Applications of M.G. Krein's Theory of Regular Symmetric Operators to Sampling Theory

The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae. One major task in sampling theory is to find concrete, non trivial realizations of this theorem. In this paper we provide a new approach to this subject on the basis of the M. G. Krein's theory of representation of simple regular symmetric operators having deficiency indices (1,1). We show that the resulting sampling formulae have the form of Lagrange interpolation series. We also characterize the space of functions reconstructible by our sampling formulae. Our construction allows a rigorous treatment of certain ideas proposed recently in quantum gravity.Comment: 15 pages; v2: minor changes in abstract, addition of PACS numbers, changes in some keywords, some few changes in the introduction, correction of the proof of the last theorem, and addition of some comments at the end of the fourth sectio

Resonances in Models of Spin Dependent Point Interactions

In dimension $d=1,2,3$ we define a family of two-channel Hamiltonians obtained as point perturbations of the generator of the free decoupled dynamics. Within the family we choose two Hamiltonians, $\hat H_0$ and \hat H_\ve, giving rise respectively to the unperturbed and to the perturbed evolution. The Hamiltonian $\hat H_0$ does not couple the channels and has an eigenvalue embedded in the continuous spectrum. The Hamiltonian \hat H_\ve is a small perturbation, in resolvent sense, of $\hat H_0$ and exhibits a small coupling between the channels. We take advantage of the complete solvability of our model to prove with simple arguments that the embedded eigenvalue of $\hat H_0$ shifts into a resonance for \hat H_\ve. In dimension three we analyze details of the time behavior of the projection onto the region of the spectrum close to the resonance.Comment: Changes in the proof of theorem 3, few misprints corrected, 21 page

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page

Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions

© 2020 The Authors. Mathematische Nachrichten published by Wiley‐VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.fi=vertaisarvioitu|en=peerReviewed

Linking Catastrophe Modeling and Stochastic Optimization Techniques for Integrated Catastrophe Risk Analysis and Management

Planning regional economic developments and social welfare without addressing issues related to mitigation and adaptation to low probability-high consequences catastrophe risks may lead to dangerous clustering of people, production facilities, and infrastructure in hazard-prone areas thereby critically increasing regional vulnerability. The endogeneity of the risks on production allocation and land use decisions represents new challenges for regional sustainable development planning. This chapter argues that catastrophe risk analysis and management have to be addressed with an Integrated Assessment and Management Model (IAMM) linking catastrophe risk modeling (CRM) with stochastic optimization (STO) techniques for the design of optimal and robust mitigation and adaptation strategies for dealing with catastrophe risks of all kinds. IAMM enables us to address the challenging characteristics on policies, mutually dependent losses, the lack of information, the need for long-term perspectives and geographically explicit models, the involvement of various agents (such as individuals, farmers, producers, consumers, governments, insurers, investors), safety and security standards, and the need for robust decisions. Safety and security criteria relate to Value-at-Risk and Conditional Value at Risk measures generalizing the well-known risk criteria and indicators used for regulating engineering, critical infrastructure, energy, water, agricultural safety and security requirements. These are key indicators for dealing with low probability-high consequences risks. The linkage between CRM and STO is established through an iterative stochastic quasigradient procedure (SQG) defining a sequential “searching” process, which resembles an adaptive learning environment and improvement of decisions from data and simulations, i.e., the so-called Adaptive Monte Carlo optimization. The SQG methods are applicable in cases when traditional stochastic approximation, gradient or stochastic gradient methods do not work, in particular, to general two-stage problems with implicitly defined goals and constraints functions, nonsmooth and possibly discontinuous performance indicators, risk and uncertainties shaped by decision of various agents

Impedance of functionalized CNT/epoxy resin composites

The aim of this work is to study AC electrical properties of functionalized CNT/epoxy resin composites with different weight content of CNTs fillers. Experimental results for composites with different weight content of CNT filler have mostly quantitative differences and can be modeled using the same equivalent circuit consisting of connected in parallel resistance R (simulating resistance of nanotubes) and constant phase element CPE (taking into account spread in values of the resistance and capacitance of the intertube contact barriers).Белорусский Республиканский Фонд Фундаментальных Исследовани