Abstract:
The first Geogarypus found in Rovno amber appears to be conspecific with Geogarypus gorskii Henderickx 2005, a species known from Eocene Baltic amber.

Abstract:
Roncus elbulli sp. n. is described from Cap de Creus Nature Park (Catalonia, Spain). The new species is morphologically close to Roncus cadinensis Zaragoza, 2007 (Barcelona province), but differs by being smaller in size anda more robust chela with a different microsetae pattern. The new species seems to be restricted to coastal semiarid slopes with garrigue vegetation. A key to the Spanish species of the genus Roncus is provided.

Differential equations to describe elasticity are derived without the use of stress or strain. The points within the body are the independent parameters instead of strain and surface forces replace stress tensors. These differential equations are a continuous analytical model that can then be solved using any of the standard techniques of differential equations. Although the equations do not require the definition stress or strain, these quantities can be calculated as dependent parameters. This approach to elasticity is simple, which avoids the need for multiple definitions of stress and strain, and provides a simple experimental procedure to find scalar representations of material properties in terms of the energy of deformation. The derived differential equations describe both infinitesimal and finite deformations.

Abstract:
The equations of Euler-Lagrange elasticity describe elastic deformations
without reference to stress or strain. These equations as previously published
are applicable only to quasi-static deformations. This paper extends these
equations to include time dependent deformations. To accomplish this, an
appropriate Lagrangian is defined and an extrema of the integral of this
Lagrangian over the original material volume and time is found. The result is a
set of Euler equations for the dynamics of elastic materials without stress or
strain, which are appropriate for both finite and infinitesimal deformations of
both isotropic and anisotropic materials. Finally, the resulting equations are
shown to be no more than Newton's Laws applied to each infinitesimal volume of
the material.

Abstract:
Linear algebra provides insights into the description of elasticity without stress or strain. Classical descriptions of elasticity usually begin with defining stress and strain and the constitutive equations of the material that relate these to each other. Elasticity without stress or strain begins with the positions of the points and the energy of deformation. The energy of deformation as a function of the positions of the points within the material provides the material properties for the model. A discrete or continuous model of the deformation can be constructed by minimizing the total energy of deformation. As presented, this approach is limited to hyper-elastic materials, but is appropriate for infinitesimal and finite deformations, isotropic and anisotropic materials, as well as quasi-static and dynamic responses.

Abstract:
We compute numerically eigenvalues and eigenfunctions of the quantum Hamiltonian that describes the quantum mechanics of a point particle moving freely in a particular three-dimensional hyperbolic space of finite volume and investigate the distribution of the eigenvalues.

Abstract:
We investigate the numerical computation of Maass cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r=40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.

Abstract:
The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-mass system is highly nonlinear. Utilizing Mathematica [1] the equation of motion is solved numerically. The kinematics of the particle namely, its position, velocity and acceleration as a function of time, are displayed in three separate phase diagrams. Energy of the oscillator is analyzed. The nonlinear motion of the charged particle is set into an actual three-dimensional setting and animated for a comprehensive understanding.

Abstract:
The electronic structure, energy band structure, total density of states (DOS) and electronic density of perovskite SrTiO_{3} in the cubic phase are calculated by the using full potential-linearized augmented plane wave (FP-LAPW) method in the framework density functional theory (DFT) with the generalized gradient approximation (GGA) by WIEN2k package. The calculated band structure shows a direct band gap of 2.5 eV at the Γ point in the Brillouin zone.The total DOS is compared with experimental x-ray photoemission spectra. From the DOS analysis, as well as charge-density studies, I have conclude that the bonding between Sr and TiO_{2} is mainly ionic and that the TiO_{2} entities bond covalently.The calculated band structure and density of state of SrTiO_{3} are in good agreement with theoretical and experimental results.