The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that if 0<p<1, 0<q<1, ℝ, while if 0<p<1, 1≤q<+∞, ∝, and if 1≤p<+∞, 0<q<1, ℝ. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.     

Synthesis and Pd-catalyzed coupling of1-C-stannylated glycals

Abstract

1-Tributylstannyl glycals were applied as versatile tools in the Pd(0)-mediated synthesis of glycal phthalonitrile conjugates. Likewise, selective homo-coupling of 1-tributylstannyl glycals furnishing C1-C1’ linked glycal dimers was investigated by using Pd(II)-species. For both Stille type couplings the rate-accelerating effect of copper(I) thiophene-2-carboxylate (CuTC) was exploited. The synthesis of stannylated glycal precursors was significantly improved by establishing a one-pot two-step procedure via glycosyl sulfoxides.     

New trends in polylactide (PLA)-based materials: “Green” PLA-Calcium sulfate (nano)composites tailored with flame retardant properties

Starting from gypsum, a by-product of lactic acid fabrication process, novel “green” composites have been produced by melt-blending polylactide (PLA) and this filler after a previous specific dehydration to obtain anhydrite II (AII). Such a material is potentially interesting in biodegradable/rigid packaging and in technical applications requiring rigidity, heat resistance and dimensional stability. In order to obtain PLA-AII composites characterized by specific end-use flame retardant properties, the addition of selected organo-modified layered silicates (OMLS) was considered. Co-addition of AII and OMLS leads to PLA (nano)composites characterized by good (nano)filler dispersion, thermal stability and adequate mechanical resistance. The flame retardant properties as shown by cone calorimetry showed significant increase in the ignition time compared to neat PLA and a substantial decrease, i.e., ca. 40%, of the maximum rate of heat release, whereas the UL94 HB test was successfully passed revealing non-dripping effect and extensive char formation. The study represents a new approach in formulating novel PLA grades with improved characteristic features.     

Embedding polynomial matrices of one variable

A non square matrix with coefficients in K[z] can (if a condition on its minors is satisfied) be embedded into a square matrix with determinant 1. Finding theoretically and in an algorithmic way an embedding of small degree is solved by a construction with vector bundles on the projective line over K.     

Four applications of majorization to convexity in the calculus of variations

The resemblance between the Horn-Thompson theorem and a recent theorem by Dacorogna-Marcellini-Tanteri indicates that Schur-convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity, such as rank one convexity or quasiconvexity. In Theorem 6.6, we give simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant.Majorization is used in order to give a very short proof of a theorem of Thompson and Freede [R.C. Thompson, L.J. Freede, Eigenvalues of sums of Hermitian matrices III, J. Res. Nat. Bur. Standards B 75B (1971) 115-120], Ball [J.M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics, in: R.J. Knops (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. 1, Res. Notes Math., 17, Pitman, 1977, pp. 187-241], or Le Dret [H. Le Dret, Sur les fonctions de matrices convexes et isotropes, CR Acad. Sci. Paris, Série I 310 (1990) 617-620], concerning the convexity of a class of isotropic functions which appear in nonlinear elasticity.Next we prove (Theorem 7.3) a lower semicontinuity result for functionals with the form _∫Ωw(D?(x))dx, with w(F)=h(lnV_F). Here F=R_FU_F=V_FR_F is the usual polar decomposition of F∈gl(n,R), and lnV_F is Hencky’s logarithmic strain.We close this paper with a compact proof of Dacorogna-Marcellini-Tanteri theorem, based only on classical results about majorization. The mentioned resemblance of this theorem with the Horn-Thompson theorem is thus explained.     

Consistent implementation of real fluid EOS in pseudopotential lattice Boltzmann models

Pseudopotential lattice Boltzmann models have emerged as successful methods to simulate liquid-vapor coexistence systems. However, the equation of state (EOS) of such systems, which is found to be thermodynamically consistent, is unique and lacks the potential to cover a broad range of physical fluids. In this study, we employ multiple pseudopotentials and extend the consistent EOS to enhance the capability of pseudopotential models in reproducing a wider range of thermodynamic states. The new system has the format which preserves the consistency between the lattice pressure tensor and the free energy density. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.