On the existence of a common eigenvector for all matrices in the commutant of a single matrix

Recent theoretical work has shown that the complete set of polarized elastic light-scattering studies should yield information about scatterer structure that has so far hardly been utilized. We present here calculations of angular dependences of light-scattering matrix elements for spheres near the Rayleigh and Rayleigh-Gans-Debye limits. The significance of single matrix elements is documented on examples that show how different matrix elements respond to changes in particle parameters. It appears that in the small-particle limit (Rg/λ < 0.1) we do not loose much information by ignoring "large particle" observables.

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PP-070 Generation of protective CTLs against the influenza A virus using single matrix epitope fused to protein transduction domain of Tat of HIV

International Journal of Infectious Diseases ◽

10.1016/s1201-9712(11)60223-3 ◽

2011 ◽

Vol 15 ◽

pp. S65

Author(s):

M. Khanna ◽

P. Kumar ◽

B. Kumar ◽

A. Banerjea

Keyword(s):

Influenza A Virus ◽

Influenza A ◽

Protein Transduction ◽

Protein Transduction Domain ◽

Single Matrix

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Single-matrix formulation of a time domain acoustic model of the vocal tract with side branches

Speech Communication ◽

10.1016/j.specom.2007.08.001 ◽

2008 ◽

Vol 50 (3) ◽

pp. 179-190 ◽

Cited By ~ 13

Author(s):

Parham Mokhtari ◽

Hironori Takemoto ◽

Tatsuya Kitamura

Keyword(s):

Time Domain ◽

Vocal Tract ◽

Acoustic Model ◽

Matrix Formulation ◽

Single Matrix

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Minimum entropy deconvolution and simplicity: A noniterative algorithm

Geophysics ◽

10.1190/1.1441919 ◽

1985 ◽

Vol 50 (3) ◽

pp. 394-413 ◽

Cited By ~ 43

Author(s):

Carlos A. Cabrelli

Keyword(s):

Synthetic Data ◽

Computational Method ◽

Minimum Entropy ◽

Autocorrelation Matrix ◽

Numerical Tests ◽

Convolution Model ◽

Single Input ◽

Definition Of ◽

Single Matrix ◽

New Criterion

Minimum entropy deconvolution (MED) is a technique developed by Wiggins (1978) with the purpose of separating the components of a signal, as the convolution model of a smooth wavelet with a series of impulses. The advantage of this method, as compared with traditional methods, is that it obviates strong hypotheses over the components, which require only the simplicity of the output. The degree of simplicity is measured with the Varimax norm for factor analysis. An iterative algorithm for computation of the filter is derived from this norm, having as an outstanding characteristic its stability in presence of noise. Geometrical analysis of the Varimax norm suggests the definition of a new criterion for simplicity: the D norm. In case of multiple inputs, the D norm is obtained through modification of the kurtosis norm. One of the most outstanding characteristics of the new criterion, by comparison with the Varimax norm, is that a noniterative algorithm for computation of the deconvolution filter can be derived from the D norm. This is significant because the standard MED algorithm frequently requires in each iteration the inversion of an autocorrelation matrix whose order is the length of the filter, while the new algorithm derived from the D norm requires the inversion of a single matrix. On the other hand, results of numerical tests, performed jointly with Graciela A. Canziani, show that the new algorithm produces outputs of greater simplicity than those produced by the traditional MED algorithm. These considerations imply that the D criterion yields a new computational method for minimum entropy deconvolution. A section of numerical examples is included, where the results of an extensive simulation study with synthetic data are analyzed. The numerical computations show in all cases a remarkable improvement resulting from use of the D norm. The properties of stability in the presence of noise are preserved as shown in the examples. In the case of a single input, the relation between the D norm and the spiking filter is analyzed (Appendix B).

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ARITHMETIC ON A QUINTIC THREEFOLD

International Journal of Mathematics ◽

10.1142/s0129167x01001118 ◽

2001 ◽

Vol 12 (08) ◽

pp. 943-972 ◽

Cited By ~ 8

Author(s):

CATERINA CONSANI ◽

JASPER SCHOLTEN

Keyword(s):

Modular Form ◽

Theta Series ◽

Continuous System ◽

Galois Representation ◽

Hilbert Modular Form ◽

Galois Action ◽

Hilbert Modular ◽

Common Eigenvector ◽

Quintic Threefold ◽

Real Quadratic

This paper investigates some aspects of the arithmetic of a quintic threefold in Pr 4 with double points singularities. Particular emphasis is given to the study of the L-function of the Galois action ρ on the middle ℓ-adic cohomology. The main result of the paper is the proof of the existence of a Hilbert modular form of weight (2, 4) and conductor 30, on the real quadratic field [Formula: see text], whose associated (continuous system of) Galois representation(s) appears to be the most likely candidate to induce the scalar extension [Formula: see text]. The Hilbert modular form is interpreted as a common eigenvector of the Brandt matrices which describe the action of the Hecke operators on a space of theta series associated to the norm form of a quaternion algebra over [Formula: see text] and a related Eichler order.

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Achieving high thermal stability of different rare-earth ions in a single matrix host via the manipulation of the local structure by a solid solution

Physical Chemistry Chemical Physics ◽

10.1039/d0cp00612b ◽

2020 ◽

Vol 22 (28) ◽

pp. 16294-16300

Author(s):

Xiuxia Yang ◽

Lei Zhao ◽

Zhichao Liu ◽

Shuyu Tian ◽

Hao Zhang ◽

...

Keyword(s):

Thermal Stability ◽

Solid Solution ◽

Rare Earth ◽

Local Structure ◽

Local Environment ◽

High Thermal Stability ◽

Rare Earth Ions ◽

Single Matrix ◽

Thermal Stability Of

Manipulating the local environment of CAS by substitution of Al3+–Y3+ for Si4+–Ca2+ to achieve more stability in the structure of CYA.

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A New Approach to Evaluate Planetary Perturbations on a Cloud of Dust in Low Eccentricity Heliocentric Orbits

International Astronomical Union Colloquium ◽

10.1017/s0252921100084955 ◽

1985 ◽

Vol 85 ◽

pp. 381-384 ◽

Cited By ~ 1

Author(s):

Bo. Å. S. Gustafson

Keyword(s):

Dust Cloud ◽

Frame Of Reference ◽

Orbital Elements ◽

New Approach ◽

Gravitational Perturbations ◽

Time Integral ◽

Common Coordinate System ◽

Heliocentric Orbits ◽

Single Matrix ◽

Over Time

AbstractDynamical perturbations on ensembles of particles in heliocentric orbits of low eccentricity are integrated over time. The dust is perturbed by radiation pressure, Poynting-Robertson drag, their corpuscular counterparts, and by gravitation due to any number of planets. A dust cloud is represented by a set of centroids and orbital dispersions (about the centroids). Gravitational perturbations on the centroid are derived from a single matrix, valid for any planet, in the appropriate frame of reference. After transformation of the time derivatives to a common coordinate system, the perturbation rates are summed up and integrated. The time dependence of the planets’ orbital elements are evaluated inside the time integral.

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A New Matrix Formula for the Inverse Laplace Transformation

Journal of Basic Engineering ◽

10.1115/1.3609592 ◽

1967 ◽

Vol 89 (2) ◽

pp. 269-272 ◽

Cited By ~ 13

Author(s):

C. F. Chen ◽

R. E. Yates

Keyword(s):

Laplace Transformation ◽

Transfer Functions ◽

High Order ◽

Partial Fraction ◽

Inverse Laplace Transformation ◽

Numerical Errors ◽

Matrix Operations ◽

Simple Matrix ◽

Matrix Formula ◽

Single Matrix

A new matrix formula for the inverse Laplace transformation is established. After substituting the eigenvalues and coefficients and performing some simple matrix operations, one can obtain the inverse Laplace transformation of the function in question. The regular Heaviside techniques involving partial fraction expansions, function differentiations, and so on, are avoided. Since the formula is general, it is particularly advantageous for use on high-order transfer functions; since the formula is exact, the results have no numerical errors. Hundreds of commonly used transform pairs can be replaced by this single matrix formula.

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Laplace and Extended Adjacency Matrices for Isomorphism Detection of Kinematic Chains Using the Characteristic Polynomial Approach

Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2005-84609 ◽

2005 ◽

Cited By ~ 1

Author(s):

Rajesh Pavan Sunkari ◽

Linda C. Schmidt

Keyword(s):

Characteristic Polynomial ◽

Spectral Properties ◽

Kinematic Chain ◽

Detection Algorithm ◽

Isomorphism Problem ◽

Characteristic Polynomials ◽

Kinematic Chains ◽

Laplace Matrix ◽

Adjacency Matrices ◽

Single Matrix

The kinematic chain isomorphism problem is one of the most challenging problems facing mechanism researchers. Methods using the spectral properties, characteristic polynomial and eigenvectors, of the graph related matrices were developed in literature for isomorphism detection. Detection of isomorphism using only the spectral properties corresponds to a polynomial time isomorphism detection algorithm. However, most of the methods used are either computationally inefficient or unreliable (i.e., failing to identify non-isomorphic chains). This work establishes the reliability of using the characteristic polynomial of the Laplace matrix for isomorphism detection of a kinematic chain. The Laplace matrix of a graph is used extensively in the field of algebraic graph theory for characterizing a graph using its spectral properties. The reliability in isomorphism detection of the characteristic polynomial of the Laplace matrix was comparable with that of the adjacency matrix. However, using the characteristic polynomials of both the matrices is superior to using either method alone. In search for a single matrix whose characteristic polynomial unfailingly detects isomorphism, novel matrices called the extended adjacency matrices are developed. The reliability of the characteristic polynomials of these matrices is established. One of the proposed extended adjacency matrices is shown to be the best graph matrix for isomorphism detection using the characteristic polynomial approach.

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