One of the most commonly observed surface structures on the prokaryotic cell envelopes is monomolecular crystalline array of proteinaceous subunits termed Surface Layers or S-layers. Due their self assembly ability and the highly ordered, regular structure down to the nanometer scale, S-layers were demonstrated to possess a great potential for nanobiotechnological applications. Some probiotic b...

In the present paper, for a positive integer $r$, we study bi-periodic $r$-Fibonacci sequence and its family of companion sequences, $r$-Lucas type $s$ with $1 \leq s r$, which extend classical Fibonacci Lucas sequences. Afterwards, establish link between Furthermore, give their properties as linear recurrence relations, generating functions, explicit formulas Binet forms.

Based on two integration steps, an optimization framework is proposed in this work for the synthesis and design of complex distillation sequence. The first step is to employ heat integration in sequence and reduce the heat consumption and total annual cost of the process. The second one is to increase the exergetic efficiency of sequence by generating power in implemented expanders in sequence....

In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuz...

In this paper, we exhibit a sequence of strongly connected aperiodic weakly monotonic automata, whose level increases with the number of states. Mathematics Subject Classification: 20M35, 68Q45, 20M07

let $p$ be a prime number greater than three. in this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(s)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm ext}_a^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{z}_p,mathbb{z}_p)$ up to nonzero scalar in the adams spectral sequence, where $ngeq m+2>5$, $0leq sext}_a^{s+2,q[(s+2)p...

‎Let $p$ be a prime with $pgeq 7$ and $q=2(p-1)$‎. ‎In this paper‎ ‎we prove the existence of a nontrivial product of‎ ‎filtration $s+4$ in the stable homotopy groups of spheres‎. ‎This nontrivial‎ ‎product is shown to be represented up to a nonzero scalar by‎ ‎the product element $widetilde{gamma}_{s}b_{n-1}g_{0}in‎ ‎{Ext}_{mathcal{A}}^{s+4,(p^n+sp^2+sp+s)q+s-3}(mathbb{Z}/p,mathbb{Z}/p)$‎ ‎in ...

1. Throughout this paper, c 1 , c2 , . . . denote absolute constants ; ko (a, fl, . . .), kr (a, f3, . . .), . . ., xo (a, /3, . . .), . . . denote constants depending only on the parameters a, /l, . . . ; v(n) denotes the number of the prime factors of the positive integer n, counted according to their multiplicity . The number of the elements of a finite set S is denoted by I S I . Let k, n b...