SUMMARY An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring Z N , N = pq for two distinct odd primes p and q. The result is a generalization of an estimate of exponential sums on rational point groups of elliptic curves over finite fields. The bound is applied to showing the pseudoran-domness of a large family of binar...

The implementation of maximum likelihood parallel factor analysis (MLPARAFAC) in conjunction with the direct exponential curve resolution algorithm (DECRA) is described. DECRA takes advantage of the intrinsic exponential structure of some bilinear data sets to produce trilinear data by a simple shifting scheme, but this manipulation generates an error structure that is not optimally handled by ...

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show t...

A C curve interpolation scheme for monotonic data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The monotone rational cubic spline scheme has a unique representation.

A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It constructed from Pad\'e expansions matrix exponential a system first-order ordinary differential equations formulated in state-space. computationally efficient developed exploiting techniques polynomial factorization partial fractions rational functions, by deco...

Recent high resolution CO observations of normal and starburst galaxies at Owens Valley Millimeter Array are summarized. While normal disk galaxies generally show exponential distribution which follows the optical blue light, starburst galaxies are often characterized by a compact (1 kpc) nuclear complex whose surface gas mass density is strongly correlated with the observed large infrared lumi...

Rational exponential integrators (REXI) are a class of numerical methods that well suited for the time integration linear partial differential equations with imaginary eigenvalues. Since these can be parallelized in (in addition to spatial parallelization is commonly performed) they exploit modern high performance computing systems. In this paper, we propose novel REXI scheme drastically improv...