Accurate WKB Approximation for a 1D Problem with Low Regularity

2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.

Using Physical Quantities in Applied Mathematical Problems with Maple

The present article discusses units of measure and their base units, work environments built in the Units package of the computer algebra system Maple. An analysis is drawn of the tools of the application in connection with the use of physical quantities and their features. Maple’s main commands are arranged in groups depending on the function. Some applied mathematical problems are given as examples making use of derivative, integral and differential equations.

Stability of an Optimal Schedule for a Job-Shop Problem with Two Jobs

The usual assumption that the processing times of the operations are known in advance is the strictest one in scheduling theory. This assumption essentially restricts practical aspects of deterministic scheduling theory since it is not valid for the most processes arising in practice. The paper is devoted to a stability analysis of an optimal schedule, which may help to extend the significance of scheduling theory for decision-making in the real-world applications. The term stability is generally used for the phase of an algorithm, at which an optimal solution of a problem has already been found, and additional calculations are performed in order to study how solution optimality depends on variation of the numerical input data.

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

Solving the Task Assignment Problem with a Variable Neighborhood Search

In this paper a variable neighborhood search (VNS) approach for the task assignment problem (TAP) is considered. An appropriate neighborhood scheme along with a shaking operator and local search procedure are constructed specifically for this problem. The computational results are presented for the instances from the literature, and compared to optimal solutions obtained by the CPLEX solver and heuristic solutions generated by the genetic algorithm. It can be seen that the proposed VNS approach reaches all optimal solutions in a quite short amount of computational time.

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

Towards New Teaching in Mathematics How to Realize Inquiry Based and Problem Oriented Mathematics Lessons?

Дагмар Рааб Математиката е вълнуваща и забавна. Можем ли да убедим учениците, че това може да стане действителност. Задачите са най-важните инструменти за учителите по математика, когато планират уроците си. Планът трябва да съдържа идеи как да се очертае и как да се жалонира пътят, по който учениците ще стигнат до решението на дадена задача. Учителите не трябва да очакват от учениците си просто да кажат кой е отговорът на задачата, а да ги увлекат в процеса на решаване с подходящи въпроси. Ролята на учителя е да помогне на учениците • да бъдат активни и резултатни при решаването на задачи; • самите те да поставят задачи; • да модифицират задачи; • да откриват закономерности; • да изготвят стратегии за решаване на задачи; • да откриват и изследват различни начини за решаване на задачи; • да намират смислена връзка между математическите си знания и проблеми от ежедневието. В доклада са представени избрани и вече експериментирани примери за това как учители и ученици могат да намерят подходящ път към нов тип преживявания в преподаването и изучаването на училищната математика.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

Vector Combinatorial Problems in a Space of Combinations with Linear Fractional Functions of Criteria

The paper considers vector discrete optimization problem with linear fractional functions of criteria on a feasible set that has combinatorial properties of combinations. Structural properties of a feasible solution domain and of Pareto–optimal (efficient), weakly efficient, strictly efficient solution sets are examined. A relation between vector optimization problems on a combinatorial set of combinations and on a continuous feasible set is determined. One possible approach is proposed in order to solve a multicriteria combinatorial problem with linear- fractional functions of criteria on a set of combinations.

Realization of an Optimal Schedule for the Two-machine Flow-Shop with Interval Job Processing Times

Non-preemptive two-machine flow-shop scheduling problem with uncertain processing times of n jobs is studied. In an uncertain version of a scheduling problem, there may not exist a unique schedule that remains optimal for all possible realizations of the job processing times. We find necessary and sufficient conditions (Theorem 1) when there exists a dominant permutation that is optimal for all possible realizations of the job processing times. Our computational studies show the percentage of the problems solvable under these conditions for the cases of randomly generated instances with n ≤ 100 . We also show how to use additional information about the processing times of the completed jobs during optimal realization of a schedule (Theorems 2 – 4). Computational studies for randomly generated instances with n ≤ 50 show the percentage of the two- machine flow-shop scheduling problems solvable under the sufficient conditions given in Theorems 2 – 4.

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Well-Posedness and Conditioning of Optimization Problems

AMS subject classification: 49K40, 90C31.