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45* diagonal

The diagonal elements of this matrix approximate the variances of the corresponding parameters. The square roots of these variances are estimates of the standard errors in the parameters and, in effect, are a measure of the uncertainties of those parameters. [Pg.102]

The off-diagonal elements of the variance-covariance matrix represent the covariances between different parameters. From the covariances and variances, correlation coefficients between parameters can be calculated. When the parameters are completely independent, the correlation coefficient is zero. As the parameters become more correlated, the correlation coefficient approaches a value of +1 or -1. [Pg.102]

Simulations of the adaptive reconstruction have been performed for a single slice of a porosity in ferritic weld as shown in Fig. 2a [11]. The image matrix has the dimensions 230x120 pixels. The number of beams in each projection is M=131. The total number of projections K was chosen to be 50. For the projections the usual CT setup was used restricted to angels between 0° and 180° with the uniform step size of about 3.7°. The diagonal form of the quadratic criteria F(a,a) and f(a,a) were used for the reconstruction algorithms (5) and (6). [Pg.124]

Manual thresholding by detecting peaks of matrix diagonal (4) to segment X-Rays images. [Pg.231]

Let u be a vector valued stochastic variable with dimension D x 1 and with covariance matrix Ru of size D x D. The key idea is to linearly transform all observation vectors, u , to new variables, z = W Uy, and then solve the optimization problem (1) where we replace u, by z . We choose the transformation so that the covariance matrix of z is diagonal and (more importantly) none if its eigenvalues are too close to zero. (Loosely speaking, the eigenvalues close to zero are those that are responsible for the large variance of the OLS-solution). In order to liiid the desired transformation, a singular value decomposition of /f is performed yielding... [Pg.888]

The simplest way to obtain X is to diagonalize S, take the reciprocal square roots of the eigenvalues and then transfomi the matrix back to its original representation, i.e. [Pg.39]

Note that h is simply the diagonal matrix of zeroth-order eigenvalues In the following, it will be assumed that the zeroth-order eigenfunction a reasonably good approximation to the exact ground-state wavefiinction (meaning that Xfi , and h and v will be written in the compact representations... [Pg.47]

It is important to realize that while the uppennost diagonal elements of these matrices are numbers, the other diagonal element is a matrix of dimension N. Specifically, these are the matrix representations of Hq and Fin the basis q which consists of all the original set, apart from i.e. [Pg.47]

The off-diagonal elements in this representation of h and v are the zero vector of lengtii (for h) and matrix elements which couple the zeroth-order ground-state eigenfunction members of the set q (for v) ... [Pg.47]

Nevertheless, equation (A 1.1.145) fonns the basis for the approximate diagonalization procedure provided by perturbation theory. To proceed, the exact ground-state eigenvalue and correspondmg eigenvector are written as the sums... [Pg.48]

However, if the zeroth-order ground-state energy is well separated from low lying excited states, the diagonal... [Pg.49]

If only zero-order states from the same polyad are conpled together, this constitutes a fantastic simplification in the Flamiltonian. Enonnons compntational economies result in fitting spectra, becanse the spectroscopic Flamiltonian is block diagonal in the polyad nnmber. That is, only zero-order states within blocks with the same polyad number are coupled the resulting small matrix diagonalization problem is vastly simpler than diagonalizing a matrix with all the zero-order states conpled to each other. [Pg.66]

The rocksalt stmcture is illustrated in figure Al.3.5. This stmcture represents one of the simplest compound stmctures. Numerous ionic crystals fonn in the rocksalt stmcture, such as sodium chloride (NaCl). The conventional unit cell of the rocksalt stmcture is cubic. There are eight atoms in the conventional cell. For the primitive unit cell, the lattice vectors are the same as FCC. The basis consists of two atoms one at the origin and one displaced by one-half the body diagonal of the conventional cell. [Pg.99]

That is, in the basis rj.F.irjjthe Hamiltonian matrix is block diagonal in Fand and we can rewrite (equation A1.4.8) as... [Pg.139]

The Hamiltonian matrix factorizes into blocks for basis functions having connnon values of F and rrip. This reduces the numerical work involved in diagonalizing the matrix. [Pg.139]

Having done this we solve the Scln-ddinger equation for the molecule by diagonalizing the Hamiltonian matrix in a complete set of known basis fiinctions. We choose the basis functions so that they transfonn according to the irreducible representations of the synnnetry group. [Pg.140]

The Hamiltonian matrix will be block diagonal in this basis set. There will be one block for each irreducible representation of the synnnetry group. [Pg.140]

It is well known that the trace of a square matrix (i.e., the sum of its diagonal elements) is unchanged by a similarity transfonnation. If we define the traces... [Pg.149]

If we start with an t -dimensional representation of A consisting of the matrices M, M2, M3,. .., it may be that we can find a matrix V such that when it is used with ( equation A1.4.34) it produces an equivalent representation M, M 2, M 3,. .. each of whose matrices is in the same block diagonal form. For example, the nonvanishing elements of each of the matrices could fonn an upper-left-comer ... [Pg.151]

In solving the secular equation it is important to know which of the off-diagonal matrix elements " I wanish since this will enable us to simplify the equation. [Pg.160]

The value of the vanishing integral rule is that it allows the matrix H to be block diagonalized. This occurs if... [Pg.160]


See other pages where 45* diagonal is mentioned: [Pg.131]    [Pg.6]    [Pg.233]    [Pg.323]    [Pg.889]    [Pg.892]    [Pg.32]    [Pg.40]    [Pg.40]    [Pg.40]    [Pg.41]    [Pg.41]    [Pg.46]    [Pg.46]    [Pg.46]    [Pg.48]    [Pg.49]    [Pg.49]    [Pg.51]    [Pg.64]    [Pg.64]    [Pg.67]    [Pg.75]    [Pg.99]    [Pg.139]    [Pg.151]    [Pg.159]    [Pg.161]    [Pg.161]    [Pg.161]   
See also in sourсe #XX -- [ Pg.153 ]

See also in sourсe #XX -- [ Pg.48 ]

See also in sourсe #XX -- [ Pg.369 ]

See also in sourсe #XX -- [ Pg.17 , Pg.28 ]




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Adsorption sites diagonal-fourfold-hollow

Algebra diagonal matrix

Algebra, diagonal vector spaces

Alkaline earth metals diagonal relationships

Aluminum beryllium diagonal relationship

Aluminum diagonal relationship with beryllium

Application of the Uniqueness Principle and Diagonal Effect

Avoiding the Diagonalization Step—Density Matrix-Based SCF

Block Diagonal Hamiltonians

Block diagonal Newton-Raphson

Block diagonal Newton-Raphson optimization

Block diagonal method

Block diagonalization of the electronic

Block diagonalization of the electronic Hamiltonian

Block diagonalized matrix

Block-diagonal

Block-diagonal Newton-Raphson method

Block-diagonal form

Block-diagonal formulations

Block-diagonal structure

Block-diagonalization

Block-diagonalization of the Hamiltonian matrix

Boron diagonal effect

Boron diagonal relationship with silicon

Canonical diagonalization

Claus diagonal formula

Computational matrix diagonalization

Data lateral, diagonal

Davidson diagonalization technique

Density matrix diagonal elements

Diagonal Born-Oppenheimer corrections

Diagonal Born-Oppenheimer corrections DBOC)

Diagonal Properties

Diagonal Spin-Orbit Parameters

Diagonal argument

Diagonal band of Broca

Diagonal bands

Diagonal behavior

Diagonal color transform

Diagonal controller

Diagonal correction

Diagonal crack

Diagonal determinant

Diagonal diagrams

Diagonal diffusion, 517 pairs

Diagonal dominance

Diagonal effect

Diagonal effect/properties

Diagonal element

Diagonal element coupling

Diagonal element quantization

Diagonal elements in a matrix

Diagonal elements linear inequalities

Diagonal elements of a matrix

Diagonal energies

Diagonal force field

Diagonal form

Diagonal gap condition

Diagonal glide

Diagonal glide planes

Diagonal hybridization

Diagonal interaction

Diagonal linear discriminant analysis

Diagonal local approximation

Diagonal local approximation Hamiltonian

Diagonal loops

Diagonal map

Diagonal mass matrix

Diagonal matrices, expectation values

Diagonal matrix

Diagonal matrix elements

Diagonal matrix of eigenvalues

Diagonal method

Diagonal mirror

Diagonal ordering

Diagonal peaks

Diagonal plane of symmetry

Diagonal planes

Diagonal plot

Diagonal product

Diagonal relationship

Diagonal relationships in the periodic

Diagonal relationships in the periodic table

Diagonal representability problem

Diagonal representation

Diagonal rule

Diagonal scaling

Diagonal set

Diagonal signals

Diagonal similarities

Diagonal similarities in the Periodic

Diagonal similarities in the Periodic Table

Diagonal spray

Diagonal subgroup

Diagonal symmetry

Diagonal system

Diagonal tension

Diagonal tension, reinforced concrete

Diagonal twist

Diagonal wiring

Diagonal-corrected vibrational

Diagonal-corrected vibrational adiabatic hyperspherical

Diagonal-corrected vibrational model

Diagonalization

Diagonalization

Diagonalization discrete-basis

Diagonalization of matrices

Diagonalization of the Dirac characters

Diagonalization of the internal kinetic energy

Diagonalization of the potential energy

Diagonalization procedure

Diagonalization repeated

Diagonalization techniques

Diagonalization transformation

Diagonalization, operator space

Diagonalization-least squares

Diagonalization-least squares procedure

Diagonalized matrix

Diagonalizing matrices

Diagonally dominant

Diffusion equation diffusivity diagonalization method

Direct Diagonalization Versus Algebraic Approaches

Direct diagonalization

Direct-diagonalization , electronic structure

Direct-diagonalization algorithm

Direct-diagonalization algorithm calculations

Disorder Off-diagonal

Disorders diagonal

Distortion, diagonal

Distortion, diagonal rhomboidal

Dynamic diagonal disorder term

Effective Hamiltonian diagonalizing

Efficient diagonalization of the interaction matrix

Eigenvalue equations Hamiltonian diagonalization

Eigenvector expansion Hamiltonian diagonalization

Eigenvectors diagonalization transformation

Electrophoresis diagonal

Energy matrices diagonalization

Exact diagonalization

Filter diagonalization

Filter diagonalization method

Filter diagonalization technique

Finding Eigenvalues by Diagonalization

First diagonal branch occlusion

Fock matrix block-diagonality

Fock matrix diagonalization

Fock operator diagonal matrix elements

Fourier component diagonalization transformations

Full matrix diagonalization

Funnel diagonally distorted

Grooved diagonal

Hamilton matrix diagonalization

Hamiltonian diagonalization

Hamiltonian diagonalization: computer program

Hamiltonian diagonalize

Hamiltonian equations diagonalization techniques

Hamiltonian matrix, diagonalizing

Hamiltonian modes diagonalization

Hamiltonian operator diagonalization

Helical or diagonal cracks

Hessian matrix diagonalization

Interactive matrix diagonalization

Inversion and Diagonalization

Iterative diagonalization

Jacobi Algorithm for Diagonalization Using a Computer

Jacobi matrix diagonalization

Lanczos diagonalization procedure

Leading diagonal

Length of diagonal

Linear inequalities for diagonal elements

Lithium diagonal relationship with

Lithium diagonal relationship with magnesium

Low-storage filter-diagonalization

Magnesium diagonal relationship with

Main diagonal

Matrices diagonally dominate

Matrix block diagonal

Matrix diagonal dominance

Matrix diagonalization

Matrix diagonalization behavior)

Matrix diagonalization eigenvalues

Matrix diagonalization perturbation method

Matrix diagonalization power method

Matrix diagonalization problem

Matrix diagonalization procedures

Matrix diagonalization, open-shell molecules

Matrix predominantly diagonal

Matrix principal diagonal

Matrix types, column diagonal

Molecular dynamics matrix diagonalization

Nontrivial diagonal matrix

Nucleus of the diagonal band

Numerical implementation of diagonalization solutions

Off-Diagonal Matrix Elements of Total Hamiltonian between Unsymmetrized Basis Functions

Off-Diagonal Part

Off-Diagonal Spin-Orbit Parameters

Off-diagonal

Off-diagonal blocks

Off-diagonal coupling

Off-diagonal coupling constant

Off-diagonal elastic constants

Off-diagonal elements

Off-diagonal force constant

Off-diagonal intensity

Off-diagonal long-range order

Off-diagonal matrix elements

Off-diagonal peaks

Off-diagonal points

Off-diagonal tensor components

Off-diagonal terms

Off-diagonal terms of the Hamiltonian

Orbital representation, diagonal elements

Other Diagonal Approximations

Periodic table diagonal line

Periodic table diagonal relationships

Periodicity diagonal relationship

Previous using three-diagonal matrix

Principal diagonal

Pseudo-diagonal

Recursive diagonalization methods

Reference states, diagonal

Remove Diagonal

Repeated diagonalization technique

Rydberg Hamiltonian, diagonalized

SPECTRAL-Diagonal-SAR

SPECTRAL-Diagonal-SAR Approach

Singular value diagonalization

Spatial representation diagonal elements

Spin-orbit diagonal matrix elements

Stable diagonal

Storing and Diagonalizing the Hessian

Structure refinement with block diagonal

Structure refinement with block diagonal least squares

Symmetry coordinates, Hamiltonian diagonalization

Symmetry elements diagonal

Synchronous diagonal

Tensor diagonalization

The Diagonal Effect

The Off-Diagonal Hypervirial Theorem

The Tri-Diagonal Matrix Algorithm

The diagonalized quasi-analytical (DQA) approximation

Tightness diagonal

Toward Well-Defined Analytic Block-Diagonal Hamiltonians

Tri diagonal

Tri-diagonal matrix

Tri-diagonal matrix algorithm

Triad-Containing Diagonal Loops

Truncation-diagonalization analysis

Uniqueness of Beryllium and Diagonal Relationship to Aluminum

Unitary Similarity Diagonalization of a Square Hermitian Matrix

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