‎In this paper‎, ‎first we develop the duality concept for $g$-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every $g$-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎$g$-frames and generalize some resu...

Early mouse embryos express two morphological subtypes of intracisternal A-type particles, one resembling those occurring in mouse tumors (referred to as IAP) and the other apparently specific for early embryos [referred to as IAP(epsilon)]. Using cloned fragments of IAP genes as labeled probes in dot-hybridization experiments, we detected IAP-related RNA sequences in mouse oocytes and preimpla...

Let d be a fixed positive integer and let ε > 0. It is shown that for every sufficiently large n ≥ n0(d, ε), the d-dimensional unit cube can be decomposed into exactly n smaller cubes such that the ratio of the side length of the largest cube to the side length of the smallest one is at most 1 + ε. Moreover, for every n ≥ n0, there is a decomposition with the required properties, using cubes of...

In this article we study the asymptotic behavior of small eigenvalues Riemann surfaces for large genus. We show that any positive integer $k$, as genus $g$ goes to infinity, smallest $k$-th eigenvalue in thick part moduli space is uniformly comparable $\frac{1}{g^2}$ $g$. proof upper bound, constant $\epsilon>0$, will construct a closed surface $\epsilon$-thick such it admits pants decompositio...

Abstract We review the relation between half-BPS Wilson–’t Hooft line operators in ${\mathcal{N}}=2$ supersymmetric gauge theories on twisted space-time $S^1 \times_\epsilon \mathbb{R}^2 \times \mathbb{R}$ and transfer matrices constructed from trigonometric L-operators of an integrable system.

The evolution of the probabilities of genetic identity within and between the loci of a multigene family is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, and the location dependence of th...

In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Ga...

Recently, in paper [14], we have introduced the following deformed $(\alpha, \beta)$-metric: $$ F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta where $\alpha=\sqrt{a_{ij}y^{i}y^{j}}$ is a Riemannian metric; $\beta=b_{i}y^{i}$ 1-form, $\left|\epsilon\right|<2\sqrt{a+1}$ real parameter and $a\in \left(\frac{1}{4},+\infty\right)$ positive scalar. The aim of...

an equitable domination has interesting application in the contextof social networks. in a network, nodes with nearly equal capacitymay interact with each other in a better way. in the societypersons with nearly equal status, tend to be friendly. in thispaper, we introduce new variant of equitable domination of agraph. basic properties and some interesting results have beenobtained.