Inverse eigenvalue problem for discrete three-diagonal Sturm-Liouville operator and the continuum limit

In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schroedinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This derivation is more correct in comparison with previous works which used only single-diagonal matrix. It is demonstrated that inverse problem procedure is nothing else than well known Gram-Schmidt orthonormalization in Euclidean space for special vectors numbered by the space coordinate index. All the results of usual inverse problem with continuous coordinate are reobtained by employing a limiting procedure, including the Goursat problem -- equation in partial derivatives for the solutions of the inversion integral equation.Comment: 19 pages There were made some additions (and reformulations) to the text making the derivation of the results more precise and understandabl

Электроснабжение производственных объектов станкостроительного завода ООО «ССЗ», г. Симбирск

Выпускная квалификационная рабoта 171с., 17 рис., 33 табл., 40источников, 14 прил. Ключевые слова: электроснабжение, линия, завод, трансформатор, подстанция, электро-приемник, нагрузка, оборудование, ток, напряжение. Объектом изучения является электрическая часть «Симбирского станкостроительного завода». Целью дипломной рабoты является, проектирование схемы электроснабжения предприятия, выбор оборудования. Процесс прохождения практики на изучаемом объекте, включил в себя сбор исходных данных по предприятию. По результатам исследования создана схема по электроснабжению от подстанции энергосистемы, до конечного электро-приемника. Произведён выбор: коммутационных оборудований, кабеля и проводов, а также сделаны необходимые проверки. В работе отражен экономический расчет на капитальные затрFinal qualifying rabota 171s., 17 fig., 33 tab., 40istochnikov 14 adj. Keywords: electricity, line, plant, transformer substation, electric receiver, load equipment, current, voltage. The object of study is a part of the electric "Simbirsk machine-tool plant". The aim of the thesis is raboty, designing enterprise power scheme, the choice of equipment. The process of practice in the target object, including the collection of baseline data on the enterprise. The study established the scheme for electricity from the substation power supply system, up to the final electro-receiver. MANUFACTURED choice of switching equipment, cables and wires, as well as the necessary checks are made. The paper reflects the economic calculation of capital costs for the implementation of the scheme adopted. Yo

KurSL: model of anharmonic coupled oscillations based on Kuramoto coupling and Sturm–Liouville problem

Physiological signaling is often oscillatory and shows nonlinearity due to complex interactions of underlying processes or signal propagation delays. This is particularly evident in case of brain activity which is subject to various feedback loop interactions between different brain structures, that coordinate their activity to support normal function. In order to understand such signaling in health and disease, methods are needed that can deal with such complex oscillatory phenomena. In this paper, a data-driven method for analyzing anharmonic oscillations is introduced. The KurSL model incorporates two well-studied components, which in the past have been used separately to analyze oscillatory behavior. The Sturm–Liouville equations describe a form of a general oscillation, and the Kuramoto coupling model represents a set of oscillators interacting in the phase domain. Integration of these components provides a flexible framework for capturing complex interactions of oscillatory processes of more general form than the most commonly used harmonic oscillators. The paper introduces a mathematical framework of the KurSL model and analyzes its behavior for a variety of parameter ranges. The significance of the model follows from its ability to provide information about coupled oscillators’ phase dynamics directly from the time series. KurSL offers a novel framework for analyzing a wide range of complex oscillatory behaviors, such as the ones encountered in physiological signals

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg-Marchenko type uniqueness theorems are derived for both discrete and continuous non-self-adjoint systems too

TrustedPals: Secure Multiparty Computation Implemented with Smart Cards

We study the problem of Secure Multi-party Computation (SMC) in a model where individual processes contain a tamper-proof security module, and introduce the TrustedPals framework, an efficient smart card based implementation of SMC for any number of participating entities in such a model. Security modules can be trusted by other processes and can establish secure channels between each other. However, their availability is restricted by their host, that is, a corrupted party can stop the computation of its own security module as well as drop any message sent by or to its security module. We show that in this model SMC can be implemented by reducing it to a fault-tolerance problem at the level of security modules. Since the critical part of the computation can be executed locally on the smart card, we can compute any function securely with a protocol complexity which is polynomial only in the number of processes (that is, the complexity does not depend on the function which is computed), in contrast to previous approaches

Inverse spectral problems for Sturm-Liouville operators with singular potentials

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized.Comment: Submitted to Inverse Problem

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page

Detecting Botnets Through Log Correlation

Botnets, which consist of thousands of compromised machines, can cause a significant threat to other systems by launching Distributed Denial of Service attacks, keylogging, and backdoors. In response to this threat, new effective techniques are needed to detect the presence of botnets. In this paper, we have used an interception technique to monitor Windows Application Programming Interface system calls made by communication applications. Existing approaches for botnet detection are based on finding bot traffic patterns. Our approach does not depend on finding patterns but rather monitors the change of behaviour in the system. In addition, we will present our idea of detecting botnet based on log correlations from different hosts