43 research outputs found
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 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, and \hat
H_\ve, giving rise respectively to the unperturbed and to the perturbed
evolution. The Hamiltonian 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 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 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