We describe a simple geometrical derivation of the formula for reflection of light from a uniformly moving plane mirror directly from the postulates of special relativity.

Aleksandar Gjurchinovski Aleksandar Skeparovski

In order to measure the radial displacements of facets on surface of a growing spherical Cu_{2-\delta}Se crystal with sub-nanometer resolution, we have investigated the reliability and accuracy of standard method of Fourier analysis of fringes obtained applying digital laser interferometry method. Guided by the realistic experimental parameters (density and orientation of fringes), starting from 2-dimensional model interferograms and using unconventional custom designed Gaussian filtering window and unwrapping procedure of the retrieved phase, we have demonstrated that for considerable portion of parameter space the non-negligible inherent phase retrieval error is present solely due to non-integer number of fringes within the digitally recorded image (using CCD camera). Our results indicate the range of experimentally adjustable parameters for which the generated error is acceptably small. We also introduce a modification of the (last part) of the usual phase retrieval algorithm which significantly reduces the error in the case of small fringe density.

Jadranko Gladic Zlatko Vucic Davorin Lovric

As is well known, Buss' theory of bounded arithmetic $S^{1}_{2}$ proves $\Sigma_{0}^{b}(\Sigma_{1}^{b})-LIND$; however, we show that Allen's $D_{2}^{1}$ does not prove $\Sigma_{0}^{b}(\Sigma_{1}^{b})-LLIND$ unless $P = NC$. We also give some interesting alternative axiomatisations of $S^{1}_{2}$.

Aleksandar Ignjatovic

In this paper we describe a procedure to simplify any given triangulation of the 3-sphere using Pachner moves. We obtain an explicit exponential-type bound on the number of Pachner moves needed for this process. This leads to a new recognition algorithm for the 3-sphere.

Aleksandar Mijatovic

Asymptotic formulas for $\sum_{\kappa_j\le K}\alpha_j H_j^k(1/2)$ are proved when $k = 3,4$, where $H_j(s)$ is the Hecke series.

Aleksandar Ivić

An asymptotic formula for the number of $n \le x$ such that $n$ does not divide $P(n)!$ is given, where P(n) is the largest prime factor of $n$.

Aleksandar Ivić

We discuss some problems in number theory posed by Djuro Kurepa (1907-1993), including his classical left factorial hypothesis that an odd prime $p$ does not divide $0! + 1! + ... + (p-1)!$.

Aleksandar Ivić Žarko Mijajlović

This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.

Aleksandar Ivić

Some identities for the Riemann zeta-function are proved, using properties of the Mellin transform and M\"untz's identity.

Aleksandar Ivić

We present a derivation of the relativistic length-contraction formula based on Lorentz space-time transformations on non-simultaneous events. Our derivation avoids the disputable story about the stationary observer and its simultaneous measurements of object's end-points.

Aleksandar Gjurchinovski