Nonadaptive search problem with sets of equal sum

Emil Kolev

Displaying similar documents to “Nonadaptive search problem with sets of equal sum”

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An n by n skew-symmetric type (-1; 1)-matrix K =[ki;j ] has 1’s on the main diagonal and ±1’s elsewhere with ki;j =-kj;i . The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n ≡ 0 mod 4 (skew-Hadamard matrices), but for n ≡ 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1;...

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In this paper we consider Bessel equations of the type $t^{2} X^{(2)} (t) + t X^{(1)} (t) + (t^{2} I - A^{2}) X (t) = 0$ , where A is an n $\times$ n complex matrix and X(t) is an n $\times$ m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.

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In this paper I present the Kronecker-Capelli theorem which states that a system of linear equations has a solution if and only if the rank of its coefficient matrix is equal to the rank of its augmented matrix.MML identifier: MATRIX15, version: 7.8.09 4.97.1001