for any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. the condition is that every minimal ideal of the ring consist entirely of bounded elements. it is not too stringent, and is satisfied, for instance, by rings of conti...

in this paper we study some results on noetherian semigroups. we  show that if  $s_s$ is an  strongly  faithful $s$-act and $s$ is a duo weakly noetherian, then we have the following.

Memristors have pinched hysteresis loops in the V − I plane. Ideal memristors are everywhere non-linear, cross at zero and are rotationally symmetric. In this paper we extend memristor theory to produce different types of non-ideality and find that: including a background current (such as an ionic current) moves the crossing point away from zero; including a degradation resistance (that increas...

We study the initial ideal of binomial edge ideal in degree 2 ([in<(JG)]2), associated to a graph G. We computed dimension, depth, Castelnuovo-Mumford regularity, Hilbert function and Betti numbers of [in<(JG)]2 for some classes of graphs. AMS Mathematics Subject Classification (2010): 05E40, 16E30

We prove the uniqueness of chemical equilibrium for an ideal mixture of ideal gases in a closed, spatially homogeneous volume. Uniqueness, a fundamental issue of chemical physics, is incompletely justified in textbooks and much of the scientific literature. We first reproduce a little known proof by Zel’dovich and show in a more direct fashion than originally presented that a unique equilibrium...

In Yoshida [11], a method to find ideal points and boundary slopes from an ideal triangulation was introduced. But the method only gives a necessary condition which the valuation corresponding to an ideal point satisfies. We give a simple sufficient condition for the existence of the corresponding ideal points.