We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials and one interval limiting spectrum. Our starting point is the result of [21] on the representation of the reproducing matrix kernels of orthogonal ensembles in terms of scalar reproducing kernel of corresponding unitary ensemble.

The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval time-varying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

We consider the concept of generalized Kolmogorov–Sinai entropy, where instead of the Shannon entropy function, we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this function, we show that this isomorphism invariant is linearly dependent on the Kolmogorov–Sinai entropy.

We study a two parameter family of piecewise linear transformations on the interval [0, 1] which have negative slope. We show that the nonwandering set consists of finitely many periodic orbits and an invariant set L which is topologically transitive and the disjoint union of finitely many closed intervals. We determine the number of these intervals.

In this paper, we consider the method for reconstructing a signal from a finite number of samples. In shift-invariant space framework, we derive an aproximately min-max optimal interpolator to to reconstruct a signal on an interval. An effective non-iterative algorithm for signal reconstruction is given also. Numerical examples show the effectiveness of the proposed method.

We construct examples of topologically conjugate unimodal maps, such that both of them have an absolutely continuous invariant measure, but for one of them that measure is finite, and for another one it is σ-finite and infinite on every interval. The work is based on the results of Al-Khal, Bruin and Jakobson [2].

This thesis is about scalable formal verification techniques for software. A verification technique is scalable if it is able to scale to reasoning about real (rather than synthetic or toy) programs. Scalable verification techniques are essential for practical program verifiers. In this work, we consider three key characteristics of scalability: precision, performance and automation. We explore...

in this paper, we give connection between the order of the generalized baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. moreover, we give a necessary and sufficient condition in which the generalized baer-invariant of a pair of groups can be embedded into the generalized baer-invariant of pair of its factor groups.