinyl iodides are synthesized by methods such as iodination and substitution reaction. Vinyl iodides with well-defined geometry (regiochemistry and stereochemistry) are important in synthesis since many natural products and drugs that have specific structure and dimension. Example of regiochemistry is whether the iodid... | Vinyl iodide functional group | 0.777799 |
97,310 | It does not isomerized to E geometry because of low reactivity of radical InCl2 with intermediate complex (no second addition). If second addition occurs then isomerization will occur through diindium intermediate. They confirm a radical mechanism in a mechanistic study with alkyne and alkene cyclization. | Vinyl iodide functional group | 0.777799 |
97,311 | The Oshima group have demonstrated using hydroindation with HInCl selectively favors Z geometry. They suggested that the reaction proceeds by a radical mechanism. They predict that HInCl adds to alkyne by radical addition in a Z geometry. | Vinyl iodide functional group | 0.777799 |
97,312 | The advantage of this technique is this technique can tolerate a wide range of functional groups. Z selective β-vinyl iodides are slightly more difficult to introduce than E-β-vinyl iodides, often requiring more than one step. Hydroalumination and hydroboration usually proceed by syn fashion, therefore selectively favo... | Vinyl iodide functional group | 0.777799 |
97,313 | The E geometry selectivity is not cause by sterics but rather the reaction itself is not concerted. In a mechanistic study, they observed isomerization, which suggest E geometry product is more favored than Z geometry. The difference of results between halogen exchange and E-vinyl ether reaction is that only when there... | Vinyl iodide functional group | 0.777799 |
97,314 | The scope of this exchange for regiochemistry and stereochemistry is currently unexplored. Halogen-exchange can also be done with zirconium derivatives that retain olefin’s geometry The Marek group have further investigated using zirconium catalyst on E or Z vinyl ethers, which selective for E-vinyl ethers. The zirconi... | Vinyl iodide functional group | 0.777799 |
97,315 | Another method is the Takai olefination which uses iodoform and chromium(II) chloride to make vinyl iodide from aldehyde with high stereoselectivity for E geometry. For high stereoselectivity for Z geometry, Stork-Zhao olefination proceeds by Wittig-like reaction. High yields and Z stereoselectivity occurred at low tem... | Vinyl iodide functional group | 0.777799 |
97,316 | If the R group is big, the solvent is unable to participate, leading to retention of olefin's geometry Zakarian's group then decided to run the reaction in HFIP, which gave high retention of olefin geometry. They reasoned that HFIP is a low nucleophilicity solvent, unlike acetonitrile. In addition, they observed accele... | Vinyl iodide functional group | 0.777799 |
97,317 | They observed retention of olefin geometry in some vinyl silyl substrates while inversion in others. They reasoned that the R group's size had an effect on the geometry of the olefin. If the R group is small, the solvent acetonitrile can participate in the reaction leading to inversion of the olefin's geometry. | Vinyl iodide functional group | 0.777799 |
97,318 | In organic chemistry, a vinyl iodide (also known as an iodoalkene) functional group is an alkene with one or more iodide substituents. Vinyl iodides are versatile molecules that serve as important building blocks and precursors in organic synthesis. They are commonly used in carbon-carbon forming reactions in transitio... | Vinyl iodide functional group | 0.777799 |
97,319 | In particle physics, the Peccei–Quinn theory is a well-known, long-standing proposal for the resolution of the strong CP problem formulated by Roberto Peccei and Helen Quinn in 1977. The theory introduces a new anomalous symmetry to the Standard Model along with a new scalar field which spontaneously breaks the symmetr... | Peccei–Quinn symmetry | 0.777798 |
97,320 | The second theorem states that local broadcasting is only possible when the state is a classical probability distribution. This means that a state can only be broadcast locally if it does not have any quantum correlations. Luo reconciled this theorem with the generalized no-broadcast theorem by making the conjecture th... | No-broadcast theorem | 0.777798 |
97,321 | The theorem also includes a converse: if two quantum states do commute, there is a method for broadcasting them: they must have a common basis of eigenstates diagonalizing them simultaneously, and the map that clones every state of this basis is a legitimate quantum operation, requiring only physical resources independ... | No-broadcast theorem | 0.777798 |
97,322 | In physics, the no-broadcasting theorem is a result of quantum information theory. In the case of pure quantum states, it is a corollary of the no-cloning theorem. The no-cloning theorem for pure states says that it is impossible to create two copies of an unknown state given a single copy of the state. Since quantum s... | No-broadcast theorem | 0.777798 |
97,323 | Here, the word "broadcast" is used in the sense of conveying the state to two or more recipients. For multiple recipients to each receive the state, there must be, in some sense, a way of duplicating the state. The no-broadcast theorem generalizes the no-cloning theorem for mixed states. | No-broadcast theorem | 0.777798 |
97,324 | Starting in 1907, the United States Food and Drug Administration began investigating saccharin as a result of the Pure Food and Drug Act. Harvey Wiley, then the director of the bureau of chemistry for the FDA, viewed it as an illegal substitution of a valuable ingredient, sugar, by a less valuable ingredient. In a clas... | Sodium Saccharin | 0.777794 |
97,325 | They have almost similar subjects like PT graduation course in developed countries and can practice either independently or multidisciplines. However, due to lack of National Council the syllabus of BPT varies from state to state in the country. After the graduation Physiotherapist (PTs') could go for further specializ... | Physical therapy education | 0.777794 |
97,326 | In Australia, a few different programs are available at both undergraduate and post graduate level. The physiotherapy degree can be undertaken over a four-year period as an undergraduate or two to three years post graduate with the early components being predominantly theoretical including basic anatomy, biology, physi... | Physical therapy education | 0.777794 |
97,327 | All physiotherapy degree courses consist of a mix of theoretical and practical teaching sessions and include a compulsory 1000 hours of clinical practice spread across each of the academic years. Pre-registration Physiotherapy training consists of advanced study within each of three distinct areas of UK Physiotherapy p... | Physical therapy education | 0.777794 |
97,328 | In Canada, entry-level physiotherapy education is offered at 14 universities. All of these university programs are at the Master's level, meaning that applicants must have already completed an undergraduate degree prior to applying. Many universities also offer graduate programs in physiotherapy, rehabilitation, or rel... | Physical therapy education | 0.777794 |
97,329 | In Bangladesh, the Bachelor of Science in physiotherapy (BPT) course is provided by the Medicine Faculty of University of Dhaka, University of Rajshahi and Gono University. The BPT curriculum includes Anatomy, Physiology, Biochemistry, Pathology & Microbiology, Biomechanics, Radiology & Imaging, Orthopedics & Rheumatol... | Physical therapy education | 0.777794 |
97,330 | In the United Arab Emirates the Bachelor Of Physiotherapy (BPT) consists of a four-year undergraduate degree program. In the first year of the program they are introduced to pre-clinical subjects such as Anatomy, Physiology, Biochemistry, Human Behaviour & Socialisation & Basic Medical Electronics & Computers. The stud... | Physical therapy education | 0.777794 |
97,331 | The Journal of Inorganic Biochemistry is a monthly peer-reviewed scientific journal covering research on the inorganic aspects of biochemistry, such as metalloenzymes and metallobiomolecules. The journal was established in 1971 as Bioinorganic Chemistry, obtaining its current name in 1979. Since 1996, the editor-in-chi... | Journal of Inorganic Biochemistry | 0.777793 |
97,332 | In mathematics, an isotropic manifold is a manifold in which the geometry does not depend on directions. Formally, we say that a Riemannian manifold ( M , g ) {\displaystyle (M,g)} is isotropic if for any point p ∈ M {\displaystyle p\in M} and unit vectors v , w ∈ T p M {\displaystyle v,w\in T_{p}M} , there is an isome... | Isotropic manifold | 0.777792 |
97,333 | "Covalent gold" (PDF). Physical Chemistry Chemical Physics. 12 (31): 8694–8705. | Aurosilane | 0.777791 |
97,334 | However, Szilard had not been able to achieve a neutron-driven chain reaction with neutron-rich light atoms. In theory, if the number of secondary neutrons produced in a neutron-driven chain reaction was greater than one, then each such reaction could trigger multiple additional reactions, producing an exponentially in... | Einstein letter | 0.777791 |
97,335 | opened the Fifth Washington Conference on Theoretical Physics with Enrico Fermi on January 26, 1939. The results were quickly corroborated by experimental physicists, most notably Fermi and John R. Dunning at Columbia University.Hungarian physicist Leo Szilard realized that the neutron-driven fission of heavy atoms cou... | Einstein letter | 0.777791 |
97,336 | Resource consumption accounting (RCA) is formally defined as a dynamic, fully integrated, principle-based, and comprehensive management accounting approach that provides managers with decision support information for enterprise optimization. RCA emerged as a management accounting approach around 2000 and was subsequent... | Accounting management | 0.777788 |
97,337 | Interferometric visibility – which quantifies interference contrast in opticsPages displaying wikidata descriptions as a fallback Mutual coherence function Degree of coherence – Measurement in quantum optics Van Cittert–Zernike theorem Michelson stellar interferometer – astronomical instrument for measuring angular dia... | Coherence theory (optics) | 0.777788 |
97,338 | In physics, coherence theory is the study of optical effects arising from partially coherent light and radio sources. Partially coherent sources are sources where the coherence time or coherence length are limited by bandwidth, by thermal noise, or by other effect. Many aspects of modern coherence theory are studied in... | Coherence theory (optics) | 0.777788 |
97,339 | The NanoSIMS has been used in many different areas of materials science. It is able to map hydrogen and deuterium at microstructurally relevant scales which is important for studies of hydrogen embrittlement in metals although there are significant challenges associated with accurately detecting hydrogen and deuterium. | Nanoscale secondary ion mass spectrometry | 0.777785 |
97,340 | NanoSIMS can also be used to examine the elemental and isotopic composition of microparticles preserved in the rock record. The types of elements and isotopic ratios can help determine if the material is of biological origin. NanoSIMS was first used in this field of paleobiology in 2005 by Robert et al. In this study, ... | Nanoscale secondary ion mass spectrometry | 0.777785 |
97,341 | The high resolution that it offers allows intracellular measurement of accumulations and fluxes of molecules containing various stable isotopes. NanoSIMS can be used for pure cultures, co-cultures, and mixed community samples.The first use of NanoSIMS in biology was by Peteranderl and Lechene in 2004, who used a protot... | Nanoscale secondary ion mass spectrometry | 0.777785 |
97,342 | Initially developed for geochemical and related research, NanoSIMS is now utilized by a wide variety of fields, including biology and microbiology. In biomedical research, NanoSIMS is also referred to as multi-isotope imaging mass spectrometry (MIMS). The 50 nm resolution allows unprecedented resolution of cellular and... | Nanoscale secondary ion mass spectrometry | 0.777785 |
97,343 | The Canadian Penning Trap Mass Spectrometer (CPT) is one of the major pieces of experimental equipment that is installed on the ATLAS superconducting heavy-ion linac facility at the Physics Division of the Argonne National Laboratory. It was developed and operated by physicist Guy Savard and a collaboration of other sc... | Canadian Penning Trap Mass Spectrometer | 0.777785 |
97,344 | NanoSIMS can capture the spatial variability of isotopic and elemental measurements of sub-micron areas, grains or inclusions from geological, materials science and biological samples. This instrument can characterise nanostructured materials with complex composition that are increasingly important candidates for energ... | Nanoscale secondary ion mass spectrometry | 0.777785 |
97,345 | In molecular biology, Small nucleolar RNA snoM1 is a non-coding RNA (ncRNA) molecule which functions in the biogenesis (modification) of other small nuclear RNAs (snRNAs). This type of modifying RNA is located in the nucleolus of the eukaryotic cell which is a major site of snRNA biogenesis. It is known as a small nucl... | Small nucleolar RNA snoM1 | 0.777785 |
97,346 | 1983 – Computer simulations sophisticated enough to provide relatively reliable results of growth and evolution of the large-scale structure emerged and yielded insight on key features of the large-scale galaxy distribution. 1985 – Details of the supercluster and void structure of the Perseus–Pisces region were surveye... | Cosmic voids | 0.777782 |
97,347 | Study of cosmic voids within the discipline of astrophysics began in the mid-1970s when redshift surveys led two separate teams of astrophysicists in 1978 to identify superclusters and voids in the distribution of galaxies and Abell clusters. The new redshift surveys revolutionized the field of astronomy by adding dept... | Cosmic voids | 0.777782 |
97,348 | The United States' National Security Agency (NSA), an intelligence agency of the federal government, publishes many documents on the history and technology of cryptology, cryptography, and cryptanalysis through various publications. Cryptolog is published monthly by PI, Techniques and Standards, for the Personnel of Op... | National Security Agency academic publications | 0.777782 |
97,349 | Works for small or low algebraic degree S-boxes or small S-boxes. In addition to AND and XOR operations. | Higher-order differential cryptanalysis | 0.777781 |
97,350 | To implement an attack using higher order derivatives, knowledge about the probability distribution of the derivative of the cipher is needed. Calculating or estimating this distribution is generally a hard problem but if the cipher in question is known to have a low algebraic degree, the fact that derivatives reduce t... | Higher-order differential cryptanalysis | 0.777781 |
97,351 | In cryptography, higher-order differential cryptanalysis is a generalization of differential cryptanalysis, an attack used against block ciphers. While in standard differential cryptanalysis the difference between only two texts is used, higher-order differential cryptanalysis studies the propagation of a set of differ... | Higher-order differential cryptanalysis | 0.777781 |
97,352 | This motivates defining the derivative of a function f: F 2 n → F 2 n {\displaystyle f:\mathbb {F} _{2}^{n}\to \mathbb {F} _{2}^{n}} at a point α {\displaystyle \alpha } as Using this definition, the i {\displaystyle i} -th derivative at ( α 1 , α 2 , … , α i ) {\displaystyle (\alpha _{1},\alpha _{2},\dots ,\alpha _{i}... | Higher-order differential cryptanalysis | 0.777781 |
97,353 | A continuous-slowing-down model is used for electron transport that includes positrons, k x-rays, and bremsstrahlung but does not include external or self-induced fields. Important standard features that make MCNP very versatile and easy to use include a powerful general source, criticality source, and surface source; ... | Monte Carlo N-Particle Transport Code | 0.77778 |
97,354 | Monte Carlo N-Particle Transport (MCNP) is a general-purpose, continuous-energy, generalized-geometry, time-dependent, Monte Carlo radiation transport code designed to track many particle types over broad ranges of energies and is developed by Los Alamos National Laboratory. Specific areas of application include, but a... | Monte Carlo N-Particle Transport Code | 0.77778 |
97,355 | The Queen Elisabeth Medical Foundation (QEMF) is a Belgian non-profit organization, founded in 1926 by Elisabeth of Bavaria, wife of Albert I. She founded the organization, based on her experience with the wounded from the front-line during the First World War. The foundation wants to encourage laboratory research and ... | Queen Elisabeth Medical Foundation | 0.777779 |
97,356 | This form of the theorem is useful in Antenna theory, where one has often to consider harmonic fields propagating in the space. In this case, using phasor notation, E ( t ) = E e j ω t {\displaystyle E(t)=Ee^{j\omega t}} and H ( t ) = H e j ω t {\displaystyle H(t)=He^{j\omega t}} . Then the following mathematical ident... | Poynting's theorem | 0.777777 |
97,357 | Using the divergence theorem, Poynting's theorem can also be written in integral form: where S is the energy flow, given by the Poynting Vector. u {\displaystyle u} is the energy density in the volume. ∂ V {\displaystyle \partial V\!} is the boundary of the volume. The shape of the volume is arbitrary but fixed for the... | Poynting's theorem | 0.777777 |
97,358 | The derivation of the statement is dependent on the assumption that the materials the equation models can be described by a set of susceptibility properties that are linear, isotropic, homogenous and independent of frequency. The assumption that the materials have no absorption must also be made. A modification to Poyn... | Poynting's theorem | 0.777777 |
97,359 | Germain identified such an auxiliary prime q {\displaystyle q} for every prime less than 100. The theorem and its application to primes p {\displaystyle p} less than 100 were attributed to Germain by Adrien-Marie Legendre in 1823. | Sophie Germain's theorem | 0.777777 |
97,360 | Specifically, Sophie Germain proved that at least one of the numbers x {\displaystyle x} , y {\displaystyle y} , z {\displaystyle z} must be divisible by p 2 {\displaystyle p^{2}} if an auxiliary prime q {\displaystyle q} can be found such that two conditions are satisfied: No two nonzero p t h {\displaystyle p^{\mathr... | Sophie Germain's theorem | 0.777777 |
97,361 | In number theory, Sophie Germain's theorem is a statement about the divisibility of solutions to the equation x p + y p = z p {\displaystyle x^{p}+y^{p}=z^{p}} of Fermat's Last Theorem for odd prime p {\displaystyle p} . | Sophie Germain's theorem | 0.777777 |
97,362 | Placental insufficiency as a result of smoking has been shown to have a causal effect in the development of pre-eclampsia. While some previous studies have suggested that carbon monoxide from cigarette smoke may have a protective effect against preeclampsia, a recent study conducted by the Genetics of Pre-Eclampsia Con... | Intrauterine hypoxia | 0.777774 |
97,363 | The S-procedure or S-lemma is a mathematical result that gives conditions under which a particular quadratic inequality is a consequence of another quadratic inequality. The S-procedure was developed independently in a number of different contexts and has applications in control theory, linear algebra and mathematical ... | S-procedure | 0.777774 |
97,364 | The Interaction Flow Modeling Language (IFML) is a standardized modeling language in the field of software engineering. IFML includes a set of graphic notations to create visual models of user interactions and front-end behavior in software systems. The Interaction Flow Modeling Language was developed in 2012 and 2013 ... | Interaction Flow Modeling Language | 0.777773 |
97,365 | Conditions that guarantee that a function with a closed graph is necessarily continuous are called closed graph theorems. Closed graph theorems are of particular interest in functional analysis where there are many theorems giving conditions under which a linear map with a closed graph is necessarily continuous. If f: ... | Closed linear operator | 0.777772 |
97,366 | In mathematics, particularly in functional analysis and topology, closed graph is a property of functions. A function f: X → Y between topological spaces has a closed graph if its graph is a closed subset of the product space X × Y. A related property is open graph.This property is studied because there are many theore... | Closed linear operator | 0.777772 |
97,367 | Let X denote the real numbers ℝ with the usual Euclidean topology and let Y denote ℝ with the indiscrete topology (where note that Y is not Hausdorff and that every function valued in Y is continuous). Let f: X → Y be defined by f(0) = 1 and f(x) = 0 for all x ≠ 0. Then f: X → Y is continuous but its graph is not close... | Closed linear operator | 0.777772 |
97,368 | Thus, the ring of functions can be taken to be the ring of polynomial functions. The above can be considered to be an additional requirement imposed on the ring; it is sometimes called the bootstrap. In physics, a special case of the operator product algebra is known as the operator product expansion. | Polynomials on vector spaces | 0.777772 |
97,369 | The operator product algebra is an associative algebra of the form A i ( x ) B j ( y ) = ∑ k f k i j ( x , y , z ) C k ( z ) {\displaystyle A^{i}(x)B^{j}(y)=\sum _{k}f_{k}^{ij}(x,y,z)C^{k}(z)} The structure constants f k i j ( x , y , z ) {\displaystyle f_{k}^{ij}(x,y,z)} are required to be single-valued functions, rat... | Polynomials on vector spaces | 0.777772 |
97,370 | When the polynomials are valued not over a field k, but over some algebra, then one may define additional structure. Thus, for example, one may consider the ring of functions over GL(n,m), instead of for k = GL(1,m). In this case, one may impose an additional axiom. | Polynomials on vector spaces | 0.777772 |
97,371 | This suggests the following: given a vector space V, let k be the commutative k-algebra generated by the dual space V ∗ {\displaystyle V^{*}} , which is a subring of the ring of all functions V → k {\displaystyle V\to k} . If we fix a basis for V and write t i {\displaystyle t_{i}} for its dual basis, then k consists o... | Polynomials on vector spaces | 0.777772 |
97,372 | In mathematics, the ring of polynomial functions on a vector space V over a field k gives a coordinate-free analog of a polynomial ring. It is denoted by k. If V is finite dimensional and is viewed as an algebraic variety, then k is precisely the coordinate ring of V. The explicit definition of the ring can be given as... | Polynomials on vector spaces | 0.777772 |
97,373 | Mathematical consideration of process architectures may be found in CCS and the π-calculus. The structure of a process system, or its architecture, can be viewed as a dualistic relationship of its infrastructure and suprastructure. The infrastructure describes a process system's component parts and their interactions. | Process architecture | 0.777772 |
97,374 | These equations induce equivalence classes on the free algebra; the quotient algebra then has the algebraic structure of a group. Some structures do not form varieties, because either: It is necessary that 0 ≠ 1, 0 being the additive identity element and 1 being a multiplicative identity element, but this is a nonident... | Carrier set | 0.777772 |
97,375 | Thus, for example, groups have a signature containing two operators: the multiplication operator m, taking two arguments, and the inverse operator i, taking one argument, and the identity element e, a constant, which may be considered an operator that takes zero arguments. Given a (countable) set of variables x, y, z, ... | Carrier set | 0.777772 |
97,376 | The study of varieties is an important part of universal algebra. An algebraic structure in a variety may be understood as the quotient algebra of term algebra (also called "absolutely free algebra") divided by the equivalence relations generated by a set of identities. So, a collection of functions with given signatur... | Carrier set | 0.777772 |
97,377 | Algebraic structures are defined through different configurations of axioms. Universal algebra abstractly studies such objects. One major dichotomy is between structures that are axiomatized entirely by identities and structures that are not. | Carrier set | 0.777772 |
97,378 | Here are some of the most common existential axioms. Identity element A binary operation ∗ {\displaystyle *} has an identity element if there is an element e such that for all x in the structure. Here, the auxiliary operation is the operation of arity zero that has e as its result. Inverse element Given a binary operat... | Carrier set | 0.777772 |
97,379 | {\displaystyle x\mapsto -x.} Also, in universal algebra, a variety is a class of algebraic structures that share the same operations, and the same axioms, with the condition that all axioms are identities. What precedes shows that existential axioms of the above form are accepted in the definition of a variety. | Carrier set | 0.777772 |
97,380 | Also, when computing in an algebraic structure, one generally uses explicitly the auxiliary operations. For example, in the case of numbers, the additive inverse is provided by the unary minus operation x ↦ − x . | Carrier set | 0.777772 |
97,381 | {\displaystyle f(X,\varphi (X))=g(X,\varphi (X)).} The introduction of such auxiliary operation complicates slightly the statement of an axiom, but has some advantages. Given a specific algebraic structure, the proof that an existential axiom is satisfied consists generally of the definition of the auxiliary function, ... | Carrier set | 0.777772 |
97,382 | In a slight abuse of notation, the word "structure" can also refer to just the operations on a structure, instead of the underlying set itself. For example, the sentence, "We have defined a ring structure on the set A {\displaystyle A} ", means that we have defined ring operations on the set A {\displaystyle A} . For a... | Carrier set | 0.777772 |
97,383 | If all axioms defining a class of algebras are identities, then this class is a variety (not to be confused with algebraic varieties of algebraic geometry). Identities are equations formulated using only the operations the structure allows, and variables that are tacitly universally quantified over the relevant univers... | Carrier set | 0.777772 |
97,384 | An example of positron emission (β+ decay) is shown with magnesium-23 decaying into sodium-23: 2312Mg → 2311Na + e+ + νeBecause positron emission decreases proton number relative to neutron number, positron decay happens typically in large "proton-rich" radionuclides. Positron decay results in nuclear transmutation, ch... | Beta plus decay | 0.777771 |
97,385 | MINLOG is a proof assistant developed at the University of Munich by the team of Helmut Schwichtenberg. MINLOG is based on first order natural deduction calculus. It is intended to reason about computable functionals, using minimal rather than classical or intuitionistic logic. The primary motivation behind MINLOG is t... | MINLOG | 0.777768 |
97,386 | It will then make a rudimentary attempt at SLAM in order to keep the object in place. 3D Viewer can post a file to the Remix 3D website, open it in Paint 3D, or send it to the Print 3D app (formerly 3D Builder) for 3D printing. When in Mixed Reality mode, the 3D Viewer can also capture photos and videos of the scene th... | Microsoft 3D Viewer | 0.777768 |
97,387 | Zhang was born in China, and moved to Gosford on the Central Coast (New South Wales), Australia at age eight. She credits her mother's stories explaining the scientific basis of various phenomena with stimulating her interest in science. She moved to Sydney to attend the University of Sydney, where she completed a Bach... | Jenny Zhang (chemist) | 0.777766 |
97,388 | Jenny Zhenqi Zhang is a Chinese-Australian chemist and BBSRC David Phillips Research Fellow of the Department of Chemistry, University of Cambridge, where she is also a Fellow of Corpus Christi College (2019-present). She was awarded the 2020 RSC Felix Franks Biotechnology Medal for her research into re-wiring photosyn... | Jenny Zhang (chemist) | 0.777766 |
97,389 | In her independent career, she has continued to work on the re-wiring of photosynthesis but now focuses on doing so in live cells. She also became a Fellow of Corpus Christi College, where she is now Director of Studies in Natural Sciences Chemistry. Zhang was recognised for her contributions to semi-artificial photosy... | Jenny Zhang (chemist) | 0.777766 |
97,390 | Zhang's doctoral research was in the area of bioinorganic chemistry, and she worked on the development of a platinum-based library of chemotherapeutic candidates featuring anthraquinone ligands and redox activity. This involved using a variety of imaging techniques (including those based on synchrotron radiation) to st... | Jenny Zhang (chemist) | 0.777766 |
97,391 | The implicit function theorem provides a continuously differentiable function ( K , M ) ↦ ( λ i ( K , M ) , x i ( K , M ) ) {\displaystyle (K,M)\mapsto (\lambda _{i}(K,M),x_{i}(K,M))} hence the expansion with little o notation: λ i = λ 0 i + δ λ i + o ( ‖ δ K ‖ + ‖ δ M ‖ ) {\displaystyle \lambda _{i}=\lambda _{0i}+\del... | Eigenvalue perturbation | 0.777762 |
97,392 | (1962). Studies in perturbation theory. IV. Solution of eigenvalue problem by projection operator formalism. Journal of Mathematical Physics, 3(5), 969-982. | Eigenvalue perturbation | 0.777762 |
97,393 | Simon, B. (1982). Large orders and summability of eigenvalue perturbation theory: a mathematical overview. International Journal of Quantum Chemistry, 21(1), 3-25. | Eigenvalue perturbation | 0.777762 |
97,394 | In classical mechanics, we may find generalized eigenvalues when we look for vibrations of multiple degrees of freedom systems close to equilibrium; the kinetic energy provides the mass matrix M {\displaystyle M} , the potential strain energy provides the rigidity matrix K {\displaystyle K} . To get details, for exampl... | Eigenvalue perturbation | 0.777762 |
97,395 | In the entry applications of eigenvalues and eigenvectors we find numerous scientific fields in which eigenvalues are used to obtain solutions. Generalized eigenvalue problems are less widespread but are a key in the study of vibrations. They are useful when we use the Galerkin method or Rayleigh-Ritz method to find ap... | Eigenvalue perturbation | 0.777762 |
97,396 | In the case where all the matrices are Hermitian positive definite and all the eigenvalues are distinct, λ i = λ 0 i + x 0 i ⊤ ( δ K − λ 0 i δ M ) x 0 i x i = x 0 i ( 1 − 1 2 x 0 i ⊤ δ M x 0 i ) + ∑ j = 1 j ≠ i N x 0 j ⊤ ( δ K − λ 0 i δ M ) x 0 i λ 0 i − λ 0 j x 0 j {\displaystyle {\begin{aligned}\lambda _{i}&=\lambda ... | Eigenvalue perturbation | 0.777761 |
97,397 | In mathematics, an eigenvalue perturbation problem is that of finding the eigenvectors and eigenvalues of a system A x = λ x {\displaystyle Ax=\lambda x} that is perturbed from one with known eigenvectors and eigenvalues A 0 x 0 = λ 0 x 0 {\displaystyle A_{0}x_{0}=\lambda _{0}x_{0}} . This is useful for studying how se... | Eigenvalue perturbation | 0.777761 |
97,398 | These were used by the NA61/SHINE experiment.Similarly, Linac 3 accelerated xenon ions in 2017 for NA61's fixed-target physics programme. On October 12, 2017, these were delivered to the Large Hadron Collider (LHC) for a unique run of data taking: For the first time, xenon ions were accelerated and collided in the LHC.... | Linac4 | 0.777761 |
97,399 | Alternatively, using bromine, sulfur hexafluoride can be synthesized from SF4 and CoF3 at lower temperatures (e.g. 100 °C), as follows: There is virtually no reaction chemistry for SF6. A main contribution to the inertness of SF6 is the steric hindrance of the sulfur atom, whereas its heavier group 16 counterparts, suc... | SF6 | 0.777761 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.