Abstract:
Review of the book by Oana M. Oprean Romania’s Accession to the European Union and Its Impact on the Roma Minority, Saarbr cken, LAP Lambert Academic Publishing, 2012, ISBN 978-3-8465-8671-6, 73p.

Abstract:
The Lambert W function, implicitly defined by W(x) exp{W(x)}=x, is a "new" special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can also be used to gain a new perspective on the distribution of primes.

Abstract:
We prove sharp bounds for the product and the sum of a pair of hyperbolic adjacent sides of hyperbolic Lambert quadrilaterals in the unit disk.

Abstract:
We prove sharp bounds for the product and the sum of two hyperbolic distances between the opposite sides of hyperbolic Lambert quadrilaterals in the unit disk. Furthermore, we study the images of Lambert quadrilaterals under quasiconformal mappings from the unit disk onto itself and obtain sharp results in this case, too.

Abstract:
The calculation of volumes of polyhedra in the three-dimensional Euclidean, spherical and hyperbolic spaces is very old and difficult problem. In particular, an elementary formula for volume of non-euclidean simplex is still unknown. One of the simplest polyhedra is the Lambert cube Q(\alpha,\beta,\gamma). By definition, Q(\alpha,\beta,\gamma) is a combinatorial cube, with dihedral angles \alpha,\beta and \gamma assigned to the three mutually non-coplanar edges and right angles to the remaining. The hyperbolic volume of Lambert cube was found by Ruth Kellerhals (1989) in terms of the Lobachevsky function \Lambda(x). In the present paper the spherical volume of Q(\alpha,\beta,\gamma) is defined in the terms of the function \delta(\alpha,\theta) which can be considered as a spherical analog of the Lobachevsky function \Delta(\alpha,\theta)=\Lambda(\alpha + \theta) - \Lambda(\alpha - \theta)

Abstract:
The goal of this paper is to analyze the discrete Lambert map x to xg^x modulo a power of a prime p which is important for security and verification of the ElGamal digital signature scheme. We use p-adic methods (p-adic interpolation and Hensel's Lemma) to count the number of solutions x of xg^x congruent to c modulo powers of an odd prime p and c, g are fixed integers. At the same time, we discover special patterns in the solutions.

Abstract:
We show how the generalized Lambert series sum(n>=1, x*q^n/(1-x*q^n)) can be computed with Theta convergence. This allows the computation of the sum of the inverse Fibonacci numbers without splitting the sum into even and odd part. The method is a special case of an expression for the more general series sum(n>=0, t^n/(1-x*q^n)), which can be obtained from either the Rogers-Fine identity or an identity by Osler and Hassen.

Abstract:
The orbital boundary value problem, also known as Lambert Problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revoltuion case, in only two iterations. The resulting algorithm is compared to Gooding's procedure revealing to be numerically as accurate, while having a smaller computational complexity.