Reaction of N-2-(1-Carbethoxy) - and N-2-(1-acyl)-benzimidazoimidates with Grignard Reagents. Synthesis of 1,3,5-Oxadiazino-(1,2-a)benzimidazoles

Reaction of ethyl chloroformate and acyl chlorides with iminoesters derived from 2- aminobenzimidazole, followed by Grignard reagent condensation leads to a variety of oxadiazinobenzimidazoles in good yield.     

Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets

The existence and the convergence (up to a subsequence) of the Moreau-Yosida regularization for the state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets are established. Then, by a reparametrization technique, the existence of solutions for bounded variation continuous state-dependent sweeping processes with nonregular (subsmooth and positively alpha-far) sets is proved. An application to vector hysteresis is discussed, where it is shown that the Play operator with positively alpha-far sets is well defined for bounded variation continuous inputs.     

Recursive polynomial interpolation algorithm (RPIA)

Two difference schemes are derived for numerically solving the one-dimensional time distributed-order fractional wave equations. It is proved that the schemes are unconditionally stable and convergent in the \(L^{\infty }\) norm with the convergence orders O(τ ² + h ²+Δγ ²) and O(τ ² + h ⁴+Δγ ⁴), respectively, where τ,h, and Δγ are the step sizes in time, space, and distributed order. A numerical example is implemented to confirm the theoretical results.     

Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids

In this contribution we present the least-squares finite element method (LSFEM) for the incompressible Navier-Stokes equations. In detail, we consider a non-Newtonian fluid flow, which is described by a power-law model, see [1]. The second-order problem is reformulated by introducing a first-order div-grad system consisting of the equilibrium condition, the incompressibility condition and the constitutive equation, which are written in residual forms, see [2]. Here, higher-order finite elements which are an important aspect regarding accuracy for the present formulation are investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integration formulas via the Fenchel subdifferential of nonconvex functions

Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the ε-subdifferential and the Fenchel subdifferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the ε-subdifferential of the nominal function or of the subdifferential of its weak lsc envelope.     

Invariant sets and Lyapunov pairs for differential inclusions with maximal monotone operators

We give different conditions for the invariance of closed sets with respect to differential inclusions governed by a maximal monotone operator defined on Hilbert spaces, which is subject to a Lipschitz continuous perturbation depending on the state. These sets are not necessarily weakly closed as in [3], [4], while the invariance criteria are still written by using only the data of the system. So, no need to the explicit knowledge of neither the solution of this differential inclusion, nor the semi-group generated by the maximal monotone operator. These invariant/viability results are next applied to derive explicit criteria for a-Lyapunov pairs of lower semi-continuous (not necessarily weakly-lsc) functions associated to these differential inclusions. The lack of differentiability of the candidate Lyapunov functions and the consideration of general invariant sets (possibly not convex or smooth) are carried out by using techniques from nonsmooth analysis.     

On the existence of the biharmonic Green kernels and the adjoint biharmonic functions

We study the existence and the regularity of the biharmonic Green kernel in a Brelot biharmonic space whose associated harmonic spaces have Green kernels. We show by some examples that this kernel does not always exist. We then introduce and study the adjoint of the given biharmonic space. This study was initiated by Smyrnelis, however, it seems that several results were incomplete and we clarify them here.     

Tangency conditions for multivalued mappings

We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.     

Origin of semiconductor and half-metallic behaviors in the perovskite materials RbXF3 (X = Co,Mn, Fe or V): A GGA + U approach

In this paper, we study and discuss the structural, and electronic properties of the RbXF3 (X = Co, Mn, V or Fe) Perovskite Materials using the Density Functional Theory (DFT). Also, the origin of both semi-conductor (SM) and half-metallic (HM) characters have been outlined. The density functional theory (DFT) has been applied to illustrate the physical properties of the RbXF₃ (X = Co, Mn, Fe or V) perovskite materials. The generalized gradient approximation introduced by Perdew–Burke and Ernzerhof (GGA-PBE) with Hubbard correction has been used for modeling the physical properties of the RbXF₃ (X = Co, Mn, V or Fe) perovskite compounds. The total and partial densities of states of each solar perovskite RbVF₃ (X = Co, Mn, Fe or V) material have been illustrated and discussed. In addition, the contribution of the different elements: Rb, Co, Mn, Fe, V and F, has been investigated revealing the most contributing ones in the valance and conduction bands. The magnetic behavior of the studied solar perovskites RbVF₃ (X = Co, Mn, Fe or V) materials, has been outlined. It is found that the perovskites RbCoF₃ and RbFeF₃ are half-metallic, while the materials RbMnF₃ and RbVF₃ exhibit a semi-conductor behavior.