A method of fundamental solutions for two-dimensional heat conduction

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.

A procedure for the reconstruction of a stochastic stationary temperature field

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Solvability and asymptotics of the heat equation with mixed variable lateral conditions and applications in the opening of the exocytotic fusion pore in cells

We investigate a mixed problem with variable lateral conditions for the heat equation that arises in modelling exocytosis, i.e. the opening of a cell boundary in specific biological species for the release of certain molecules to the exterior of the cell. The Dirichlet condition is imposed on a surface patch of the boundary and this patch is occupying a larger part of the boundary as time increases modelling where the cell is opening (the fusion pore), and on the remaining part, a zero Neumann condition is imposed (no molecules can cross this boundary). Uniform concentration is assumed at the initial time. We introduce a weak formulation of this problem and show that there is a unique weak solution. Moreover, we give an asymptotic expansion for the behaviour of the solution near the opening point and for small values in time. We also give an integral equation for the numerical construction of the leading term in this expansion.

Uses of frontier efficiency methodologies and multi-criteria decision making for performance measurement in the energy sector

Guest editorial Ali Emrouznejad is a Senior Lecturer at the Aston Business School in Birmingham, UK. His areas of research interest include performance measurement and management, efficiency and productivity analysis as well as data mining. He has published widely in various international journals. He is an Associate Editor of IMA Journal of Management Mathematics and Guest Editor to several special issues of journals including Journal of Operational Research Society, Annals of Operations Research, Journal of Medical Systems, and International Journal of Energy Management Sector. He is in the editorial board of several international journals and co-founder of Performance Improvement Management Software. William Ho is a Senior Lecturer at the Aston University Business School. Before joining Aston in 2005, he had worked as a Research Associate in the Department of Industrial and Systems Engineering at the Hong Kong Polytechnic University. His research interests include supply chain management, production and operations management, and operations research. He has published extensively in various international journals like Computers & Operations Research, Engineering Applications of Artificial Intelligence, European Journal of Operational Research, Expert Systems with Applications, International Journal of Production Economics, International Journal of Production Research, Supply Chain Management: An International Journal, and so on. His first authored book was published in 2006. He is an Editorial Board member of the International Journal of Advanced Manufacturing Technology and an Associate Editor of the OR Insight Journal. Currently, he is a Scholar of the Advanced Institute of Management Research. Uses of frontier efficiency methodologies and multi-criteria decision making for performance measurement in the energy sector This special issue aims to focus on holistic, applied research on performance measurement in energy sector management and for publication of relevant applied research to bridge the gap between industry and academia. After a rigorous refereeing process, seven papers were included in this special issue. The volume opens with five data envelopment analysis (DEA)-based papers. Wu et al. apply the DEA-based Malmquist index to evaluate the changes in relative efficiency and the total factor productivity of coal-fired electricity generation of 30 Chinese administrative regions from 1999 to 2007. Factors considered in the model include fuel consumption, labor, capital, sulphur dioxide emissions, and electricity generated. The authors reveal that the east provinces were relatively and technically more efficient, whereas the west provinces had the highest growth rate in the period studied. Ioannis E. Tsolas applies the DEA approach to assess the performance of Greek fossil fuel-fired power stations taking undesirable outputs into consideration, such as carbon dioxide and sulphur dioxide emissions. In addition, the bootstrapping approach is deployed to address the uncertainty surrounding DEA point estimates, and provide bias-corrected estimations and confidence intervals for the point estimates. The author revealed from the sample that the non-lignite-fired stations are on an average more efficient than the lignite-fired stations. Maethee Mekaroonreung and Andrew L. Johnson compare the relative performance of three DEA-based measures, which estimate production frontiers and evaluate the relative efficiency of 113 US petroleum refineries while considering undesirable outputs. Three inputs (capital, energy consumption, and crude oil consumption), two desirable outputs (gasoline and distillate generation), and an undesirable output (toxic release) are considered in the DEA models. The authors discover that refineries in the Rocky Mountain region performed the best, and about 60 percent of oil refineries in the sample could improve their efficiencies further. H. Omrani, A. Azadeh, S. F. Ghaderi, and S. Abdollahzadeh presented an integrated approach, combining DEA, corrected ordinary least squares (COLS), and principal component analysis (PCA) methods, to calculate the relative efficiency scores of 26 Iranian electricity distribution units from 2003 to 2006. Specifically, both DEA and COLS are used to check three internal consistency conditions, whereas PCA is used to verify and validate the final ranking results of either DEA (consistency) or DEA-COLS (non-consistency). Three inputs (network length, transformer capacity, and number of employees) and two outputs (number of customers and total electricity sales) are considered in the model. Virendra Ajodhia applied three DEA-based models to evaluate the relative performance of 20 electricity distribution firms from the UK and the Netherlands. The first model is a traditional DEA model for analyzing cost-only efficiency. The second model includes (inverse) quality by modelling total customer minutes lost as an input data. The third model is based on the idea of using total social costs, including the firm’s private costs and the interruption costs incurred by consumers, as an input. Both energy-delivered and number of consumers are treated as the outputs in the models. After five DEA papers, Stelios Grafakos, Alexandros Flamos, Vlasis Oikonomou, and D. Zevgolis presented a multiple criteria analysis weighting approach to evaluate the energy and climate policy. The proposed approach is akin to the analytic hierarchy process, which consists of pairwise comparisons, consistency verification, and criteria prioritization. In the approach, stakeholders and experts in the energy policy field are incorporated in the evaluation process by providing an interactive mean with verbal, numerical, and visual representation of their preferences. A total of 14 evaluation criteria were considered and classified into four objectives, such as climate change mitigation, energy effectiveness, socioeconomic, and competitiveness and technology. Finally, Borge Hess applied the stochastic frontier analysis approach to analyze the impact of various business strategies, including acquisition, holding structures, and joint ventures, on a firm’s efficiency within a sample of 47 natural gas transmission pipelines in the USA from 1996 to 2005. The author finds that there were no significant changes in the firm’s efficiency by an acquisition, and there is a weak evidence for efficiency improvements caused by the new shareholder. Besides, the author discovers that parent companies appear not to influence a subsidiary’s efficiency positively. In addition, the analysis shows a negative impact of a joint venture on technical efficiency of the pipeline company. To conclude, we are grateful to all the authors for their contribution, and all the reviewers for their constructive comments, which made this special issue possible. We hope that this issue would contribute significantly to performance improvement of the energy sector.

Reconstruction of a stationary flow from boundary data using iterative methods

In this paper, three iterative procedures (Landweber-Fridman, conjugate gradient and minimal error methods) for obtaining a stable solution to the Cauchy problem in slow viscous flows are presented and compared. A section is devoted to the numerical investigations of these algorithms. There, we use the boundary element method together with efficient stopping criteria for ceasing the iteration process in order to obtain stable solutions.

Reconstruction of an acoustically sound-soft obstacle from one incident field and the far field pattern

The problem considered is that of determining the shape of a plane acoustically sound-soft obstacle from the knowledge of the far-field pattern for one time-harmonic incident field. An iterative procedure is proposed based on two boundary integrals representing the incident field and the far-field pattern, respectively. Numerical examples are included which show that the procedure gives accurate numerical approximations in relatively few iterations.

A Prototype of an Extension to the UDDI Registry Allowing Pubilcation and Search Based on Subjective Evaluations

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko and Lubomir Tschakalo , So a, July, 2006.

Generalized Nets Model of an E-Learning System Software Architecture

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko ff and Lubomir Tschakaloff , Sofi a, July, 2006.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

Financial Education Through Mathematics and IT Curricula: Pocket Money Management

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Financial Decisions via Methods of Guaranteed Control Theory

AMS subject classification: 93C95, 90A09.

Recent Developments in Digital Mathematics Libraries

The paper presents recent developments in the domain of digital mathematics libraries towards the envisioned 21st Century Global Library for Mathematics. The Bulgarian Digital Mathematical Library BulDML and the Czech Digital Mathematical Library DML-CZ are founding partners of the EuDML Initiative and through it contribute to the sustainable development of the European Digital Mathematics Library EuDML and to the global advancements in this area.

A New Characterization of Weighted Peetre K-Functionals (II)

2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.