The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence of the spectral formula chi(G)=sum_x (-1)^dim(x) = p(G)-n(G), where p(G) is the number of positive eigenvalues and n(G) is the number of negati...

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...

A class of recombinant phage lambda clones are recovered from human genomic libraries on Escherichia coli recB21 recC22 sbcB15 cells, which fail to form plaques on wild-type cells. We report experiments which address the mechanism of this inhibition. The introduction of the recombination-stimulating sequence chi into one such clone allows growth of this phage on Rec+ cells. In addition, the ins...

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic mapping. Then, obtain some best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, provide examples to show the effectiveness our results.

The recombination hotspot Chi, 5' G-C-T-G-G-T-G-G 3', stimulates the RecBCD recombination pathway of Escherichia coli. We have determined, with precision greater than previously reported, the distribution of Chi-stimulated exchanges around a Chi site in phage lambda. Crosses of lambda phages with single base-pair mutations surrounding a Chi site were conducted in and analyzed on mismatch correc...

In lytic cycle crosses with Red-Gam-lambda phage, particles were examined that had undergone an Int-mediated exchange. It was assumed that this exchange dimerized the circular lambda, making it packageable. Among these Int-mediated recombinants, particles were identified that had, in addition, enjoyed a close double exchange mediated by the RecBC pathway. Such close double exchanges indicate lo...

In this manuscript, we prove the existence and uniqueness of a common fixed point for continuous self-mapping over closed subset Hilbert space satisfying non-linear rational type contraction condition.

Sharp bounds are obtained for expressions involving Zeta and related functions at a distance of one apart. Since Euler discovered in 1736 a closed form expression for the Zeta function at the even integers, a comparable expression for the odd integers has not been forthcoming. The current article derives sharp bounds for the Zeta, Lambda and Eta functions at a distance of one apart. The methods...

In this paper, as a geometric approach to the fixed-point theory, we prove new fixed-figure results using notion of k-ellipse on metric space. For purpose, are inspired by Caristi type mapping, Kannan contraction, Chatterjea contraction and Ćirić contraction. After that, give some existence uniqueness theorems fixed k-ellipse. We also support our obtained with illustrative examples. Finally, pr...

In the present paper we analyze construction of fundamental analytic solutions (FAS) for generalized Kulish-Sklyanin models (KSM) vanishing (VBC) and constant boundary conditions (CBC). Using FAS one can reduce direct inverse scattering problems Lax operator to a Riemann-Hilbert problem (RHP). For VBC find two $\chi^+(x,t,\lambda) $ $\chi^-(x,t,\lambda) in upper/lower $\mathbb{C}_\pm$ complex $...