In this paper, by using the concept of frames, two iterative methods are constructed to solve the operator equation $ Lu=f $ where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint linear operator on a separable Hilbert space $ H $. These schemes are analogous with steepest descent method which is applied on a preconditioned equation obtained by frames instead. We then investigate their convergence via corresponding convergence rates, which are formed by the frame bounds. We also investigate the optimal case, which leads to the exact solution of the equation. The first scheme refers to the case where $H$ is a real separable Hilbert space, but in the second scheme, we drop this assumption.

In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from a Hilbert $C^{\ast}$-module $\mathcal{H}$ to itself denoted by $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $. We give some properties relating to some constructions of integral $K$-operator frames and to operators preserving integral $K$-operator frame and we establish some new results.

Let $K$ be a bounded operator. $K$-frames are ordinary frames for the range $K$. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range $K$. Here we define the $K$-orthonormal basis and the $K$-Riesz basis, and then we describe their properties. As might be expected, the $K$-bases differ from the ordinary ones mentioned in this article.

In this study the main endeavor is to model dependence structure between crude oil prices of West Texas Intermediate (WTI) and Brent - Europe. The main activity is on concentrating copula technique which is powerful technique in modeling dependence structures. Beside several well known Archimedean copulas, three new Archimedean families are used which have recently presented to the literature. Moreover, convex combination of these copulas also are investigated on modeling of the mentioned dependence structure. Modeling process is relied on 318 data which are average of the monthly prices from Jun-1992 to Oct-2018.

‎Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $\ell^1(S)$ with coefficients in $\ell^\infty(S)$ (and also $\ell^1(S)^{(2n-1)}$ for $n\in \mathbb{N}$) are equal.

In this work systems of sines $sin left(n+beta right)t,, , n=1,2, ldots,$ and cosines $cos left(n-beta right)t,, , n=0,1,2, ldots,$ are considered, where $beta in R-$is a real parameter. The subspace $M^{p,alpha } left(0,pi right)$ of the Morrey space $L^{p,alpha } left(0,pi right)$ in which continuous functions are dense is considered. Criterion for the completeness, minimality and basicity of these systems with respect to the parameter $beta $ in the subspace $M^{p,alpha } left(0,pi right)$, $1<p <+infty, $ are found.

Despite the growing growth of technology, handwritten signature has been selected as the first option between biometrics by users. In this paper, a new methodology for offline handwritten signature verification and recognition based on the Shearlet transform and transfer learning is proposed. Since, a large percentage of handwritten signatures are composed of curves and the performance of a signature verification/recognition system is directly related to the edge structures, subbands of shearlet transform of signature images are good candidates for input information to the system. Furthermore, by using transfer learning of some pre-trained models, appropriate features would be extracted. In this study, four pre-trained models have been used: SigNet and SigNet-F (trained on offline signature datasets), VGG16 and VGG19 (trained on ImageNet dataset). Experiments have been conducted using three datasets: UTSig, FUM-PHSD and MCYT-75. Obtained experimental results, in comparison with the literature, verify the effectiveness of the presented method in both signature verification and signature recognition.

In this paper we consider (extended) metaplectic representation of the semidirect product $G_{\mathbb{J}}=\mathbb{R}^{2d}\times\mathbb{J}$ where $\mathbb{J}$ is a closed subgroup of $Sp(d,\mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{\mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Finally, we rewrite the dual conditions, by using the Wigner distribution and obtain more reconstruction formulas.

In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.

In this paper, at first, we introduce $alpha_{mu}$-admissible, $Z_mu$-contraction and $N_{mu}$-contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions via $alpha$-admissible simulation mappings, as well. Our results can be viewed as extension of the corresponding results in this area. Moreover, some examples and an application to functional integral equations are given to support the obtained results.