In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

In this paper, a design method for a robust PI/PID controller for fuzzy parametric uncertain systems is proposed. An uncertain Linear Time Invariant (LTI) system with fuzzy coefficients is referred as fuzzy parametric uncertain system. The fuzzy coefficients are approximated by intervals (crisp sets) using the nearest interval approximation approach to obtain an interval system. Further, a robu...

Abstract We define a class of invariants, which we call homological for persistence modules over finite poset. Informally, invariant is one that respects some data and takes values in the free abelian group generated by set indecomposable modules. focus particular on groups “spread modules,” are sometimes called “interval modules” theory literature. show both dimension vector rank equivalent to...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.

We consider stochastic perturbations of expanding maps of the interval where the noise can project the trajectory outside the interval. We estimate the escape rate as a function of the amplitude of the noise and compare it with the purely diffusive case. This is done under a technical hypothesis which corresponds to stability of the absolutely continuous invariant measure against small perturba...

To examine a possible biological mechanism for a cognitive timer, the stochastic dynamics of a network of neurons possessing two stable states ("on" and "off" states) is studied. The fraction of on neurons existing at t = 0 remains large for an extended interval, and then abruptly falls. The distribution of the lengths of the interval is scale invariant in the following sense: The ratio (k root...

One-dimensional Fisher-Wright diffusion process on the interval $(0,1)$ with mutations is considered. This a widely known model in population genetics. The goal of paper an exponential recurrence process, which also implies rate convergence towards invariant measure.

Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful functions is further specified. Several already known results for comparison meaningful functions and invariant functions are obtained as consequences of our description.