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Localization-protected quantum order , the ground state is ferromagnetically ordered with spins aligned along the z { \ displaystyle z } axis for j > h { \ displaystyle j > h }, but is a paramagnet for j < h { \ displaystyle j < h } and at any finite temperature ( fig 1a ). deep in the ordered phase, the system has tw...
Localization-protected quantum order
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Probability current : j = ρ v, { \ displaystyle \ mathbf { j } = \ rho \ mathbf { v }, } where ρ { \ displaystyle \ rho } is the mass density of the fluid and v is its velocity ( also the group velocity of the wave ). in the classical limit, we can associate the velocity with ∇ s m, { \ displaystyle { \ tfrac { \ nabl...
Probability current
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Nakajima–Zwanzig equation q } } \ \ \ end { matrix } } \ right ) l \ left ( { \ begin { matrix } { \ mathcal { q } } \ \ { \ mathcal { p } } \ \ \ end { matrix } } \ right ) \ rho. } the dynamics of the projected state p ρ { \ displaystyle { \ mathcal { p } } \ rho }, under any idempotent projection operator ( where p...
Nakajima–Zwanzig equation
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RNA interference fda approved the first sirna - based drug ( patisiran ) in 2018. givosiran and lumasiran later won fda approval for the treatment of ahp and ph1 in 2019 and 2020, respectively. inclisiran received ema approval in 2020 for the treatment of high cholesterol and is currently under review by the fda. = = ...
RNA interference
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Computer-aided auscultation contexts ). = = auscultogram = = the sounds of auscultation can be depicted using symbols to produce an auscultogram. it is used in cardiology training. = = mediate and immediate auscultation = = mediate auscultation is an antiquated medical term for listening ( auscultation ) to the intern...
Computer-aided auscultation
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Edge wave in fluid dynamics, an edge wave is a surface gravity wave fixed by refraction against a rigid boundary, often a shoaling beach. progressive edge waves travel along this boundary, varying sinusoidally along it and diminishing exponentially in the offshore direction. = = references = = = = further reading = = ...
Edge wave
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Brandes' algorithm } } } } is known as the pair dependency of s t { \ displaystyle st } on v { \ displaystyle v }, and represents the proportion of the shortest s { \ displaystyle s } – t { \ displaystyle t } paths which travel via v { \ displaystyle v }. the betweenness centrality is simply the sum of the pair depend...
Brandes' algorithm
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Grouped data of the mean of the population from which the data are drawn can be calculated from the grouped data as : x = f x f. { \ displaystyle { \ bar { x } } = { \ frac { \ sum { f \, x } } { \ sum { f } } }. } in this formula, x refers to the midpoint of the class intervals, and f is the class frequency. note tha...
Grouped data
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Positive-real function left half s - plane. to accommodate such functions in the definition of pr, it is therefore necessary to relax the condition that the function be real for all real s, and only require this when s is positive. thus, a possibly irrational function z ( s ) is pr if and only if z ( s ) is analytic i...
Positive-real function
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Compound (linguistics) chest, which has been made reddish - yellow by the saffron from the bosom of kamala ( lakshmi ), an adjective of rama in the kakabhushundi ramayana. a compound of 16 words and 44 syllables. - योग - नयाय - वशषिक - परव - मीमासा - वदानत - नारद - शाणडिलय - भकति - सतर - गीता - वालमीकीय - रामायण - भाग...
Compound (linguistics)
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General recursive function here, the class of μ - recursive functions remains the same, which follows from kleene's normal form theorem ( see below ). the only difference is, that it becomes undecidable whether a specific function definition defines a μ - recursive function, as it is undecidable whether a computable (...
General recursive function
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Geometric calculus { i _ { 1 } } \ right ) \ wedge \ left ( dx ^ { i _ { 2 } } e _ { i _ { 2 } } \ right ) \ wedge \ cdots \ wedge \ left ( dx ^ { i _ { k } } e _ { i _ { k } } \ right ) \ \ & = \ left ( e _ { i _ { 1 } } \ wedge e _ { i _ { 2 } } \ wedge \ cdots \ wedge e _ { i _ { k } } \ right ) dx ^ { i _ { 1 } } ...
Geometric calculus
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Glossary of genetics and evolutionary biology is the earliest developmental stage. = = see also = = outline of evolution index of evolutionary biology articles glossary of cellular and molecular biology glossary of cellular and molecular biology ( 0 – l ) glossary of cellular and molecular biology ( m – z ) = = refere...
Glossary of genetics and evolutionary biology
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Ford–Fulkerson algorithm 2006 ). " chapter 7 : extensions to the maximum - flow problem ". algorithm design. pearson education. pp. 378 – 384. isbn 0 - 321 - 29535 - 8. samuel gutekunst ( 2019 ). engri 1101. cornell university. backman, spencer ; huynh, tony ( 2018 ). " transfinite ford – fulkerson on a finite network...
Ford–Fulkerson algorithm
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Permutationally invariant quantum state tomography number of independent real parameters of p i { \ displaystyle \ varrho _ { \ rm { pi } } } for n { \ displaystyle n } qubits scales as n 3. { \ displaystyle \ sim n ^ { 3 }. } the number of local measurement settings scales as n 2. { \ displaystyle \ sim n ^ { 2 }. } ...
Permutationally invariant quantum state tomography
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Tokenization (data security) ' s maintenance workload increases significantly. for ensuring database consistency, token databases need to be continuously synchronized. apart from that, secure communication channels must be built between sensitive data and the vault so that data is not compromised on the way to or from...
Tokenization (data security)
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Quasiperiodic function in mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. a function f { \ displaystyle f } is quasiperiodic with quasiperiod ω { \ displaystyle \ omega } if f ( z + ω ) = g ( z, f ( z ) ) { \ displaystyle f ( z + \ omega ) = g ( z, f ( z ) ) },...
Quasiperiodic function
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Bayes linear statistics of probability. de finetti, b. ( 1937 ) “ la prevision : ses lois logiques, ses sources subjectives, ” annales de l'institut henri poincare, - " foresight : its logical laws, its subjective sources, " ( translation of the 1937 article in french ) in h. e. kyburg and h. e. smokler ( eds ), studi...
Bayes linear statistics
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Unitary element 1 } = ( a ^ { * } ) ^ { - 1 } ( b ^ { * } ) ^ { - 1 } = ab }. in particular, a u { \ displaystyle { \ mathcal { a } } _ { u } } forms a multiplicative group. the element a { \ displaystyle a } is normal. the adjoint element a ∗ { \ displaystyle a ^ { * } } is also unitary, since a = ( a ∗ ) ∗ { \ displ...
Unitary element
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The Neutral Theory of Molecular Evolution ##omic data studied and the statistical tools used to detect positive selection. for example, bayesian methods for the detection of selected codon sites and mcdonald - kreitman tests have been criticized for their rate of erroneous identification of positive selection. = = see...
The Neutral Theory of Molecular Evolution
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Non-autonomous mechanics q \ to \ mathbb { r } } coordinated by ( t, q i, p i ) { \ displaystyle ( t, q ^ { i }, p _ { i } ) } and endowed with the canonical poisson structure. the dynamics of hamiltonian non - autonomous mechanics is defined by a hamiltonian form p i d q i − h ( t, q i, p i ) d t { \ displaystyle p _...
Non-autonomous mechanics
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Cell damage as indicated by the observation that 89 % of spontaneously occurring base substitution mutations are caused by introduction of ros - induced single - strand damages followed by error - prone replication past these damages. oxidative dna damages usually involve only one of the dna strands at any damaged sit...
Cell damage
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DNA-binding domain repeat arrays have been shown to contract upon dna binding and a two - state search mechanism has been proposed whereby the elongated tale begins to contract around the dna beginning with a successful thymine recognition from a unique repeat unit n - terminal of the core tal - effector repeat array....
DNA-binding domain
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Actin-binding protein ##onin tor2 tubulin biv = = u = = ulapualide utrophin unc - 87 unc - 60 ( adf / cofilins ) = = v = = vasp vav verprolin vdac vibrio cholerae rtx toxin villin vinculin vitamin d - binding protein = = w = = wip wasp = = y = = y - box proteins ypka ( yopo ) = = z = = zipper protein zo - 1 zyxin = = ...
Actin-binding protein
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Nonribosomal code can predict the amino acid sequence of the produced small peptide. nrps, nrps - like or nrps - pks complexes also exist and have domain variations, additions and / or exclusions. = = supporting examples = = the a - domains have 8 amino acid - long non - ribosomal signatures. ltkvghig → asp ( aspartic...
Nonribosomal code
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Pendulum (mechanics) pendulum period valid for all possible amplitudes, to which experimental data could be compared, was sought. in 2008, lima derived a weighted - average formula with this characteristic : t ≈ r a 2 t lima + k 2 t cromer r a 2 + k 2, { \ displaystyle t \ approx { \ frac { r \, a ^ { 2 } \, t _ { \ t...
Pendulum (mechanics)
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Justesen code }, } where ℓ { \ displaystyle \ ell } is the greatest integer satisfying i = 1 ℓ ( 2 m i ) ≤ n − k + 1 { \ displaystyle \ sum _ { i = 1 } ^ { \ ell } { \ binom { 2m } { i } } \ leq n - k + 1 }. ( see macwilliams / macwilliams for a proof. ) = = see also = = concatenated error correction code linear code ...
Justesen code
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Inductive probability out as bayes'law. p ( a ∧ b ) = p ( a ) p ( b | a ) = p ( b ) p ( a | b ) { \ displaystyle p ( a \ land b ) = p ( a ) p ( b | a ) = p ( b ) p ( a | b ) } this law describes the relationship between prior and posterior probabilities when new facts are learnt. written as quantities of information b...
Inductive probability
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SeaBASS (data archive) the seawifs bio - optical archive and storage system ( seabass ) is a data archive of in situ oceanographic data used to support satellite remote sensing research of ocean color. seabass is used for developing algorithms for satellite - derived variables ( such as chlorophyll - a concentration )...
SeaBASS (data archive)
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Direct function a direct function ( dfn, pronounced " dee fun " ) is an alternative way to define a function and operator ( a higher - order function ) in the programming language apl. a direct operator can also be called a dop ( pronounced " dee op " ). they were invented by john scholes in 1996. they are a unique co...
Direct function
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Multicopy single-stranded DNA strand extending from the 3'- oh needs somehow to spiral down the binding cleft without being blocked by steric hindrance. to overcome this issue, the msdna reverse transcriptase clearly would require special features not shared by other rts. = = references = = = = further reading = = lam...
Multicopy single-stranded DNA
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Gene regulatory circuit nutrient availability and developmental signals, and react in accordance to changes in their surroundings. in plant synthetic biology, genetic regulatory circuits can be used to program traits to increase crop plant efficiency by increasing their robustness to environmental stressors. additiona...
Gene regulatory circuit
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Height function tate height, or canonical height, is a quadratic form on the mordell – weil group of rational points of an abelian variety defined over a global field. it is named after andre neron, who first defined it as a sum of local heights, and john tate, who defined it globally in an unpublished work. = = = wei...
Height function
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Detention center (cell biology) a nucleolar detention center ( dc ) is a region of the cell in which certain proteins are temporarily detained in periods of cellular stress. dcs are absent from cells under normal culture conditions, but form in response to specific environmental triggers. the detention of numerous pro...
Detention center (cell biology)
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Reality structure { im } \ { v \ } } in this case, the complex conjugate of a vector v is defined as follows : v = re { v } − i im { v } { \ displaystyle { \ overline { v } } = \ operatorname { re } \ { v \ } - i \, \ operatorname { im } \ { v \ } } this map v ↦ v { \ displaystyle v \ mapsto { \ overline { v } } } is ...
Reality structure
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Bond graph . j − − − c { \ displaystyle j \ ; { \ overset { \ textstyle } { \ underset { \ textstyle } { - \! \! \! - \! \! \! - \! \! \! \ rightharpoonup \! \! \! } } } \ ; \ c } = = = two - port elements = = = these elements have two ports. they are used to change the power between or within a system. when convertin...
Bond graph
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Engineering geology geological society of america ; centennial special volume 3 legget, robert f., editor, 1982, geology under cities : geological society of america ; reviews in engineering geology, volume v, 131 pages ; contains nine articles by separate authors for these cities : washington, dc ; boston ; chicago ;...
Engineering geology
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Protein aggregation predictors computational methods that use protein sequence and / or protein structure to predict protein aggregation. the table below, shows the main features of software for prediction of protein aggregation = = table = = = = see also = = phasage toolbox amyloid protein aggregation = = references ...
Protein aggregation predictors
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Gene transfer agent there is one 17. 8 kb area with phage - like structural genes in the bacterial genome, but their link to gta production is not yet experimentally proven. = = = vta ( methanococcus voltae ) = = = m. voltae is an archaean ; its gta is known to transfer 4. 4 kb dna fragments but has not been otherwise...
Gene transfer agent
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Kuranishi structure from k q { \ displaystyle k _ { q } } to k p { \ displaystyle k _ { p } }. in addition, the coordinate changes must satisfy the cocycle condition, namely, whenever q ∈ f p, r ∈ f q { \ displaystyle q \ in f _ { p }, \ r \ in f _ { q } }, we require that p q ∘ q r = p r, ^ p q ∘ ^ q r = ^ p r { \ di...
Kuranishi structure
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Transcript of unknown function transcripts of unknown function ( tufs ) is the name that has been suggested for known rna transcripts of dna whose function is unclear. most are probably ncrnas, such as rnai or snornas, but could also represent a whole new class of ncrna. their dna sequences reside in the intergenic or...
Transcript of unknown function
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Weyl equation \ sigma } } ^ { \ nu } p _ { \ nu } \ right ) \ left ( \ sigma ^ { \ mu } p _ { \ mu } \ right ) \ chi = \ left ( \ sigma ^ { \ nu } p _ { \ nu } \ right ) \ left ( { \ bar { \ sigma } } ^ { \ mu } p _ { \ mu } \ right ) \ chi = p _ { \ mu } p ^ { \ mu } \ chi = \ left ( e ^ { 2 } - { \ vec { p } } \ cdo...
Weyl equation
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Distributed agile software development located in the u. s. and seven offshore companies were located in india. the findings are summarized in the following table : from this we learn that all case studies emphasized the first value of the agile manifesto which states that individuals and interactions should be valued...
Distributed agile software development
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Mesangial cell then occurs due to insufficient degradation by matrix metalloproteinases. increased glucose levels results in the activation of metabolic pathways leading to increased oxidative stress. this in turn results in the over - production and accumulation of advanced glycosylation end products responsible for ...
Mesangial cell
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Offshore concrete structure barge in the ardjuna field ( indonesia ). this barge is built of reinforced and prestressed concrete containing cylindrical tanks each having a cross - section perpendicular to its longitudinal axes that comprises a preferably circular curved portion corresponding to the bottom. = = major o...
Offshore concrete structure
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Small interfering RNA 2020, alnylam and vir pharmaceuticals announced a partnership and have started working on a rnai therapy that would treat severe cases of covid - 19. other companies that have had success in developing a pipeline of sirna therapies are dicerna pharmaceuticals, partnered eli lilly and company and ...
Small interfering RNA
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Kernel (statistics) = = kernel functions in common use = = = several types of kernel functions are commonly used : uniform, triangle, epanechnikov, quartic ( biweight ), tricube, triweight, gaussian, quadratic and cosine. in the table below, if k { \ displaystyle k } is given with a bounded support, then k ( u ) = 0 {...
Kernel (statistics)
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Market data between authority and destination breaks off, all requests made from the client will be dropped. a server ( authority ) can handle large client - connections, though usually a relatively small number of clients are connected to the same server at the same time. a client ( destination ) usually has a small ...
Market data
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Optical material optical materials are transparent materials from which optical lenses, prisms, windows, waveguides, and second - surface mirrors can be made. they are required in most optical instruments. most optical materials are rigid solids, but flexible and elastic materials are used for special functions. conta...
Optical material
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Integral element [ f 1, …, f n ] { \ displaystyle k [ f _ { 1 }, \ ldots, f _ { n } ] } for a regular sequence ( f 1, …, f n ) { \ displaystyle ( f _ { 1 }, \ ldots, f _ { n } ) }? ]
Integral element
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International Journal of Data Warehousing and Mining the international journal of data warehousing and mining ( ijdwm ) is a quarterly peer - reviewed academic journal covering data warehousing and data mining. it was established in 2005 and is published by igi global. the editor - in - chief is david taniar ( monash ...
International Journal of Data Warehousing and Mining
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Morphology (architecture and engineering) - class residential developments. certain activities are unable to afford the costs of the most desirable locations, as seen in the case of low - income residential areas and high land with a much sought - after view. one real - world example of this model is the multiple nucl...
Morphology (architecture and engineering)
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Quantum Cheshire cat \ displaystyle | b \ rangle }, respectively. additionally, an out - of the - plane polarization operator is defined as σ = | 0 ⟩ ⟨ 1 | + | 1 ⟩ ⟨ 0 |, { \ displaystyle \ sigma _ { \ perp } = | 0 \ rangle \ langle 1 | + | 1 \ rangle \ langle 0 |, } this operator can be thought as a measure of angula...
Quantum Cheshire cat
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Sampled data system in systems science, a sampled - data system is a control system in which a continuous - time plant is controlled with a digital device. under periodic sampling, the sampled - data system is time - varying but also periodic ; thus, it may be modeled by a simplified discrete - time system obtained by...
Sampled data system
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Parameterized approximation algorithm kernelization scheme ( psaks ) is an α - approximate kernelization algorithm that computes a polynomial - sized kernel and for which α can be set to 1 + ε { \ displaystyle 1 + \ varepsilon } for any ε > 0 { \ displaystyle \ varepsilon > 0 }. for example, while the connected vertex...
Parameterized approximation algorithm
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Gene trapping gene trapping is a high - throughput approach that is used to introduce insertional mutations across an organism's genome. = = method = = trapping is performed with gene trap vectors whose principal element is a gene trapping cassette consisting of a promoterless reporter gene and / or selectable genetic...
Gene trapping
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Quantum capacity \ mathcal { s } } \ left \ { e _ { a ^ { n } } ^ { \ dagger } e _ { b ^ { n } } \ in n \ left ( { \ mathcal { s } } \ right ) \ right \ } } ≤ a n, b n ∈ t δ p n, b n = a n pr { e a n } 2 − ( n − k ) { \ displaystyle \ leq \ sum _ { a ^ { n }, b ^ { n } \ in t _ { \ delta } ^ { \ mathbf { p } ^ { n } }...
Quantum capacity
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DNA methylation and zheng, et al. together with biological assay, these methods greatly facilitate the dna methylation analysis. = = see also = = 5 - hydroxymethylcytosine 5 - methylcytosine 7 - methylguanosine decrease in dna methylation i ( ddm1 ), a plant methylation gene demethylating agent differentially methylat...
DNA methylation
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Quantum programming embedded language, using haskell as the host language. for this reason, quantum programs written in quipper are written in haskell using provided libraries. for example, the following code implements preparation of a superposition = = references = = = = further reading = = mingsheng, ying ( 2024 )....
Quantum programming
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Frame (linear algebra) } is a hilbert space, x { \ displaystyle x } a locally compact space, and μ { \ displaystyle \ mu } is a locally finite borel measure on x { \ displaystyle x }. then a set of vectors in h { \ displaystyle h }, { f x } x ∈ x { \ displaystyle \ { f _ { x } \ } _ { x \ in x } } with a measure μ { \...
Frame (linear algebra)
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Wetware (biology) the term wetware is used to describe the protocols and molecular devices used in molecular biology and synthetic biology. where biological components and systems are treated in a similar manner to software, and similar development models and methodologies are applied, the term'wetware'can be used to ...
Wetware (biology)
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CSS code in quantum error correction, css codes, named after their inventors, robert calderbank, peter shor and andrew steane, are a special type of stabilizer code constructed from classical codes with some special properties. an example of a css code is the steane code. = = construction = = let c 1 { \ displaystyle ...
CSS code
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Cole–Vishkin algorithm } ( g ) } to be the least k for which such a matrix w { \ displaystyle w } exists. then χ v ( g ) ≤ χ ( g ). { \ displaystyle \ chi _ { v } ( g ) \ leq \ chi ( g ). } lovasz number : the lovasz number of a complementary graph is also a lower bound on the chromatic number : ( g ) ≤ χ ( g ). { \ d...
Cole–Vishkin algorithm
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Integro-differential equation in mathematics, an integro - differential equation is an equation that involves both integrals and derivatives of a function. = = general first order linear equations = = the general first - order, linear ( only with respect to the term involving derivative ) integro - differential equati...
Integro-differential equation
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Wannier equation ] ν l ( k ) = δ λ, ν { \ displaystyle \ sum _ { \ mathbf { k } } \ left [ \ phi _ { \ lambda } ^ { l } ( \ mathbf { k } ) \ right ] ^ { \ star } \, \ phi _ { \ nu } ^ { r } ( \ mathbf { k } ) = \ sum _ { \ mathbf { k } } \ left [ \ phi _ { \ lambda } ^ { r } ( \ mathbf { k } ) \ right ] ^ { \ star } \...
Wannier equation
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Solution (chemistry) ##s dissolve in polar solvents, forming polar bonds or hydrogen bonds. as an example, all alcoholic beverages are aqueous solutions of ethanol. on the other hand, non - polar solutes dissolve better in non - polar solvents. examples are hydrocarbons such as oil and grease that easily mix, while be...
Solution (chemistry)
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Membrane structure membrane structures are spatial structures made out of tensioned membranes. the structural use of membranes can be divided into pneumatic structures, tensile membrane structures, and cable domes. in these three kinds of structure, membranes work together with cables, columns and other construction m...
Membrane structure
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Neural network quantum states network, computing the expectation value is an exponentially costly operation in n { \ displaystyle n }, stochastic techniques based, for example, on the monte carlo method are used to estimate e ( w ) { \ displaystyle e ( w ) }, analogously to what is done in variational monte carlo, see...
Neural network quantum states
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Tensor calculus symmetric and antisymmetric parts on two indices : a α β γ = a ( α β ) γ + a [ α β ] γ { \ displaystyle a _ { \ alpha \ beta \ gamma \ cdots } = a _ { ( \ alpha \ beta ) \ gamma \ cdots } + a _ { [ \ alpha \ beta ] \ gamma \ cdots } } as can be seen by adding the above expressions for a ( αβ ) γ⋅⋅⋅ and...
Tensor calculus
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Quantum field theory ##c { \ left \ langle 0 \ left | t \ left \ { \ phi _ { i } ( x ) \ phi _ { i } ( y ) \ exp \ left [ - i \ int _ { - t } ^ { t } dt \, h _ { i } ( t ) \ right ] \ right \ } \ right | 0 \ right \ rangle } { \ left \ langle 0 \ left | t \ left \ { \ exp \ left [ - i \ int _ { - t } ^ { t } dt \, h _...
Quantum field theory
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Structure mining and unbiased representation of input and output is enough. a particularly relevant area where finding the appropriate structure and model is the key issue is text mining. xpath is the standard mechanism used to refer to nodes and data items within xml. it has similarities to standard techniques for na...
Structure mining
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Scenedesmus obliquus mitochondrial code ##r, t ), tryptophan ( trp, w ), tyrosine ( tyr, y ), valine ( val, v ) = = differences from the standard code = = = = systematic range and comments = = scenedesmus obliquus = = see also = = list of genetic codes = = references = = this article incorporates text from the united ...
Scenedesmus obliquus mitochondrial code
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List of fluid mechanics journals this is a list of scientific journals related to the field of fluid mechanics. = = see also = = list of scientific journals list of physics journals list of materials science journals
List of fluid mechanics journals
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Classical electromagnetism and special relativity the theory of special relativity plays an important role in the modern theory of classical electromagnetism. it gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a lorentz transformation from one inertial ...
Classical electromagnetism and special relativity
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Barnes G-function pi z } { \ pi } } \ right ) + \ log \ gamma ( z ) + { \ frac { 1 } { 2 \ pi } } \ operatorname { cl } _ { 2 } ( 2 \ pi z ) } adamchik ( 2003 ) has given an equivalent form of the reflection formula, but with a different proof. replacing z with 1 / 2 − z in the previous reflection formula gives, after...
Barnes G-function
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Routhian mechanics in classical mechanics, routh's procedure or routhian mechanics is a hybrid formulation of lagrangian mechanics and hamiltonian mechanics developed by edward john routh. correspondingly, the routhian is the function which replaces both the lagrangian and hamiltonian functions. although routhian mech...
Routhian mechanics
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List of protein structure prediction software this list of protein structure prediction software summarizes notable used software tools in protein structure prediction, including homology modeling, protein threading, ab initio methods, secondary structure prediction, and transmembrane helix and signal peptide predicti...
List of protein structure prediction software
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Lyapunov equation the lyapunov equation, named after the russian mathematician aleksandr lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. in particular, the discrete - time lyapunov equation ( also known as stein equation ) for x { \ displaystyle x } is a x a h − x + q = 0 { \...
Lyapunov equation
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Algebra of physical space ′ = l u l †. { \ displaystyle u \ rightarrow u ^ { \ prime } = lul ^ { \ dagger }. } = = = four - momentum paravector = = = the four - momentum in aps can be obtained by multiplying the proper velocity with the mass as p = m u, { \ displaystyle p = mu, } with the mass shell condition translat...
Algebra of physical space
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Calculus on Euclidean space { 0 } | = r } - \ int _ { | z - z _ { 0 } | = \ epsilon } \ right ) { \ frac { f } { z - z _ { 0 } } } dz. } letting → 0 { \ displaystyle \ epsilon \ to 0 } we then get : 2 π i f ( z 0 ) = | z − z 0 | = r f z − z 0 d z + | z − z 0 | ≤ r ∂ f ∂ z d z ∧ d z z − z 0. { \ displaystyle 2 \ pi i \...
Calculus on Euclidean space
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Neural network Gaussian process } \ right ] ; 0, \ sigma _ { w } ^ { 2 } \ left [ { \ begin { array } { cc } k ^ { l - 1 } ( x, x ) & k ^ { l - 1 } ( x, x') \ \ k ^ { l - 1 } ( x ', x ) & k ^ { l - 1 } ( x ', x') \ end { array } } \ right ] + \ sigma _ { b } ^ { 2 } \ right ) \ end { aligned } } } so, in the infinite ...
Neural network Gaussian process
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Routhian mechanics ##φ ). applying the lagrangian approach there are two nonlinear coupled equations to solve. the θ equation is d d t ∂ l ∂ θ = ∂ l ∂ θ ⇒ m ℓ 2 θ ¨ = m ℓ 2 sin θ cos θ 2 − m g ℓ sin θ, { \ displaystyle { \ frac { d } { dt } } { \ frac { \ partial l } { \ partial { \ dot { \ theta } } } } = { \ frac { ...
Routhian mechanics
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Calculus on Euclidean space . for every test function φ { \ displaystyle \ varphi }, we have : ⟨ h ′, φ ⟩ = − 0 ∞ φ ′ d x = φ ( 0 ). { \ displaystyle \ langle h ', \ varphi \ rangle = - \ int _ { 0 } ^ { \ infty } \ varphi'\, dx = \ varphi ( 0 ). } let δ a { \ displaystyle \ delta _ { a } } denote the linear functiona...
Calculus on Euclidean space
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4,082
Expectation value (quantum mechanics) mechanics, in the strict sense ), the states considered are generally normal. however, in other areas of quantum theory, also non - normal states are in use : they appear, for example. in the form of kms states in quantum statistical mechanics of infinitely extended media, and as ...
Expectation value (quantum mechanics)
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Weyl equation rm { l } } \ mapsto d _ { \ rm { l } } ^ { \ prime } = sd _ { \ rm { l } } s ^ { \ dagger } \ qquad d _ { \ rm { r } } \ mapsto d _ { \ rm { r } } ^ { \ prime } = \ left ( s ^ { \ dagger } \ right ) ^ { - 1 } d _ { \ rm { r } } s ^ { - 1 } } whereas the weyl spinors transform as ψ l ↦ ψ l ′ = ( s † ) − 1...
Weyl equation
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