The main result of the paper is the derivation of the evolution equation of the tensorial texture coefficients of the crystallite orientation distribution function (codf). The evolution equation of each coefficient depends on the complete codf and the lattice spin, which is a constitutive quantity. For the solution of the differential equation based on a finite number of coefficients, the codf ...

In this paper we wish to prove that under certain conditions the Fourier coefficients of the Eisenstein series for an arithmetic group acting on a tube domain are all rational numbers. Let G be a connected, simply-connected, semisimple, and almost Q-simple linear algebraic group defined over the rational number field Q. Let R be the real number field. Then GR is connected, and we assume that if...

In Fourier analysis, since Fourier coefficients are computable and applicable, people have established many nice results by assuming monotonicity of the coefficients. Generally speaking, it became an important topic how to generalize monotonicity. In many studies the generalization follows by this way (see, for example, [8] for definitions): (coefficients) nonincreasing ⇒ quasimonotone ⇒ regula...

This article focuses on the theta series on the 6-fold cover of GL2. We investigate the Fourier coefficients τ(r) of the theta series, and give partially proven, partially conjectured values for τ(π)2, τ(π2) and τ(π4) for prime values π.

We show that essentially the speed of decay of the Fourier sine coefficients of a function in a Lebesgue space is comparable to that of the corresponding coefficients with respect to the basis formed by the generalized sine functions sin p,q .

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a(p) = 2p~ @ ) cos 0(p). Since we know the truth of the Ramanujan-Petersson conjecture, it follows that the 0(p)'s are real. Inspired by the Sato-Tate conjecture for elliptic curves, Serre [14] conjectured that the 0(p)'s are uniformly distributed in the interval [0, rc] with respect to the 1 measure -sin2OdO. Following Serre, we shall refer to this as the Sato-Tate r~ conjecture, there being n...

Continued fraction expansions for the eigenvalues A= A(I', h2 ) and for the Fourier coefficients c~n/co are given by Tamir and Wang in [2]. These relations are valid both in the s table (I' real) and unstable (I' complex) regions . F (I') == C~,.1Co is numerically evaluated and depicted. It is seen from the graphs in [2] that the given formulas for C~,JCO are not particularly suitable for numer...

Computing the Fourier transform is a basic building block used in numerous applications. For data intensive applications, even the O(N logN) running time of the Fast Fourier Transform (FFT) algorithm may be too slow, and sub-linear running time is necessary. Clearly, outputting the entire Fourier transform in sub-linear time is infeasible, nevertheless, in many applications it suffices to find ...

Uncompressed images occupy more memory and it contains redundant data. For storage and transmission efficiency compression is required. The purpose of image compression is to reduce the number of bits to represent in image while maintaining visual quality of images. In this paper we implement the Fast Fourier co efficient Transform with non overlapping 3 x 3, 9 x 9 and 27x 27 block sizes of the...