We associate to any given circulant complex matrix C another one E(C) such that E(E(C)) = C∗ the transpose conjugate of C. All circulant Hadamard matrices of order 4 satisfy a condition C4 on their eigenvalues, namely, the absolute value of the sum of all eigenvalues is bounded above by 4. We prove by a “descent” that uses our operator E that the only circulant Hadamard matrices of order n > 4,...

$^{229}$Th is a promising candidate for developing nuclear optical clock and searching the new physics beyond standard model. Accurate knowledge of properties very important. In this work, we calculate hyperfine-structure constants first four states $^{229}$Th$^{3+}$ using relativistic coupled-cluster method based on Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with lowest-order...

Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in l1 and l2-norm based reconstruction algorithms. Such linear systems can...

Transfer matrix functional relations for the generalized τ 2 (t q) model Abstract The N-state chiral Potts model in lattice statistical mechanics can be obtained as a " descendant " of the six-vertex model, via an intermediate " Q " or " τ 2 (t q) " model. Here we generalize this to obtain a column-inhomogeneous τ 2 (t q) model, and derive the functional relations satisfied by its row-to-row tr...

Eigenvectors of a max-min matrix characterize stable states of the corresponding discrete-events system. Investigation of the max-min eigenvectors of a given matrix is therefore of a great practical importance. The eigenproblem in max-min algebra has been studied by many authors. Interesting results were found in describing the structure of the eigenspace, and algorithms for computing the maxim...

The recursive algorithm of a (fast) discrete wavelet transform, as well as its generalizations, can be described as repeated applications of block-Toeplitz operators or, in the case of periodized wavelets, multiplications by block circulant matrices. Singular values of a block circulant matrix are the singular values of some matrix trigonometric series evaluated at certain points. The norm of a...

Kirchhoo's Matrix Tree Theorem permits the calculation of the number of spanning trees in any given graph G through the evaluation of the determinant of an associated matrix. In the case of some special graphs Boesch and Prodinger 9] have shown how to use properties of Chebyshev polyno-mials to evaluate the associated determinants and derive closed formulas for the number of spanning trees of g...

Circulant matrix embedding is one of the most popular and efficient methods for the exact generation of Gaussian stationary univariate series. Although the idea of circulant matrix embedding has also been used for the generation of Gaussian stationary random fields, there are many practical covariance structures of random fields where classical embedding methods break down. In this work, we pro...

We show that the Waring number over a finite field Fq, denoted as g(k,q), when exists coincides with diameter of generalized Paley graph ?(k,q)=Cay(Fq,Rk) Rk={xk:x?Fq?}. find infinite new families exact values g(k,q) from characterization graphs ?(k,q) which are also Hamming proved by Lim and Praeger in 2009. Then, we every positive integer is for some pair (k,q) q not prime. Finally, lower bou...

In this paper, we gives an upper bound estimation of the spectral norm for matrices A and B such that the entries in the first row of n×n r-circulant matrix A = Circr(a1, a2, . . . , an) and n×n symmetric r-circulant matrix B = SCircr(a1, a2, . . . , an) are ai = Pi or ai = P 2 i or ai = Pi−1 or ai = P 2 i−1, where {Pi}i=0 is Padovan sequence. At the last section, some illustrative numerical ex...