An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

Multi-wavelength source using low drive-voltage amplitude modulators for optical communications

A simple and cost-effective technique for generating a flat, square-shaped multi-wavelength optical comb with 42.6 GHz line spacing and over 0.5 THz of total bandwidth is presented. A detailed theoretical analysis is presented, showing that using two concatenated modulators driven with voltages of 3.5 Vp are necessary to generate 11 comb lines with a flatness below 2dB. This performance is experimentally demonstrated using two cascaded Versawave 40 Gbit/s low drive voltage electro-optic polarisation modulators, where an 11 channel optical comb with a flatness of 1.9 dB and a side-mode-suppression ratio (SMSR) of 12.6 dB was obtained.

The UK MPharm (1) - are we over reliant on traditional teaching methods?

Introduction-The design of the UK MPharm curriculum is driven by the Royal Pharmaceutical Society of Great Britain (RPSGB) accreditation process and the EU directive (85/432/EEC).[1] Although the RPSGB is informed about teaching activity in UK Schools of Pharmacy (SOPs), there is no database which aggregates information to provide the whole picture of pharmacy education within the UK. The aim of the teaching, learning and assessment study [2] was to document and map current programmes in the 16 established SOPs. Recent developments in programme delivery have resulted in a focus on deep learning (for example, through problem based learning approaches) and on being more student centred and less didactic through lectures. The specific objectives of this part of the study were (a) to quantify the content and modes of delivery of material as described in course documentation and (b) having categorised the range of teaching methods, ask students to rate how important they perceived each one for their own learning (using a three point Likert scale: very important, fairly important or not important). Material and methods-The study design compared three datasets: (1) quantitative course document review, (2) qualitative staff interview and (3) quantitative student self completion survey. All 16 SOPs provided a set of their undergraduate course documentation for the year 2003/4. The documentation variables were entered into Excel tables. A self-completion questionnaire was administered to all year four undergraduates, using a pragmatic mixture of methods, (n=1847) in 15 SOPs within Great Britain. The survey data were analysed (n=741) using SPSS, excluding non-UK students who may have undertaken part of their studies within a non-UK university. Results and discussion-Interviews showed that individual teachers and course module leaders determine the choice of teaching methods used. Content review of the documentary evidence showed that 51% of the taught element of the course was delivered using lectures, 31% using practicals (includes computer aided learning) and 18% small group or interactive teaching. There was high uniformity across the schools for the first three years; variation in the final year was due to the project. The average number of hours per year across 15 schools (data for one school were not available) was: year 1: 408 hours; year 2: 401 hours; year 3: 387 hours; year 4: 401 hours. The survey showed that students perceived lectures to be the most important method of teaching after dispensing or clinical practicals. Taking the very important rating only: 94% (n=694) dispensing or clinical practicals; 75% (n=558) lectures; 52% (n=386) workshops, 50% (n=369) tutorials, 43% (n=318) directed study. Scientific laboratory practices were rated very important by only 31% (n=227). The study shows that teaching of pharmacy to undergraduates in the UK is still essentially didactic through a high proportion of formal lectures and with high levels of staff-student contact. Schools consider lectures still to be the most cost effective means of delivering the core syllabus to large cohorts of students. However, this does limit the scope for any optionality within teaching, the scope for small group work is reduced as is the opportunity to develop multi-professional learning or practice placements. Although novel teaching and learning techniques such as e-learning have expanded considerably over the past decade, schools of pharmacy have concentrated on lectures as the best way of coping with the huge expansion in student numbers. References [1] Council Directive. Concerning the coordination of provisions laid down by law, regulation or administrative action in respect of certain activities in the field of pharmacy. Official Journal of the European Communities 1985;85/432/EEC. [2] Wilson K, Jesson J, Langley C, Clarke L, Hatfield K. MPharm Programmes: Where are we now? Report commissioned by the Pharmacy Practice Research Trust., 2005.

An efficient knowledge transfer solution to a novel SMDP formalization of a broker's decision problem

This paper introduces a new technique for optimizing the trading strategy of brokers that autonomously trade in re- tail and wholesale markets. Simultaneous optimization of re- tail and wholesale strategies has been considered by existing studies as intractable. Therefore, each of these strategies is optimized separately and their interdependence is generally ignored, with resulting broker agents not aiming for a glob- ally optimal retail and wholesale strategy. In this paper, we propose a novel formalization, based on a semi-Markov deci- sion process (SMDP), which globally and simultaneously op- timizes retail and wholesale strategies. The SMDP is solved using hierarchical reinforcement learning (HRL) in multi- agent environments. To address the curse of dimensionality, which arises when applying SMDP and HRL to complex de- cision problems, we propose an ecient knowledge transfer approach. This enables the reuse of learned trading skills in order to speed up the learning in new markets, at the same time as making the broker transportable across market envi- ronments. The proposed SMDP-broker has been thoroughly evaluated in two well-established multi-agent simulation en- vironments within the Trading Agent Competition (TAC) community. Analysis of controlled experiments shows that this broker can outperform the top TAC-brokers. More- over, our broker is able to perform well in a wide range of environments by re-using knowledge acquired in previously experienced settings.

Solving a Direct Marketing Problem by Three Types of ARTMAP Neural Networks

An important task for a direct mailing company is to detect potential customers in order to avoid unnecessary and unwanted mailing. This paper describes a non-linear method to predict profiles of potential customers using dARTMAP, ARTMAP-IC, and Fuzzy ARTMAP neural networks. The paper discusses advantages of the proposed approaches over similar techniques based on MLP neural networks.

Some new Results for Additive Self-Dual Codes over GF(4)

* Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.

Efficient Computing of some Vector Operations over GF(3) and GF(4)

The problem of efficient computing of the affine vector operations (addition of two vectors and multiplication of a vector by a scalar over GF (q)), and also the weight of a given vector, is important for many problems in coding theory, cryptography, VLSI technology etc. In this paper we propose a new way of representing vectors over GF (3) and GF (4) and we describe an efficient performance of these affine operations. Computing weights of binary vectors is also discussed.

Asymmetric Cipher Protocol Using Decomposition Problem

The asymmetric cipher protocol based on decomposition problem in matrix semiring M over semiring of natural numbers N is presented. The security parameters are defined and preliminary security analysis is presented.

Multi-wavelength source using low drive-voltage amplitude modulators for optical communications

A simple and cost-effective technique for generating a flat, square-shaped multi-wavelength optical comb with 42.6 GHz line spacing and over 0.5 THz of total bandwidth is presented. A detailed theoretical analysis is presented, showing that using two concatenated modulators driven with voltages of 3.5 Vp are necessary to generate 11 comb lines with a flatness below 2dB. This performance is experimentally demonstrated using two cascaded Versawave 40 Gbit/s low drive voltage electro-optic polarisation modulators, where an 11 channel optical comb with a flatness of 1.9 dB and a side-mode-suppression ratio (SMSR) of 12.6 dB was obtained.

The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3

Recently Garashuk and Lisonek evaluated Kloosterman sums K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In this paper, we will give an answer to this problem. The result allows us to count the number of elements a in F3m belonging to each of these two classes.

Maximization of a Linear Utility Function over the Set of the Housing Market Short-Term Equilibria

AMS subject classification: 90C05, 90A14.

Estimation of IRT Parameters over a Small Sample. Bootstrapping of the Item Responses

2000 Mathematics Subject Classification: 97C40.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Four-leg converters with improved common current sharing and selective voltage-quality enhancement for islanded microgrids

Four-leg dc-ac power converters are widely used for the power grids to manage grid voltage unbalance caused by the interconnection of single-phase or three-phase unbalanced loads. These converters can further be connected in parallel to increase the overall power rating. The control of these converters poses a particular challenge if they are placed far apart with no links between them (e.g., in islanded microgrids). This challenge is studied in this paper with each four-leg converter designed to have improved common current sharing and selective voltage-quality enhancement. The common current sharing, including zero sequence component, is necessary since loads are spread over the microgrid and they are hence the common responsibility of all converters. The voltage-quality enhancement consideration should however be more selective since different loads have different sensitivity levels towards voltage disturbances. Converters connected to the more sensitive load buses should therefore be selectively triggered for compensation when voltage unbalances at their protected buses exceed the predefined thresholds. The proposed scheme is therefore different from conventional centralized schemes protecting only a common bus. Simulation and experimental results obtained have verified the effectiveness of the proposed scheme when applied to a four-wire islanded microgrid.