Higher Regularity of H?lder Continuous Solutions of Parabolic Equations with Singular Drift Velocities

Motivated by an equation arising in magnetohydrodynamics, we prove that H?lder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space?Ctime Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314?C328, 1995), combined with energy estimates, without any minimality assumption on the H?lder exponent of the weak solutions.     

Solution of Finite-Dimensional Variational Inequalities Using Smooth Optimization with Simple Bounds

The variational inequality problem is reduced to an optimization problem with a differentiable objective function and simple bounds. Theoretical results are proved, relating stationary points of the minimization problem to solutions of the variational inequality problem. Perturbations of the original problem are studied and an algorithm that uses the smooth minimization approach for solving monotone problems is defined.     

Investigation of the unusual behavior of projectile fragments using nuclear chemistry techniques

In recent years the question of the unusual behavior of projectile fragments formed in the interaction of relativistic heavy ions with copper nuclei was studied using nuclear chemistry techniques. As targets we used various copper disk arrangements. It is not the intention of this conference contribution to give a complete account of the entire procedure and its results. However, we want to present a few more recent experimental findings, some of them even in a preliminary form. We want to stimulate the discussion about the entire problem which might be part of the so-called anomalon phenomenon, as observed in the field of relativistic heavy ion interactions with a few other techniques such as nuclear emulsions or bubble chambers.     

Hydrothermal Synthesis and Crystal Structure of a Novel Polyoxometalate K(C_4N_2H_(12))_4(C_4N_2H_(11))_(2-)[Mo_8~ⅤMo_4~ⅥCdP_8O_(54)(OH)_8]F·6H_2O

The title compound 1 has been synthesized by the reaction of H_2MoO_4, CdCl_2, H_3PO_4, KF, piperazine hexahydrate and water in aqueous solution under mild hydrothermal conditions. Single-crystal X-ray analysis reveals that the title compound crystallizes in the triclinic system, space group P(-1) with a = 14.049(3), b = 15.972(3), c = 20.043(4) (A), α = 85.82(3), β = 81.28(3),γ = 67.15(3)°, V= 4095.9(14) (A)~3, M_r = 3204.62, Z=2,D_c = 2.598 g/cm~3,μ = 2.360 mm~(-1), F(000) = 3124, the final R = 0.0314, wR = 0.0826 and S = 0.989 for 18592 observed reflections with I > 2σ(I). The crystal packing is stabilized by N-H…O and O-H…O intra- and intermolecular hydrogen bonds to form an infinite 3D network.