Seasonal variations of the composition,structural features,and antitumor properties of polysaccharides from <Emphasis Type="Italic">Padina pavonica</Emphasis> (Lebanon) as a function of composition

The variation of the polysaccharide composition of the brown alga Padina pavonica from the Mediterranean Sea was studied as a function of the collection season (April–July). It was shown that the principal polysaccharide (8.0-13.3% of dry alga weight) was alginic acid. Its content did not undergo significant changes from April to July. The content of water-soluble polysaccharides (laminarans and fucoidans) was low (<0.3% of dry alga weight). Water-soluble polysaccharides of the studied alga were practically pure fucoidan. The amount of laminarans was insignificant (<0.01% of dry alga weight). The content of fucoidans increased in alga samples from May through July. It was shown that P. pavonica is a promising source of alginic acids, which have a high capacity for gelation, and fucoidans, which exhibit antitumor action against RPMI-7951 human melanoma cells.     

A note on representations for the inverses of tridiagonal matrices

In this note, we propose an explicit representation with the nested sums for the entries of the inverses of general tridiagonal nonsingular matrices. Its equivalence with other particular representations, based on the combinatorial expressions or the continued fractions, is considered. In addition, an analytical representation for the entries of the finite sections of the resolvent of Jacobi matrices, in terms of its related orthogonal polynomials, is observed.     

Effect of Microalgae Polysaccharides on Biochemical and Metabolomics Pathways Related to Plant Defense in Solanum lycopersicum

Applied Biochemistry and Biotechnology - Microalgae are photosynthetic microorganisms that produce several bioactive molecules that have received considerable attention in scientific and industrial...     

Linear recurrence relations in the algebra of matrices and applications

We study here some linear recurrence relations in the algebra of square matrices. With the aid of the Cayley–Hamilton Theorem, we derive some explicit formulas for Aⁿ (nr) and e^tA for every r×r matrix A, in terms of the coefficients of its characteristic polynomial and matrices A^j, where 0jr−1.     

Some explicit formulas for the polynomial decomposition of the matrix exponential and applications

This paper is devoted to the study of some formulas for polynomial decomposition of the exponential of a square matrix A. More precisely, we suppose that the minimal polynomial M_A(X) of A is known and has degree m. Therefore, e^tA is given in terms of P₀(A),…,P_m−1(A), where the P_j(A) are polynomials in A of degree less than m, and some explicit analytic functions. Examples and applications are given. In particular, the two cases m=5 and m=6 are considered.     

Parabolic–Elliptic Chemotaxis Model with Space–Time Dependent Logistic Sources on $$\mathbb {R}^N$$ R N . III: Transition Fronts

Journal of Dynamics and Differential Equations - The current work is the third of a series of three papers devoted to the study of asymptotic dynamics in the following parabolic–elliptic...