The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined indices, is invariant under taking duals. In this paper, we generalize the to regularized by showing that, although suitably generalized operator not duals, between its at an index and dual written explicitly in terms of gamma function.

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

Abstract For a finite abelian p -group A and subgroup $\Gamma \le \operatorname {\mathrm {Aut}}(A)$ , we say that the pair $(\Gamma ,A)$ is fusion realizable if there saturated system ${\mathcal {F}}$ over $S\ge A$ such $C_S(A)=A$ $\operatorname {Aut}}_{{\mathcal {F}}}(A)=\Gamma $ as subgroups of . In this paper, develop tools to show certain representations are not in sense. example, show, for...

In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

We prove a local-global compatibility result in the mod $p$ Langlands program for $\mathrm{GL}_2(\mathbf{Q}_{p^f})$. Namely, given global residual representation $\bar{r}$ that is sufficiently generic at $p$, we diagram occurring corresponding Hecke eigenspace of completed cohomology determined by restrictions to decomposition groups $p$. If these are moreover semisimple, show $(\varphi,\Gamma)...

The 4 dimensional (4d) Jordan totient matrix which is described by the aid of famous Jordan's function and some new double sequence spaces as domain this aforementioned have been examined Erdem Demiriz . In present paper, first all we define two using 4d show that newly are Banach with their norm. Then, give inclusion relations including spaces. Moreover, compute $\alpha$-, $\beta(bp)$- $\gamma...

We show that various duals that occur in optimization and constraint satisfaction can be classified as inference duals, relaxation duals, or both. We discuss linear programming, surrogate, Lagrangean, superadditive, and constraint duals, as well as duals defined by resolution and filtering algorithms. Inference duals give rise to nogood-based search methods and sensitivity analysis, while relax...

in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...