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Longer titles found: Linear combination of atomic orbitals (view), Symmetry-adapted linear combination (view)

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PLATO (Package for Linear-combination of ATomic Orbitals) is a suite of programs for electronic structure calculations. It receives its name from the choice

quadratic function of a multinormal variable (normal vector), or a linear combination of different normal variables and squares of normal variables. Equivalently

In algebraic topology, a k-chain is a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes)

of the circuit F(x) when a linear combination of signals ax1(t) + bx2(t) is applied to it is equal to the linear combination of the outputs due to the

In mathematics, a formal sum, formal series, or formal linear combination may be: In group theory, an element of a free abelian group, a sum of finitely

multi-electron system. Mathematically, configuration simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification

low-lying excited states or in bond-breaking situations). It uses a linear combination of configuration state functions (CSF), or configuration determinants

Tibshirani. Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then the LARS algorithm provides

local coordinates. In a local coordinate system, a one-form is a linear combination of the differentials of the coordinates: α x = f 1 ( x ) d x 1 + f

the complex amplitude (phasor). A linear combination of such functions can be represented as a linear combination of phasors (known as phasor arithmetic

and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known

In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability

theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the same distribution

predictions are exactly correct and a value of 0 indicating that no linear combination of the independent variables is a better predictor than is the fixed

function has an elementary antiderivative, then this antiderivative is a linear combination of logarithms, where the coefficients and the arguments of the logarithms

expressing the signature of a smooth closed oriented manifold by a linear combination of Pontryagin numbers called the L-genus. It was used in the proof

is known as a linear combination of experts. It can be seen that most forms of neural network are some subset of a linear combination: the standard neural

new position ( x 1 {\textstyle x_{1}} ) can then be expressed as a linear combination of the search vectors i.e. x 1 = x 0 + ∑ i = 1 N α i s i {\textstyle

that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural numbers,

similar but simpler variance swaps, which can be replicated with a linear combination of options and a dynamic position in futures. The difference between

decision theory, the weighted sum model (WSM), also called weighted linear combination (WLC) or simple additive weighting (SAW), is the best known and simplest

environment. In essence, PRT computes the illumination of a point as a linear combination of incident irradiance. An efficient method must be used to encode

the elements of the identity matrix. Functions can be written as a linear combination of the basis functions, f ( t ) = ∑ j = 1 n b j u j ( t ) , {\displaystyle

algebra) Largest remainder method (voting systems) Level-set method Linear combination of atomic orbitals molecular orbital method (molecular orbitals) Method

constraints. Importantly, the spectrum produced by a mixture forms a linear combination of the component spectra, enabling relative chemical content to be

S2CID 19777585. Bausch, J. (2013). "On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String

two-form can be expressed as a linear combination of tensor products of pairs of vectors, especially a linear combination of tensor products of pairs of

considered a non-linear approach as the mapping cannot be represented as a linear combination of the original variables as possible in techniques such as principal

mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology

common divisor of any two elements exists and can be written as a linear combination of them (Bézout's identity). In particular, the existence of efficient

polynomials. Any product of Schur polynomials can be written as a linear combination of Schur polynomials with non-negative integral coefficients; the

vectors, such that every column of the matrix can be written as a linear combination of those vectors. For the nonnegative rank, it is required that the

vectors, such that every column of the matrix can be written as a linear combination of those vectors. For the nonnegative rank, it is required that the

numbers is rationally independent if none of them can be written as a linear combination of the other numbers in the collection with rational coefficients

expresses a function of a matrix f(A) as a matrix polynomial, namely a linear combination of that function's values on the eigenvalues of A. Let A be a diagonalizable

psychophysical data. The probability of response is related to a linear combination of predictors by means of a sigmoid link function (e.g. probit, logit

Bravais lattice. (Note that the plane is not always orthogonal to the linear combination of direct or original lattice vectors h a 1 + k a 2 + ℓ a 3 {\displaystyle

T_{0}} is a constant scalar field 3. T 0 {\displaystyle T_{0}} is a linear combination of products of delta functions δ a b {\displaystyle \delta _{a}^{b}}

the 1953 horror film, It Came from Outer Space. The game is a non-linear combination of dialogue boxes and several types of action scenes, typical of contemporary

to be independent of each other and therefore can be written as a linear combination: These two parameters are treated as independent terms because of

correspondence has valence k if and only if it is homologous to a linear combination a(C×1) + b(1×C) – kΔ where Δ is the diagonal of C×C. The Chasles–Cayley–Brill

non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties

chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. A CSF must not be confused with a configuration

induced characters states that a character on a finite group is a linear combination with integer coefficients of characters induced from elementary subgroups

represent Y. It works by finding the linear combination of X variables, i.e. X1, X2 etc., and linear combination of Y variables, i.e. Y1, Y2 etc., which

ways one can represent a vector (weight) as a non-negative integer linear combination of the positive roots Δ + ⊂ Δ {\displaystyle \Delta ^{+}\subset \Delta

filter for each orientation, a steerable filter is synthesized from a linear combination of a small, fixed set of "basis filters". This approach is efficient

method of modeling the behavior of a viscoelastic material using a linear combination of springs and dashpots to represent elastic and viscous components

Slater-type functions (STFs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. They are named after

whose value is uncertain at contract date, can be decomposed as a linear combination of its Arrow–Debreu securities, and thus as a weighted sum of its

(again, up to the specific choice of normalization). By a simple linear combination of solid harmonics of ±m these functions are transformed into real

{\displaystyle M} , such that every element of M {\displaystyle M} is a linear combination of these vectors with non-negative integer coefficients. The semigroup

network, and secondly connect a desired output signal by a trainable linear combination of all these response signals. Another feature of the ESN is the autonomous

theory, Eaton's inequality is a bound on the largest values of a linear combination of bounded random variables. This inequality was described in 1974

Slater determinants for the description of the wavefunction as a linear combination of these determinants. Based on the freedom left for the occupation

There is another possible branching, under which the hypercharge is a linear combination of an SU(5) generator and χ. This is known as flipped SU(5). Another

statistics, an L-estimator (or L-statistic) is an estimator which is a linear combination of order statistics of the measurements. This can be as little as

methods, often for the surface. The solutions are represented with the linear combination of pre-defined basis functions; generally, the coefficients of these

completed his PhD in mathematics in 1939 with a thesis entitled, "Linear Combination of Data with Least Error of Differences". Buchan was awarded an MBE

methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely used

resulting coefficients are made to minimize the error between the linear combination of test functions, and actual solution, in a chosen norm. It is often

determined by setting z = 1 in such an equation. Here F is a non-zero linear combination of the third-degree monomials ⁠ x 3 , y 3 , z 3 , x 2 y , x 2 z ,

coefficients of the linear combination of those basis polynomials that give the spline on that interval c0, ..., ck–2 Add up that linear combination of basis polynomial

time associated with that signal. By representing any signal as the linear combination of the wavelet functions, we can localize the signals in both time

suppose some linear combination of the vectors is 0. Applying ⁠ A − λ I , {\displaystyle A-\lambda I,} ⁠ we get some linear combination of pi, with the

{\displaystyle T=a{\dot {\gamma }}(t)+bt{\dot {\gamma }}(t)} is a linear combination of trivial Jacobi fields and I ( t ) {\displaystyle I(t)} is orthogonal

generating set of a module M, then every element of M is a (finite) R-linear combination of some elements of Γ; i.e., for each x in M, there are r1, ..., rm

algorithm, in computational fluid dynamics Simple function, a finite linear combination of indicator functions of measurable sets Simple machine, a mechanical

absent or invisible. The "strength" of an interpersonal tie is a linear combination of the amount of time, the emotional intensity, the intimacy (or mutual

many c e {\displaystyle c_{e}} are nonzero. It is called a formal linear combination of elements of E. A similar argument shows that every free left (resp

an update function in which each bit of the state is updated by a linear combination of the same bit and a function of a subset of its less significant

manifold is a cobordism invariant, and in particular is given by some linear combination of its Pontryagin numbers. For example, in four dimensions, it is

The superposition principle means that a linear combination of inputs to the system produces a linear combination of the individual zero-state outputs (that

a reproducing kernel Hilbert space can be represented as a finite linear combination of kernel products evaluated on the input points in the training set

inequality Eaton's inequality, a bound on the largest absolute value of a linear combination of bounded random variables Emery's inequality Entropy power inequality

finite-dimensional linear space, a quadratic form x↦f(x) is always a (finite) linear combination of products x↦g(x) h(x) of two linear functionals g and h. Therefore

basis. The transformation that describes the new basis vectors as a linear combination of the old basis vectors is defined as a covariant transformation

t_{k}(x_{k})=1} and that t k ( x ) {\displaystyle t_{k}(x)} is a linear combination of the right powers of e i x {\displaystyle e^{ix}} . Upon using the

of roots of unity. A quadratic Gauss sum can be interpreted as a linear combination of the values of the complex exponential function with coefficients

Rutledge) was entitled "The Approximation of Functions and Integrals by a Linear Combination of Functions".On January 2, 1933 he married Charlotte Louise Zander

such that any dominant integral weight is a non-negative integer linear combination of the fundamental weights. The corresponding irreducible representations

of ways for expressing a given number as a (non-negative, integer) linear combination of a fixed set of relatively prime numbers. In particular, if { a

{\displaystyle \Delta } is a root of Φ {\displaystyle \Phi } which is a linear combination of elements of Δ {\displaystyle \Delta } with nonnegative coefficients

packets are called "native packets". The source node then creates a linear combination of K packets and forwards them. The code vector represents the random

of the Logarithmic Schrödinger equation, it has been found that a linear combination of Gaussons can very accurately approximate excited states as well

(n − 1)d in the representation of atomic orbitals (AOs) – is used in a linear combination with the ligand orbitals, forming a very stable bonding orbital with

construct a system of equations restricting the coefficients of the linear combination to satisfy the ODE. This method is not as general as variation of

recurrence relation expresses the values of a sequence of numbers as a linear combination of earlier values; for instance, the Fibonacci numbers may be defined

p_{2},\ldots ,p_{n}} are pairwise disjoint components of e, any real linear combination of p 1 , p 2 , … , p n {\displaystyle p_{1},p_{2},\ldots ,p_{n}} is

eigenstate can be decomposed into a linear combination of the initial eigenstates: the coefficients in the linear combination consist of Wigner rotation matrix

the characterisation of differences in group means in regards to a linear combination of multiple dependent variables, while simultaneously controlling

polynomial p(t) of degree at most d is uniquely expressible as a linear combination ∑ k = 0 d a k ( t k ) {\textstyle \sum _{k=0}^{d}a_{k}{\binom {t}{k}}}

linear combination of the functions e ± 2 3 x 3 / 2 x 1 / 4 . {\displaystyle {\frac {e^{\pm {\frac {2}{3}}x^{3/2}}}{x^{1/4}}}.} However, the linear combination

degrees of freedom. The electric charge arises as the particular linear combination (nontrivial) of YW (weak hypercharge) and the T3 component of weak

is predicting the pKa of an ionizable group. The pKa equation is a linear combination of a few features, including: depth, number of hydrogen bond, electrostatic

the target of the k-SVD algorithm is to represent the signal as a linear combination of atoms in D {\displaystyle D} . The k-SVD algorithm follows the

variables is again Gaussian distributed, that is the same as saying every linear combination of ( X t 1 , … , X t k ) {\displaystyle (X_{t_{1}},\ldots ,X_{t_{k}})}

{\displaystyle l} is the angular momentum quantum number, is approximated by a linear combination of n {\displaystyle n} primitive GTOs ϕ l α m j {\displaystyle \phi

measures a type of normalized prediction error and its distribution is a linear combination of χ2 variables of degree 1. All models are wrong Model selection

two corresponding outputs, if you take a linear combination of those two inputs you will get a linear combination of the outputs. An example of a linear

consisting of a linear combination of arbitrary kernels over different domains. The coefficients or weights of the linear combination can be learned as

"deterministic" time series, in the sense that it is completely determined as a linear combination of its past values (see e.g. Anderson (1971) Ch. 7, Section 7.6.3

below that of the ground state for one of the operators or for a linear combination of the two. The idea behind this is that the circle denoting the uncertainty

strategy consists of identifying similar pairs of stocks and taking a linear combination of their price so that the result is a stationary time-series. We

K=-\lambda ^{2}} for convenience. Then, T ( t ) {\displaystyle T(t)} is a linear combination of sine and cosine functions, T ( t ) = A cos ⁡ c λ t + B sin ⁡ c

use a predefined set of kernels and learn an optimal linear or non-linear combination of kernels as part of the algorithm. Reasons to use multiple kernel

is a linear combination of powers t j {\displaystyle t^{j}} with integer coefficients. Hence the number P {\displaystyle P} is a linear combination (with

be defined by a known linear combination of these two constants. For instance, the elongation along [110] is a linear combination of λ 100 {\displaystyle

simple ring. Every element can be written in a unique way as a R-linear combination of monomials of the form X a D b  mod  I {\displaystyle X^{a}D^{b}{\text{

A self-concordant function is a function satisfying a certain differential inequality, which makes it particularly easy for optimization using Newton's

complete set of generators for the algebra. They are not unique: any linear combination of these three fields is still a Killing field. There are several

Born–Oppenheimer approximation). The many-electron function is generally a linear combination of many simpler electron functions with the dominant function being

Born–Oppenheimer approximation). The many-electron function is generally a linear combination of many simpler electron functions with the dominant function being

\nu \rho \sigma }\,d^{d}x,} but in four dimensions this term is a linear combination of the other two terms and a surface term. See Gauss–Bonnet gravity

J_{ij}=1} , is in the adjacency algebra of the graph (meaning it is a linear combination of powers of A). Let G be a k-regular graph with diameter D and eigenvalues

\sigma _{f}={\frac {\sigma }{\sqrt {n}}}.} When f is a set of non-linear combination of the variables x, an interval propagation could be performed in

series. This however conflicts with a fact that an average (or any linear combination) of assets with lognormal distribution does not follow lognormal distribution

n-dimensional position vector. A position vector can be expressed as a linear combination of basis vectors: r = ∑ i = 1 n x i e i = x 1 e 1 + x 2 e 2 + ⋯ +

U(1)χ varies from article/book to article. The hypercharge Y/2 is a linear combination (sum) of the following: ( 1 15 0 0 0 0 0 1 15 0 0 0 0 0 1 15 0 0 0

be represented by a cycle in the Floer chain complex, formally a linear combination α H = a 1 x 1 + a 2 x 2 + ⋯ {\displaystyle \alpha _{H}=a_{1}x_{1}+a_{2}x_{2}+\cdots

}{2}}{\left(v-{\mu }_{j}\right)}^{2}\right)} is directly modeled as a linear combination of radial basis function kernels, where γ {\displaystyle \gamma }

where the strain energy density function W {\displaystyle W\,} is a linear combination of two invariants of the left Cauchy–Green deformation tensor B {\displaystyle

{\displaystyle a\in {\mathfrak {b}}} , so a {\displaystyle a} is a left linear combination a = ∑ j u j a j {\displaystyle a=\sum _{j}u_{j}a_{j}} of the coefficients

linear or not, applied to a plane wave yields a plane wave. Any linear combination of plane waves with the same normal vector n → {\displaystyle {\vec

derivatives of ε over all αi is not sufficient. If ψ(α) is expressed as a linear combination of other functions (αi being the coefficients), as in the Ritz method

SMPTE C, or Rec. 709). For the Rec. 709 (and sRGB) primaries, the linear combination, based on pure colorimetric considerations and the definition of relative

allows us to numerically compute v n {\displaystyle v_{n}} as a finite linear combination of the basis vectors in V n {\displaystyle V_{n}} . The key property

obtains an orthonormal basis of eigenvectors. A can be written as a linear combination of pairwise orthogonal projections, called its spectral decomposition

colors that are spectral, since a linear combination of spectral colors will be matched by the same linear combination of their (IS, IM, IL) matches. Note

Memberships, in which the fuzzy membership of each object is updated by a linear combination of the fuzzy memberships of its nearest neighbors. Cluster construction

said to not have any column descents. We want to express eS as a linear combination of standard polytabloids, i.e. polytabloids associated to standard

with applications in convex minimization. Convex combination - a linear combination of points where all coefficients are non-negative and sum to 1. All

properties: Every root α ∈ Φ {\displaystyle \alpha \in \Phi } is a linear combination of elements of Δ {\displaystyle \Delta } with integer coefficients

{\displaystyle P_{\mu }=(M,0,0,0)} ) and Z {\displaystyle Z} is a linear combination of the central charges. This inequality is the BPS bound. States that

set of weights for each point that best describes the point as a linear combination of its neighbors. Finally, it uses an eigenvector-based optimization

of observables, namely that any state can be written as a convex linear combination of so-called pure states. According to Lawrence Narici and Edward

spacetime. It follows that any normal vector can be expressed as a linear combination of two future directed null vectors, normalised by: k+ · k− = −2 The

} , which is a linear combination of various | L m L S m S ⟩ {\displaystyle \vert Lm_{L}Sm_{S}\rangle } . The exact linear combination, however, is unnecessary

the number of edges Number of connected components Circuit rank, a linear combination of the numbers of edges, vertices, and components diameter, the longest

define decision boundaries in many machine learning algorithms such as linear-combination (oblique) decision trees, and perceptrons. In a vector space, a vector

result of any Adams operation is naturally a vector bundle, not a linear combination of ones in K-theory. Treating the line bundle direct factors formally

bilinearity of the inner product, this squared norm can be expanded into a linear combination of ‖ f ( x ) ‖ 2 , {\displaystyle \|f(x)\|^{2},} ‖ f ( y ) ‖ 2 , {\displaystyle

}^{\gamma }~.} One may prefer the recast version, resulting from a linear combination of the above, λ β α ⋅ λ δ γ = 2 δ δ α δ β γ − 2 3 δ β α δ δ γ   .

meaning that it represents a linear combination of the dependent variables yi. The weights in this linear combination are functions of the regressors

modifications to an S-box could significantly weaken DES. Any S-box where any linear combination of output bits is produced by a bent function of the input bits is

punctured domain (an open domain minus one point in the interior) is a linear combination of a harmonic function in the unpunctured domain with a scaled fundamental

{\displaystyle \mathbb {Z} } -linear combination of classes of complex subvarieties of X {\displaystyle X} . (Such a linear combination is called an algebraic

meaning that it represents a linear combination of the dependent variables yi. The weights in this linear combination are functions of the regressors

 Y(x2))). For locations x1, x2, ..., xN ∈ D the variance of every linear combination X = ∑ i = 1 N w i Z ( x i ) {\displaystyle X=\sum _{i=1}^{N}w_{i}Z(x_{i})}

as a linear combination of eta-quotients in Mk′(Γ0(N)) and then divide out by ηg. The result will be an expression of f as a linear combination of eta

(Sα + X)/n for α < β, where n is a positive integer and X is an integral linear combination of the numbers xα for α < β. Then the group generated by these numbers

definite, the cosine function is positive definite as a nonnegative linear combination of the above functions: cos ⁡ ( x ) = 1 2 ( e i x + e − i x ) = 1

mixing angle θP = −11.5°), so that the actual quark composition is a linear combination of these formulae. That is: ( cos ⁡ θ P − sin ⁡ θ P sin ⁡ θ P    

appearing in one-loop renormalization of QED or QCD may be written as a linear combination of terms in the form ∫ d d k ( 2 π ) d k μ 1 ⋯ k μ n ( ( k + q 1 )

functions and exponentials is called an exponential monomial, and a linear combination of these is then an exponential polynomial on G. Ritt's theorem states

the product a i a j {\displaystyle a_{i}a_{j}} decomposes as the linear combination of basis elements a k {\displaystyle a_{k}} . Combinatorial proof

in statistics, pattern recognition, and machine learning to find a linear combination of features that characterizes or separates two or more classes of

are linearly dependent, v ℓ + 1 {\displaystyle v_{\ell +1}} is a linear combination of v 0 , … , v ℓ {\displaystyle v_{0},\ldots ,v_{\ell }} . Applying

rectangular cuboid, with a unique minimal surface interior defined as a linear combination of the four vertices, creating a saddle surface. This example shows

if an input is a weighted linear combination of different signals, the output is a similarly weighted linear combination of the corresponding output

codes).[citation needed] Efficient parallelization. The use of a linear combination of numerical atomic orbitals makes SIESTA a DFT code. SIESTA can produce

Wikimedia Commons has media related to Sigmoid functions. Step function – Linear combination of indicator functions of real intervals Sign function – Function

pair of matrices. Conversely, any square matrix with zero trace is a linear combination of the commutators of pairs of matrices. Moreover, any square matrix

2-dimensional. An arbitrary state for a qubit can be written as a linear combination of the Pauli matrices, which provide a basis for 2 × 2 {\displaystyle

recognize that since the price of a security can be returned as a linear combination of its state prices (contingent claim analysis) so, conversely, pricing-

obtained the set of solutions to a linear differential equation, any linear combination of the solutions will, because of the superposition principle, also

coefficients within each column to assign each matroid element a linear combination of these transcendentals. The converse is false: not every algebraic

Slater type orbitals (STOs) and atomic shielding constants, 1931: linear combination of atomic orbitals, van der Waals forces (with Jack Kirkwood, as a

{\displaystyle \Phi =\sum _{H}\Phi _{H}(x)dx_{H},} is written as a linear combination of sixteen basis forms indexed by H {\displaystyle H} , which runs

Hartree–Fock wavefunction as the ground determinant, one takes a linear combination of the ground and excited determinants Φ I {\displaystyle \Phi _{I}}

2021-04-13. Witkovsky, V. (2001). "Computing the Distribution of a Linear Combination of Inverted Gamma Variables". Kybernetika. 37 (1): 79–90. MR 1825758

unobserved location x 0 {\displaystyle x_{0}} , is calculated from a linear combination of the observed values z i = Z ( x i ) {\displaystyle z_{i}=Z(x_{i})}

given partially ordered set Chain (algebraic topology), a formal linear combination of k-simplices Chain complex, a generalization of the algebraic topology

such as e, π and ln(2), which will lead to an expression for x as a linear combination of these constants. A typical approach in experimental mathematics

{(p-3)(p-1)(p+1)(p+3)}{5!}}x^{5}-\cdots .} The general solution is any linear combination of these two. When p is a non-negative integer, one or the other of

that consists of identifying similar pairs of stocks and taking a linear combination of their price so that the result is a stationary time-series. Investors

showing that a bounded linear functional can be written as a finite linear combination of positive ones. In its original form by Frigyes Riesz (1909) the

can do this by decomposing | s ⟩ {\displaystyle |s\rangle } into a linear combination of | ψ 1 ⟩ {\displaystyle |\psi _{1}\rangle } and | ψ 2 ⟩ {\displaystyle

domain if and only if any two elements in it have a gcd that is a linear combination of the two. A Bézout domain is thus a GCD domain, and (4) gives yet

, an are some constants, then the characteristic function of the linear combination of the Xi variables is φ a 1 X 1 + ⋯ + a n X n ( t ) = φ X 1 ( a 1

line and frame synchronization pulses. The color video signal is a linear combination of the luminance (Y) of the picture and a chrominance subcarrier which

variables are again Skellam-distributed. It is sometimes claimed that any linear combination of two Skellam distributed variables are again Skellam-distributed

generalized variance. Applied to one vector, the covariance matrix maps a linear combination c of the random variables X onto a vector of covariances with those

usual Ising basis, acting on any linear combination of past configurations, it produces the same linear combination but with the spin at position i of

states that a stochastic process can be represented as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation

tunneling, an energy splitting between the bonding and anti-bonding linear combination of states with opposite magnetization classical ground states arises

is not itself linearly independent, because there is a non-trivial linear combination making it zero: 1 ⋅ 0 = 0 {\displaystyle 1\cdot \mathbf {0} =\mathbf

1021/ed500813d. Chen, E.; Chang, T. (1998). "Walsh Diagram and the Linear Combination of Bond Orbital Method". Journal of Molecular Structure: THEOCHEM

w. H 500×100. 100 hidden vectors h concatenated into a matrix c 500-long context vector = H * w. c is a linear combination of h vectors weighted by w.

it can be written as the sum of a sum matrix S and a non-negative linear combination of LL-UR block matrices. The sum matrix is defined in terms of a sequence

_{n=1}^{e}\sum _{m=1}^{d}b_{m,n}(u_{m}w_{n}),} which shows that x is a linear combination of the umwn with coefficients from K; in other words they span M over

simulation. This truncated expansion is then implemented via the linear combination of unitaries (LCU) technique for Hamiltonian simulation. Namely, one

considered a new space, where each term vector ti was expressed as a linear combination of 2n vectors mr where r = 1...2n. For a document dk and a query q

{\displaystyle (X,\Delta )} where Δ {\displaystyle \Delta } is a formal linear combination of prime divisors with rational coefficients such that K X + Δ {\displaystyle

or is inconsistent. It is inconsistent if and only if 0 = 1 is a linear combination (with polynomial coefficients) of the equations (this is Hilbert's

two-dimensional because every point in the plane can be described by a linear combination of two independent vectors. The dot product of two vectors A = [A1

try to separate lightness from chroma signals in an RGB input using linear combination. As the input RGB values are gamma-corrected, such a separation does

} The last term is not tangential to M, but can be expressed as a linear combination of the tangent space base vectors using the Christoffel symbols as

problem in LFSR-based stream ciphers: Non-linear combination of several bits from the LFSR state; Non-linear combination of the output bits of two or more LFSRs

bit is shifted into each of the three shift registers using a non-linear combination of taps from that and one other register; one bit of output is produced

notions of positivity. A form is called strongly positive if it is a linear combination of products of semi-positive forms, with positive real coefficients

}{\partial t}}+\Omega {\frac {\partial }{\partial \varphi }}} , the linear combination of the time translation and axisymmetry Killing vectors which is null

_{f}(\partial _{\mu }O)(x)=\partial _{\mu }\left(\pi _{f}(O)(x)\right)} is a linear combination of ∂ μ O {\displaystyle \partial _{\mu }O} and ⁠ O {\displaystyle

acting on | Φ 0 ⟩ {\displaystyle |\Phi _{0}\rangle } , produces a linear combination of excited determinants from the reference wave function (see section

Economics 6, no. 1 (2015): 123–152. Andrews, Isaiah. "Conditional linear combination tests for weakly identified models." Econometrica 84, no. 6 (2016):

linearly independent, i.e., no state variable can be written as a linear combination of the other state variables, or the system cannot be solved. The

f ( z + γ ) = f ( z ) {\displaystyle f(z+\gamma )=f(z)} for every linear combination γ = m ω 1 + n ω 2 {\displaystyle \gamma =m\omega _{1}+n\omega _{2}}

\mu } if λ − μ {\displaystyle \lambda -\mu } is expressible as a linear combination of positive roots with non-negative real coefficients. A weight λ

\lambda _{2}} , the solution to L y = 0 {\displaystyle Ly=0} is a linear combination of the solutions to each of ( x D − λ 1 I ) y = 0 {\displaystyle (xD-\lambda

where T is any cycle such that dim T = codim Z (The intersection is a linear combination of points and we add the intersection multiplicities at each point

design and analyze analog IIR filters. A signal is represented as linear combination of its previous samples. Coefficients of the combination are called

rational arguments the Hurwitz zeta function may be expressed as a linear combination of Dirichlet L-functions and vice versa: The Hurwitz zeta function

signal x ∈ R N {\textstyle \mathbf {x} \in \mathbb {R} ^{N}} as a linear combination of a few atoms in the redundant dictionary D ∈ R N × M , M ≫ N {\textstyle

rational arguments the Hurwitz zeta function may be expressed as a linear combination of Dirichlet L-functions and vice versa: The Hurwitz zeta function

the z being bilinear forms in the x and y: that is, each z is a K-linear combination of terms of the form xi yj.: 127  We call a triple ( r , s , n ) {\displaystyle

}}=g({\boldsymbol {\eta }})\,.} Here η is an intermediate variable representing a linear combination, containing the regression parameters, of the explanatory variables

Therefore, the quantum state of the deuterium is a superposition (a linear combination) of the s = 1, l = 0 state and the s = 1, l = 2 state, even though

C_{i}}c_{j}} , then s1 = 0 for all i ≥ 2, si can be written as a rational linear combination of the cj's in all the Ck with k < i. This means that si is in the

b; c; z). Gauss showed that 2F1(a, b; c; z) can be written as a linear combination of any two of its contiguous functions, with rational coefficients

According to this theorem, any such valuation can be expressed as a linear combination of the intrinsic volumes; for instance, in two dimensions, the intrinsic

h ∗ {\displaystyle {\mathfrak {h}}^{*}} such that each root is a linear combination of α 1 , … , α l {\displaystyle \alpha _{1},\dots ,\alpha _{l}} with

corresponding dual basis). Since a general mixed dyadic tensor is a linear combination of decomposable tensors of the form f ⊗ v {\displaystyle f\otimes

whilst inside it is spacelike. Furthermore, considering a particular linear combination of ∂ / ∂ t {\displaystyle \partial /\partial t} and ∂ / ∂ ϕ {\displaystyle

x^{i}}}\right|_{p}.} This formula therefore expresses v {\displaystyle v} as a linear combination of the basis tangent vectors ∂ ∂ x i | p ∈ T p M {\textstyle \left

for all but finitely many g ∈ G {\displaystyle g\in G} so that the linear combination is finite. The (size of the) support of an element a = ∑ g λ g g {\displaystyle

{\mathcal {H}}_{k}} . 2. Functions in an RKHS are in the closure of the linear combination of the kernel at given points, f ( x ) = ∑ i k ( x i , x ) c i {\displaystyle

algorithms. For equally-spaced values, a polynomial interpolation is a linear combination of the known values. If the discrete time signal is estimated to obey

under rigid motions of R n {\displaystyle \mathbb {R} ^{n}} is a linear combination of the quermassintegrals (or, equivalently, of the intrinsic volumes)

of an abelian group A is linearly independent (over Z) if the only linear combination of these elements that is equal to zero is trivial: if ∑ α n α a α

posterior to the actual scan, eigen flat fields can be computed. A linear combination of the most important eigen flat fields can then be used to individually

space V with the space V∗ by first decomposing the tensor into a linear combination of simple tensors, and then applying a factor from V∗ to a factor

\mathbb {C} } . Using this data, one can define a c-divisor as a formal linear combination D = ∑ i k i C i + ∑ ∞ λ ∞ X ∞ {\displaystyle D=\sum _{i}k_{i}C_{i}+\sum

in SUSY D = 10 gauge theory is the hexagon which has a particular linear combination of the two-form gauge field strength and Ricci tensor, F 6 ,   F 4

{\displaystyle -\lambda y=\operatorname {ad} _{\mathfrak {h}}(y)x} is a linear combination of eigenvectors of ad h ⁡ ( y ) {\displaystyle \operatorname {ad}

coordinate fields x μ {\displaystyle x^{\mu }} . The metric is thus a linear combination of tensor products of one-form gradients of coordinates. The coefficients

sequence or scaling mask. The wavelet proper is obtained by a similar linear combination, ψ ( x ) = ∑ k = 0 M − 1 b k ϕ ( 2 x − k ) {\displaystyle \psi (x)=\sum

Mittag-Leffler star of ƒ at a. Each polynomial in this series is a linear combination of the first several terms in the Taylor series expansion of ƒ around a

m {\displaystyle m} independent plane wave solutions of which any linear combination is also a solution: ψ ∝ ∑ j = 1 m A j e i k j ⋅ r {\displaystyle \psi

eigenvectors is known. Moreover, the eigenvectors are not unique because any linear combination of eigenvectors for the same eigenvalue is also an eigenvector for

linearization of the R′G′B′ components to RGB is needed before the linear combination. Relative luminance should not be confused with luma Y ′ {\displaystyle

an ambient air sample has particulate matter contributions from a linear combination of emission sources. If the chemical compositions of local sources

the definition of the algorithm below. The final classifier is a linear combination of weak hypotheses and is evaluated in the same manner as most other

Examples Viscoelastic Kelvin material, Maxwell material "Parallel" linear combination of elastic and viscous effects Some lubricants, whipped cream, Silly

decreases in intensity. The two transitions are describable as a linear combination of the parent modes. Fermi resonance does not lead to additional bands

to zero, and each exponent β ( m ) {\displaystyle \beta (m)} is a linear combination of α ( i ) {\displaystyle \alpha (i)} with integer coefficients. Then

covalency. The VBCI model describes the ground and excited state as a linear combination of the metal-based d-state and the ligand-based charge transfer state

For any set of independent continuous random variables, for any linear combination of those variables, its characteristic function (which uniquely determines

that a 2 + b 2 + c 2 = 1 {\displaystyle a^{2}+b^{2}+c^{2}=1\,} the linear combination a I + b J + c K {\displaystyle aI+bJ+cK\,} is a complex structures

Inside the spheres, they can be any smooth continuation, such as a linear combination of polynomials or Bessel functions. The PAW method is typically combined

relation algorithm (such as the Inverse Symbolic Calculator) to find a linear combination of mathematical constants that matches this value. For example, the

codimension-i subvarieties of V. An algebraic cycle means a finite linear combination of subvarieties; so an equivalent statement is that every element

coefficients within each column to assign each matroid element a linear combination of these transcendentals. For fields of characteristic zero (such

determinant. In other words, in this case, every invariant polynomial is a linear combination of powers of the determinant polynomial. So in this case, k [ V ]

k, then each element of Ek can be expressed in a unique way as a linear combination of elements from among the spaces Ωp,q with p + q = k. More succinctly

iγ a non-real zero. The Dirichlet L-functions may be written as a linear combination of the Hurwitz zeta function at rational values. Fixing an integer

of f. Then, f(r) = 0, which can be rearranged to express rk as a linear combination of powers of r less than k. This equation can be used to reduce away

+ Q2, then P2 = 2P3 + Q3, etc. finally expresses P as an integral linear combination of points Qi and of points whose height is bounded by a fixed constant

closed under squaring, the non-real basis element u squares to a linear combination of 1 and u: u 2 = a 0 + a 1 u {\displaystyle u^{2}=a_{0}+a_{1}u} for

quantum numbers: The quantum states in the system can be described as linear combination of these 8 states. However, in the presence of spin–orbit interaction

understanding of the spectrum. This quantification is achieved via linear combination. Linear combination requires knowledge of the underlying spectral shapes, referred

input parameters are x and y. # The function, named f, returns a linear combination of x and y. f <- function(x, y) { z <- 3 * x + 4 * y # An explicit

gradient problem. Ridge functions are multivariate functions acting on a linear combination of the input variables. Often used examples include:[clarification

the membrane into triangles and a computer is used to determine the linear combination of the functions that represent the displacement which solves a complex

classifier, decrease if correctly Form the final strong classifier as the linear combination of the T classifiers (coefficient larger if training error is small)

This is known as exchange degeneracy. More generally, consider a linear combination of such states, | Ψ ⟩ {\displaystyle |\Psi \rangle } . For the best

arbitrary solution a k {\displaystyle a_{k}} can be written as a linear combination of such geometric solutions, and the eigenvalues of largest complex

wavelength. The fact that the luminance function could be constructed by a linear combination of the RGB color matching functions was not guaranteed by any means

expressed through Pontryagin numbers. For the theorem describing the linear combination of Pontryagin numbers giving the signature see Hirzebruch signature

a simplified model of a neuron y {\displaystyle y} that returns a linear combination of its inputs x using presynaptic weights w: y ( x )   =   ∑ j = 1

conformal symmetry. Any correlation function can be written as a linear combination of conformal blocks: functions that are determined by conformal symmetry

x y {\displaystyle f(x,y)=e^{xy}} cannot be expressed as a finite linear combination of smooth functions in C ∞ ( R x ) ⊗ C ∞ ( R y ) . {\displaystyle

&\dots ,&{\mathbf {x} }^{(n+1)}\end{bmatrix}}} so that x(n+1) is a linear combination of x′, …, x(n−1). Consider the matrix A = [ x ˙ , x ¨ , … , x ( n

direction. The total derivative d f a {\displaystyle df_{a}} is a linear combination of linear functionals and hence is itself a linear functional. The

Poisson brackets of the three-metric and its conjugate momentum with a linear combination of the spatial diffeomorphism and Hamiltonian constraint. The vanishing

extended linearly to a general k-form (which is expressible as a linear combination of basic simple k {\displaystyle k} -forms) ω = f I d x I , {\displaystyle

functions must be Bloch waves here. The solution in the crystal is then a linear combination of an incoming wave and a wave reflected from the surface. For z>0

{a}}^{\dagger }} : and any state of the system can be expressed as a linear combination of the states | n ⟩ ∝ ( a ^ † ) n | 0 ⟩ . {\displaystyle |n\rangle

functions for a given angular quantum number. To address this, a linear combination of two d-type GTOs can be used to reproduce a canonical d function

}e_{3}+a_{5}e_{1}e_{3}+a_{6}e_{1}e_{2}+a_{7}e_{1}e_{2}e_{3}.} The linear combination of the even degree elements of Cl3,0(R) defines the even subalgebra

proper, i.e. dim(A ∩ B) = dim A + dim B − dim X, then A · B is a linear combination of the irreducible components of A ∩ B, with coefficients the intersection

Scaling is necessary because the plot is based on interpolation (linear combination) of consecutive pairs of variables. Therefore, the variables must

multiplication above it follows that each column in the product matrix WH is a linear combination of the 10 column vectors in the features matrix W with coefficients

a custom benchmark for each portfolio to be developed, using the linear combination of style indices that best replicate portfolio style allocation, and

XANES spectra of an unknown sample to those of known "standards". Linear combination fitting of several different standard spectra can give an estimate

a linear combination of the constraints, with positive coefficients, such that the coefficients of x in the constraints are at least cT. This linear combination

signatures and 2. the radiometric signature at the instrument head is a linear combination of that of the different surface types, with the weights taking on

is the Planck constant. Thus a system like an atom consists of a linear combination of modes of definite energy. These energies are characteristic of

have had the foregrounds removed as far as possible: the "internal linear combination" map of the WMAP collaboration and a similar map prepared by Max Tegmark

{\displaystyle \mathbf {x} } in the domain are approximated by the linear combination of RBFs: The derivatives are approximated as such: where N {\displaystyle

three-dimensional because every point in space can be described by a linear combination of three independent vectors. A vector can be pictured as an arrow

distributed, then so is DX for any matrix D with full row rank. Thus any linear combination of the components of X is elliptical (though not necessarily with

\nolimits _{i}n_{i}p_{i}} is a divisor (meaning a formal integer-linear combination of points of C). We can define u ( D ) = ∑ i n i u ( p i ) {\displaystyle

{\displaystyle ZY_{\alpha _{i_{1}}}\cdots Y_{\alpha _{i_{M}}}} as a linear combination of products of Lie algebra elements with the raising operators X α

Electronic Structure Method for Complex Materials: The orthogonalized linear combination of atomic orbitals. The Magnetism of Amorphous Metals and Alloys.

}.} Two arbitrary distinct points on the line can be written as a linear combination of A {\displaystyle \mathbf {A} } and B {\displaystyle \mathbf {B}

{\displaystyle K(n,p)=\sum _{x=1}^{p}e(nx^{3}/p)} is easily seen to be a linear combination of the Kummer sums. In fact it is 3P where P is one of the Gaussian

states are discarded (finite-dimensional space), it would consist of a linear combination of Pauli strings P ^ i {\displaystyle {\hat {P}}_{i}} consisting of

respect to x {\displaystyle x} , we can write this function as a linear combination of the f λ {\displaystyle f_{\lambda }} . In particular, we know the

equation can be quite complicated. Still, it can be analyzed as a linear combination of simple solutions that are sinusoidal plane waves with various directions

Hooft–Polyakov monopoles. Because the electromagnetic charge Q is a linear combination of some SU(2) generator with ⁠Y/2⁠, these monopoles also have quantized

the Fourier transform (the fourth roots of unity ±1 and ±i) and any linear combination of eigenfunctions with the same eigenvalue gives another eigenfunction

function of a baseline hazard h 0 ( t ) {\displaystyle h_{0}(t)} and a linear combination of explanatory variables: log ⁡ h ( t ) = f ( h 0 ( t ) , α + β 1