We show a reduction of Hilbert’s tenth problem to the solvability of the matrix equation A1 1 A i2 2 · · ·A ik k = Z over non-commuting integral matrices, where Z is the zero matrix, thus proving that the solvability of the equation is undecidable. This is in contrast to the case whereby the matrix semigroup is commutative in which the solvability of the same equation was shown to be decidable ...

Let A be a k × k matrix over a ring R; let GM (A, R) be the digraph with vertex set R k , and an arc from v to w if and only if w = Av. In this paper, we determine the numbers and lengths of the cycles of GM (A, R) for k = 2 in the following two cases. (a) R = F F q , the q–element finite field, and (b) R = Z Z/nZ Z and GCD(n, det(A)) = 1. This extends previous results for k = 1 and R = Z Z/nZ ...

The traditional way to model the visual appearance of the image is to define the spatial interactions of the image voxels in terms of their neighboring voxels. A new spatial interaction model was developed for the 3D lung data by extracting new spatial features based on NMF. Let GNx,y,z ∈ QIx×Iy×Iz be the image signals of the neighborhood of the voxel (x, y, z). By including the image signals o...

Bu makalede, değişken bir çıkış gerilimi ve kademeli olarak değişen frekansı elde etmek için tek fazlı matris dönüştürücü ile birlikte Z-kaynak ağı kullanılan alternatif akım-alternatif akım (AA-AA) yapısı incelenmiştir. yapısında, hem düşürülebilmekte de yükseltilebilmektedir. Matris dönüştürücü, doğrudan AA-AA dönüşüm yaparken anahtarlama stratejisi frekansını değiştirme imkânı sağlamaktadır....

This paper deals with bi-matrix games random payoffs. Using probability tools, we propose a solution based on the concept of Z-equilibrium. Then, give sufficient conditions its existence. Further, problem computation this is transformed into determination Pareto optimal solutions deterministic bi-criteria minimization problem. Finally, provide illustrative numerical examples.

Let A be a matrix with the absolute values of all eigenvalues strictly larger than one, and let Z 0 be a subset of Z such that n 2 Z 0 implies n + 1 2 Z 0. Denote the space of all compactly supported distributions by D 0 , and the usual convolution between two compactly supported distributions f and g by f g.

We prove that for any n × n matrix, A, and z with |z| ≥ ‖A‖, we have that ‖(z − A)−1‖ ≤ cot( π 4n )dist(z, spec(A)). We apply this result to the study of random orthogonal polynomials on the unit circle.

Already for a long time it is known that quaternionic polynomials whose coefficients are located only at one side of the powers, may have two classes of zeros: isolated zeros and spherical zeros. Only recently a classification of the two types of zeros and a means to compute all zeros of such polynomials have been developed. In this investigation we consider quaternionic polynomials whose coeff...

By providing a matrix version of Koenig's theorem we reduce the problem of evaluating the coeecients of a monic factor r(z) of degree h of a power series f (z) to that of approximating the rst h entries in the rst column of the inverse of an innnite Toeplitz matrix in block Hessenberg form. This matrix is reduced to a band matrix if f (z) is a polynomial. We devise a suitable algorithm, based o...

In this paper, convolutional network coding is formulated by means of matrix power series representation of the local encoding kernel (LEK) matrices and global encoding kernel (GEK) matrices to establish its theoretical fundamentals for practical implementations. From the encoding perspective, the GEKs of a convolutional network code (CNC) are shown to be uniquely determined by its LEK matrix K...