Linear diffusion layer is an important part of lightweight block ciphers and hash functions. This paper presents an efficient class of lightweight 4x4 MDS matrices such that the implementation cost of them and their corresponding inverses are equal. The main target of the paper is hardware oriented cryptographic primitives and the implementation cost is measured in terms of the required number ...

canine brucellosis is a zoonotic infectious disease caused by brucella canis. this bacterium can be transmitted to humans as well as other dogs. it is a significant cause of reproductive failure, predominantly in kennels. the aim of this study was to determine the seroprevalence of brucella canis infection in companion dogs referred to the veterinary hospital of shahid chamran university of ahv...

We explore combinatorial matrix patterns of order n for which some matrix entries are necessarily nonzero, some entries are zero, and some are arbitrary. In particular, we are interested in when the pattern allows any monic characteristic polynomial with real coefficients, that is, when the pattern is spectrally arbitrary. We describe some order n patterns that are spectrally arbitrary. We show...

Many applications give rise to structured, in particular T-palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P (λ)x = 0, where P (λ) is a T-palindromic matrix polynomial, it is convenient to use palindromic linearizations to ensure that the symmetries in the eigenvalues, elementary divisors, and minimal indices of P (λ) due to the palindromicity are preserved. I...

Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial has no nonreal roots, but typically nonreal roots are much more numerous than the real ones. We dramatically accelerate the known algorithms in this case by...

Many applications give rise to structured, in particular T-palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P (λ)x = 0, where P (λ) is a T-palindromic matrix polynomial, it is convenient to use palindromic linearizations to ensure that the symmetries in the eigenvalues, elementary divisors, and minimal indices of P (λ) due to the palindromicity are preserved. I...

Many applications give rise to structured, in particular T-palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P (λ)x = 0, where P (λ) is a T-palindromic matrix polynomial, it is convenient to use palindromic linearizations to ensure that the symmetries in the eigenvalues, elementary divisors, and minimal indices of P (λ) due to the palindromicity are preserved. I...

We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...

An efficient method for construction of J-unitary matrix polynomials is proposed, associated with companion functions the last row which a polynomial in 1/t. The relies on Wiener-Hopf factorization theory and stems from recently developed J-spectral algorithm certain Hermitian functions.

The classes of clean and nil-clean rings are closed with respect standard constructions as direct products and (triangular) matrix rings, cf. [12] resp. [4], while the classes of weakly (nil-)clean rings are not closed under these constructions. Moreover, while all matrix rings over fields are clean, [12] when we consider nil-clean rings there are strongly restrictions: if a matrix ring over a ...