Hamiltonian Formulation of FRW Equations of Cosmology

We give a general Hamiltonian formulation of the Friedmann-Robertson-Walker (FRW) fundamental equations of a homogeneous and isotropic universe in the Standard Cosmological model. It gives some interesting insight on the 3-curvature of the universe, which is found to be obtained in terms of the scale factor (also termed radius of the universe) and its first derivative. It also leads to an easy determination of the Schrödinger equation for the (R) wave function of the universe, in the radiative era.     

General decay of solutions of a viscoelastic equation

In this paper we consider the following viscoelastic equation:

     

Some applications of the strong approximation of the integrated empirical copula processes

The purpose of the present paper is to provide a strong invariance principle for the integrated empirical copula process [introduced in a series of papers by Henze and Nikitin in the univariate setting] with the rate of the approximation for multivariate empirical processes. The applications discussed here are change-point detection in multivariate copula models and the integrated empirical copula process with estimated parameter. Finally, a general notion of bootstrapped integrated empirical copula process, constructed by exchangeably weighting sample, is presented.     

Synthesis and characterization of spinel LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript> nanoparticles prepared by high-energy milling and hydrothermal method

Spinel LiMn₂O₄ has been known to be a technologically important, environmental-friendly, and low-cost cathode material used in Li-based rechargeable batteries, and it is also widely available. Nanoparticle spinel LiMn₂O₄ has been synthesized by the top-down, high-energy milling, and hydrothermal methods. SEM images, X-ray diffraction patterns, and neutron high-resolution powder diffraction patterns have confirmed the nanocrystalline nature of the spinel LiMn₂O₄ samples. Raman and Fourier transform infrared (FTIR) measurements show typical absorption and vibration spectra typical for the spinel LiMn₂O₄ showing the formation of various metallic bonds in the sample. The strongest Raman and FTIR signals come from the higher frequency region, with weaker signals appearing in the lower frequency range.     

A primal-mixed formulation for the strong coupling of quasi-Newtonian fluids with porous media

In this work we analyze a primal-mixed finite element method for the coupling of quasi-Newtonian fluids with porous media in 2D and 3D. The flows are governed by a class of nonlinear Stokes and linear Darcy equations, respectively, and the transmission conditions on the interface between the fluid and the porous medium are given by mass conservation, balance of normal forces and the Beavers-Joseph-Saffman law. We apply a primal formulation in the Stokes domain and a mixed formulation in the Darcy formulation. The “strong coupling” concept means that the conservation of mass across the interface is introduced as an essential condition in the space where the velocity unknowns live. In this way, under some assumptions on the nonlinear kinematic viscosity, a generalization of the Babu?ka-Brezzi theory is utilized to show the well posedness of the primal-mixed formulation. Then, we introduce a Galerkin scheme in which the discrete conservation of mass is imposed approximately through an orthogonal projector. The unique solvability of this discrete system and its Strang-type error estimate follow from the generalized Babu?ka-Brezzi theory as well. In particular, the feasible finite element subspaces include Bernadi-Raugel elements for the Stokes flow, and either the Raviart-Thomas elements of lowest order or the Brezzi-Douglas-Marini elements of first order for the Darcy flow, which yield nonconforming and conforming Galerkin schemes, respectively. In turn, piecewise constant functions are employed to approximate in both cases the global pressure field in the Stokes and Darcy domain. Finally, several numerical results illustrating the good performance of both discrete methods and confirming the theoretical rates of convergence, are provided.     

On the decay rates of Timoshenko system with second sound

In this work, we study the well‐posedness and the asymptotic stability of a one‐dimensional linear thermoelastic Timoshenko system, where the heat conduction is given by Cattaneo's law and the coupling is via the displacement equation. We prove that the system is exponentially stable provided that the stability number χ_τ=0. Otherwise, we show that the system lacks exponential stability. Furthermore, in the latter case, we show that the solution decays polynomially. Copyright © 2015 John Wiley & Sons, Ltd.     

One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane $${\mathbb{C}_{J}}$$

In this paper, we introduce one-parameter homothetic motions in the generalized complex number plane (\({\mathfrak{p}}\)-complex plane)

$$\mathbb{C}_{J}=\left\{x+Jy:\,\,\, x,y \in \mathbb{R},\quad J^2=\mathfrak{p},\quad \mathfrak{p} \in \{-1,0,1\} \right\} \subset \mathbb{C}_\mathfrak{p}$$

where

$$\mathbb{C}_\mathfrak{p}=\{x+Jy:\,\,\, x,y \in \mathbb{R}, \quad J^2=\mathfrak{p}\}$$

such that \({-\infty < \mathfrak{p} < \infty}\). The velocities, accelerations and pole points of the motion are analysed. Moreover, three generalized complex number planes, of which two are moving and the other one is fixed, are considered and a canonical relative system for one-parameter planar homothetic motion in \({\mathbb{C}_{J}}\) is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, during the one-parameter homothetic motions, is obtained with the aim of this canonical relative system.