On R. Chapman's "evil determinant": case p ≡ 1 (mod 4)
For p ≡ 1 (mod 4), we prove the formula (conjectured by R. Chapman) for the determinant of the (p+1)/2 × (p+1)/2 matrix with .
On some generalizations of the Vandermonde matrix and their relations with the Euler beta-function.
On the asymptotics of certain Wiener--Hopf-plus-Hankel determinants.
On the Brualdi-Liu conjecture for the even permanent.
On the coefficients of the max-algebraic characteristic polynomial and equation
No polynomial algorithms are known for finding the coefficients of the characteristic polynomial and characteristic equation of a matrix in max- algebra. The following are proved: (1) The task of finding the max-algebraic characteristic polynomial for permutation matrices encoded using the lengths of their constituent cycles is NP-complete. (2) The task of finding the lowest order finite term of the max-algebraic characteristic polynomial for a matrix can be converted to the assignment problem....
On the computation of the minimal polynomial of a polynomial matrix
The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples.
On the determinantal inequalities.
On the dispersions of the polynomial maps over finite fields.
On the Fischer inequality
On the Frobenius condition number of positive definite matrices.
On the function .
On the matrix negative Pell equation
Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) with d ∈ N for nonsingular , i=1,...,n.
On the Maximum Value of a Class of Determinants
On the non-quadraticity of values of the q-exponential function and related q-series
On the order of linear dependence of real functions
On the permanents of certain circulant matrices and related Toeplitz matrices. (Über die Permanente gewisser zirkulanter Matrizen und damit zusammenhängender Toeplitz-Matrizen.)
On uniform symmetrization of analytic matrix functions
On-line Ramsey theory.
Optimal design in small amplitude homogenization
This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of H-measures we are able to prove general existence theorems for small amplitude optimal design and to provide...
Orthogonality of immanants