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.     

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.     

Metal-organic frameworks exhibiting strong anion-pi interactions

Coordination polymers offer a significant potential for applications in adsorption, guest and anion recognition and sensing. Their structure commonly provides binding sites for such specific interactions as pi-pi stacking and XH...pi hydrogen bonding. The latter reflects the ability of the pi-cloud to interact with positively polarized atoms. An electrostatic interaction between anionic species and electron deficient heterocycles, which parallels the above binding scheme, is also possible and very recently the existence of anion-pi interactions was proved in the solid state and in solution. This effect may be significant also for biomolecule/solution interfaces, as it occurs in protein structures. In fact, such interactions could be especially relevant for host-guest chemistry of coordination polymers, particularly for functionalization of hydrophobic crystal cavities and for the design of geometrically rigid anion receptors. However, typical electron deficient heterocycles such as 1,3,5-triazines and 1,2,4,5-tetrazines are very weak donors and they are hardly suitable for bridging metal ions and the generation of coordination frameworks. As a system that combines efficient donor properties towards transition metal ions and a pronounced ability for anion-pi interactions we have developed unsubstituted pyridazino[4,5-d]pyridazine, which was readily accessible by a novel one-pot synthesis involving inverse electron demand Diels-Alder cycloaddition (Scheme 1). Unusual anion binding properties of the ligand may be clearly related to its electron-deficiency (LUMO energy -1.591 vs. -0.288 eV for the parent pyridazine), influenced also by N-coordination to such Lewis acids as metal ions.     

Stabilization of polystyrene by styrylquinoline containing methacrylates

Abstract

The thermostability of polysterene with/without new styrylquinoline containing methacrylic fragments has been described in the present work. Polystyrene and copolymers based on styrene and new methacrylic styrylquinoline containing monomers were synthesized by free radical thermoinitiated polymerization in the presence of 2,2′-azobisisobutyronitrile (1?wt%) as initiator at inert atmosphere. The impact of 2-[2-(4-methoxyphenyl)ethenyl]quinolin-8-yl 2-methylpropyl-2-enoate (М1), 2-(2-phenylethenyl)quinolin-8-yl 2-methylpropyl-2-enoate (М2), 2-[2-(4-nitrophenyl)ethenyl]quinolin-8-yl 2-methylpropyl-2-enoate (М3) on thermal stability of polystyrene was investigated. The thermostability of polystyrene and copolymers ST:M1, ST:M2, ST:M3 were studied by dynamic thermograviametric analysis. It was shown that destruction of polystyrene with corresponding units M1-M2 starts at 41–42°С higher, than reference polystyrene.     

Cyclotomic factors of the descent set polynomial

We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorization patterns. We explore the question of when particular cyclotomic factors divide these polynomials. As an instance we deduce that the proportion of odd entries in the descent set statistics in the symmetric group Sn only depends on the number on 1's in the binary expansion of n. We observe similar properties for the signed descent set statistics.     

Access to C-protected β-amino-aldehydes via transacetalization of 6-alcoxy tetrahydrooxazinones and use for pseudo-peptide synthesis

Efficient access to masked β-amino-aldehydes was performed starting from 6-alcoxy tetrahydrooxazinone 6a–d (6-ATO). Transacetalization leads to the opening of the cycle to form either unsymmetric acetal 7 or symmetric acetals 16–18. These amino acetals are key compounds, obtained with 99% ee, which can be engaged in efficient peptide coupling. This method could easily provide peptides aldehydes or small amido aldehydes as exemplified with the formal synthesis of ent-Maraviroc.