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Longer titles found: Orthogonality (mathematics) (view), Orthogonality (programming) (view), Orthogonality (term rewriting) (view), Orthogonality principle (view), Hyperbolic orthogonality (view), Schur orthogonality relations (view), Anderson orthogonality theorem (view)

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Banach spaces for which the image of the unit ball is bounded. Birkhoff orthogonality Two vectors x and y in a normed linear space are said to be Birkhoff

valuable from the perspective of an artificial intelligence. Bostrom's "orthogonality thesis" argues instead that, with some technical caveats, almost any

AVR is a family of microcontrollers developed since 1996 by Atmel, acquired by Microchip Technology in 2016. These are modified Harvard architecture 8-bit

In database systems, atomicity (/ˌætəˈmɪsəti/; from Ancient Greek: ἄτομος, romanized: átomos, lit. 'undividable') is one of the ACID (Atomicity, Consistency

The Petrov–Galerkin method is a mathematical method used to approximate solutions of partial differential equations which contain terms with odd order

orthogonality to P 0 {\displaystyle P_{0}} and P 1 {\displaystyle P_{1}} , and so on. P n {\displaystyle P_{n}} is fixed by demanding orthogonality to

Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. This method is

In the absence of reflexivity we have to distinguish left and right orthogonality. In a reflexive space the left and right radicals agree and are termed

That is, a sesquilinear form is reflexive precisely when the derived orthogonality relation is symmetric. A σ-sesquilinear form φ is called (σ, ε)-Hermitian

|Hjk|=1 for j,k=1,2,…,N{\displaystyle |H_{jk}|=1{\text{ for }}j,k=1,2,\dots ,N} orthogonality: HH†=NI{\displaystyle HH^{\dagger }=NI}, where †{\displaystyle \dagger

polynomials named after Giulio Racah, as their orthogonality relations are equivalent to his orthogonality relations for Racah coefficients. The Racah polynomials

In mathematics, a symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the

The Cotlar–Stein almost orthogonality lemma is a mathematical lemma in the field of functional analysis. It may be used to obtain information on the operator

stationary point of the Lagrangian under variations of ψi and RI, with the orthogonality constraint. M I R ¨ I = − ∇ I E [ { ψ i } , { R I } ] {\displaystyle

In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight

Wong et al. presented an analysis of the problems that the pairwise orthogonality assumption of the vector space model (VSM) creates. From here they extended

In mathematics, Stieltjes–Wigert polynomials (named after Thomas Jan Stieltjes and Carl Severin Wigert) are a family of basic hypergeometric orthogonal

Orthogonal is a science fiction trilogy by Australian author Greg Egan taking place in a universe where, rather than three dimensions of space and one

Structured Query Language (SQL) (/ˌɛsˌkjuːˈɛl/ S-Q-L, often /ˈsiːkwəl/ "sequel" for historical reasons[clarification needed]) is a domain-specific language

In mathematics, the Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by

morphism w such that the following diagram commutes. The difference with orthogonality is that w is not necessarily unique. A weak factorization system (E

In the context of computer programming, magic is an informal term for abstraction; it is used to describe code that handles complex tasks while hiding

Kravchuk polynomials or Krawtchouk polynomials (also written using several other transliterations of the Ukrainian surname Кравчу́к) are discrete orthogonal

+1};q)_{n}}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x).} Orthogonality is defined by the unimono nature of the polynomials' convergence at

P_{n}^{(\alpha ,\beta )}(1)={n+\alpha \choose n},} and satisfy the orthogonality condition ∫−11(1−x)α(1+x)βPm(α,β)(x)Pn(α,β)(x)dx=2α+β+12n+α+β+1Γ(n+

{\stackrel {\mathrm {def} }{=}}\ {\frac {1}{(x+1){\sqrt {x}}}}} The orthogonality of the Chebyshev rational functions may be written:

w(x;\lambda ,\phi )=|\Gamma (\lambda +ix)|^{2}e^{(2\phi -\pi )x}} and the orthogonality relation is given by ∫ − ∞ ∞ P n ( λ ) ( x ; ϕ ) P m ( λ ) ( x ; ϕ )

in Rn{\displaystyle \mathbb {R} ^{n}} it yields a lattice basis with orthogonality defect at most nn{\displaystyle n^{n}}, unlike the 2n2/2{\displaystyle

orthogonal rate 1 STBCs, that provide ISI free transmissions due to orthogonality. The design of STBCs is based on the so-called diversity criterion derived

In mathematics, the q-Bessel polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A

Kravchuk polynomials or Krawtchouk polynomials (also written using several other transliterations of the Ukrainian surname Кравчу́к) are discrete orthogonal

φ(t) are slowly varying functions compared to 2πft, the assumption of orthogonality is a common one. Authors often call it a narrowband assumption, or a

)\cdot \mathbf {\Phi } _{\ell 'm'}(\mathbf {r} )&=0.\end{aligned}}} The orthogonality relations allow one to compute the spherical multipole moments of a

{\displaystyle L} are generalized Laguerre polynomials. They satisfy the orthogonality relation ∑ x = 0 ∞ μ x x ! C n ( x ; μ ) C m ( x ; μ ) = μ − n e μ n

u ] , {\displaystyle {\begin{bmatrix}p&t\\q&u\end{bmatrix}},} which orthogonality demands satisfy the three equations 1 = p 2 + t 2 , 1 = q 2 + u 2 ,

AA∗=A∗A=nI{\displaystyle AA^{\ast }=A^{\ast }A=nI}. This implies the desired orthogonality relationship for the characters: i.e., ∑k=1nfk∗(gi)fk(gj)=nδij{\displaystyle

The Open Biological and Biomedical Ontologies (OBO) Foundry is a group of people dedicated to build and maintain ontologies related to the life sciences

{49}{96}}x^{3}-{\frac {21}{320}}x^{5}} ; The Bateman polynomials satisfy the orthogonality relation ∫ − ∞ ∞ F m ( i x ) F n ( i x ) sech 2 ⁡ ( π x 2 ) d x = 4

+4)}{2}}\left({\frac {z-1}{2}}\right)^{2}.} The Jacobi polynomials satisfy the orthogonality condition ∫ − 1 1 ( 1 − x ) α ( 1 + x ) β P m ( α , β ) ( x ) P n (

sequences, which are now called Brenke–Chihara polynomials, and found their orthogonality relations. Brenke, W. C. (1945), "On generating functions of polynomial

Riesz lemma or Riesz inequality. It can be seen as a substitute for orthogonality when the normed space is not an inner product space. Riesz's lemma — Let

}(k)J_{\nu }(kr)\,k\,\mathrm {d} k,} which can be readily verified using the orthogonality relationship described below. Inverting a Hankel transform of a function

{3}\\j_{5}&j_{4}&j_{7}\end{Bmatrix}}.} The 9-j symbols satisfy this orthogonality relation: ∑j7j8(2j7+1)(2j8+1){j1j2j3j4j5j6j7j8j9}{j1j2j3′j4j5j6′j7j

detailed list of their properties. The dual Hahn polynomials have the orthogonality condition ∑s=ab−1wn(c)(s,a,b)wm(c)(s,a,b)ρ(s)[Δx(s−12)]=δnmdn2{\displaystyle

contribution to the operator and norm inequality. He has developed the orthogonality in Hilbert C*-modules and has significant contributions to operator

In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown

1&-h_{\mbox{o}}\rightarrow 1\\-g_{\mbox{e}}&h_{\mbox{e}}\end{pmatrix}}} Orthogonality means that the adjoint matrix P∗{\displaystyle \scriptstyle P^{*}} is

{\displaystyle \tan \phi =(Z/p)/((1-e^{2})N+h)/(N+h)).} The orthogonality of the coordinates is confirmed via differentiation:

expression when another j is equal to zero. The 6-j symbols satisfy this orthogonality relation: ∑ j 3 ( 2 j 3 + 1 ) { j 1 j 2 j 3 j 4 j 5 j 6 } { j 1 j 2

In mathematics, the Legendre rational functions are a sequence of orthogonal functions on [0, ∞). They are obtained by composing the Cayley transform with

(b+ix)\,\Gamma (c-ix)\,\Gamma (d-ix).} In particular, they satisfy the orthogonality relation 12π∫−∞∞Γ(a+ix)Γ(b+ix)Γ(c−ix)Γ(d−ix)pm(x;a,b,c,d)pn(x;a,b,c

PDP–11 uses memory-mapped I/O and so the same move instruction is used; orthogonality even enables moving data directly from an input device to an output

some subsets are orthogonal. Assuming 0 ≤ m ≤ ℓ, they satisfy the orthogonality condition for fixed m: ∫ − 1 1 P k m P ℓ m d x = 2 ( ℓ + m ) ! ( 2 ℓ

in Zygo interferometers and the open source software DFTFringe. The orthogonality in the radial part reads ∫ 0 1 2 n + 2 R n m ( ρ ) 2 n ′ + 2 R n ′ m

finite orthogonality. However, for some special cases in which the parameters depend in a particular way on the polynomial degree infinite orthogonality can

Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups

In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of

Modula-3, and Self. The main goals of the project were extensibility, orthogonality, efficiency, and ease-of-use. The language supports multiple dispatch

systematic errors such as polar misalignment, mechanical and optical non-orthogonality, lack of roundness in telescope mounting drive gears, as well as for

In object-oriented programming, a class is an extensible program-code-template for creating objects, providing initial values for state (member variables)

off-diagonal components of the metric tensor are a direct result of the non-orthogonality of the basis vectors of the coordinates, since by definition: g i j

In analytic number theory, the Petersson trace formula is a kind of orthogonality relation between coefficients of a holomorphic modular form. It is a

In analytic number theory, the Petersson trace formula is a kind of orthogonality relation between coefficients of a holomorphic modular form. It is a

systematic errors such as polar misalignment, mechanical and optical non-orthogonality, lack of roundness in telescope mounting drive gears, as well as for

its tone and not at all to the others; this independence provides the orthogonality. Like other M-ary orthogonal schemes, the required Eb/N0 ratio for a

Lp functions for 1 < p < ∞. It is typically used as a substitute for orthogonality arguments which only apply to Lp functions when p = 2. One implementation

In special functions, a topic in mathematics, spin-weighted spherical harmonics are generalizations of the standard spherical harmonics and—like the usual

the orthogonality of r i {\displaystyle {\boldsymbol {r}}_{i}} and conjugacy of p i {\displaystyle {\boldsymbol {p}}_{i}} . Due to the orthogonality of

also requires that these two metrics satisfy a transversality (or "orthogonality") condition, habtbc=0{\displaystyle h^{ab}t_{bc}=0}. Thus, one defines

m_{2}\rangle \equiv \langle j_{1}\,m_{1}\,j_{2}\,m_{2}|J\,M\rangle } The first orthogonality relation is ∑ J = | j 1 − j 2 | j 1 + j 2 ∑ M = − J J ⟨ j 1 m 1 j 2

ISBN 978-0-691-08247-9. Stein, Elias (1993). Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press. ISBN 0-691-03216-5

ascertained. The eigenvectors have very important properties called orthogonality properties. These properties can be used to greatly simplify the solution

{\displaystyle \Gamma (x,\alpha +1,1)} denotes the gamma distribution then the orthogonality relation can be written as ∫ 0 ∞ L n ( α ) ( x ) L m ( α ) ( x ) Γ (

{\displaystyle \ E_{a}^{j}=q_{ab}\ E_{j}^{b}~.} We then have the two orthogonality relationships  δjk=qab Eaj Ebk ,{\displaystyle \ \delta ^{jk}=q^{ab}\

transformation between these two bases, and this unitarity implies the orthogonality relations (2j3+1)∑m1m2(j1j2j3m1m2m3)(j1j2j3′m1m2m3′)=δj3,j3′δm3,m3′{j1j2j3}

p-subgroups. The second and third main theorems allow refinements of orthogonality relations for ordinary characters which may be applied in finite group

In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The

introducing the Hamilton–Jacobi equation approach to mechanics. The orthogonality of mechanical trajectories characteristic of geometrical optics to the

antennas, 12 signals can be extracted from the receiver because of the orthogonality of the transmitted signals. That is, a 12-element virtual antenna array

these estimators are mathematically equivalent to those based on "orthogonality conditions" (Sargan, 1958, 1959) or "unbiased estimating equations"

orthogonal polynomials. He also studied moment problems and found the orthogonality measure for several orthogonal polynomials. This includes the q-ultraspherical

Jn(kρ){\displaystyle J_{n}(k\rho )} , the orthogonality of Jn{\displaystyle J_{n}}, along with the orthogonality relationships of Φn(φ){\displaystyle \Phi

the dimension of the lattice. One measure of nearly orthogonal is the orthogonality defect. This compares the product of the lengths of the basis vectors

isomorphism A ≅ A ^ {\displaystyle A\cong {\widehat {A}}} and 2) the orthogonality relations: ∑ a ∈ A η ( a ) = { | A |  if  η = η 0 0  if  η ≠ η 0 {\displaystyle

expansion coefficients can then, in principle, be computed using the orthogonality relationships: aj,k=2j∫−∞∞f(t)⋅w∗(2jt−k)dta~j,k=2j∫−∞∞f(t)⋅w(2jt−k)

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets

Orbitals from different pairs are forced to be orthogonal - the strong orthogonality condition. This condition simplifies the calculation but can lead to

the orthogonality of the density with spiciness and the used scaling factor of potential temperature and salinity. McDougall claims that orthogonality should

ideal dual-polarization system lies its foundation onto the perfect orthogonality of the two polarization states, and any of the single-polarized interfaces

Orbitals from different pairs are forced to be orthogonal - the strong orthogonality condition. This condition simplifies the calculation but can lead to

P_{n}(x;c;q)={}_{3}\phi _{2}(q^{-n},q^{n+1},x;q,cq;q,q)} . They obey the orthogonality relation ∫ c q q P m ( x ; c ; q ) P n ( x ; c ; q ) d x = q ( 1 − c

measurement space (called innovation sequence, which naturally includes the orthogonality principle in its derivations to yield an independence relation and therefore

44=4\cdot 33}. For m,n∈N{\displaystyle m,n\in \mathbb {N} } the following orthogonality relation holds: ∫−∞∞gn(−iy)gm(iy)ysinh⁡πydy=12nδmn.{\displaystyle \int

_{i=1,2,3}UW_{i,j}} A fundamental property of origami matrices, called orthogonality, is that the order in which dimensions are contracted does not matter

harmonic, integrating over the solid angle Ω, and utilizing the above orthogonality relationships. This is justified rigorously by basic Hilbert space theory

q)} and se n ( x , q ) {\displaystyle {\text{se}}_{n}(x,q)} satisfy orthogonality relations ∫ 0 2 π ce n ce m d x = ∫ 0 2 π se n se m d x = δ n m π ∫

Self-reflexivity (see Self-reference) Bilinear form § Reflexivity and orthogonality Reflectivism Reflexive (disambiguation) Reflexive operator algebra –

_{i}\}_{i=p+1}^{M}} that spans the noise subspace. In order to measure the degree of orthogonality of e{\displaystyle \mathbf {e} } with respect to all the vi∈UN{\displaystyle

K. (2019). "Multi-Objective Model Updating Optimization Considering Orthogonality". Journal of Computational and Nonlinear Dynamics. 14 (6): 1–11. doi:10

whose sum stays below the identity. Such pairs are called orthogonal; orthogonality reflects simultaneous measurability of observables. An effect algebra

j we are able to find the magnitude of the interorbital angle. The orthogonality condition implies the relation known as Coulson's theorem:   1 + λ i

ISBN 978-0201616224. Dave Thomas, interviewed by Bill Venners (2003-10-10). "Orthogonality and the DRY Principle". Retrieved 2006-12-01. Object Oriented Software

_{2}&\gamma \\&&\nu \end{pmatrix}}.} Also, they follow the following orthogonality relations, ∑ ν 1 , ν 2 ( μ 1 μ 2 γ ν 1 ν 2 ν ) ( μ 1 μ 2 γ ′ ν 1 ν 2

steric complementarity while maintaining biochemical competence and orthogonality to the wild type pair. Typically, a "bumped" ligand/inhibitor analog

Semigroup Vector space Affine representation Character theory Great orthogonality theorem Maschke's theorem Monstrous moonshine Projective representation

The Dolinar Receiver is a device based upon the Kennedy receiver that may be used to discriminate between two or more low-amplitude coherent states of

variables is valuable as it enables multiple PPG applications, including orthogonality in systems with multiple protecting groups. As the removal of a PPG

Maria; Pérez, T. E.; Piñar, M. A.; Ronveaux, A. (1999). "Non-standard orthogonality for Meixner Polynomials" (PDF). Electron. Trans. Numer. Anal. 9: 1–25

with λi<1{\displaystyle \lambda _{i}<1} remain unchanged due to their orthogonality to the constant left vector at λ=1{\displaystyle \lambda =1}. The gap

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a sequence of random

MR 2723248. Costas-Santos, R.S.; Sánchez-Lara, J.F. (September 2011). "Orthogonality of q-polynomials for non-standard parameters". Journal of Approximation

which the absolute value of its determinant is 1, also because of the orthogonality. Using these facts and the form of the VMF density, it follows that:

MR 2723248. Costas-Santos, R.S.; Sánchez-Lara, J.F. (September 2011). "Orthogonality of q-polynomials for non-standard parameters". Journal of Approximation

character functions of representations. These properties follow from the orthogonality relations for characters of representations of finite groups. For any

Programming, Systems, Languages, and Applications Open/closed principle Orthogonality Overload Package Parametric overloading Parameterized classes Parnas's

coefficient for ri has to be nonnegative. The third is true because orthogonality is a symmetric relation. And lastly, let Dij=δij(ri,ri){\displaystyle

restricted to relatively small molecules, largely due to the lack of orthogonality between valence bond orbitals and between valence bond structures, while

+2k)\int _{0}^{\infty }f(z){\frac {J_{\nu +2k}(z)}{z}}\,dz} due to the orthogonality relation ∫ 0 ∞ J α ( z ) J β ( z ) d z z = 2 π sin ⁡ ( π 2 ( α − β )

MR 2723248. Costas-Santos, R.S.; Sánchez-Lara, J.F. (September 2011). "Orthogonality of q-polynomials for non-standard parameters". Journal of Approximation

Hyperdimensional computing (HDC) is an approach to computation, particularly artificial intelligence. HDC is motivated by the observation that the cerebellum

NMF. When the orthogonality constraint H H T = I {\displaystyle \mathbf {H} \mathbf {H} ^{T}=I} is not explicitly imposed, the orthogonality holds to a large

include calculating grid quantities (e.g. aspect ratios, skewness, orthogonality and stretch factors), normalizing data; Deriving flow field functions

if their normal vectors are orthogonal and in a nondefinite metric orthogonality does not imply transversality. Given a smooth manifold of dimension

(1984), "A survey of basic stability theory, with particular emphasis on orthogonality and regular types", Israel Journal of Mathematics, 49 (1–3): 181–238

arithmetic, unlimited-sized lists and strings, and other features supporting orthogonality and ease of use by novices ABC was originally a monolithic implementation

W.; Jaschke, Paul R. (2019-03-15). "Measuring Amber Initiator tRNA Orthogonality in a Genomically Recoded Organism" (PDF). ACS Synthetic Biology. 8 (4):

{1-x^{2}}}}. Zernike polynomials are defined on the unit disk and have orthogonality of both radial and angular parts. Walsh functions and Haar wavelets

transport of the spin tensor along the trajectory – but one preserving orthogonality to the momentum vector k μ {\displaystyle k^{\mu }} rather than to the

integral, exchanging the order of integration and summation, and using the orthogonality of the cosines, the entropy may be written: H=−c0−2∑m=1∞ϕmcm=−ln⁡(1

load-bearing structures and internal partitions creating, through the orthogonality of the entrance gallery and the entrance hall of the Palace, a unique

computation, Information Causality, Macroscopic Locality, and Local Orthogonality. All these principles limit the set of possible correlations in non-trivial

computation, Information Causality, Macroscopic Locality, and Local Orthogonality. All these principles limit the set of possible correlations in non-trivial

images of the parallels and meridians intersect at right angles. This orthogonality property is a consequence of the angle-preserving property of the stereographic

Cheikh, Y. Ben; Lamiri, I.; Ouni, A. (2009), "On Askey-scheme and d-orthogonality, I: A characterization theorem", Journal of Computational and Applied

Sons. Stein, Elias (1993), Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton University Press. Bruss, F. Thomas

v{\displaystyle v} in Vh.{\displaystyle V_{h}.} We used the a{\displaystyle a}-orthogonality of u−uh{\displaystyle u-u_{h}} and v−uh∈Vh{\displaystyle v-u_{h}\in

properties: Its eigenvalues are real, λi = λi* Its eigenfunctions obey an orthogonality condition, ⟨ f i , f j ⟩ = 0 {\displaystyle \langle f_{i},f_{j}\rangle

defined on the interval [ a , b ] {\displaystyle [a,b]} satisfying the orthogonality condition ∫ a b P m ( x ) P n ( x ) w ( x ) d x = K n δ m , n , {\displaystyle

363–366. E. Torrance, Strictly convex spaces via semi-inner-product space orthogonality, Proceedings of the American Mathematical Society 26 (1970), 108–110

transform has a non-trivial kernel, but from the no-slip condition follows orthogonality of the vorticity flow to the kernel. Special Weber's transform is an

the positive operator-valued measure (POVM), where the need for the orthogonality implied by projection operators is replaced by the idea of a set of

unit from stratum k if Hhk = −1 and the second unit if Hhk = +1. The orthogonality of rows of H ensures that our choices are uncorrelated between half-samples

, where matrix multiplication works as intended because of the orthogonality of the projections. In order to identify A with a matrix ring over a

{\displaystyle D} satisfies D = D ⊥ {\displaystyle D=D^{\perp }} , where orthogonality is with respect to the symmetric bilinear form on V × V ∗ {\displaystyle

condition numbers of random matrices, the geometry of algorithms with orthogonality constraints, the geometry of the generalized singular value decomposition

data operations on an RDF graph should result in another RDF graph Orthogonality: data operations are independent of the context in which they are used

x2+y2≤1,n≥0,|m|≤n{\displaystyle x^{2}+y^{2}\leq 1,n\geq 0,|m|\leq n} and orthogonality on the unit disk is given as ∫02π∫01r[Vnl(rcos⁡θ,rsin⁡θ)]∗×Vmk(rcos⁡θ

directions to fight this stability issue: Prevent the loss of orthogonality, Recover the orthogonality after the basis is generated. After the good and "spurious"

}c_{m}\phi _{n}\int _{\Gamma }e^{i(m-n)\theta }\,d\theta }. Using the orthogonality of the Fourier basis, the integral may be reduced to: H=−∑n=−∞∞cnϕn{\displaystyle

1007/BF02392052 Elias Stein, Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press, 1993. ISBN 0-691-03216-5

feature engineering methods have been reported in literature, including Orthogonality constrained factorization for hard clustering and manifold learning

coefficients χ(a)); the converse is also true, as a consequence of the orthogonality relations for the group (Z/nZ)×. In other words, the Gaussian periods

a fixed point is rotation Euler's theorem (differential geometry) – Orthogonality of the directions of the principal curvatures of a surface Euler's theorem

{\displaystyle Q} and Λ {\displaystyle \Lambda } are also real. To see orthogonality, suppose x {\displaystyle \mathbf {x} } and y {\displaystyle \mathbf

coefficients χ(a)); the converse is also true, as a consequence of the orthogonality relations for the group (Z/nZ)×. In other words, the Gaussian periods

for finite groups has a square character table with row and column orthogonality properties. With a slightly different definition of conjugacy classes

Murphy, Timothy S. (1993). Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton: Princeton University Press. ISBN 0-691-03216-5

Merrifield in 1977. For peptide synthesis via automated machine, the orthogonality of the Fmoc group (basic cleavage), the tert‑butyl group (acidic cleavage)

High angle of attack typically ranges from 60 to 80 degrees. (3) The orthogonality between the surface of the wing and ascending trajectory of the sea

that are both closed and co-closed: that is, of harmonic forms. Here, orthogonality is defined with respect to the L2 inner product on Ωk(M){\displaystyle

integral, exchanging the order of integration and summation, and using the orthogonality of the cosines, the entropy may be written: H=ln⁡(2πI0(κ))−κϕ1=ln⁡(

r^{2}\left|R_{l}(r)\right|^{2}=1} which in general does not impose orthogonality in l{\displaystyle l}. Because an individual primitive Gaussian function

Shelah's classification program, such as regular types, forking, and orthogonality, allowed these ideas to be carried to greater generality, especially

Bn{\displaystyle B_{n}} from the initial conditions by taking advantage of the orthogonality of Fourier components. mode n = 1 mode n = 2 Consider a rectangular

 486 Stein, Elias (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press. Atiyah, Michael

C\lambda ^{-n/2}.} Elias Stein, Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press, 1993. ISBN 0-691-03216-5

proved two of Saffari's conjectures, the phase problem and the near orthogonality conjecture. In 2007, working with Borwein, Ferguson, and Lockhart, he

to the remaining eigenvector of A, with eigenvalue 1, because of the orthogonality of the eigenvectors of A. A vector is said to be rotating if it changes

Programming, Lecture Notes in Computer Science 130, Springer-Verlag. 1987: Orthogonality and Spacetime Geometry, Universitext Springer-Verlag ISBN 0-387-96519-X

\mu }\right)^{-1}.} We must also have an equivalent condition to the orthogonality condition of the Poincaré transformations: AAT+BC=DDT+CB{\displaystyle

of q1,…,qk−1{\displaystyle q_{1},\dots ,q_{k-1}}. This ensures the orthogonality of all the generated vectors. The algorithm breaks down when qk is the

c_{k}\epsilon ^{1/k}} . Elias Stein, Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press, 1993. ISBN 0-691-03216-5

multi-threaded multiprocessor, or networked—under a single model. Its orthogonality allows processes computing in different languages and platforms to interoperate

of T moreover σ(U) = K and σ(V) = σ(T) \ K. A key property is mutual orthogonality. If L is another open and closed set in the subspace topology on σ(T)

distinctive modulation characteristics, including Spreading Factor orthogonality, and the capability for below noise-floor communication. This adaptation

849–854. MR0045131 doi:10.1090/S0002-9939-1951-0045131-2 Tadasi Nakayama. Orthogonality relation for Frobenius- and quasi-Frobenius-algebras . Proc. Amer. Math

"Pyrrolysyl-tRNA synthetase:tRNAPyl structure reveals the molecular basis of orthogonality". Nature. 457 (7233): 1163–1167. Bibcode:2009Natur.457.1163N. doi:10

subsequent pairs are found by using eigenvalues of decreasing magnitudes. Orthogonality is guaranteed by the symmetry of the correlation matrices. Another way

ISSN 0022-4715. S2CID 13923422. Lewis, Peter J. (1997). "Quantum Mechanics, Orthogonality, and Counting". The British Journal for the Philosophy of Science. 48

where Pn has degree n. But the above answer for the case r = 2 gives an orthogonality relation, whence the Pn's are the Laguerre polynomials (up to a sign

turbine axis could be vertical or horizontal, the only requirement is orthogonality to the flow. The GHT is a unidirectional turbine, operating under a

have a high degree of column collinearity, NIPALS suffers from loss of orthogonality of PCs due to machine precision round-off errors accumulated in each

ISSN 0022-4715. S2CID 13923422. Lewis, Peter J. (1997). "Quantum Mechanics, Orthogonality, and Counting". The British Journal for the Philosophy of Science. 48

original on December 10, 2012. Retrieved November 14, 2011. "Crackpotness Orthogonality - ScienceBits". www.sciencebits.com. Smith, Douglas L.; Dietrich, Jane

{red}\lambda _{2}}<b^{2}<{\color {red}\lambda _{3}}<a^{2}\ .} Proof of the orthogonality of the surfaces: Using the pencils of functions Fλ(x,y

fully recovers the set of all two-point quantum correlators. Local Orthogonality (LO). This principle applies to multipartite Bell scenarios, where n{\displaystyle

form an orthogonal basis. This is a major difference with PCA where orthogonality is imposed onto loadings (and not the scores). A number of variants

Orthogonality of the directions of the principal curvatures of a surface

R_{ijkl}R^{ijkl}=S_{ijkl}S^{ijkl}+E_{ijkl}E^{ijkl}+W_{ijkl}W^{ijkl}.} This orthogonality can be represented without indices by ⟨S,E⟩g=⟨S,W⟩g=⟨E,W⟩g=0,{\displaystyle

importing the classical code, it must satisfy the dual-containing (or self-orthogonality) constraint. Researchers have found many examples of classical codes

absurd final goals, e.g. making paperclips), a concept he calls the orthogonality thesis. He argues that an AI with the ability to improve itself might

determined. Substitute (9) and (10) back to (8) and considering the orthogonality of sine functions we get u n ′ ( t ) + α n 2 π 2 L 2 u n ( t ) = h n

its neighbours: it is not confined to a 4.3125 kHz wide channel. The orthogonality of COFDM makes this possible without interference. Up to 15 bits per

iterations. On the other hand, GMRES tends to suffer less from loss of orthogonality. The MINRES method iteratively calculates an approximate solution of

with Vladimir Nikolaevich Sorokin: Rational approximations and orthogonality. AMS. 1991. L. D. Faddeev; A. A. Gonchar; B. S. Kashin; A. I. Kostrikin;

1093/biomet/72.1.1. ISSN 0006-3444. Cox, D. R.; Reid, N. (1987). "Parameter Orthogonality and Approximate Conditional Inference". Journal of the Royal Statistical

Nevertheless, because these polynomials can be defined in terms of orthogonality with respect to a nonnegative weight function, the entire theory of

theorem or the variational principle have been used. The choice of orthogonality product used to establish the eigenmode base. Some references use the

vectors, p, one concludes that every rotation matrix, Q, satisfies the orthogonality condition, Q T Q = I . {\displaystyle Q^{\mathsf {T}}Q=I.} Rotations

Astronomi och Fysik. 30: 1–18. 1948. Löwdin, Per-Olov (1950). "On the non-orthogonality problem connected with the use of atomic wave functions in the theory

_{k}}\right|^{\frac {2}{\alpha }}d\theta _{1}\cdots d\theta _{n}} This orthogonality property is unaffected by normalization. The normalization defined above

agents may have various possible final goals. Note that by Bostrom's orthogonality thesis, final goals of knowledgeable agents may be well-bounded in space

⟩ {\textstyle T|n\rangle } that is orthogonal to the first one. The orthogonality property is crucial, as it means that the two eigenstates | n ⟩ {\textstyle

the transverse part of X a ; b {\displaystyle {X^{a}}_{;b}} . This orthogonality relation holds only when X is a timelike unit vector of a Lorentzian

apparent orthogonality of the Big Five was largely due to the nature of the analysis techniques used to derive it rather than any inherent orthogonality. Through

expanding the internal field in terms of SVWFs and exploiting their orthogonality on spherical surfaces, one arrives at an expression for the T-matrix

dimension of the last irreducible representation. Finally using the orthogonality of irreducible representations, we can complete the character table

_{k}}\right|^{\frac {2}{\alpha }}d\theta _{1}\cdots d\theta _{n}} This orthogonality property is unaffected by normalization. The normalization defined above

8245–8252. doi:10.1021/j100084a048. Löwdin, Per‐Olov (1950). "On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory

can be repeated for a prescribed number of times to correct for non-orthogonality. Predictor step Guess the pressure field p ∗ {\displaystyle p^{*}} and

these estimators are mathematically equivalent to those based on "orthogonality conditions" (Sargan, 1958, 1959) or "unbiased estimating equations"

new performance measures should be orthogonal to existing metrics. Orthogonality, or non-redundancy, does not necessarily indicate null correlation.

certainly be normalized, as it is the sum of two normalized wavefunctions. Orthogonality must be established so that the two hybrid orbitals can be involved

expanding the internal field in terms of SVWFs and exploiting their orthogonality on spherical surfaces, one arrives at an expression for the T-matrix

_{k}^{T}\mathbf {w} _{k}{\sqrt {P_{k}}}s_{k}+n_{k},\quad k=1,2,\ldots ,K} The orthogonality condition can be expressed in matrix form as HTW=Q{\displaystyle \mathbf

neoclassical characteristics, interpreted in the width of the streets and the orthogonality of their blocks. These followed the sinuosities of the river, due to

optimal constants when the functions are assumed to satisfy certain orthogonality constraints. Such results are naturally applicable to many problems

supplied to the medium. Xenobiological systems are designed to convey orthogonality to natural biological systems. A (still hypothetical) organism that

eiω2t⟨2|{\displaystyle e^{i\omega _{2}t}\langle 2|}, and using the orthogonality condition of eigenstates ⟨i|j⟩=δi,j{\displaystyle \langle i|j\rangle

surface atoms. Further the energy of the system will increase due to the orthogonality of wavefunctions of the approaching atom and surface atoms. This Pauli

him. Under the Petersson metric it is shown that we can define the orthogonality on the space of modular forms as the space of cusp forms and its orthogonal

which again come from the Hodge–Riemann bilinear relations. These are: Orthogonality: FpHk(Xb, C) is orthogonal to Fk − p + 1Hk(Xb, C) with respect to Q

Wright BW, Jaschke PR (April 2019). "Measuring Amber Initiator tRNA Orthogonality in a Genomically Recoded Organism". ACS Synthetic Biology. 8 (4): 675–685

→ 2 {\displaystyle {\vec {r}}_{1},{\vec {r}}_{2}} are noisy and the orthogonality condition of the attitude matrix (or the direction cosine matrix) is

1140/epjd/e2004-00192-1. S2CID 117346954. de Castro, Antonio S. (April 4, 2007). "Orthogonality criterion for banishing hydrino states from standard quantum mechanics"

of p. This coordinate system is automatically isothermal, since the orthogonality of du{\displaystyle du} and dv{\displaystyle dv} implies the diagonality

allow real eigenvalues to be found, corresponding to measurements. Orthogonality allows a suitable basis set of vectors to represent the state of the

Ain=i{\displaystyle {\mathcal {A}}_{i_{n}=i}} have the properties of all-orthogonality: two sub tensors Ain=i{\displaystyle {\mathcal {A}}_{i_{n}=i}} and Ain=j{\displaystyle

paperclips. Lantz argues that Universal Paperclips reflects a version of the orthogonality thesis, which states that an agent can theoretically have any combination

Wm roughly covers the band [1/2m−1, 1/2m]. From those inclusions and orthogonality relations, especially V 0 ⊕ W 0 = V − 1 {\displaystyle V_{0}\oplus W_{0}=V_{-1}}

W.; Jaschke, Paul R. (2019-03-11). "Measuring Amber Initiator tRNA Orthogonality in a Genomically Recoded Organism". ACS Synthetic Biology. 8 (4): 675–685

a given channel, there exists a canonical form distinguished by the orthogonality relation of Kraus operators, Tr⁡Ai†Aj∼δij{\displaystyle \operatorname

(as measured by the residuals) at the highest level are uncorrelated. Orthogonality of regressors to random effects The regressors must not correlate with

perspective obtained from the entrance door of the Palazzetto through the orthogonality of the entrance gallery with the facade of the palace overlying to the

& Hall. ISBN 9780412494406. Cox, D. R.; Reid, N. (1987). "Parameter orthogonality and approximate conditional inference (with discussion)". J. Royal Statistical

camera itself. If some of the intrinsic parameters are given as data (orthogonality of the image or optical center coordinates) the number of images required

constraints on the six Plücker coordinates are the homogeneity constraint the orthogonality constraint A line representation is minimal if it uses four parameters

and voltages by using the circuit topology. Roth translates Kron’s "orthogonality conditions" into exact sequences of homology or cohomology. Roth’s interpretation

Kazuo; Nakamura, Gen; Oharu, Shinnosuke (1986-01-01). "Riesz's lemma and orthogonality in normed spaces" (PDF). Hiroshima Mathematical Journal. 16 (2). Hiroshima

Hamiltonian, and form an overcomplete basis which consequentially lacks orthogonality. The coherent states are indexed by α ∈ C and expressed in the |n⟩ basis

P_{2}(x)={\frac {1}{2}}(3x^{2}-1)\,,\quad \dots } Note especially the orthogonality relations ⟨Pi,Pj⟩L2([−1,1])=22i+1δij∀i,j∈N0.{\displaystyle \left\langle

different principal components are orthogonal. In order to achieve orthogonality, additional constraints must be enforced. The following equivalent definition

of the work concerning "real" orthogonal polynomials (i.e. with the orthogonality condition defined on the real line) and Hermitian random matrices. Perhaps

the new town in other districts. Structure, however, maintained the orthogonality of the monumental complex of the Jesuit College and by a dense corollary

selectively when necessary. (The main benefit of the sib byte is the orthogonality and more powerful addressing modes it provides, which make it possible

be hyperbolic-orthogonal if ⟨z, w⟩ = 0. While analogous to ordinary orthogonality, particularly as it is known with ordinary complex number arithmetic

25l..55E. doi:10.1063/1.3071146. Gelman, Harry (1968). "The second orthogonality conditions in the theory of proper and improper rotations: Derivation

Selecting a basis formed from vectors that spans the lattice, neither orthogonality nor unit length is guaranteed, only linear independence. However the

different principal components are orthogonal. In order to achieve orthogonality, additional constraints must be enforced. The following equivalent definition

conditions. The alkyne is not as small, but it still has the stability and orthogonality necessary for in vivo labeling. Cyclooctynes are traditionally the most

Selecting a basis formed from vectors that spans the lattice, neither orthogonality nor unit length is guaranteed, only linear independence. However the

the compiler. This also reduced the number of addressing modes and orthogonality. The computer designs based on this theory were called reduced instruction

the new town in other districts. Structure, however, maintained the orthogonality of the monumental complex of the Jesuit College and by a dense corollary

differentiate it from the local field using either the approximate orthogonality or the harmonic property. The background field can also be directly

_{g}\notin H^{\perp }\end{cases}}} Proof This can be derived from the orthogonality of characters. The characters of G{\displaystyle G} form an orthonormal

analysis for the Couette flow), the cross terms arising from the non-orthogonality of the eigenvalues can increase transiently. Thus, the total energy

x)\qquad n=1,2,\ldots } with the real eigenvalues n2π2; the well-known orthogonality of the sine functions follows as a consequence of A being symmetric

these terms, the delta function provides a suggestive statement of the orthogonality property of the Fourier kernel on R. Formally, one has ∫ − ∞ ∞ e i 2

step can be proved by using a Taylor series expansion, and using the orthogonality of the states | g ⟩ {\displaystyle |{\text{g}}\rangle } and | e ⟩ {\displaystyle

reflection," Optics Commun. 31, 257—258 (December 1979). A. E. Siegman, "Orthogonality properties of optical resonator eigenmodes," Opt. Commun. 31, 369—373

"Random Sampling-High Dimensional Model Representation (RS-HDMR) and orthogonality of its different order component functions". Journal of Physical Chemistry

boundary conditions. Here, the projections are accomplished by the orthogonality of the solenoidal and irrotational function spaces. The discrete form

{intersection, orthogonal sum, orthogonal complement, inclusion, and orthogonality} respectively, where Q1⊥Q2≡Q1⊃¬Q2{\displaystyle Q_{1}\bot Q_{2}\equiv

associated plane.) Listing's law can be deduced without starting with the orthogonality assumption. If one assumes that all achieved eye orientations can be

Geometric figures are objects in space; Logical independence is geometric orthogonality; Numbers are sets, object collections, physical segments, points on

coordinate chart, and (in a Lorentzian manifold), so do the notions of orthogonality and length. Thus, just like vector fields and other geometric quantities

their approaches, these derivations share a common topic—proving the orthogonality of the residuals and conjugacy of the search directions. These two properties

Bagaria; C. Casacuberta; A.R.D. Mathias & J. Rosický (2015). "Definable orthogonality classes in accessible categories are small". Journal of the European

gammas will themselves satisfy the Clifford relations, because of the orthogonality of the Lorentz transformation. By the fundamental theorem, one may replace

X-e_{X}(Y)} is orthogonal to the space M of all functions of Y. This orthogonality condition, applied to the indicator functions f ( Y ) = 1 Y ∈ H {\displaystyle

Random Sampling-High Dimensional Model Representation (RS-HDMR) and orthogonality of its different order component functions. Journal of Physical Chemistry

we return to the rotation matrix R. It follows from its realness and orthogonality that we can find a U such that: RU=U(eiϕ000e−iϕ000±1){\displaystyle

point in between is a copy of the corresponding bit of an endpoint. Orthogonality, x ⊥ y: Point x is orthogonal to point y, or the two are perpendicular