SUSY-hierarchy of one-dimensional reflectionless potentials

A class of one-dimensional reflectionless potentials, an absolute transparency of which is concerned with their belonging to one SUSY-hierarchy with a constant potential, is studied. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless potentials, have a simple analytical view and are expressed through finite number of elementary functions (unlike some reflectionless potentials, which are constructed on the basis of soliton solutions or are shape invariant in one or many steps with involving scaling of parameters, and are expressed through series), is obtained. An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible), i.e. which has the form $V(x) = \pm \alpha / |x-x_{0}|^{n}$ (where $\alpha$ and $x_{0}$ are constants, $n$ is natural number), is fulfilled. It is shown that such a potential can be reflectionless at n = 2 only. A SUSY-hierarchy of the inverse power reflectionless potentials is constructed. Isospectral expansions of this hierarchy is analyzed.Comment: 33 pages, 10 files of figures in EPS format, LaTeX v.2e, ElsArt styl

Ethical aspects on partnership Christian Orthodox Church – medical institutions concerning the organ transplantation

The explosive technological progress in medicine generated a need of ethic, moral and religious evalution concerning new medical achievements. In this way, the present study reveals an Orthodox Cristian point of view on such contradictory medical practice as it is the organ transplantation. The quintessence of study resides in fact that Orthodox Church conception regarding the organ transplantation is aproving, however, this practice should be limited in certain bioethic and biotheological requirements, so it could be religiously accepted

Geometric singular perturbation theory for stochastic differential equations

We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths of the stochastic system are concentrated in a neighbourhood of the slow manifold, which we construct explicitly. Depending on the dynamics of the reduced system, the results cover time spans which can be exponentially long in the noise intensity squared (that is, up to Kramers' time). We obtain exponentially small upper and lower bounds on the probability of exceptional paths. If the slow manifold contains bifurcation points, we show similar concentration properties for the fast variables corresponding to non-bifurcating modes. We also give conditions under which the system can be approximated by a lower-dimensional one, in which the fast variables contain only bifurcating modes.Comment: 43 pages. Published version. Remarks added, minor correction

Проблема создания и внедрения апипрепаратов в Украине

Представлены основные направления исследований кафедры аптечной технологии лекарств НФаУ по созданию и внедрению отечественных апипрепаратов в Украине. Создано четыре биологически активные субстанции из прополиса, обножки пчелиной, на основе которых теоретически и экспериментально обоснованы составы и технология лекарственных препаратов в форме таблеток, мазей, суппозиториев, капсул и др. Получено разрешение к медицинскому применению и промышленному производству 10 лекарственных препаратов. Пять лекарственных препаратов различной направленности действия: противовоспалительного, антимикробного, андрогенного, противотуберкулезного, противолучевого, находятся на стадиях доклинического и клинического изучения.Проблема создания и внедрения апипрепаратов в Украин

The effect of additive noise on dynamical hysteresis

We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the forcing and on noise intensity, there are three qualitatively different types of hysteresis cycles. Below a critical noise intensity, the random area enclosed by hysteresis cycles is concentrated near the deterministic area, which is different for small and large driving amplitude. Above this threshold, the area of typical hysteresis cycles depends, to leading order, only on the noise intensity. In all three regimes, we derive mathematically rigorous estimates for expectation, variance, and the probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure

Indexing multi-dimensional uncertain data with arbitrary probability density functions

Research Session 26: Spatial and Temporal DatabasesIn an "uncertain database", an object o is associated with a multi-dimensional probability density function (pdf), which describes the likelihood that o appears at each position in the data space. A fundamental operation is the "probabilistic range search" which, given a value p q and a rectangular area r q, retrieves the objects that appear in r q with probabilities at least p q. In this paper, we propose the U-tree, an access method designed to optimize both the I/O and CPU time of range retrieval on multi-dimensional imprecise data. The new structure is fully dynamic (i.e., objects can be incrementally inserted/deleted in any order), and does not place any constraints on the data pdfs. We verify the query and update efficiency of U-trees with extensive experiments.postprintThe 31st International Conference on Very Large Data Bases (VLDB 2005), Trondheim, Norway, 30 August-2 September 2005. In Proceedings of 31st VLDB, 2005, v. 3, p. 922-93

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System