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The main objective is to develop an efficient BEM scheme for the numerical solution of two‐dimensional heat problems. Our scheme will be of the re‐initialization type, in which the domain integrals are computed by a recursion relation which depends only on the boundary temperature and flux at previous time step. To obtain the re‐initialization approach, we will use in the integral representation formula a Green function corresponding to zero temperature in a box containing the original domain, instead of using the classical free space fundamental solution. This Green function is given in terms of the original fundamental solution plus a regular solution of the heat equation inside the domain under consideration. It can therefore be used in the integral representation formula of the heat equation (direct formulation) to obtain the solution of a heat problem in such a domain. The Green function mentioned can be obtained by the images method, and the resulting source series can also be rewritten in terms of a double Fourier series, that we will use in the domain integral of the integral representation formula to transform such integral into equivalent surface integrals.

With the development of economy, China’s OFDI constantly increase in recent year. Meanwhile, OFDI has spillover effect on economic development and technological development of home country. Thus, accurate OFDI prediction is a prerequisite for the effective development of international investment strategies. The purpose of this paper is to predict China’s OFDI accurately using a novel multivariable grey prediction model with Fourier series.

This paper applied a multivariable grey prediction model, GM(1,N), to forecast China’s OFDI. In order to improve the prediction accuracy and without changing local characteristics of grey model prediction, this paper proposed a novel grey prediction model to improve the performance of the traditional GM(1,N) model by combining with residual modification model using GM(1,1) model and Fourier series.

The coefficients indicate that the export and GDP have positive influence on China’s OFDI, and, according to the prediction result, China’s OFDI shows a growing trend in next five years.

This paper proposed an effective multivariable grey prediction model that combined the traditional GM(1,N) model with a residual modification model in order to predict China’s OFDI. Accurate forecasting of OFDI provides reference for the Chinese Government to implement international investment strategies.

The purpose of this paper is to survey briefly how harmonic analyis started and developed throughout the centuries to reach its modern status and its surprisingly wide range of applications.

The author traces applications of harmonic analysis back to Mesopotamia, ancient Egypt and the Indus Valley, showing how the Greeks have applied trigonometry and influenced its birth, then the important developments in India in the sixth century laying the first brick to modern trigonometry with the definition of the sinus, then medieval India founding modern mathematical analysis. Trigonometry was developed further by the Arabs until the fourteenth century, then by the Europeans. The eighteenth century in France was particularly important when Bernoulli solved, with an infinite trigonometric series, the vibrating string problem, then Fourier, who studied these series extensively. The author goes on to harmonic analysis on locally compact groups, and ends up with a quick personal view on harmonic analysis nowadays. The last section of the paper presents some of the modern applications. Harmonic analysis is, of course, still used for navigation but also has many other very surprising applications such as signal processing, quantum mechanics, neuroscience, tomography, etc.

The power of harmonic analysis lies in giving the solutions to various problems as infinite series of basic functions, so to be able to produce algorithms for FFT boxes, it must be understood how these series came about and the convergence of these series.

The review should be useful to people interested in studying and/or applying harmonic analysis.

This study aims to propose a mathematical model for stacked multicell converters (SMCs), to be exploited in the analytic determination of natural voltage balancing dynamics of the flying-capacitor (FC) stacked multicell multilevel converters, i.e. investigations of the start-up behavior, dynamic response, and natural voltage balancing phenomenon.

The crux of the proposed strategy is based on the closed-form analytic solution derivation for the switching functions used in the switching of the SMCs operated under phase disposition (PD) and phase shifted carrier (PSC) pulse width modulation (PD-PSC-PWM) technique. Hence, the suggested approach develops an analytic solution for the Fourier series and associated Fourier coefficients pertinent to the switching functions of the SMCs by obtaining the switching instants of the PD-PSC-PWM modulator in terms of Kapteyn series when the frequency of the triangular carrier waveform (fc) and that of the sinusoidal reference waveform (fr) have an integer ratio, i.e. f _c  · f _r −1=k, k∈N.

This approach results into a model, first order differential equation based model, which can be readily developed for the SMCs with any number of levels expediting the investigation of their performance. Furthermore, by an experimental scrutiny conducted on a 4×2-cell-nine-level topology of an SMC, it is inferred that under PD-PSC-PWM modulation technique, FC voltages balance naturally for higher number of stacks and cells, therefore the natural balancing exist for high-level SMCs.

Despite the sophistication of the proposed methodology and mathematical model, this study presents an alternative approach with high potential of applicability for derivation of the multilevel converter mathematical model exploiting the Kapteyn (Bessel-Fourier) series.

Numeric computation results of the proposed analytic model for the SMCs and the simulation results as well as investigational measurements taken from 2×2-cell-five-level and 4×2-cell-nine-level experimental set-ups are presented in order to substantiate the suggested approach, derived model, and verification of natural balancing.

This article and its innovations are original.

The paper aims to propose a system that uses a combination of techniques to suggest weld requirements for ships parts. These suggestions are evaluated, decisions are made and then weld parameters are sent to a program generator.

A pattern recognition system recognizes shipbuilding parts using shape contour information. Fourier‐descriptors provide information and neural networks make decisions about shapes.

The system has distinguished between various parts and programs have been generated so that the methods have proved to be valid approaches.

The new system used a rudimentary curvature metric that measured Euclidean distance between two points in a window but the improved accuracy and ease of implementation can benefit other applications concerning curve approximation, node tracing, and image processing, but especially in identifying images of manufactured parts with distinct corners.

A new proposed system has been presented that uses image processing techniques in combination with a computer‐aided design model to provide information to a multi‐intelligent decision module. This module will use different criteria to determine a best weld path. Once the weld path has been determined then the program generator and post‐processor can be used to send a compatible program to the robot controller. The progress so far is described.

The purpose of this paper is to present a method for analyzing higher magnetic force harmonics in electrical machines based on electromagnetic finite element simulation.

Sampling of air gap field solution data allows for a Fourier decomposition of magnetic forces and flux densities. A two‐dimensional convolution gives insight into the spectral decomposition of forces responsible for acoustic noise, vibration and higher torque harmonics.

The proposed approach seems especially suitable for synchronous machine models. The influence of magnetic circuit design parameters that are difficult to calculate analytically on the harmonic air gap content can be analyzed and the spectral force decomposition illustrated by means of space vectors.

The approach is generalized to the convolution and analysis of arbitrarily sampled two‐dimensional data in this paper.

The purpose of this paper is to present an analytical calculation for estimating the leakages field distribution in surface-mounted permanent magnet synchronous motors (SMPMSMs) according to a sub-domain field model for eccentricity fault detection.

The magnetic field domain is classified into four sub-domains of PMs, air gap, stator core and outer region. In the proposed method, the governing equations taking the rotor eccentricity effect into account per region and the interface boundary conditions between sub-domains are formulated using the regular perturbation technique, Taylor series and Fourier series expansion. Maxwell's equations are solved in different regions in the polar coordinate system regarding the boundary conditions.

The radial and tangential components of electromagnetic field distribution in all sub-domains of one SMPMSM are obtained using the proposed method analytically. Finite element analysis is used to validate the results of the proposed method; the results indicated that the analytical model matches the finite-element prediction up to 30% eccentricity, except for some peak values that depend on the harmonic order value. The results of this paper demonstrated that in the event of eccentricity, an asymmetric magnetic field is generated in the outer region of the machine. Although its amplitude is small, it can be an indicator for detecting eccentricity faults from the outside environment of the machine.

The formulas presented in this paper can be applied as a new technique for detecting eccentricity faults in these motors from the outside environment.

The flying capacitor converter (FFC) balances the clamping capacitor voltages naturally when phase shifted carrier modulation is used. Several models that describe this mechanism, and to estimate the time constants following a perturbation, are discussed in the literature. However, due to the model complexity, numerical methods must be used to evaluate these models. This paper aims to present a closed form expression, using a reference table, that describes a maximum bound for the voltage balancing time constant.

The FCC is analysed in the frequency domain. A decomposition of the characteristic matrix that describes the voltage balancing mechanism is used. The resulting real symmetric matrix is factorised by using approximations of the load characteristics at the frequencies of interest.

The minimum eigenvalue of the factorised matrix is used to determine a maximum bound for the time constant of the voltage balancing. Since the factorised matrix is independent of variations in switching frequency and load, the eigenvalue of interest can be calculated once and tabulated.

The closed form expression can be used for quick calculations of the maximum time constant under different operating conditions. Furthermore, the expression provides considerable insight into the influences circuit design choices have on the balancing mechanism.

Drape of the fabric is its ability to hang freely in graceful folds when some area of it is supported over a surface and the rest is unsupported. When two‐dimensional fabrics are converted to three‐dimensional garment forms, a number of operations are required which affect drape behaviour of the fabric while present in garment form. In the present study, the effect of sewing and fusing of interlining on drape behaviour of men's suiting fabrics is investigated.Design/methodology/approach – The effect of sewing and fusing of interlining on drape behaviour of men's suiting fabrics is investigated. Comparisons were also made between different stitches (chain stitch and lock stitch), different seams for lock stitch and different types of interlinings for their effect on drape behaviour of fabrics. In addition to drape coefficient and number of folds, a new drape parameter – average amplitude to average radius (A/r) ratio – was also defined and calculated for drape image geometry.Findings – Drape coefficient has a good to strong correlation with A/r ratio and number of folds for most of the shell, sewn and interlining fused fabrics except for a few cases. A/r defines image in a more descriptive manner than drape coefficient. Drape coefficient changes with the types of seams and stitches used, as well as with the interlining used.Originality/value – This paper provides information on the effects of sewing (seams and stitch types) and fused interlining on drape behaviour of men's suiting fabrics.

Describes some parts of Wiener’s significant contribution to mathematics in as simple and non‐technical a language as possible. Looks at Wiener’s early research and how he applied integration theory to potential theory, but not without first explaining the background to integration theory. Then describes one of Wiener’s most important works – that on Brownian motion, and how other theories such as harmonic analysis flowed from his study of Brownian motion. Concludes with a brief chronology of Wiener’s life.