Recently, infinite and finite dimensional Generalized Hilbert tensors have been introduced. In this paper, the authors further introduce infinite and finite dimensional Generalized Cesaro tensors as a generalization of Cesaro matrices and discuss the properties of these structured tensors. Next, some  upper bounds of $Z_{1}$-spectral radius of Generalized Cesaro tensors  and  Generalized Hilbert tensors are given,  which improves the existing ones. Finally, we obtain conditions under which a Generalized Cesaro tensor is column sufficient tensor.

The relativistic Dirac equation under spin symmetry is investigated for Generalized Morse potential. We calculated the eigenvalues and the corresponding wave function by using the Nikiforov-Uvarov method. We also discussed two special cases: attractive radial and Deng-Fan potentials. We have also reported some numerical results and figures to show the effect of tensor interaction.

This paper aims to extend a Krylov subspace technique based on an in-complete orthogonalization of Krylov tensors (as a multidimensional exten-sion of the common Krylov vectors) to solve Generalized Sylvester tensor equations via the Einstein product. First, we obtain the tensor form of the quasi-GMRES method, and then we lead to the direct variant of the proposed algorithm. This approach has the great advantage that it uses previous data in each iteration and has a low computational cost. More-over, an upper bound for the residual norm of the approximate solution is found. Finally, several experimental problems are given to show the acceptable accuracy and efficiency of the presented method.

In this paper, we introduce the concept of Generalized difference lacunary weak convergence of sequences. Using the concept of difference operator, we have introduced some new classes of sequences. We investigated several of its algebraic and topological properties, such as solidness, symmetry and monotone. We gave appropriate examples and detailed discussions to validate our established  failure instances and definitions. Further, we have established some inclusion relations of the introduced sequence spaces with other sequence spaces, in particularly with the weak Ces`aro summable sequences.

Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with tensor data. Precisely, the goal of MDA  is to find mode-specific projections that optimally separate tensor data from different classes. However, to solve this task, standard MDA methods use alternating optimization heuristics involving the computation of a succession of tensor-matrix products. Such approaches are most of the time difficult to solve and not natural, highligthing the difficulty to formulate this problem in fully tensor form. In this paper, we propose to solve multilinear discriminant analysis (MDA) by using the concept of transform domain (TD) recently proposed in [15]. We show here that moving MDA to this specific transform domain make its resolution easier and more natural. More precisely, each frontal face of the transformed tensor is processed independently to build a separate optimization sub-problems easier to solve. Next, the obtained solutions are converted into projective tensors by inverse transform. By considering a large number of experiments, we show the effectiveness of our approach with respect to existing MDA methods.

The present paper aims to study about (ϵ)-LP-Sasakian manifolds with the Generalized symmetric metric connection. We have an example satisfying (ϵ)-LP-Sasakian manifolds with the Generalized symmetric metric connection. Further, we studied D-conformally-flat and ξ-D-conformally flat curvature conditions in (ϵ)-LP-Sasakian manifolds with the Generalized symmetric metric connection.

The Markowitz-based portfolio selection turns to an NP-hard problem when considering cardinality constraints. In this case, existing exact solutions like quadratic programming may not be efficient to solve the problem. Many researchers, therefore, used heuristic and metaheuristic approaches in order to deal with the problem. This work presents Asexual Reproduction Optimization (ARO), a model-free metaheuristic algorithm inspired by the asexual reproduction, in order to solve the portfolio optimization problem including cardinality constraint to ensure the investment in a given number of different assets and bounding constraint to limit the proportions of fund invested in each asset. This is the first time that this relatively new metaheuristic is applied in the field of portfolio optimization, and we show that ARO results in better quality solutions in comparison with some of the well-known metaheuristics stated in the literature. To validate our proposed algorithm, we measured the deviation of the obtained results from the standard efficient frontier. We report our computational results on a set of publicly available benchmark test problems relating to five main market indices containing 31, 85, 89, 98, and 225 assets. These results are used in order to test the efficiency of our proposed method in comparison to other existing metaheuristic solutions. The experimental results indicate that ARO outperforms Genetic Algorithm (GA), Tabu Search (TS), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) in most of test problems. In terms of the obtained error, by using ARO, the average error of the aforementioned test problems is reduced by approximately 20 percent of the minimum average error calculated for the above-mentioned algorithms.

Abstract : In this paper it is attempted to reconstruct the depositional environment of the Jeirud Formation in Aro section. The Jeirud Formation (Late Devonian) is composed of about 45 meters of clastic sedimentary units in the southwest of Firoozkuh city, southern Alborz area. To carry out this research a field work was done during which a precise and detailed sedimentary log of the section was prepared and 52 samples from different lithologies of the formation were collected. Thin sections were prepared from all conglomeratic and sandstone samples, besides some thin sections were prepared from mudrocks and just 1 sample of paleosoil and then all were petrographically studied. In the study area, both basal and top boundary of the Jeirud Formation is disconformable with Mila and Mobarak formations respectively. All facies in the section include clastics (conglomerates, sandstones, mudstones and a paleosoil horizon). The facies were classified based on Miall classification so that conglomeratic facies comprise Gcm and Gmm; sandstone facies comprise Sh, Sp and Sm and mudrocks include Fl and Fm facies. Combined field and lab studies resulted in identification of two sedimentary facies associations including channel fill and flood plain facies associations. The reconstructed sedimentary environment of the Jeirud Formation in the Aro area represents a braided river depositional environment. The lower parts of this formation represent a finning-upward sequence which indicates deposition within a braided river channel subenvironment (conglomerates and sandstones) and the upper part is dominated with mudrocks with a paleosoil horizon representing deposition in a flood plain subenvironment.

The recurrence and birecurrence property in Finsler space have been studied by the Finsleriangeometrics. The aim of this paper is to obtain the necessary and sufficient condition for Cartan’s secondcurvature tensor that is recurrnt and birecurrent in Generalized BP−recurrent space and GeneralizedBP−birecurrent space, respectively. We discuss certain identities belong to the mentioned spaces. Further,we end up this paper with some illustrative examples.

Recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. Using this machinery, we have defined the concept of symmetric curvature. This concept is natural and is related to the notions divergence and Laplacian of vector fields. This concept is also related to the derivations on the algebra of symmetric forms which has been discussed by the authors. We introduce a new class of geometric vector fields and prove some basic facts about them. We call these vector fields affinewise. By contraction of the symmetric curvature, we define two new curvatures which have direct relations to the notions of divergence, Laplacian, and the Ricci tensor.