Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces

We find necessary and sufficient conditions for a finite K–bi–invariant measure on a compact Gelfand pair (G,K) to have a square–integrable density. For convolution semigroups, this is equivalent to having a continuous density in positive time. When (G,K) is a compact Riemannian symmetric pair, we study the induced transition density for G–invariant Feller processes on the symmetric space X = G/K. These are obtained as projections of K–bi–invariant Lévy processes on G, whose laws form a convolution semigroup. We obtain a Fourier series expansion for the density, in terms of spherical functions, where the spectrum is described by Gangolli’s Lévy–Khintchine formula. The density of returns to any given point on X is given by the trace of the transition semigroup, and for subordinated Brownian motion, we can calculate the short time asymptotics of this quantity using recent work of Bañuelos and Baudoin. In the case of the sphere, there is an interesting connection with the Funk–Hecke theorem.     

Size dependence of incipient dislocation plasticity in Ni3Al

Molecular dynamics simulations are carried out to study the incipient dislocation plasticity in Ni3Al. Dislocation nucleation is found to occur preferentially at energetic atomic clusters with larger-than-average relative displacements. From the simulated distribution of the atomic relative displacements, a scaling model is proposed to predict the size dependence of the incipient plasticity condition in real-sized specimens.     

Electronic structure of germanium monohydrides Ge(n)H, n = 1-3

Quantum chemical calculations were applied to investigate the electronic structure of germanium hydrides, Ge(n)H (n = 1, 2, 3), their cations, and anions. Computations using a multiconfigurational quasi-degenerate perturbation approach (MCQDPT2) based on complete active space wave functions (CASSCF), multireference perturbation theory (MRMP2), and density functional theory reveal that Ge(2)H has a (2)B(1) ground state with a doublet-quartet gap of approximately 39 kcal/mol. A quasidegenerate (2)A(1) state has been derived to be 2 kcal/mol above the ground state (MCQDPT2/aug-cc-pVTZ). In the case of the cation Ge(3)H(+) and anion Ge(3)H(-), singlet low-lying electronic states are derived, that is, (1)A' and (1)A(1), respectively. The singlet-triplet energy gap is estimated to 6 kcal/mol for the cation. An "Atoms in Molecules" (AIM) analysis shows a certain positive charge on the Ge(n) (n = 1, 2, 3) unit in its hydrides, in accordance with the NBO analysis. The topologies of the electron density of the germanium hydrides are different from that of the lithium-doped counterparts. On the basis of our electron localization function (ELF) analysis, the Ge-H bond in Ge(2)H is characterized as a three-center-two-electron bond. Some key thermochemical parameters of Ge(n)H have also been derived.     

Electronic properties of 3,3'-dimethyl-5,5'-bis(1,2,4-triazine): towards design of supramolecular arrangements of N-heterocyclic Cu(I) complexes

A new efficient and safe synthesis of 3,3'-dimethyl-5,5'-bis-(1,2,4-triazine) is presented. The electron-density distribution and electrostatic properties (charge, electrostatic potential) of this molecule were analyzed. These properties were derived from a high-resolution single-crystal X-ray diffraction experiment at 100 K and compared to the results obtained from ab initio DFT quantum-mechanical calculations. Comparisons of its electrostatic potential features and integrated atomic charges (quantum theory of atoms in molecules, QTAIM) have been made with those of related molecules such as bipyrimidine ligands. Two methods were used to derive integrated charges: one is based on the conventional analytical procedure and the second uses a steepest-ascent numerical algorithm. Excellent agreement was obtained between these two methods. Charges and electrostatic potential were used as predictive indices of metal chelation and discussed in the light of complexation abilities of the title compound and related molecules. The crystal structure of a Cu(I) complex of 3,3'-dimethyl-5,5'-bis(1,2,4-triazine) is reported here. In the solid state, this complex forms a three-dimensional multibranch network with open channels in which counterions and solvent molecules are located. This architecture involves both cis and trans isomers of the title compound.     

Constituents from the Fruiting Bodies of Trametes cubensis and Trametes suaveolens in Vietnam and Their Anti-Inflammatory Bioactivity

It is reported that various fungi have been used for medicine and edible foods. The tropical Trametes genus is popular and well-known in Vietnam for its health effects and bioactivities. In this study, the fruiting bodies of the edible fungi T. cubensis and T. suaveolens were collected in Vietnam. The preliminary bioactivity screening data indicated that the methanol extracts of the fruiting bodies of T. cubensis and T. suaveolens displayed significant inhibition of superoxide anion generation and elastase release in human neutrophils. Therefore, the isolation and characterization were performed on these two species by a combination of chromatographic methods and spectrometric analysis. In total, twenty-four compounds were identified, and among these (1–3) were characterized by 1D-, 2D-NMR, and HRMS analytical data. In addition, the anti-inflammatory potentials of some purified compounds were examined by the cellular model for the inhibition of superoxide anion generation and elastase release in human neutrophils. Among the isolated compounds, (5,14), and (19) displayed significant anti-inflammatory potential. As the results suggest, the extracts and isolated compounds from T. cubensis and T. suaveolens are potential candidates for the further development of new anti-inflammatory lead drugs or natural healthy foods.     

Stacking patterns of thieno[3,2‐b]thiophenes functionalized by sequential palladium‐catalyzed Suzuki and Heck cross‐coupling reactions

The crystal structures of three 5‐alkenyl‐2‐arylthieno[3,2‐b]thiophenes, namely 3,6‐dibromo‐5‐(4‐tert‐butylstyryl)‐2‐(naphthalen‐1‐yl)thieno[3,2‐b]thiophene, C₂₈H₂₂Br₂S₂, (I), 3,6‐dibromo‐5‐(4‐methylstyryl)‐2‐(naphthalen‐1‐yl)thieno[3,2‐b]thiophene, C₂₅H₁₆Br₂S₂, (II), and 3,6‐dibromo‐2‐(4‐tert‐butylphenyl)‐5‐(4‐methylstyryl)thieno[3,2‐b]thiophene, C₂₅H₂₂Br₂S₂, (III), have been determined in order to evaluate the geometry of the molecules. The π‐conjugated system containing the thieno[3,2‐b]thiophene skeleton, the ethylene bridge and the phenyl rings is almost planar. The aromatic ring directly attached to the thieno[3,2‐b]thiophene moiety is not coplanar with the thieno[3,2‐b]thiophene moiety itself due to steric hindrance of the bromo substituent. The crystal packings are characterized by π–π stacking [only for (II)] and C—Br...π interactions. The long axes of the molecules in (I) are oriented in two directions; for the two other structures the long axis is oriented in one direction only.     

Preparation of chitosan nanoparticles by spray drying,and their antibacterial activity

Chitosan nanoparticles were prepared from chitosan of different molecular weight by spray drying. The morphology of the particles was characterized by SEM, and size distribution and zeta potential were determined. The effects of chitosan solution concentration, molecular weight of chitosan, and size of the spray dryer nozzles on average size, size distribution and zeta potential of chitosan nanoparticles were investigated. The effects of chitosan nanoparticles and chitosan nanoparticles–amoxicillin complex on Staphylococcus aureus were also tested. The results showed that the average size of chitosan nanoparticles were in the range 95.5–395 nm and zeta potentials were 39.3–45.7 mV, depending on the concentration and molecular weight of the chitosan. The lower the concentration and molecular weight of the chitosan, the smaller the chitosan nanoparticles and the higher the zeta potential. Testing for antibacterial activity against S. aureus indicated that chitosan nanoparticles strongly inhibited growth of the bacteria; the minimum inhibitory concentration, 20 μg/mL, was lower than those of chitosan solution or amoxicillin. The antibacterial capacity of chitosan nanoparticles also depended on the size, zeta potential, and molecular weight of the chitosan. Complexation of chitosan nanoparticles with amoxicillin improved the antibacterial activity of amoxicillin.     

Transition from deterministic to stochastic deformation

Theory predicts that deformation that occurs by emission of strain bursts falls into two regimes, one in which the burst emission remains a stochastic process as strain increases, and another in which the emission of bursts settles into a deterministic process for large strains. The stochastic regime occurs when the burst emission rate decreases with strain, and in this case, large statistical scatter persists in the stress–strain response on repeated measurements. The deterministic regime occurs when the emission rate increases with strain, and the scatter in the corresponding stress–stress behaviour diminishes at large strains. The strength at the same strain in the stochastic regime is also higher than in the deterministic regime. Factors that affect the burst emission rate include the number of sources as well as the stress dependence of the efficiency of the sources.     

Performance guarantee for edf under overload

Earliest deadline first (edf) is a widely used algorithm for online deadline scheduling. It has been known for long that edf is optimal for scheduling an underloaded, single-processor system; recent results on the extra-resource analysis of edf further revealed that edf when using moderately faster processors can achieve optimal performance in the underloaded, multi-processor setting. This paper initiates the extra-resource analysis of edf for overloaded systems, showing that edf supplemented with a simple form of admission control can provide a similar performance guarantee in both the single and multi-processor settings.