Cell transfer and monomial positivity

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generating functions of Stanley's (P,ω)-partitions. T.L. was supported in part by NSF DMS-0600677.     

Three polymorphs of 3‐(3‐phenyl‐1H‐1,2,4‐triazol‐5‐yl)‐2H‐1‐benzopyran‐2‐one formed from different solvents

The polymorphic study of 3‐(3‐phenyl‐1H‐1,2,4‐triazol‐5‐yl)‐2H‐1‐benzopyran‐2‐one, C₁₇H₁₁N₃O₂, was performed due to its potential biological activity and revealed three polymorphic modifications in the triclinic space group P, the monoclinic space group P2₁ and the orthorhombic space group Pbca. These polymorphs have a one‐column layered type of crystal organization. The strongest interactions between the molecules of the studied structures is stacking between π‐systems, while N—H…N and C—H…O hydrogen bonds link stacked columns forming layers as a secondary basic structural motif. C—H…π hydrogen bonds were observed between neighbouring layers and their role is the least significant in the formation of the crystal structure. Packing differences between the polymorphic modifications are minor and can be identified only using an analysis based on a comparison of the pairwise interaction energies.     

Biological properties of two enantiomorphic forms of N‐(2,6‐dimethylphenyl)‐4‐hydroxy‐2,2‐dioxo‐1H‐2λ6,1‐benzothiazine‐3‐carboxamide,a structural analogue of piroxicam

The title benzothiazine‐3‐carboxamide, C₁₇H₁₆N₂O₄S, crystallized in two enantiomorphic crystal forms with the space groups P3₂ and P3₁ despite the absence of a classic stereogenic atom. The molecular structures are mirror images of each other. Only one sulfonyl O atom takes part in intramolecular hydrogen bonding as a proton acceptor and this atom is different in the two enantiomorphic structures. As a result, the S atom becomes a pseudo‐stereogenic centre. This fact is worth taking into account due to the different biological activities of the enantiomorphic forms. One form possesses a high analgesic activity, while the other form revealed a high anti‐inflammatory activity.     

3D [Ag-Mg] polyanionic frameworks in the La4Ag10Mg3 and La4Ag10.3Mg12 new ternary compounds

The crystal structures of two new ternary phases, La₄Ag₁₀Mg₃ and La₄Ag_10.3Mg₁₂, were refined from X-ray single crystal diffraction data. La₄Ag₁₀Mg₃ crystallizes in the Ca₄Au₁₀In₃ structure type, an ordered variant of the binary Zr₇Ni₁₀ compound: orthorhombic, Cmce, oS68, a=14.173(5), b=10.266(3), c=10.354(3) Å, Z=4, wR₂=0.0826, 676 F² values, 50 variables. La₄Ag_10.3Mg₁₂ represents a new structure type: orthorhombic, Cmmm, oS116-10.32, a=9.6130(3), b=24.9663(8), c=9.6333(2) Å, Z=4, wR₂=0.0403, 1185 F² values, 101 variables. The structural analysis of both compounds, highlighting a significant contraction of the Ag-Mg distances, suggests the existence of three-dimensional [Ag-Mg] networks hosting La atoms. LMTO calculations applied to La₄Ag₁₀Mg₃ indicate that the strongest bonds occur for Ag-Ag and Ag-Mg interactions, and confirm the presence of a 3D_∞[Ag₁₀Mg₃]^δ− polyanionic framework balanced by positively charged La atoms.     

Long-time behavior of solutions for quasilinear hyperbolic hemivariational inequalities with application to piezoelectricity problem

We consider quasilinear autonomous inclusions of hyperbolic type. The dynamics of all weak solutions defined on the positive semi-axis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. The classes of mathematical models for piezoelectric fields containing the multidimensional law are studied. The conditions of the output of each weak solution for this problem at stationary states are given. We consider as a particular case the piezoelectric model for PZT-4 piezoceramics as one of the possible applications.     

Reinstallation of the COMPASS-D tokamak in IPP ASCR

The COMPASS-D tokamak, originally operated by UKAEA at Culham, UK, will be reinstalled at the Institute of Plasma Physics (IPP) AS CR. The COMPASS device was designed as a flexible tokamak in the 1980s mainly to explore the MHD physics. Its operation (with D-shaped vessel) began at the Culham Laboratory of the Association EURATOM/ UKAEA in 1992.The COMPASS-D tokamak will have the following unique features after putting in operation on IPP Prague. It will be the smallest tokamak with a clear H-mode and ITER-relevant geometry. ITER-relevant plasma conditions will be achieved by installation of two neutral beam injection systems (2 × 300 kW), enabling co-and counter-injections. Redeployment of the existing LH system (400 kW) is also envisaged. A comprehensive set of diagnostics focused mainly on the edge plasma will be installed.The scientific programme proposed for the COMPASS-D tokamak installed in IPP Prague will benefit from these unique features of COMPASS-D and consist of two main scientific projects, both highly relevant to ITER-Edge plasma physics (H-mode studies) and Wave-plasma interaction studies.The COMPASS-D tokamak will offer an important research potential as a small, flexible and low-cost facility with ITER-relevant geometry.     

Determination of eddy transport coefficients in thermo-lattice Boltzmann modeling of two-dimensional turbulence

Thermal Lattice Boltzmann (TLBE) techniques are used to consider the time evolution of free-decaying two dimensional (2D) turbulence induced by a double velocity shear layer. In particular, we consider the effect of this turbulence at a Reynolds number of 2555 on a strong temperature gradient. Since all structures are resolved on the 1024×1024 grid, the Smagorinsky model is employed to compute directly the eddy viscosity and eddy diffusivity. These transport coefficients play an integral part in large eddy simulations at very high Reynolds numbers where a direct simulation cannot resolve all excited scales. TLBE codes have the virtue of being readily extended to 3D, can readily handle nonperiodic geometries, and are ideally suited for multi-parallel computer architectures.This work was supported by a joint US-Czech DoE Grant #93066. Computations were performed under the auspices of the SPP (Special Parallel Processing) on the C90 at NERSC.