Space of images of the mixed Riesz hyperbolic B-potential and analytic continuation

In this paper we prove semigroup properties for the mixed Riesz hyperbolic B-potential, find its analytic continuation and describe a space of images of mixed hyperbolic Riesz B-potentials. This problem is closely related to the problem of inversion of the weighted Radon transform on Lorentzian manifold

Noise-induced escape in an excitable system

We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation

On recovery of the singular differential Laplace-Bessel operator from the Fourier-Bessel transform

This paper is devoted to the problem of the best recovery of a fractional power of the B-elliptic operator of a function on R₊ᴺby its Fourier-Bessel transform known approximately on a convex set with the estimate of the difference between Fourier-Bessel transform of the function and its approximation in the metri

Generalized compactness in linear spaces and its applications

The class of subsets of locally convex spaces called $\mu$-compact sets is considered. This class contains all compact sets as well as several noncompact sets widely used in applications. It is shown that many results well known for compact sets can be generalized to $\mu$-compact sets. Several examples are considered. The main result of the paper is a generalization to $\mu$-compact convex sets of the Vesterstrom-O'Brien theorem showing equivalence of the particular properties of a compact convex set (s.t. openness of the mixture map, openness of the barycenter map and of its restriction to maximal measures, continuity of a convex hull of any continuous function, continuity of a convex hull of any concave continuous function). It is shown that the Vesterstrom-O'Brien theorem does not hold for pointwise $\mu$-compact convex sets defined by the slight relaxing of the $\mu$-compactness condition. Applications of the obtained results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad

Advances in and Issues With Minimally Invasive Surgery for Rectal Cancer in Elderly Patients

Colorectal cancer ranks third after breast cancer in terms of incidence and second after lung cancer in terms of mortality.Management of rectal cancer requires a multidisciplinary approach, with the surgical management playing the main role. There are currently three resective techniques that complement the traditional open surgery: laparoscopic surgery, robotic surgery, and transanal total mesorectal excision.Rectal cancer in elderly patients is particularly hard to diagnose and treat surgically due to multiple comorbidities and limited functional reserve. Treatment of such patients may be associated with poorer outcomes after both open and minimally invasive surgery.This article reviews the current state of advances in minimally invasive surgery for rectal cancer in general and in elderly patients in particular

On properties of the space of quantum states and their application to construction of entanglement monotones

We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using these results we analyze two infinite-dimensional versions (discrete and continuous) of the convex roof construction of entanglement monotones, which is widely used in finite dimensions. It is shown that the discrete version may be 'false' in the sense that the resulting functions may not possess the main property of entanglement monotones while the continuous version can be considered as a 'true' generalized convex roof construction. We give several examples of entanglement monotones produced by this construction. In particular, we consider an infinite-dimensional generalization of the notion of Entanglement of Formation and study its properties.Comment: 34 pages, the minor corrections have been mad