In this paper, we derive the general expression for the entries of the positive integer powers of the Min matrix A = [min{i, j}],i, j = 1, 2, . . ., n of arbitrary order. Also, we give Maple 18 procedures in order to verify our calculations.

In this paper,  rstly we derive a general expression for the mth power (m 2 N) for one type of tridiagonal matrices of even order. Secondly we present a method for computing integer powers of the antitridiagonal matrices that is corresponding with these matrices. Then, we present some examples to illustrate our results and give Maple 18 procedure in order to verify our calculations.

In traditional Data Envelopment Analysis (DEA) approaches, inputs and outputs are usually considered as exact and real values. The relative efficiency of the Decision Making Units (DMUs) is evaluated and it is known that the factors are inputs and/or outputs. However, there are some conditions under which the efficiency of DMUs should be calculated while the data are integer and ambiguous. Therefore, various integer DEA models have been proposed to determine the performance of DMUs when integer data and fuzzy factors are available. In addition, there are cases where the efficiency of DMUs should be determined when integer data and flexible factors are available. Therefore, some integer DEA methods have been proposed to calculate the performance of DMUs and specify the role of flexible measures when some of the data are integer and flexible factors are available. However, there are some situations where there are integer data, fuzzy integer measures and flexible factors. Therefore, this paper sheds light on the nature of the model to determine the efficiency of DMUs when there are integer inputs and/or outputs, flexible factors and fuzzy integer measures, and determines the role of factors with uncertain inputs or outputs. In fact, slacks are addressed and a slack-based efficiency measure (SBM) is defined to compute the performance of DMUs in the presence of flexible factors, integer data and fuzzy integer measures. The proposed approaches are demonstrated and illustrated using an example.

This paper elaborates on the government's powers - both at the domestic level and over foreign countries. The domestic power is the power against domestic lobbies, and the foreign one is the government's international power. To do so, this paper tries to evaluate the effects of these powers on the formation of free trade agreements (FTAs). The theoretical framework follows an oligopolistic-political economy. The main findings of the study show that the optimal solution for the government is paying more attention to the national welfare than lobbies' welfare. In addition, larger FTA helps the government have lower dependency on the lobbies. The paper indicates that the effects of foreign power on FTAs and shows that a larger FTA does not have always positive effects on expanding the FTAs. The effects depend on both domestic and foreign powers that are precisely described through this paper. The issues dealt here are not only theoretically interesting but are relevant while designing domestic and foreign policies.

In the legal- political system of Iran, resolving dispute and regulation of the powers relations, especially on thirty five years of the Islamic Republic history that led into the revision and modification of the Constitution, is special and unique issue that derived from the power distribution type in governance system of this country. Disputes and conflict jurisdictions problems sometimes results in unprecedented disputations that indicates different explanations from law. In recent years, this problem, despite some apparently regards again brought back into the political arena, thus it seriously required to be redesigned and fixed. The Leader created “Supreme institution of resolving dispute and regulation of the threefold powers relation” in the political arena of country based on paragraph 7 of Article 110 of the Constitution, in culmination of disputes between the threefold powers. Research in this newly established institution and review of paragraph 7 of article 110 of the Constitution as basic system of the resolving dispute and regulation of the powers relations in Iran make the main subject in this essay.

The hegemonic state usually creates and maintains a hegemonic order in order to achieve its interests. Thus, preventing major and central wars has become the most important goal of the hegemonic state in the hegemonic order. In contrast to the hegemonic state, there are emerging powers that, according to the variables of satisfaction, role, ideology and power developments and the role they experience, try to create regional order in accordance with their principles and rules and are considered as a challenge to the hegemonic order. The question of this paper is what principles are the main strategies of emerging powers in the hegemonic order? In response to this question, and considering the assumption of power dynamics and the effect of role and satisfaction variables on the design of actors strategies in the international system, it is hypothesized that the proximity of emerging powers to hegemony leads to role changes in actors behaviors and this leads to contrastive behavioral patterns and seizing the power gap will lead to the aggressive and challenging policies of the dissatisfied emerging actor. This study tries to explain the strategies of emerging powers in the hegemonic order by focusing on the theories of power cycle, hegemonic stability and power transition.