In this paper, transient solution of two dimensional asymmetric thermal and mechanical stresses for a hollow cylinder made of piezoelectric material is developed. Transient temperature distribution, as function of radial and circumferential directions and time with general thermal boundary-conditions, is analytically obtained, using the method of separation of variables and<br...

The Constant Elasticity of Variance (CEV) model is mathematically presented and then used in a Credit-Equity hybrid framework. Next, we propose extensions to the CEV model with default: firstly by adding a stochastic volatility diffusion uncorrelated from the stock price process, then by more generally time changing Bessel processes and finally by correlating stochastic volatility moves to the ...

The classical theory of Gaussian quadrature assumes a positive weight function. We will show that in some cases Gaussian rules can be constructed with respect to an oscillatory weight, yielding methods with complex quadrature nodes and positive weights. These rules are well suited for highly oscillatory integrals because they attain optimal asymptotic order. We show that for the Fourier oscilla...

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis −∞ < E < ∞ instead of being bounded from below 0 ≤ E < ∞ (“Fer...

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they res...

Two standard tools for signal analysis are the short{time Fourier transform and the continuous wavelet transform. These tools arise as matrix coeecients of square integrable representations of the Heisenberg and aane groups respectively, and discrete frame decompositions of L 2 arise from approximations of corresponding reproducing formulae. Here we study two groups, the so-called aane Weyl-Hei...

The frequency-domain finite-difference (FD-FD) methods have been successfully used to obtain numerical solutions of the twodimensional (2-D) Helmholtz equation. The standard second-order accurate FD-FD scheme is known to produce unwanted numerical spatial and temporal dispersions when the sampling is inadequate. Recently compact higher-order accurate FD-FD methods have been proposed to reduce t...

The structure and the properties of the eigenfunctions of the canonical integral transform are investigated. It is shown that a signal can be decomposed into a set of the orthogonal eigenfunctions of the generalized Fresnel transform. The property that the set contains a finite number of functions is obtained. The canonical integral transform, also known as the generalized Fresnel transform (GF...

Recently, the authors introduced least squares quantization table (LSQT) method to accelerate the direct Fourier transform to reconstruct magnetic resonance images acquired using a spiral trajectory. In this paper, we will discuss the LSQT further in its adaptability, reusability and choice of the number of groups. The experimental results show that the LSQT method has better adaptability for t...