A Strong Maximum Principle for parabolic equations with the p-Laplacian

We prove the Strong Maximum Principle (SMP) under suitable assumptions for a class of quasilinear parabolic problems with the p  -Laplacian, p>1$p>1$, on bounded cylindrical domains of R^N+1${\mathbb{R}}^{N+1}$,

_∂tu−_Δpu−λ|u|^p−2u≥0,${\partial }_{t}u-{\mathrm{\Delta }}_{p}u-\lambda {|u|}^{p-2}u\ge 0,$

with nonnegative initial–boundary conditions and λ≤0$\lambda \le 0$, and we give some counterexamples to the SMP if some of our assumptions are violated. We show that the Hopf Maximum Principle holds for 1<p<2$1<p<2$, and give a counterexample to it for p>2$p>2$. Also the Weak Maximum Principle for λ≤_λ1$\lambda \le {\lambda }_1$ is established.     

Effective stereoselective approach to substituted 1,4-dioxane-2,5-diones as prospective substrates for ring-opening polymerization

1. Download high-res image (151KB)
2. Download full-size image

     

Stress Integration of the Hoek-Brown Material Model Using Incremental Plasticity Theory

This paper presents the formulation of the stress integration procedure for the Hoek-Brown (HB) material model with non-associative yielding condition by using the incremental plasticity method. Main idea of this method is to reach the solution by calculating the plastic matrix according to the method of incremental plasticity (used for elastic constitutive matrix corrections), and with the use of the total strain increment. Computational procedure is implemented within the PAK program package. Results of this procedure were compared with the solutions obtained by other program that contains this material model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New Type of Nanocomposite CsH2PO4-UiO-66 Electrolyte with High Proton Conductivity

New (1−x)CsH₂PO₄–xUiO-66 electrolytes with high proton conductivity and thermal stability at 230–250 °C were developed. The phase composition and proton conductivity of nanocomposites (x = 0–0.15) were investigated in detail. As shown, the UiO-66 matrix is thermally and chemically suitable for creating composites based on CsH₂PO₄. The CsH₂PO₄ crystal structure remains, but the degree of salt crystallinity changes in nanocomposites. As a result of interface interaction, dispersion, and partial salt amorphization, the proton conductivity of the composite increases by two orders of magnitude in the low-temperature range (up to 200 °C), depending on the UiO-66 fraction, and goes through a maximum. At higher temperatures, up to 250 °C, the conductivity of nanocomposites is close to the superprotonic values of the original salt at low UiO-66 values; then, it decreases linearly within one order of magnitude and drops sharply at x > 0.07. The stability of CsH₂PO₄-UiO-66 composites with high proton conductivity was shown. This creates prospects for their use as proton membranes in electrochemical devices.     

Behavior of Solutions to the Dirichlet Problem for Elliptic Systems in Convex Domains

We consider the Dirichlet problem for strongly elliptic systems of order 2m in convex domains. Under a positivity assumption on the Poisson kernel it is proved that the weak solution has bounded derivatives up to order m provided the outward unit normal has no big jumps on the boundary. In the case of second order symmetric systems in plane convex domains the boundedness of the first derivatives is proved without the assumption on the normal.     

Spatial structure of peptides determined by residual dipolar couplings analysis

The gated decoupled (13)C NMR spectra of a dipeptide (Glu-Trp) and a tetrapeptide (NAc-Ser-Phe-Val-Gly-OMe) were recorded in D(2)O and in a lyotropic alignment medium (pentaethylene glycol monododecyl ether/n-hexanol). The residual dipolar couplings were extracted as the differences between the observed couplings for the magnetic nuclei dissolved in the latter and former media. Using a computational optimization, the spatial structures of the compounds were calculated starting from their respective low energy conformations obtained on a semiempirical basis. The uniformity of each conformation was confirmed by the solid-state (13)C NMR spectra of powder samples. Differences between the starting structures and final ones, optimized when employing residual dipolar couplings, are discussed.     

On arrangements of roots for a real hyperbolic polynomial and its derivatives

In this paper we count the number ?_n^(0,k), k?n−1, of connected components in the space Δ_n^(0,k) of all real degree n polynomials which a) have all their roots real and simple; and b) have no common root with their kth derivatives. In this case, we show that the only restriction on the arrangement of the roots of such a polynomial together with the roots of its kth derivative comes from the standard Rolle's theorem. On the other hand, we pose the general question of counting all possible root arrangements for a polynomial p(x) together with all its nonvanishing derivatives under the assumption that the roots of p(x) are real. Already the first nontrivial case n=4 shows that the obvious restrictions coming from the standard Rolle's theorem are insufficient. We prove a generalized Rolle's theorem which gives an additional restriction on root arrangements for polynomials.     

Complete integrability of the asymmetric chiral O(3)-field equation in a class of rapidly decreasing functions

The direct and inverse scattering problem for the asymmetric chiral O(3)-field equation is investigated by the Gel'fand-Levitan approach. The same results for the Landau-Lifshitz equation are presented. The canonical variables are derived and the Hamiltonian perturbation theory of these equations is constructed. It is not difficult to apply the methods of the paper to any L-operator with spectral parameter on a curve of genus g > 0.     

Catalytic removal of nitric oxides from diesel exhaust over supported metal oxides catalysts

Summary A number of supported metal oxide catalysts were prepared and tested for nitrogen oxide removal from diesel engine exhaust. More than 50% of nitrogen oxides were removed using many prepared catalysts in the temperature range of 150^oC-350^oC.