In this paper, a three-dimensional solution with mixed layerwise formulation is presented for multi-layer composite plates with arbitrary geometry and boundary conditions.  In this study, the displacement field the out-of plane stresses are considered as a sum of a series of functions with unknown coefficients. The boundary conditions and the continuity of the displacement field and the traction stresses between the layers are exactly satisfied. Equilibrium and compatibility equations are also applied using the Reissner's variational principle. The results show that the mixed formulation has faster convergence than displacement based formulation, and provides more accurate values of interlaminar stresses.

In this study, a semi-analytical method based on the Reisner's mixed formulation is presented for the elastic analysis of anisotropic homogeneous solids with an edge or interior crack. In this method, the displacement and the stress fields are represented as the sum of a known function and a finite series of functions with unknown coefficients. The functions are constructed in such a way that the displacement discontinuity across the crack faces and the exact singular behavior of the stress field at the crack tip are captured, moreover all essential and natural homogeneous and inhomogeneous boundary conditions are satisfied exactly. The equilibrium and the compatibility equations are also applied with the desired accuracy using the Reissner's variational principle. Solution of the variational equation leads to a set of linear algebraic equations in terms of the unknown coefficients. After computing of the unknown coefficients, the displacement and the stress fields are obtained and subsequently the stress intensity factors (SIFs) and crack opening displacement (COD) are calculated. The results show that computing of SIFs has high convergence rate and the results of the proposed approach are in good agreement with those of the analytical solutions reported in the literature.

Characterizing simplicial complexes with vertex decomposability property is one of the main problems in combinatorial commutative algebra since they have many interesting algebraic and topological properties. In this regard introducing families of simplicial complexes with this property is of great interest and has been studied in many research papers. In this paper the Stanley-Reisner simplicial complex associated to the t-clique ideal of the complement of path graphs has been studied. For such a simplicial complex   we explain the set of facets of  and using this characterization we show that every such simplicial complex is vertex decomposable, whose shedding vertex is an endpoint of the path graph. Indeed this family of simplicial complexes are Cohen-Macaulay, since they are pure. Since edge ideals of graphs are in fact 2-clique ideals, this family of  simplicial complexes contains the independence complexes of complement of path graphs. Finally, as a consequence it is shown that the t-independence ideal of the complement of a path graph is vertex splittable and its Betti splitting is presented.

In this study, the solution of small mass impact on a moderately thick rectangular plate was derived semianalytically,based on elastic Hertzian contact law. A set of exact closed-form in-plane and transverse displacement equations are given for the first time, using the so-called Mindlin plate theory (a first-order shear deformation theory) for the plates having two opposite edges that are simply supported. The other two edges may be given any possible combination of free, simply-supported and clamped boundary conditions. The proposed analytical method is verified by observing excellent agreements to those available in the literature. Finally, the influence of boundary conditions,material properties, dimensions of the plate and initial velocity and radius of the spherical impactor on the impact parameters are examined and discussed in detail.

There has been many researches in the field of combinational commutative algebra; however, what makes this research distinct from the previous ones is its focus on monomial ideals and their connection to graphs. The present study aims at various goals one of which is analyzing the existence of linear resolution of such ideals. Concerning combinatorial commutative algebra there are numerous methods for creating connection between combinational objects and algebric objects‎. ‎This article is to study such objects through corresponding monomial ideals with graphs and simplicial complexes‎. ‎The most significant treatable ideals of simplicial complex include edge ideal and Stanly-Reisner ideal‎. Let r be a positive integer. A monomial ideal I is said to be linear in the first r steps, if for some integer d , β_(i.i+j) (I)=0 for all 0≤i

The informal Constitutional amendment is a process which alters the meaning and concept of the Constitution without changing its text. This process which may happen consciously or unconsciously as a result of the actions of governmental authorities and entities, changes the Constitution outside its formal amendment mechanism and in fact infringes that. One of the issues likely to have altered the Constitution in this way is the adoption of general policies of principle 44 by the Supreme Leader so that as a result of these policies, important evolutions have taken place in the way of investment, ownership and management of those envisioned in the beginning of the principle.
This paper seeks to examine the ratio between the general policies of principle 44 and the content of this principle with an analytic approach. The question is whether the Constitution has been changed with these policies or not. Simultaneous regard to the content of the beginning and last paragraph of principle 44, alternativeness of principle 44 from the viewpoint of Constitutional legislator, possibility of devolving the issues set forth in the beginning of the principle to non-governmental sector even prior to the adoption of the mentioned policies and other evidences all prove that the general policies have been in accordance with the Constitution and in line with principle 44.

Based on «the principle of immutability of litigation», although parties to the dispute have dominance on the thematic elements of legal claim, but also when the petition was set by the plaintiff, all of wanted things must be stipulated clearly in the offered petition by lawful condition observance, and also the defendant has defense right, under this required framework. After the trial begins, next changes have limitations which are followed in whole trial. The purpose of this principle is showing that although parties have free hearing right and defense right, but also based on the necessity of legal defense, discipline in the trial and speedy judgment consideration, they are limited on the principle of immutability of litigation. This study tries to specify position of this principle in the Iranian civil procedure and American Federal law (Federal rules of Civil procedure), basics of the principle and identify its exceptions for its better execution.

In its foreign policy, Islamic Iran has a value system derived from Islamic principles, which has been an important witness in post-revolutionary foreign policy in behavioral-value changes. These changes were due to the guidelines that Imam Khomeini (ra) gave in various decrees and orders, messages and recommendations, letters, speeches and interviews in various positions and occasions. In other words, Iran's foreign policy changed after the victory of the Islamic Revolution based on the values ​​of the revolution and was based on Islam. With the emergence of the Islamic Revolution of Iran and the formation of the Islamic Republic, the movement towards the implementation of Islamic laws and the influence of political jurisprudence on foreign policy and international relations was effective and from the very beginning a path to national independence was opened. Today, Shiite political jurisprudence is facing a new experience with the practical and tangible entry of jurists in socio-political affairs. The requirements of the new era, after the constitution, and especially the formation of the Islamic Republic, made this doubly important and made Shiite political jurisprudence the place of many reflections and questions. Due to the importance of the subject in this research, the application of selected principles of political jurisprudence in the foreign policy of the Islamic system has been analyzed. Among these principles that can be used as effective components of the Islamic system include the principle of composing hearts, the principle of expediency, the principle of invitation, the principle of increasing power and so on

Generalized Returns To Scale has been introduced to compute the rate of variation in outputs to the variation in inputs up to the Most Productive Scale Size pattern. In this paper, we  address the generalized RTS in the multiplicative models and we propose an algorithm to calculate the rate of variations in different intervals. We also demonstrate that the non-discretionary factors can be easily taken into account in the algorithm.