A Fractional Analog of the Duhamel Principle

Mathematics Subject Classification: 35CXX, 26A33, 35S10

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.

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

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.

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.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

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

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

On Seliger and Whitham`s variational principle for hydrodynamic systems from the point of view of `fictitious particles`

FAPESP, the Sao Paulo State Research Foundation[04/04611-5]

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Transanal endorectal pull-through in children with Hirschsprung`s disease-technical refinements and comparison of results with the Duhamel procedure

Purpose: Transanal endorectal pull-through (TEPT) has drastically changed the treatment of Hirschsprung`s disease (HD). A short follow-up of children Submitted to TEPT reveals results that are similar to the classic transabdominal pull-through procedures. However, few reports compare the late results of TEPT with transabdominal pull-through procedures with respect to complication rates and the fecal continence. The aims of the present work are to describe some technical refinements that we introduced in the procedure and to compare the short and long-term outcome of TEPT with the outcomes of a group of patients with HD who previously underwent the Duhamel procedure. Methods: Thirty-five patients who underwent TEPT were prospectively studied and compared to a group of 29 patients who were treated with colostomy followed by a classical Duhamel pull-through. The main modifications introduced in the TEPT group were no preoperative colon preparation, operation conducted under general anesthesia in addition to regional sacral anesthesia, use of only one purse-string Suture in the rectal mucosa before transanal submucosal dissection, and no use of retractors and electrocautery during file submucosal dissection. Results: The most frequent early complications of TEPT group were perineal dermatitis (22.8%) and anastomotic strictures (8.6%). The comparison with patients who underwent Duhamel procedure revealed no difference in the incidence of preoperative enterocolitis, the patients of the TEPT group were younger at the time of diagnosis and of surgery, they had shorter operating times, and they began oral feeding more quickly after the operation. The incidence of wound infection was lower in the TEPT group. Moreover, the TEPT and Duhamel groups showed no difference in the incidences of mortality, postoperative partial continence, and total incontinence. Although the incidences of complete continence and postoperative enterocolitis were not different, a tendency to the increased incidence in the TEPT group was observed. Conclusions: This study further supports the technical advantages, the simplicity, and the decreased incidence of complications of a primary TEPT procedure when compared to a classical form of pull-through. Sonic technical refinements are described, and no preoperative colon preparation was necessary for the patients studied here. The results show that the long-term outcomes of the modified TEPT procedure are generally better than those obtained with classical approaches. Published by Elsevier Inc.

The "ethical anthropic principle" and the religious ethics of Levinas

Why did Levinas choose Isaiah 45:7 ("I make peace and create evil: I the Lord do all that") as a superscription of his essay on evil? This article explores the role of evil in Levinas's religious ethics. The author discusses the structure of evil as revealed phenomenologically and juxtaposes it to the structure of subjectivity found in the writings of Levinas. The idea of the "ethical anthropic principle," modeled upon the cosmic anthropic principle, is then used to link evil to the responsibility of the subject. The link is subsequently extended to God. This is proposed as one way of understanding the meaning of Isaiah 45:7. © 2001 Journal of Religious Ethics, Inc.