In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

We consider the quenched and averaged (or annealed) large deviation rate functions Iq and Ia for space-time and (the usual) space-only RWRE on Z. By Jensen’s inequality, Ia ≤ Iq. In the space-time case, when d ≥ 3 + 1, Iq and Ia are known to be equal on an open set containing the typical velocity ξo. When d = 1+1, we prove that Iq and Ia are equal only at ξo. Similarly, when d = 2+1, we show th...

Educational inequality is one of the types of inequality which always pervades on an educational system. The existence of the educational inequality alongside other inequalities and their interaction are the most important in a society. This paper attempts to examine the factors that affect educational inequality in Kazeroon city. The method of present study is survey and data collection tool i...

Let .~" be a family of 2 "+1 subsets of a 2n-element set. Then the number of disjoint pairs in ~" is bounded by (1 + o(1))22". This proves an old conjecture of Erd/Ss. Let ~" be a family of 2 tl/tk+l~+~" subsets of an n-element set. Then the number of containments in ,~ is bounded by / I~1 'X (1 1/k + o(1)) k 2 :" This verifies a conjecture of Daykin and Erd/Ss. A similar Erd6s-Stone type resul...