Volume 11, 2005, Number 1

Volume 11 ▶ Number 1 ▷ Number 2Number 3Number 4

On four Smarandache’s problems
Original research paper. Pages 1–6
Krassimir T. Atanassov
Full paper (PDF, 125 Kb)

Exploring the q-Riemann Zeta function and q-Bernoulli polynomials
Original research paper. Pages 7–19
T. Kim, C. S. Ryoo, L. C. Jang and S. H. Rim
Full paper (PDF, 334 Kb) | Abstract

In this paper we study that the q-Bernoulli polynomial, which were constructed by T. Kim, are analytic continued to βs(z). A new formula for the q-Riemann Zeta function ζq(s) due to T. Kim (see [1,2,8]) in terms of nested series of ζq(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an investing phenomenon of “scattering” of the zeros of βs(z) is observed. Following the idea of q-zeta function due to T. Kim, we are going to use “Mathematica” to explore a formula for ζq(n).

Goldbach’s n-perfect numbers as a key for proving the Goldbach’s conjecture
Original research paper. Pages 20–22
Mladen Vassilev-Missana
Full paper (PDF, 1278 Kb)

Prime grids in the modular ring Z6
Original research paper. Pages 23–28
J. V. Leyendekkers and A. G. Shannon
Full paper (PDF, 42 Kb) | Abstract

Prime grids are set up in the Modular Ring Z6 for the Classes ̅26 and ̅46. The regular formation of composites intrudes into the grid in a predictable manner, which indicates that the primes form in a structures rather than a haphazard manner when viewed in this way.

Volume 11 ▶ Number 1 ▷ Number 2Number 3Number 4

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