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Articles 1 - 7 of 7
Full-Text Articles in Algebra
On The Geometry Of The Multiplier Space Of ℓPA, Christopher Felder, Raymond Cheng
On The Geometry Of The Multiplier Space Of ℓPA, Christopher Felder, Raymond Cheng
Mathematics & Statistics Faculty Publications
For p ∊ (1, ∞)\ {2}, some properties of the space Mp of multipliers on ℓpA are derived. In particular, the failure of the weak parallelogram laws and the Pythagorean inequalities is demonstrated for Mp. It is also shown that extremal multipliers on the ℓpA spaces are exactly the monomials, in stark contrast to the p = 2 case.
Dimensional Analysis: Physical Insight Gained Through Algebra, John A. Adam
Dimensional Analysis: Physical Insight Gained Through Algebra, John A. Adam
Mathematics & Statistics Faculty Publications
No abstract provided.
Fast Multipole Method Using Cartesian Tensor In Beam Dynamic Simulation, He Zhang, He Huang, Rui Li, Jie Chen, Li-Shi Luo
Fast Multipole Method Using Cartesian Tensor In Beam Dynamic Simulation, He Zhang, He Huang, Rui Li, Jie Chen, Li-Shi Luo
Mathematics & Statistics Faculty Publications
The fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed. © 2017 Author(s).
An Invariance Property Of Common Statistical Tests, N. Rao Chaganty, A. K. Vaish
An Invariance Property Of Common Statistical Tests, N. Rao Chaganty, A. K. Vaish
Mathematics & Statistics Faculty Publications
Let A be a symmetric matrix and B be a nonnegative definite (nnd) matrix. We obtain a characterization of the class of nnd solutions Σ for the matrix equation AΣA = B. We then use the characterization to obtain all possible covariance structures under which the distributions of many common test statistics remain invariant, that is, the distributions remain the same except for a scale factor. Applications include a complete characterization of covariance structures such that the chisquaredness and independence of quadratic forms in ANOVA problems is preserved. The basic matrix theoretic theorem itself is useful in other characterizing …
The Sharp Lipschitz-Constants For Feasible And Optimal-Solutions Of A Perturbed Linear Program, Wu Li
The Sharp Lipschitz-Constants For Feasible And Optimal-Solutions Of A Perturbed Linear Program, Wu Li
Mathematics & Statistics Faculty Publications
The purpose of this paper is to derive the sharp Lipschitz constants for the feasible solutions and optimal solutions of a linear program with respect to right-hand-side perturbations. The Lipschitz constants are given in terms of pseudoinverses of submatrices of the matrices involved and are proven to be sharp.
A Note On The Degree Of Approximation With An Optimal, Discrete Polynomial, J. J. Swetits, B. Wood
A Note On The Degree Of Approximation With An Optimal, Discrete Polynomial, J. J. Swetits, B. Wood
Mathematics & Statistics Faculty Publications
A saturation theorem and an asymptotic theorem are proved for an optimal, discrete, positive algebraic polynomial operator. The operator is based on the Gauss-Legendre quadrature formula.
Approximation By Discrete Operators, J. J. Swetits, B. Wood
Approximation By Discrete Operators, J. J. Swetits, B. Wood
Mathematics & Statistics Faculty Publications
A discrete, positive, weighted algebraic polynomial operator which is based on Gaussian quadrature is constructed. The operator is shown to satisfy the Jackson estimate and an optimal version is obtained.