Some Discrete Nonlinear Inequalities and Applications to Difference Equations

In this article, the authors establish some new nonlinear difference inequalities in two independent variables, which generalize some existing results and can be used as handy tools in the study of qualitative as well as quantitative properties of solutions of certain classes of difference equations.     

Identities for the Chebyshev functional involving derivatives of arbitrary order and applications

We generalize the identities of J. Pe?ari? and A.M. Fink for the Chebyshev functional. The identities are shown to be very useful in establishing various bounds for the Chebyshev functional.     

Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls

Integral means of arbitrary order, with power weights and their companion means, where the integrals are taken over balls in centered at the origin, are introduced and related mixed-means inequalities are derived. These relations are then used in obtaining Hardy and Levin-Cochran-Lee inequalities and their companion results for -dimensional balls. Finally, the best possible constants for these inequalities are obtained.

     

Complex configuration mixing method

A method analogous to the configuration interaction scheme, based on the complex molecular orbital (CMO) wavefunction as a zero-order approximation, is developed. The CMO pairing representation is employed to solve problems related to non-orthogonalities characteristic of the CMO method. This complex configuration mixing method may compete with present theories of electronic correlation in molecules.     

Analysis of the uniform magnetic field free-electron laser with scalarized photons in the microwave-spectral region

The recently developed concept of scalarized photons (formally photons of any polarization) is used to analyze the spontaneous and stimulated emission in the uniform magnetic field free-electron laser in the microwave spectral region. In fact, this free-electron laser is the simplest of many other, wiggler and wiggler-free free-electron lasers whose analyses could be done with scalarized photons in the small signal regime and whose physical parameters can be conveniently chosen for radiation to be generated in the microwave spectral region. As to the uniform magnetic field free-electron laser, which is treated here in some detail, with the electron beam energy of up to 10 MeV and the uniform magnetic field of up to 4 Tesla, the radiation (occurring with the fundamental and higher harmonic frequencies) can cover easily a 10 to 10,000 GHz spectral region.     

On refined Hardy-type inequalities with fractional integrals and fractional derivatives

The aim of this paper is to present new more general Hardy-type inequalities for different kinds of fractional integrals and fractional derivatives.     

A multiscale approach to thermoplastic deformation

The paper applies a multiscale formulation to thermoplasticity problems. The plasticity model is based on the variationally consistent formulation at the micro level. It is suitable for problems involving large strains. The temperature field is calculated at the macro level and is assumed to be homogeneous at the micro level. The proposed formulation is implemented in the Abaqus software by means of user subroutines. User subroutines are introduced both at the macro and at the micro level. The consistent tangent operator is calculated by the numerical differentiation procedure. Implementation details are briefly addressed. Finally, the methodology is verified on a representative example and relevant results are presented and discussed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Derivation and Justification of the Models of Rods and Plates From Linearized Three-Dimensional Micropolar Elasticity

In this paper we derive and mathematically justify models of micropolar rods and plates from the equations of linearized micropolar elasticity. Derivation is based on the asymptotic techniques with respect to the small parameter being the thickness of the elastic body we consider. Justification of the models is obtained through the convergence result for the displacement and microrotation fields when the thickness tends to zero. The limiting microrotation is then related to the macrorotation of the cross–section (transversal segment) and the model is rewritten in terms of macroscopic unknowns. The obtained models are recognized as being either the Reissner–Mindlin plate or the Timoshenko beam type.