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22,600 | Substitution theorem If Γ ⊢ π1: A and Γ, u:A ⊢ π2: B, then Γ ⊢ π2: B.So far the judgment "Γ ⊢ π: A" has had a purely logical interpretation. In type theory, the logical view is exchanged for a more computational view of objects. Propositions in the logical interpretation are now viewed as types, and proofs as programs... | Natural deduction system | 0.80929 |
22,601 | In the rule, "Γ, u:A" stands for the collection of hypotheses Γ, together with the additional hypothesis u. With proofs available explicitly, one can manipulate and reason about proofs. The key operation on proofs is the substitution of one proof for an assumption used in another proof. This is commonly known as a subs... | Natural deduction system | 0.80929 |
22,602 | The term natural deduction (or rather, its German equivalent natürliches Schließen) was coined in that paper: Gentzen was motivated by a desire to establish the consistency of number theory. He was unable to prove the main result required for the consistency result, the cut elimination theorem—the Hauptsatz—directly fo... | Natural deduction system | 0.80929 |
22,603 | Natural deduction grew out of a context of dissatisfaction with the axiomatizations of deductive reasoning common to the systems of Hilbert, Frege, and Russell (see, e.g., Hilbert system). Such axiomatizations were most famously used by Russell and Whitehead in their mathematical treatise Principia Mathematica. Spurred... | Natural deduction system | 0.80929 |
22,604 | In theoretical chemistry, molecular electronic transitions take place when electrons in a molecule are excited from one energy level to a higher energy level. The energy change associated with this transition provides information on the structure of the molecule and determines many of its properties, such as colour. Th... | Molecular electron transition | 0.80929 |
22,605 | Thompson's normal p-complement theorem used conditions on two particular characteristic subgroups of a Sylow p-subgroup. Glauberman improved this further by showing that one only needs to use one characteristic subgroup: the center of the Thompson subgroup. Glauberman (1968) used his ZJ theorem to prove a normal p-comp... | P-nilpotent group | 0.80929 |
22,606 | The Frobenius normal p-complement theorem is a strengthening of the Burnside normal p-complement theorem, that states that if the normalizer of every non-trivial subgroup of a Sylow p-subgroup of G has a normal p-complement, then so does G. More precisely, the following conditions are equivalent: G has a normal p-compl... | P-nilpotent group | 0.80929 |
22,607 | Initially, this optimization technique was performed without computers, instead relying on dice to determine random mutations. By 1965, the calculations were performed wholly by machine.John Henry Holland introduced genetic algorithms in the 1960s, and it was further developed at the University of Michigan in the 1970s... | Evolutionary Computation | 0.809286 |
22,608 | Since traditional gradient descent techniques produce results that may get stuck in local minima, Rechenberg and Schwefel proposed that random mutations (applied to all parameters of some solution vector) may be used to escape these minima. Child solutions were generated from parent solutions, and the more successful o... | Evolutionary Computation | 0.809286 |
22,609 | These approaches differ in the method of selection, the permitted mutations, and the representation of genetic data. By the 1990s, the distinctions between the historic branches had begun to blur, and the term 'evolutionary computing' was coined in 1991 to denote a field that exists over all four paradigms.In 1962, Law... | Evolutionary Computation | 0.809286 |
22,610 | The concept of mimicking evolutionary processes to solve problems originates before the advent of computers, such as when Alan Turing proposed a method of genetic search in 1948 . Turing's B-type u-machines resemble primitive neural networks, and connections between neurons were learnt via a sort of genetic algorithm. ... | Evolutionary Computation | 0.809286 |
22,611 | A line of research in theoretical computer science is about the number of single-bit arithmetic operations necessary to multiply two n {\displaystyle n} -bit integers. This is known as the computational complexity of multiplication. Usual algorithms done by hand have asymptotic complexity of O ( n 2 ) {\displaystyle O(... | Long multiplication | 0.809285 |
22,612 | Metal-organic compounds (jargon: metalorganics, metallo-organics) are a class of chemical compounds that contain metals and organic ligands, which confer solubility in organic solvents or volatility. Compounds with these properties find applications in materials science for metal organic vapor deposition (MOCVD) or sol... | Metal-organic compound | 0.809284 |
22,613 | In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. A dynamo is though... | Dynamo effect | 0.80928 |
22,614 | Broadly, models of the geodynamo attempt to produce magnetic fields consistent with observed data given certain conditions and equations as mentioned in the sections above. Implementing the magnetohydrodynamic equations successfully was of particular significance because they pushed dynamo models to self-consistency. T... | Dynamo effect | 0.80928 |
22,615 | Virtually all dynamos in astrophysics and geophysics are hydromagnetic dynamos. The main idea of the theory is that any small magnetic field existing in the outer core creates currents in the moving fluid there due to Lorentz force. These currents create further magnetic field due to Ampere's law. | Dynamo effect | 0.80928 |
22,616 | In organic chemistry, the vicarious nucleophilic substitution is a special type of nucleophilic aromatic substitution in which a nucleophile replaces a hydrogen atom on the aromatic ring and not leaving groups such as halogen substituents which are ordinarily encountered in SNAr. This reaction type was reviewed in 1987... | Vicarious nucleophilic substitution | 0.809278 |
22,617 | Forces of the Quantum Vacuum: An introduction to Casimir physics. World Scientific. ISBN 978-981-4632-90-4. | Casimir–Polder force | 0.809276 |
22,618 | Casimir effect description from University of California, Riverside's version of the Usenet physics FAQ. A. Lambrecht, The Casimir effect: a force from nothing, Physics World, September 2002. NASA Astronomy Picture of the Day: Casimir effect (17 December 2006) Simpson, W. M. R; Leonhardt, U. (2015). | Casimir–Polder force | 0.809276 |
22,619 | Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in turbulent water or gas illustrate the Casimir force. In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physic... | Casimir–Polder force | 0.809276 |
22,620 | Let E/F be a field extension. Algebraic extension An extension in which every element of E is algebraic over F. Simple extension An extension which is generated by a single element, called a primitive element, or generating element. The primitive element theorem classifies such extensions. Normal extension An extension... | Glossary of field theory | 0.809273 |
22,621 | In the two variable case, D ( a , b ) {\displaystyle D(a,b)} and f x x ( a , b ) {\displaystyle f_{xx}(a,b)} are the principal minors of the Hessian. The first two conditions listed above on the signs of these minors are the conditions for the positive or negative definiteness of the Hessian. For the general case of an... | Second partial derivative test | 0.809273 |
22,622 | In mathematics, the second partial derivative test is a method in multivariable calculus used to determine if a critical point of a function is a local minimum, maximum or saddle point. | Second partial derivative test | 0.809273 |
22,623 | Kroneckerian field A totally real algebraic number field or a totally imaginary quadratic extension of a totally real field. CM-field or J-field An algebraic number field which is a totally imaginary quadratic extension of a totally real field. Linked field A field over which no biquaternion algebra is a division algeb... | Glossary of field theory | 0.809273 |
22,624 | some valuation. A generalization of complete fields. Hilbertian field A field satisfying Hilbert's irreducibility theorem: formally, one for which the projective line is not thin in the sense of Serre. | Glossary of field theory | 0.809273 |
22,625 | to some valuation. Pseudo algebraically closed field A field in which every variety has a rational point. Henselian field A field satisfying Hensel lemma w.r.t. | Glossary of field theory | 0.809273 |
22,626 | Algebraic numbers The field of algebraic numbers is the smallest algebraically closed extension of the field of rational numbers. Their detailed properties are studied in algebraic number theory. Quadratic field A degree-two extension of the rational numbers. | Glossary of field theory | 0.809273 |
22,627 | Algebraic closure An algebraic closure of a field F is an algebraic extension of F which is algebraically closed. Every field has an algebraic closure, and it is unique up to an isomorphism that fixes F. Transcendental Those elements of an extension field of F that are not algebraic over F are transcendental over F. Al... | Glossary of field theory | 0.809273 |
22,628 | The degree is called the imperfect degree of F. The field F is perfect if and only if its imperfect degree is 1. For example, if F is a function field of n variables over a finite field of characteristic p>0, then its imperfect degree is pn. Algebraically closed field A field F is algebraically closed if every polynom... | Glossary of field theory | 0.809273 |
22,629 | Algebraic extension If an element α of an extension field E over F is the root of a non-zero polynomial in F, then α is algebraic over F. If every element of E is algebraic over F, then E/F is an algebraic extension. Generating set Given a field extension E/F and a subset S of E, we write F(S) for the smallest subfield... | Glossary of field theory | 0.809273 |
22,630 | Galois extension A normal, separable field extension. Primary extension An extension E/F such that the algebraic closure of F in E is purely inseparable over F; equivalently, E is linearly disjoint from the separable closure of F. Purely transcendental extension An extension E/F in which every element of E not in F is ... | Glossary of field theory | 0.809273 |
22,631 | The philosophy of biology is a subfield of philosophy of science, which deals with epistemological, metaphysical, and ethical issues in the biological and biomedical sciences. Although philosophers of science and philosophers generally have long been interested in biology (e.g., Aristotle, Descartes, and Kant), philoso... | Philosophy of biology | 0.809272 |
22,632 | History and Philosophy of the Life Sciences Journal of the History of Biology Biology & Philosophy Biological Theory Philosophy, Theory, and Practice in Biology Studies in History and Philosophy of Science | Philosophy of biology | 0.809272 |
22,633 | Standard philosophy of science seemed to leave out a lot of what characterised living organisms - namely, a historical component in the form of an inherited genotype. Philosophers of biology have also examined the notion of “teleology.” Some have argued that scientists have had no need for a notion of cosmic teleology ... | Philosophy of biology | 0.809272 |
22,634 | The old positivist approach used in physics emphasised a strict determinism and led to the discovery of universally applicable laws, testable in the course of experiment. It was difficult for biology to use this approach. | Philosophy of biology | 0.809272 |
22,635 | As individual organisms must be understood in the context of their ecosystems, holists argue, so must lower-level biological processes be understood in the broader context of the living organism in which they take part. Proponents of this view cite our growing understanding of the multidirectional and multilayered natu... | Philosophy of biology | 0.809272 |
22,636 | A prominent question in the philosophy of biology is whether biology can be reduced to lower-level sciences such as chemistry and physics. Materialism is the view that every biological system including organisms consists of nothing except the interactions of molecules; it is opposed to vitalism. As a methodology, reduc... | Philosophy of biology | 0.809272 |
22,637 | According to their explanation a lesson to be learned from the successes of cancer immunotherapy is that they emerged from decoding of basic biology.Theory in biology is to some extent less strictly formalized than in physics. Besides 1) classic mathematical-analytical theory, as in physics, there is 2) statistics-base... | Philosophy of biology | 0.809272 |
22,638 | As Krakauer et al. put it: "machine learning is a powerful means of preprocessing data in preparation for mechanistic theory building, but should not be considered the final goal of a scientific inquiry." In regard to cancer biology, Raspe et al. state: "A better understanding of tumor biology is fundamental for extrac... | Philosophy of biology | 0.809272 |
22,639 | Research in biology continues to be less guided by theory than it is in other sciences. This is especially the case where the availability of high throughput screening techniques for the different "-omics" fields such as genomics, whose complexity makes them predominantly data-driven. Such data-intensive scientific dis... | Philosophy of biology | 0.809272 |
22,640 | Ontologies such as the Gene Ontology are being used to annotate the results of biological experiments in model organisms in order to create logically tractable bodies of data for reasoning and search. The ontologies are species-neutral graph-theoretical representations of biological types joined together by formally de... | Philosophy of biology | 0.809272 |
22,641 | "Is evolution compatible with Christianity or other religious systems?" "Are there laws of biology like the laws of physics? "Ideas drawn from philosophical ontology and logic are being used by biologists in the domain of bioinformatics. | Philosophy of biology | 0.809272 |
22,642 | "Is biological materialism & deterministic molecular biology compatible with free will?" "How is rationality possible, given our biological origins?" | Philosophy of biology | 0.809272 |
22,643 | Philosophers of biology examine the practices, theories, and concepts of biologists with a view toward better understanding biology as a scientific discipline (or group of scientific fields). Scientific ideas are philosophically analyzed and their consequences are explored. Philosophers of biology have also explored ho... | Philosophy of biology | 0.809272 |
22,644 | This point cannot be overstated: biomedia depend upon an understanding of biological as informational but not immaterial. "Some approaches to the philosophy of biology incorporate perspectives from science studies and/or science and technology studies, anthropology, sociology of science, and political economy. This inc... | Philosophy of biology | 0.809272 |
22,645 | One perspective on the philosophy of biology is how developments in modern biological research and biotechnologies have influenced traditional philosophical ideas about the distinction between biology and technology, as well as implications for ethics, society, and culture. An example is the work of philosopher Eugene ... | Philosophy of biology | 0.809272 |
22,646 | International Society for the History, Philosophy, and Social Studies of Biology | Philosophy of biology | 0.809272 |
22,647 | By clarifying and restricting the use of the term “teleology” to describe and explain systems controlled strictly by genetic programmes or other physical systems, teleological questions can be framed and investigated while remaining committed to the physical nature of all underlying organic processes. While some philos... | Philosophy of biology | 0.809272 |
22,648 | The areas of application of metascience include ICTs, medicine, psychology and physics. | Metascience | 0.809271 |
22,649 | Studies have various kinds of metadata which can be utilized, complemented and made accessible in useful ways. OpenAlex is a free online index of over 200 million scientific documents that integrates and provides metadata such as sources, citations, author information, scientific fields and research topics. Its API and... | Metascience | 0.809271 |
22,650 | Scientific data science is the use of data science to analyse research papers. It encompasses both qualitative and quantitative methods. Research in scientific data science includes fraud detection and citation network analysis. | Metascience | 0.809271 |
22,651 | Scientific awards are one category of science incentives. Metascience can explore existing and hypothetical systems of science awards. For instance, it found that work honored by Nobel prizes clusters in only a few scientific fields with only 36/71 having received at least one Nobel prize of the 114/849 domains science... | Metascience | 0.809271 |
22,652 | Metascience seeks to identify poor research practices, including biases in research, poor study design, abuse of statistics, and to find methods to reduce these practices. Meta-research has identified numerous biases in scientific literature. Of particular note is the widespread misuse of p-values and abuse of statisti... | Metascience | 0.809271 |
22,653 | In response to concerns about publication bias and p-hacking, more than 140 psychology journals have adopted result-blind peer review, in which studies are pre-registered and published without regard for their outcome. An analysis of these reforms estimated that 61 percent of result-blind studies produce null results, ... | Metascience | 0.809271 |
22,654 | Metascience has revealed significant problems in psychological research. The field suffers from high bias, low reproducibility, and widespread misuse of statistics. The replication crisis affects psychology more strongly than any other field; as many as two-thirds of highly publicized findings may be impossible to repl... | Metascience | 0.809271 |
22,655 | Meta-research in the following decades found many methodological flaws, inefficiencies, and poor practices in research across numerous scientific fields. Many scientific studies could not be reproduced, particularly in medicine and the soft sciences. The term "replication crisis" was coined in the early 2010s as part o... | Metascience | 0.809271 |
22,656 | Some research is investigating scientific controversy or controveries, and may identify currently ongoing major debates (e.g. open questions), and disagreement between scientists or studies. One study suggests the level of disagreement was highest in the social sciences and humanities (0.61%), followed by biomedical an... | Metascience | 0.809271 |
22,657 | The figure at the right shows three examples beginning with clear inequality (top) and approaching equality (bottom). In the Euclidean case, equality occurs only if the triangle has a 180° angle and two 0° angles, making the three vertices collinear, as shown in the bottom example. Thus, in Euclidean geometry, the shor... | Segment addition postulate | 0.80927 |
22,658 | In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although it may be proved without these theorems. The inequality can be viewed intuitively in either R2 or R3. | Segment addition postulate | 0.80927 |
22,659 | In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclud... | Segment addition postulate | 0.80927 |
22,660 | Important examples of self-assembly in materials science include the formation of molecular crystals, colloids, lipid bilayers, phase-separated polymers, and self-assembled monolayers. The folding of polypeptide chains into proteins and the folding of nucleic acids into their functional forms are examples of self-assem... | Self-assembly | 0.809269 |
22,661 | This feature can make synthesis rather complex because of the need to control many free parameters. Yet self-assembly has the advantage that a large variety of shapes and functions on many length scales can be obtained.The fundamental condition needed for nanoscale building blocks to self-assemble into an ordered struc... | Self-assembly | 0.809269 |
22,662 | Self-assembly extends the scope of chemistry aiming at synthesizing products with order and functionality properties, extending chemical bonds to weak interactions and encompassing the self-assembly of nanoscale building blocks at all length scales. In covalent synthesis and polymerization, the scientist links atoms to... | Self-assembly | 0.809269 |
22,663 | Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, applied mathematics, and computer science, in order to address problems in ... | Chemometrics | 0.809269 |
22,664 | Chemometrics is applied to solve both descriptive and predictive problems in experimental natural sciences, especially in chemistry. In descriptive applications, properties of chemical systems are modeled with the intent of learning the underlying relationships and structure of the system (i.e., model understanding and... | Chemometrics | 0.809269 |
22,665 | Supervised multivariate classification techniques are closely related to multivariate calibration techniques in that a calibration or training set is used to develop a mathematical model capable of classifying future samples. The techniques employed in chemometrics are similar to those used in other fields – multivaria... | Chemometrics | 0.809269 |
22,666 | These are higher-order extensions of more widely used methods. For example, while the analysis of a table (matrix, or second-order array) of data is routine in several fields, multiway methods are applied to data sets that involve 3rd, 4th, or higher-orders. Data of this type is very common in chemistry, for example a ... | Chemometrics | 0.809269 |
22,667 | Specifically in terms of MSPC, multiway modeling of batch and continuous processes is increasingly common in industry and remains an active area of research in chemometrics and chemical engineering. Process analytical chemistry as it was originally termed, or the newer term process analytical technology continues to dr... | Chemometrics | 0.809269 |
22,668 | Chemometric model selection usually involves the use of tools such as resampling (including bootstrap, permutation, cross-validation). Multivariate statistical process control (MSPC), modeling and optimization accounts for a substantial amount of historical chemometric development. Spectroscopy has been used successful... | Chemometrics | 0.809269 |
22,669 | Through the 1980s three dedicated journals appeared in the field: Journal of Chemometrics, Chemometrics and Intelligent Laboratory Systems, and Journal of Chemical Information and Modeling. These journals continue to cover both fundamental and methodological research in chemometrics. At present, most routine applicatio... | Chemometrics | 0.809268 |
22,670 | Although one could argue that even the earliest analytical experiments in chemistry involved a form of chemometrics, the field is generally recognized to have emerged in the 1970s as computers became increasingly exploited for scientific investigation. The term 'chemometrics' was coined by Svante Wold in a 1971 grant a... | Chemometrics | 0.809268 |
22,671 | The Journal of Mechanics in Medicine and Biology is a peer-reviewed medical journal that was established in 2001 and is published by World Scientific. It covers research in the field of mechanics as applied to medicine and biology. | Journal of Mechanics in Medicine and Biology | 0.809265 |
22,672 | The Colombeau Algebra is defined as the quotient algebra C M ∞ ( R n ) / C N ∞ ( R n ) . {\displaystyle C_{M}^{\infty }(\mathbb {R} ^{n})/C_{N}^{\infty }(\mathbb {R} ^{n}).} Here the algebra of moderate functions C M ∞ ( R n ) {\displaystyle C_{M}^{\infty }(\mathbb {R} ^{n})} on R n {\displaystyle \mathbb {R} ^{n}} is ... | Colombeau algebra | 0.809263 |
22,673 | As a mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework, lifting the limitations of distribution theory. These algebras have found numerous applications in the fields of partial differential equations, geophysics, microloc... | Colombeau algebra | 0.809263 |
22,674 | In mathematics, a Colombeau algebra is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Such a multiplication of distributions has long ... | Colombeau algebra | 0.809263 |
22,675 | In such a case, evaluation of the function must be expressed in an unwieldy manner as or in order to use the Leibniz notation. Thus, in these cases, it may be preferable to use the Euler differential operator notation with D i {\displaystyle D_{i}} as the partial derivative symbol with respect to the i-th variable. For... | Partial derivatives | 0.809263 |
22,676 | The space(s) of Schwartz distributions can be embedded into the simplified algebra by (component-wise) convolution with any element of the algebra having as representative a δ-net, i.e. a family of smooth functions φ ε {\displaystyle \varphi _{\varepsilon }} such that φ ε → δ {\displaystyle \varphi _{\varepsilon }\to \... | Colombeau algebra | 0.809263 |
22,677 | In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The... | Partial derivatives | 0.809263 |
22,678 | Hence, the number of total base pairs is equal to the number of nucleotides in one of the strands (with the exception of non-coding single-stranded regions of telomeres). The haploid human genome (23 chromosomes) is estimated to be about 3.2 billion bases long and to contain 20,000–25,000 distinct protein-coding genes.... | Kilo base pair | 0.809263 |
22,679 | In neuroscience, repolarization refers to the change in membrane potential that returns it to a negative value just after the depolarization phase of an action potential which has changed the membrane potential to a positive value. The repolarization phase usually returns the membrane potential back to the resting memb... | Repolarization | 0.809263 |
22,680 | Full descriptions of the no-go theorems named below are given in other articles linked to their names. A few of them are broad, general categories under which several theorems fall. Other names are broad and general-sounding but only refer to a single theorem. | No-go theorem | 0.80926 |
22,681 | Bell's theorem Kochen–Specker theorem PBR theorem No-hiding theorem No-cloning theorem Quantum no-deleting theorem No-teleportation theorem No-broadcast theorem The no-communication theorem in quantum information theory gives conditions under which instantaneous transfer of information between two observers is impossib... | No-go theorem | 0.80926 |
22,682 | Antidynamo theorems is a general category of theorems that restrict the type of magnetic fields that can be produced by dynamo action. Cowling's theorem states that an axisymmetric magnetic field cannot be maintained through a self-sustaining dynamo action by an axially symmetric current. Earnshaw's theorem states that... | No-go theorem | 0.80926 |
22,683 | In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. Specifically, the term describes results in quantum mechanics like Bell's theorem and the Kochen–Specker theorem that constrain the permissible types of hidden variable theories which try to explain ... | No-go theorem | 0.80926 |
22,684 | Hegerfeldt's theorem implies that localizable free particles are incompatible with causality in relativistic quantum theory. Coleman–Mandula theorem states that "space-time and internal symmetries cannot be combined in any but a trivial way". Haag–Łopuszański–Sohnius theorem is a generalisation of the Coleman–Mandula t... | No-go theorem | 0.80926 |
22,685 | Weinberg–Witten theorem states that massless particles (either composite or elementary) with spin J > 1 2 {\displaystyle \;J>{\tfrac {1}{2}}\;} cannot carry a Lorentz-covariant current, while massless particles with spin J > 1 {\displaystyle \;J>1\;} cannot carry a Lorentz-covariant stress-energy. It is usually interpr... | No-go theorem | 0.80926 |
22,686 | In mathematics there is the concept of proof of impossibility referring to problems impossible to solve. The difference between this impossibility and that of the no-go theorems is: a proof of impossibility states a category of logical proposition that may never be true; a no-go theorem instead presents a sequence of e... | No-go theorem | 0.80926 |
22,687 | Native chemical ligation can also be performed with an N-terminal selenocysteine residue.Polypeptide C-terminal thioesters produced by recombinant DNA techniques can be reacted with an N-terminal Cys containing polypeptide by the same native ligation chemistry to provide very large semi-synthetic proteins. Native chemi... | Native chemical ligation | 0.809258 |
22,688 | Fmoc chemistry solid phase peptide synthesis techniques for generating peptide-thioesters are based on the synthesis of peptide hydrazides that are converted to peptide thioesters post-synthetically. Polypeptide C-terminal thioesters can also be produced in situ, using so-called N,S-acyl shift systems. Bis(2-sulfanylet... | Native chemical ligation | 0.809258 |
22,689 | It is carried out in aqueous solution at neutral pH, usually in 6 M guanidine.hydrochloride, in the presence of an arylthiol catalyst and typically gives near-quantitative yields of the desired ligation product. Peptide-thioesters can be directly prepared by Boc chemistry SPPS; however, thioester-containing peptides ar... | Native chemical ligation | 0.809258 |
22,690 | That is, as in the discrete case, there is a resolution of the identity where the operator-valued integral is again understood in the weak sense. If the spectrum of P has both continuous and discrete parts, then the resolution of the identity involves a summation over the discrete spectrum and an integral over the cont... | Impulse function | 0.809253 |
22,691 | The spectrum of the position (in one dimension) is the entire real line and is called a continuous spectrum. However, unlike the Hamiltonian, the position operator lacks proper eigenfunctions. The conventional way to overcome this shortcoming is to widen the class of available functions by allowing distributions as wel... | Impulse function | 0.809253 |
22,692 | A set of orthonormal wave functions is complete in the space of square-integrable functions if any wave function |ψ⟩ can be expressed as a linear combination of the {|φn⟩} with complex coefficients: with cn = ⟨φn|ψ⟩. Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the Hamiltonia... | Impulse function | 0.809253 |
22,693 | The delta function is expedient in quantum mechanics. The wave function of a particle gives the probability amplitude of finding a particle within a given region of space. Wave functions are assumed to be elements of the Hilbert space L2 of square-integrable functions, and the total probability of finding a particle wi... | Impulse function | 0.809253 |
22,694 | Higher derivatives of the delta function are known in physics as multipoles. Higher derivatives enter into mathematics naturally as the building blocks for the complete structure of distributions with point support. If S is any distribution on U supported on the set {a} consisting of a single point, then there is an in... | Impulse function | 0.809253 |
22,695 | Just as standard mathematical induction is equivalent to the well-ordering principle, structural induction is also equivalent to a well-ordering principle. If the set of all structures of a certain kind admits a well-founded partial order, then every nonempty subset must have a minimal element. (This is the definition ... | Structural induction | 0.809252 |
22,696 | Query understanding is the process of inferring the intent of a search engine user by extracting semantic meaning from the searcher’s keywords. Query understanding methods generally take place before the search engine retrieves and ranks results. It is related to natural language processing but specifically focused on ... | Query understanding | 0.809248 |
22,697 | Entity recognition is the process of locating and classifying entities within a text string. Named-entity recognition specifically focuses on named entities, such as names of people, places, and organizations. In addition, entity recognition includes identifying concepts in queries that may be represented by multi-word... | Query understanding | 0.809248 |
22,698 | There are several logic families with different characteristics (power consumption, speed, cost, size) such as: RDL (resistor–diode logic), RTL (resistor-transistor logic), DTL (diode–transistor logic), TTL (transistor–transistor logic) and CMOS. There are also sub-variants, e.g. standard CMOS logic vs. advanced types ... | Universal logic gate | 0.809245 |
22,699 | Logic gates have been made out of DNA (see DNA nanotechnology) and used to create a computer called MAYA (see MAYA-II). Logic gates can be made from quantum mechanical effects, see quantum logic gate. Photonic logic gates use nonlinear optical effects. In principle any method that leads to a gate that is functionally c... | Universal logic gate | 0.809245 |
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