Matrix continued fractions and Expansions of the Error Function

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued fraction expansions of the error function erf(A) where A is a matrix. At the end, some numerical examples illustrating the theoretical results are discussed

Cryptography based on the Matrices

In this work we introduce a new method of cryptography based on the matrices over a finite field $\mathbb{F}_{q}$, were $q$ is a power of a prime number $p$. The first time we construct the matrix $M=\left( \begin{array}{cc} A_{1} & A_{2} \\ 0 & A_{3} \\ \end{array} \right)$ were \ $A_{i}$ \ with $i \in \{1, 2, 3 \}$ is the matrix of order $n$ \ in \ $\mathcal{M}(\mathbb{F}_{q})$ - the set of matrices with coefficients in $\mathbb{F}_{q}$ - and $0$ is the zero matrix of order $n$. We prove that $M^{l}=\left( \begin{array}{cc} A_{1}^{l} & (A_{2})_{l} \\ 0 & A_{3}^{l} \\ \end{array} \right)$ were $(A_{2})_{l}=\sum\limits_{k=0}^{l-1} A_{1}^{l-1-k}A_{2}A_{3}^{k}$ for all $l\in \mathbb{N}^{\ast}$. After we will make a cryptographic scheme between the two traditional entities Alice and Bob

Production of β-glucosidases by European Armillaria species

International audienceAbstract Production of β-glucosidase was investigated in nine isolates of Armillaria representing four species found in Europe: Armillaria mellea and Armillaria ostoyae, considered to be pathogenic and moderately pathogenic, respectively, and Armillaria. gallica and Armillaria cepistipes, both considered to be non-pathogenic. β-glucosidase was predominantly produced in the rhizomorphs, while the vegetative mycelium produced only a low amount of enzyme. Pachlewski's medium containing ammonium tartrate, glucose, maltose and thiamine was very efficient in promoting differentiation and growth of rhizomorphs. In A. ostoyae and A. cepistipes, a large proportion of β-glucosidase production was endocellular, but the rhizomorphs of all species excreted significant amounts of the enzyme in the culture medium once they had grown. The pathogenic species A. ostoyae and A. mellea excreted significantly more β-glucosidase than the non-pathogenic species, indicating that this enzyme might play a key role in pathogenicity. Native intracellular β-glucosidases were visualized as three bands at 470, 164 and 82 kDa on polyacrylamide gradient gels. The native excreted enzymes exhibited two, three or four bands depending on the isolates, with molecular weights ranging from 170 to 400 kDa