This research presents a numerical tool to estimate the Green's function operator Matrix of intraplate faults. Having this Matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. This information could be employed to predict the location of future powerful earthquakes. To implement fault sliding in FE calculations, Soft Material Technique as a simple method is applied. In this technique, the fault is modeled by a flexible (very low elasticity modulus) thin element. This material not only prevents fault planes overlapping, but exhibits a good consistency with the physical behavior of fault. In other words, this material ignores the strength of neighboring rocks ready to trigger sliding. In this research, without involving the nonlinear contact problem, two sides of the fault are dislocated as one unit, and the ground surface deformation is measured.Available geodetic data provides a proper opportunity to detect underground interactions. We can express observation equations with m observation data as:Bi=åj Aij Xj + Ei (i=1, …, m)                                                                                                             (1)where Bi are the observed surface deformations, Xj the slippage components along the fault, Ei the random errors, and Aij Green’s function operators (i.e., the elastic response at a point i to a unit source at a point j on the model source region). This equation can be rewritten in a Matrix form as:B = AX + E                                                                                                                                      (2)where A is an m×n coefficient Matrix.To minimize the errors, the length of the vector E has to be minimized. It may be shown that, standard inversion equations based on the least-square method are obtained as:   X=(ATA)-1ATB                                                                                                                                (3)where superscripts T and -1 indicate the transpose and inverse of a Matrix, respectively.This relation offers a straightforward way for finding the source vector X. One of the new aspects of the present study is the calculation of the Green’s function operator Matrix A by means of FEM. This issue enables us to overcome all limitations of traditional inverse methods.How can the Green’s function operators be found by FEM? By applying unit source vectors in each degree of freedom, the relevant response of ground surface nodes is the corresponding component of the coefficient Matrix A.The proposed numerical model is first compared by available analytical approaches, and gains its proper validity, one of the Tehran faults is modeled by this method to calculate the corresponding Green's function operator Matrix.

The main goal of this article is to extend the concept of special Matrix functions through the study of modified degenerate Gamma Matrix function. For this, the modified degenerate Gamma Matrix function has been introduced and some of its properties have been established. The article also presents limit representations, asymptotic equality, and infinite product representations. The new function of Matrix argument is an analogue of the Gamma Matrix function, and the properties are analogues of those satisfied by the Gamma Matrix function. Upon taking the limit as $\lambda \to 0^{+}$, the established results reduce to the results of the Gamma Matrix function.

Suppose that the random Matrix X has a Matrix variate normal distribution with the mean Matrix Θ and covariance Matrix Σ⊗Ψ where Σ and Ψ are known positive definite covariance matrices. This paper studies the soft Bayesian shrinkage wavelet estimation of the mean Matrix Θ . Soft Bayesian shrinkage wavelet estimator is proposed based on quadratic balanced loss function and Matrix variate normal $N_{p,m}(\mathbf{0}, \mathbf{\Lambda}\otimes \mathbf{\Psi})$ prior distribution. Λ is known positive definite covariance Matrix. By using the Bayes estimator as the target estimator in the quadratic balanced loss function and Stien's unbiased risk estimate technique, the soft Bayesian shrinkage wavelet threshold is obtained. Based on the new proposed threshold, we find the soft Bayesian shrinkage wavelet estimator of Θ mean Matrix. The simulation study and two real examples to measure the performance of the presented theoretical topics are used. The results show that the soft Bayesian shrinkage wavelet estimator dominates classical shrinkage wavelet estimators.

Although the genome is defined by its primary sequence, its functional properties are determined by far more complex mechanisms and depend on multiple layers of nuclear organization. The architecture of the nucleus includes two overlapping structures: the chromatin and a framework structure named the nuclear Matrix. Ultra-structural studies reveal that the nuclear Matrix is a network consisting of branched core filaments masked with a large number of hnRNPs and regulatory proteins. This scaffold has been demonstrated to be an active and dynamic structure, anchoring the nuclear processes such as replication, transcription and splicing making nuclear domains/foci. It is postulated that the nuclear Matrix serves as a dynamic support to bring together specific DNA sequences with factors involved in the regulation of genome functions. In this review, we attempt to introduce the structure and function of nuclear Matrix as an active intra-nuclear factor, having a critical dynamic role to organize different nuclear functions. Studying in vivo variations of this epigenetic parameter has been suggested to all investigators interested in the field of chromatin structure and itsdynamics.