We consider two families of weighted zero-sum constant for finite abelian groups. For a finite abelian group (G,+), a set of weights W ⊂ Z, and an integral parameter m, the m-wise Davenport constant with weights W is the smallest integer n such that each sequence over G of length n has at least m disjoint zero-subsums with weights W . And, for an integral parameter d, the d-constrained Davenpor...

We apply the Hecke operators T (p) and T̃j(p 2) (1 ≤ j ≤ n, p prime) to a degree n theta series attached to a rank 2k Z-lattice L, n ≤ k, equipped with a positive definite quadratic form in the case that L/pL is hyperbolic. We show that the image of the theta series under these Hecke operators can be realized as a sum of theta series attached to certain closely related lattices, thereby generali...

Symmetric standard elliptic integrals are considered when one of their parameters is larger than the others. Distributional approach is used for deriving five convergent expansions of these integrals in inverse powers of the respective five possible asymptotic parameters. Four of these expansions involve also a logarithmic term in the asymptotic variable. Coefficients of these expansions are ob...

Presented here is a unified approach to evaluating the errorrate performance of digital communication systems operating over a generalized fading channel. What enables the unification is the recognition of the desirable form for alternate representations of the Gaussian and Marcum Q-functions that are characteristic of error-probability expressions for coherent, differentially coherent, and non...

I derive analytically the spectrum of the CMB fluctuations. The final result for Cl is presented in terms of elementary functions with an explicit dependence on the basic cosmological parameters. This result is in a rather good agreement with CMBFAST for a wide range of parameters around concordance model. This allows us to understand the physical reasons for dependence of the particular featur...

It is “well known” that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a function of underlying, strike, and call price, implied volatility does not belong to the class of Dfinite functions. This does not rule out all explicit expressions, but shows that implied volatility does not belong to a certain large class, which contains many elementary funct...

For any class F of total functions in the set N of the natural numbers, we define the notion of F-computable real number. A real number α is called Fcomputable if there exist one-argument functions f , g and h in F such that for any n in N the distance between the rational number f(n) − g(n) over h(n) + 1 and the number α is not greater than the reciprocal of n + 1. Most concrete real numbers p...

(ABSTRACT) This study examines perceptions of the stakeholders fifth grade students) about the Virginia Beach Elementary Guidance and Counseling Program. A survey was developed by examining guidance goals and a previous study of the program (1993). Questions covered four domains: (1) home-school relationships, (2) student personal development, (3) support for academic growth, and (4) program va...

A double sub-equation method is presented for constructing complexiton solutions of nonlinear partial differential equations (PDEs). The main idea of the method is to take full advantage of two solvable ordinary differential equations with different independent variables. With the aid of Maple, one can obtain both complexiton solutions, combining elementary functions and the Jacobi elliptic fun...

We have determined theoretically the rest mass of the muon neutrino at 50 milli-eV and the rest mass of the electron neutrino at 5 meV, as well as , to 1% accuracy, the ratio of the masses of the stable elementary particles which decay by weak decays. We assume that the particles of the neutrino branch consist of a cubic, isotropic nuclear lattice, held together by the weak nuclear force. The e...