Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Operational Calculi for the Euler Operator

2000 Mathematics Subject Classification: 44A40, 44A35

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

On the Operational Solution of a System of Fractional Differential Equations

MSC 2010: 26A33, 44A45, 44A40, 65J10

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.

Algebraic derivative estimation applied to nonlinear control of magnetic levitation.

The subject of this thesis is the real-time implementation of algebraic derivative estimators as observers in nonlinear control of magnetic levitation systems. These estimators are based on operational calculus and implemented as FIR filters, resulting on a feasible real-time implementation. The algebraic method provide a fast, non-asymptotic state estimation. For the magnetic levitation systems, the algebraic estimators may replace the standard asymptotic observers assuring very good performance and robustness. To validate the estimators as observers in closed-loop control, several nonlinear controllers are proposed and implemented in a experimental magnetic levitation prototype. The results show an excellent performance of the proposed control laws together with the algebraic estimators.

An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel

Mathematics Subject Classification: 44A40, 45B05

Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

Explicit Solution of Bitsadze-Samarskii Problem

Иван Димовски, Юлиан Цанков - В статията е намерено точно решение на задачата на Бицадзе-Самрски (1) за уравнението на Лаплас, като е използвано операционно смятане основано на некласическа двумернa конволюция. На това точно решение може да се гледа като начин за сумиране на нехармоничния ред по синуси на решението, получен по метода на Фурие.

Exact Solutions of Nonlocal Pluriparabolic Problems

MSC 2010: 44A35, 44A40

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Operational active fire mapping and burnt area identification applicable to Mexican Nature Protection Areas using MODIS and NOAA-AVHRR direct readout data

Since 1999, the National Commission for the Knowledge and Use of the Biodiversity (CONABIO) in Mexico has been developing and managing the “Operational program for the detection of hot-spots using remote sensing techniques”. This program uses images from the MODerate resolution Imaging Spectroradiometer (MODIS) onboard the Terra and Aqua satellites and from the Advanced Very High Resolution Radiometer of the National Oceanic and Atmospheric Administration (NOAA-AVHRR), which are operationally received through the Direct Readout station (DR) at CONABIO. This allows the near-real time monitoring of fire events in Mexico and Central America. In addition to the detection of active fires, the location of hot spots are classified with respect to vegetation types, accessibility, and risk to Nature Protection Areas (NPA). Besides the fast detection of fires, further analysis is necessary due to the considerable effects of forest fires on biodiversity and human life. This fire impact assessment is crucial to support the needs of resource managers and policy makers for adequate fire recovery and restoration actions. CONABIO attempts to meet these requirements, providing post-fire assessment products as part of the management system in particular for satellite-based burnt area mapping. This paper provides an overview of the main components of the operational system and will present an outlook to future activities and system improvements, especially the development of a burnt area product. A special focus will also be placed on the fire occurrence within NPAs of Mexico

Enhancing spiral-wound ultrafiltration performance for direct drinking water treatment through operational procedures improvement: A feasible option for the Sao Paulo Metropolitan Region

This work aimed to evaluate the influence of specific operational conditions on the performance of a spiral-wound ultrafiltration pilot plant for direct drinking water treatment, installed at the Guarapiranga's reservoir, in the Sao Paulo Metropolitan Region. Results from operational tests showed that the volume of permeate produced in the combination of periodic relaxation with flushing and chlorine dosage procedures was 49% higher than the volume obtained when these procedures were not used. Two years of continuous operation demonstrated that the ultrafiltration pilot plant performed better during fall and winter seasons, higher permeate flow production and reduced chemical cleanings frequency. Observed behavior seems to be associated with the algae bloom events in the reservoir, which are more frequent during spring and summer seasons, confirmed by chlorophyll-a analysis results. Concentrate clarification using ferric chloride was quite effective in removing NOM and turbidity, allowing its recirculation to the ultrafiltration feed tank. This procedure made it possible to reach almost 99% water recovery considering a single 54-hour recirculation cycle. Water quality monitoring demonstrated that the ultrafiltration pilot plant was quite efficient, and that potential pathogenic organisms, Escherichia coil and total coliforms, turbidity and apparent color removals were 100%, 95.1%, and 91.5%, respectively. (C) 2012 Elsevier B.V. All rights reserved.