in recent years, many changes have been observed in buying culture of customers and developing chain stores in iran. moreover, need to be more competition in business environments made necessary the stablishment of chain stores, the creation of competitive advantage and long relations to the costumers. regular marketing is a response to stores requirement when establishing such a win-win long r...

Using weaker versions of the cardinal function $$\psi_c(X)$$ , we derive a series new bounds for cardinality Hausdorff spaces and regular that do not involve nor its variants at all. For example, show if X is then $$|X|\leq 2^{c(X)^{\pi\chi(X)}}$$ 2^{c(X)\pi\chi(X)^{ot(X)}}$$ where $$ot(X)$$ introduced by Tkachenko, has property $$ot(X)\leq\min\{t(X),c(X)\}$$ . It follows from latter space with...

In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.

Abstract For the family of double standard maps $f_{a,b}=2x+a+({b}/{\pi }) \sin 2\pi x \pmod {1}$ we investigate structure space parameters a when $b=1$ and $b\in [0,1)$ . In first case have critical point, but for set $E_1$ positive Lebesgue measure there is an invariant absolutely continuous $f_{a,1}$ second open non-empty $E_b$ which map $f_{a,b}$ expanding. We show that as $b\nearrow 1$ , a...

Problem 198. Pi Mu Epsilon Journal 4(Fall 1967)296 A semi-regular solid is obtained by slicing off sections from the corners of a cube. It is a solid with 36 congruent edges, 24 vertices and 14 faces, 6 of which are regular octagons and 8 are equilateral triangles. If the length of an edge of this polytope is e, what is its volume? Problem E2017. American Mathematical Monthly 74(Oct 1967)1005 L...

In recent years, recombinant DNA technology has been used to design insulin molecules that overcome the limitations of regular insulin in mealtime supplementation. However, safety issues have been raised with these alternatives, as the alteration of the three-dimensional structure may alter the interaction with the insulin and/or IGF-I receptors and therefore lead to the activation of alternate...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

In security games, a defender commits to a mixed strategy for protecting a set of n targets of values αi; an attacker, knowing the defender’s strategy, chooses which target to attack and for how long. We study a natural version in which the attacker’s utility grows linearly with the time he spends at the target, but drops to 0 if he is caught. The defender’s goal is to minimize the attacker’s u...

Let $f:A\rightarrow B$ be a ring homomorphism and $K$ an ideal of $B$. Many variations the notions clean nil-clean rings have been studied by variety authors. We investigate strongly $\pi$-regular clean-like properties amalgamation $A\bowtie^{f}K$ $A$ with $B$ along respect to $f$.