On distributive residuated groupoids

In this note we extend the well-known fact (see [1], p. 45) that an implicative (or Brouwerian) lattice is distributive to a large class of residuated groupoids.     

First example of high loaded polymer-stabilized nanoclusters immobilized on hydrotalcite: effects in alkyne hydrogenation

Poly(N-vinyl-2-pyrrolidone)-stabilized Pd-nanoclusters, for the first time exclusively supported on the hydrotalcite lateral surface, showed a remarkable catalytic performance in the selective hydrogenation of 3-hexyn-1-ol, which can be ascribed to both the influence of the protecting polymer PVP as well as the nature of the support.     

Zur Erkennung der auf Fasern und Geweben fixirten Farbstoffe

Ohne Zusammenfassung     

A theoretical insight into the role of counter anions and their interactions in nitropentaamminecobalt(III) toward linkage isomerism-induced photochemical motion

Density functional theory (B3LYP, B3LYP-D3, wB97XD, M062X, and M06L) and ab initio methods (MP2 and CCSD(T)) in conjunction with 6-31+G(d,p) and LanL2DZ were employed to investigate the interaction energies between [Co(NH₃)₅NO₂]²⁺ linkage isomers and chloride and nitrate in both gas phase and solid state. The nature of the chemical bonding has been analyzed by means of the atoms in molecules, electron density shift, natural bond orbitals, symmetry adapted perturbation theory, and energy decomposition analysis. The electronic structures of the two lowest laying singlet states (S_o and S₁) of [Co(NH₃)₅NO₂](NO₃)Cl isomers were also investigated using CASSCF(6,6) with LanL2DZ and 6-31G(d) basis sets. Our results show that [Co(NH₃)₅NO₂]²⁺ linkage isomers interact more strongly with chloride than nitrate. The structures of [Co(NH₃)₅NO₂](NO₃)Cl linkage isomers and their relative stabilities were examined in gas phase and in solid state and confirmed the nitro-complex as the most stable following by a viable intermediate endo-complex. Study of the nitro-nitrito linkage isomerization in [Co(NH₃)₅NO₂](NO₃)Cl revealed that anions form strong electrostatic bonds with [Co(NH₃)₅NO₂]²⁺ leading to decrease in an activation energy compared to the [Co(NH₃)₅ONO]²⁺ isomers. A concerted action of ionic interactions and hydrogen bonds are suspected of regulating the isomerization in solid state. Assessment of various DFT methods with respect to CCSD(T) suggests M062X suitable method for [Co(NH₃)₅NO₂](NO₃)Cl linkage-isomerization study. Potential energy surface calculations at the CASSCF/6-31G(d) level of theory shows that the conical intersection (S₁/S_o) might play an important role in the photoisomerization of [Co(NH₃)₅NO₂](NO₃)Cl.     

The Boron Conundrum: Which Principles Underlie the Formation of Large Hollow Boron Cages?

Extensive optimisation calculations are performed for the B₈₀ isomers in order to find out which principles underlie the formation of large hollow boron cages. Our analysis shows that the most stable isomers contain triangular B₁₀ or rhombohedral B₁₆ building blocks. The lowest‐energy isomer has C_3v symmetry and is characterised by a belt of three interconnected B₁₆ units and two separate B₁₀ units. At the B3LYP/6‐31G(d) level of theory, this newly discovered isomer is 2.29, 1.48, and 0.54 eV below the leapfrog B₈₀ of Szwacki et al., the T_h‐B₈₀ of Wang, and the D_3d‐B₈₀ of Pochet et al., respectively. Our C_3v isomer is therefore identified as the most stable hollow cage isomer of B₈₀ presently known. Its HOMO–LUMO gap of 1.6 eV approaches that of the leapfrog B₈₀. The leapfrog principle still remains a reliable scheme for producing boron cages with larger HOMO–LUMO gaps, whereas the thermodynamically most stable B₈₀ cages are formed when all pentagonal faces are capped. We show that large hollow cages of boron retain a preference for fullerene frames. The additional capping is in accordance with the following rules: preference for capping of pentagonal faces, formation of B₁₀ and/or B₁₆ units, homogeneous distribution of the hexagonal caps, and hole density approaching 1/9. Although our most stable B₈₀ isomer still remains higher in energy than the B₈₀ core–shell structure, we show that by applying the bonding principles to larger structures it is possible to construct boron cages with higher stabilisation energy per boron atom than the core–shell structure; a prototypical example is B₁₆₀. This clearly shows the continuous competition between the two suggested construction schemes, namely, the formation of multiple‐shell structures and hollow cages.     

Mathematical analysis of a two-patch model of tuberculosis disease with staged progression

The spread of tuberculosis is studied through a two-patch epidemiological system SE₁ ? E_nI which incorporates migrations from one patch to another just by susceptible individuals. Our model is consider with bilinear incidence and migration between two patches, where infected and infectious individuals cannot migrate from one patch to another, due to medical reasons. The existence and uniqueness of the associated endemic equilibria are discussed. Quadratic forms and Lyapunov functions are used to show that when the basic reproduction ratio is less than one, the disease-free equilibrium (DFE) is globally asymptotically stable, and when it is greater than one there exists in each case a unique endemic equilibrium (boundary equilibria and endemic equilibrium) which is globally asymptotically stable. Numerical simulation results are provided to illustrate the theoretical results.     

A new look at correlations in atomic and molecular systems. I. Application of fermion monte carlo variational method

We are engaged in research directed toward the development of compact and accurate correlation functions for many-electron systems. Our computational tool is the variational method in which the many-electron integrals are calculated by Monte Carlo using the fermion Metropolis sampling algorithm. That is, a many-fermion system is simulated by sampling the square of a correlated antisymmetric wave function. The principal advantage of the method is that interelectronic distance r_ij may be included directly in the wave function without adding significant computational complexity. In addition, other quantities of physical and theoretical interest such as electron correlation functions and representations of Coulomb and Fermi “holes” are very easily obtained. Preliminary results are reported for He, H₂, and Li₂.     

Measurement of the acoustic reflectivity of sirenia (Florida manatees) at 171 kHz

The Florida manatee (Trichechus manatus latirostris) is an endangered sirenian. At present, its adult population (approximately 2200) seems stable, but tenuous. Manatee-boat collisions are a significant proportion (approximately 25%) of mortalities. Here, the potential use of active sonar for detecting manatees by quantifying sonic reflectivity is explored. In order to estimate reflectivity two methods were used. One method measured live reflections from captive animals using a carefully calibrated acoustic and co-registered optical system. The other method consisted of the analysis of animal tissue in order to obtain estimates of the sound speed and density and to predict reflectivity. The impedance measurement predicts that for a lateral view, the tissue reflectivity is close to 0.13, with a critical grazing angle of 28 degrees. Data measured from live animals indicate that substantial reflections can be recorded, however in many instances observed "empirical target strengths" were less than an experimentally dependent -48-dB threshold. Conclusions favor the hypothesis that the animals reflect substantial amounts of sound; however, the reflections can often be specular, and therefore impractical for observation by a manatee detection sonar operating at 171 kHz.