An iterative procedure for solving a Cauchy problem for second order elliptic equations

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A general route to synthesize supported isolated oxide and mixed-oxide nanoclusters at sizes below 5 nm

A simple and efficient route to prepare supported nanocrystalline oxides is presented. The synthesis procedure, i.e. in situ autocombustion of a glycine complex, allows the production of nanocrystals in a porous matrix presenting larger pore size. An example of successful formation of 2-5 nm nanocrystals is given for a single oxide (Fe2O3), a mixed-oxide structure (LaCoO3 perovskite-type) and a nickel-doped oxide. © 2011 The Royal Society of Chemistry.

Nontrivial Solutions of Quasilinear Equations In BV

The existence of a nontrivial critical point is proved for a functional containing an area-type term. Techniques of nonsmooth critical point theory are applied.

Learning Technology in Scheduling Based on the Mixed Graphs

We propose the adaptive algorithm for solving a set of similar scheduling problems using learning technology. It is devised to combine the merits of an exact algorithm based on the mixed graph model and heuristics oriented on the real-world scheduling problems. The former may ensure high quality of the solution by means of an implicit exhausting enumeration of the feasible schedules. The latter may be developed for certain type of problems using their peculiarities. The main idea of the learning technology is to produce effective (in performance measure) and efficient (in computational time) heuristics by adapting local decisions for the scheduling problems under consideration. Adaptation is realized at the stage of learning while solving a set of sample scheduling problems using a branch-and-bound algorithm and structuring knowledge using pattern recognition apparatus.

Laparoscopic greater curvature plication in morbidly obese women with type 2 diabetes:effects on glucose homeostasis, postprandial triglyceridemia and selected gut hormones

Background: Laparoscopic greater curvature plication (LGCP) is an emerging bariatric procedure that reduces the gastric volume without implantable devices or gastrectomy. The aim of this study was to explore changes in glucose homeostasis, postprandial triglyceridemia, and meal-stimulated secretion of selected gut hormones [glucose-dependent insulinotropic polypeptide (GIP), glucagon-like peptide-1 (GLP-1), ghrelin, and obestatin] in patients with type 2 diabetes mellitus (T2DM) at 1 and 6 months after the procedure. Methods: Thirteen morbidly obese T2DM women (mean age, 53.2 ± 8.76 years; body mass index, 40.1 ± 4.59 kg/m2) were prospectively investigated before the LGCP and at 1- and 6-month follow-up. At these time points, all study patients underwent a standardized liquid mixed-meal test, and blood was sampled for assessment of plasma levels of glucose, insulin, C-peptide, triglycerides, GIP, GLP-1, ghrelin, and obestatin. Results: All patients had significant weight loss both at 1 and 6 months after the LGCP (p≤0.002), with mean percent excess weight loss (%EWL) reaching 29.7 ;plusmn2.9 % at the 6-month follow-up. Fasting hyperglycemia and hyperinsulinemia improved significantly at 6 months after the LGCP (p<0.05), with parallel improvement in insulin sensitivity and HbA1c levels (p<0.0001). Meal-induced glucose plasma levels were significantly lower at 6 months after the LGCP (p<0.0001), and postprandial triglyceridemia was also ameliorated at the 6-month follow-up (p<0.001). Postprandial GIP plasma levels were significantly increased both at 1 and 6 months after the LGCP (p<0.0001), whereas the overall meal-induced GLP-1 response was not significantly changed after the procedure (p ;gt0.05). Postprandial ghrelin plasma levels decreased at 1 and 6 months after the LGCP (p<0.0001) with no significant changes in circulating obestatin levels. Conclusion: During the initial 6-month postoperative period, LGCP induces significant weight loss and improves the metabolic profile of morbidly obese T2DM patients, while it also decreases circulating postprandial ghrelin levels and increases the meal-induced GIP response. © 2013 Springer Science+Business Media New York.

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

Nonlinear Bihari Type Integral Inequalities with Maxima

Some new nonlinear integral inequalities that involve the maximum of the unknown scalar function of one variable are solved. The considered inequalities are generalizations of the classical nonlinear integral inequality of Bihari. The importance of these integral inequalities is defined by their wide applications in qualitative investigations of differential equations with "maxima" and it is illustrated by some direct applications.

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.