This work provides a complete analysis of eddy current problems, ranging from a proof of unique solvability to the analysis of a multiharmonic discretization technique. For proving existence and uniqueness, we use a Schur complement approach in order to combine the structurally different results for conducting and non-conducting regions. For solving the time-dependent problem, we take advantage...

a numerical method for solving nonlinear fredholm-volterra integral equations of general type is presented. this method is based on replacement of unknown function by truncated series of well known chebyshev expansion of functions. the quadrature formulas which we use to calculate integral terms have been imated by fast fourier transform (fft). this is a grate advantage of this method which has...

We establish two binomial coefficient–generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo p (k > 1) congruences between truncated generalized hypergeometric series, and a function which extends Greene’s ...

Abstract— In this paper, a simple Fourier series based algorithm has been used to achieve stable locomotion in an NAO biped robot, with 22 degrees of freedom that implemented in a virtual physics-based simulation environment of Robocup soccer simulation environment. The algorithm uses a Truncated Fourier Series (TFS) to generate control signal for the biped robot. To find the best angular traje...

This paper presents an overview of Nexus 3D Soccer Simulation Team. Our main concentration was on developing a new hybrid methodology for an evolutionary gait generator that uses trigonometric truncated Fourier series formulations with coefficients optimized by a Genetic Algorithm. The Fourier series is used to model joint angle trajectories of a simulated humanoid robot with 25 degrees of free...

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of α-stable distributions. Although they play a key role in modelling time-series with jumps and discontinuities, the use of α-stable distributions in inference often leads to analytically intractable problems. The infinite series representation employed in this ...

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

Geographically Weighted Regression (GWR) is the development of multiple linear regression models used in spatial data. The assumption heterogeneity results each location having different characteristics and allows relationships between response variable predictor to be unknown, hence nonparametric becomes one alternatives that can used. In addition, functions are not always same variables. This...

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has...

Nonparametric regression becomes a potential solution if the parametric assumption is too restrictive while curve assumed to be known. In multivariable nonparametric regression, pattern of each predictor variable’s relationship with response variable not always same; thus, combined estimator recommended. addition, modeling sometimes involves more than one response, i.e., multiresponse situation...