This paper is concerned with non-trivial solvability in p-adic integers of systems of additive forms. Assuming that the congruence equation ax + by + cz ≡ d (mod p) has a solution with xyz 6≡ 0 (mod p) we have proved that any system of R additive forms of degree k with at least 2 · 3R−1 · k + 1 variables, has always non-trivial p-adic solutions, provided p k. The assumption of the solubility of...

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

Abstract— A fundamental problem for control engineers is that of output tracking. The earlier approaches are restricted to certain classes of systems precluding the presence of zeros from certain regions in the complex plane, and do not reasonably take into account process and measurement noise. A technique to achieve output tracking applicable to non-minimum phase linear systems is presented w...

We study the distribution, in the space of Satake parameters, of local components of Siegel cusp forms of genus 2 and growing weight k, subject to a specific weighting which allows us to apply results concerning Bessel models and a variant of Petersson’s formula. We obtain for this family a quantitative local equidistribution result, and derive a number of consequences. In particular, we show t...

We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also correspo...

The zeros of generalized Krawtchouk polynomials are studied. Some interlacing theorems for the zeros are given. A new infinite family of integral zeros is given, and it is conjectured that these comprise most of the non-trivial zeros. The integral zeros for two families of q-Krawtchouk polynomials are classified.

We argue that the resonance-like structures Y (4260) [1, 2], Y (4360), Y (4660) [3] and Y (4635) [4], which were recently reported to have been observed in experiment, are nonresonant manifestations of the Regge zeros that appear in the production amplitude of the Resonance-Spectrum Expansion. Charmonium cc̄ states are visible on the slopes of these enhancements. In the Resonance-Spectrum Expans...

The permutation test is one of the oldest techniques for making statistical inferences. Monte Carlo methods and asymptotic formulas have been used to approximate the associated p-values. When data are truncated, however, the permutation null distribution is difficult to handle. We describe here an efficient sequential importance sampling strategy for generating permutations with restricted posi...

Natural 4 zeros texture mass matrices recently proposed by Fritzsch and Xing have been investigated by including ‘non-leading’corrections in the context of latest data regarding m t and VCKM matrix elements. Apart from accommodating m t in the range 175 ± 15 GeV, |Vcb| and |Vub/Vcb| = 0.08 ± 0.02, the analysis with maximal CP-violation predicts |Vtd| = .005 − .013. Further, the CP-violating pha...