Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...

What is nonlinear Fourier Analysis? Let us consider an example. Let Q be a domain in the plane bounded by a Jordan curve T that goes to oo. Let O be a Riemann mapping of the upper half-plane onto £2. How does O behave as a function of T? Is it continuous? smooth? realanalytic? Let's think of ourselves as calculus students; we are presented with this function, and we want to study its basic prop...

In the lecture notes on waves, we have shown that the waves on a plucked guitar string are transverse standing waves consisting of a linear superposition (i.e. sum) of harmonics of the fundamental (first harmonic) with the fundamental itself. A first-order mathematical description of the shape of the overall waveform of the transverse standing wave on a plucked guitar string is a triangle, or s...

Abstract In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is...

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...

in this research work, the frequency domain (fd) of surface geochemical data was analyzed to decompose the complex geochemical patterns related to different depths of the mineral deposit. in order to predict the variation in mineralization in the depth and identify the deep geochemical anomalies and blind mineralization using the surface geochemical data for the dalli cu-au porphyry deposit, a ...

The Fourier transforms x̂j = ∑ k xkω , k, j = 0, 1, . . . , n− 1 of a data vector x with scalar components xk indexed by n-fold planar rotations ω k define a n × n Hermitian matrix F with entries ωjk/√n, so that x̂ = √n Fx and the inverse Fourier transform is simply x = F∗x̂/√n. Here, the frequencies ω and their harmonics ω fully describe the set (Ĝ) of all n irreducible representations of the Abe...