Linear programs with an additional rank two reverse convex constraint

An efficient algorithm is developed for solving linear programs with an additional reverse convex constraint having a special structure. Computational results are presented and discussed.     

Structure and diffusion characterization of SBA-15 materials

In situ formation of the micro- and mesoporous structures of SBA-15 materials was investigated. It was found that the structure is significantly different from that for cylindrical or hexagonal pores, which suggests that the SBA-15 is more complex than an array of hexagonally ordered channels. Nitrogen adsorption isotherms at 77 K provided evidence that large (primary) mesopores are accompanied by a certain amount of significantly smaller pores with a broad distribution in the micropore/small-mesopore range within the mesoporous walls of main channels. It was found that the microporosity can be controlled by the time of heating as well as the synthesis temperature. The diffusion properties of n-heptane as a probe molecule in four selected SBA-15 samples with different micropore volumes were studied by the standard zero length column technique and related to their structural characteristics. The results have shown that the diffusion process involving n-heptane at a low concentration level takes place inside the walls of main mesoporous channels and depends on the relative content of micropores. In the samples that have a relatively high content of micropores, n-heptane diffusivities are relatively low, their activation energies are high, and the process is similar to diffusion in typical microporous adsorbents, like zeolites. As the micropore content is decreased, diffusion becomes more and more controlled by secondary mesopores of the intrawall pore structure, rendering diffusion faster and activation energies lower.     

Viscosity effect in Landau's hydrodynamical model

The Bose-Einstein distribution is used to investigate Landau's hydrohynamical model with viscosity. In case the viscosity dependence on the temperature isT ³, the correction to the multiplicity behaves like 1/E and is found to be negligible for thepp data. A discussion is presented on a possibility of reconcilingE ^1/2 and logE dependence of the multiplicity law.     

Temperature‐dependent Raman scattering study of multiferroic MnWO4

We have measured polarized Raman spectra of MnWO₄ single crystals at low temperatures, and studied the temperature dependence of the various phonon modes. From our Raman studies of the MnWO₄, a new transition temperature, ∼180 K, was found. We have completely assigned the symmetries of the 18 observed Raman modes of the MnWO₄, as expected from a group theoretical analysis. These Raman modes have been classified into three groups according to weak, intermediate and strong temperature dependence of the modes in each group. Six internal modes have been identified by their weak temperature dependence of the Raman wavenumbers. The temperature dependence of the wavenumbers of the B_g modes in Mg O bonds, modes of intermediate temperature dependence group, shows an anomalous behavior under 50 K. The phonon modes of strong temperature dependence show an anomalous change at ∼180 K in the linewidths. This is believed to be a new transition temperature which involves the changes in the inter‐WO₆ octahedra structure. Copyright © 2009 John Wiley & Sons, Ltd.     

Blowup with vorticity control for a 2D model of the Boussinesq equations

We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a vorticity stretching term and a non-local Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.     

Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients

It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada–Watanabe theorem (Yamada and Watanabe, 1971, [31,32]) and the Feller test for explosions (Feller, 1951, 1954), there exists a unique stationary distribution with respect to the Markov semigroup of transition probabilities. We consider systems on a restricted domain $D$ of the phase space $\mathbb{R}$ and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called free energy function on the density function space, we prove that the density functions, which are solutions of the Fokker–Planck equation, converge to the stationary density function exponentially under the Kullback–Leibler divergence, thus also in the total variation norm. The results show that there is a relation between the Bakry–Émery curvature dimension condition and the dissipativity condition of the transformed system under the Fisher–Lamperti transformation. Several applications are discussed, including the Cox–Ingersoll–Ross model and the Ait-Sahalia model in finance and the Wright–Fisher model in population genetics.     

On division subrings normalized by almost subnormal subgroups in division rings

Periodica Mathematica Hungarica - Let D be a division ring with infinite center, K a proper division subring of D and N an almost subnormal subgroup of the multiplicative group $$D^*$$ of D. The...     

On a backward problem for fractional diffusion equation with Riemann-Liouville derivative

In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L² and H^τ norms is considered and illustrated by numerical example.