Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

Wellposedness for the Navier–Stokes flow in the exterior of a rotating obstacle

In this paper we study the Navier–Stokes boundary‐initial value problem in the exterior of a rotating obstacle, in two and three spatial dimensions. We prove the local in time existence and uniqueness of strong solutions. Moreover, we show that the solutions are global in time, in two spatial dimensions. Copyright © 2005 John Wiley & Sons, Ltd.     

Nonexistence and symmetry theorems for elliptic systems in R N

In this paper we study Liuoville type results for the system of elliptic equations $$ - \Delta u = F(u) u \geqslant 0, u \ne 0 in R^N ,$$ when the function $F:\bar R_ + ^m \to \bar R_ + ^m $ is regular, quasi-monotone, fully coupled and has suberitical growth. WhenF has a radial dependence on the space variable we also prove symmetry results. The nonexistence theorems of the nature studied here have consequences on existence results on bounded domains, through the blow-up technique and degree theory. Our results are proved using the moving planes method.     

Pseudopotential calculations on Rb+2, Cs+2, RbH+, CsH+ and the mixed alkali dimer ions

Semi-empirical pseudopotentials are used in calculating the ground-state potentials curves for single valence-electron molecular ions. Very accurate results are obtained and a number of predictions given. The ionization energies of the neutral dimers are evaluated. A spectroscopic rule enables us to estimate the A ¹Σ⁺ state of KRb and RbCs.     

Computational Study of Cage Like (ZnO)12 Cluster Using Hybrid and Hybrid Meta Functionals

Density Functional Theory employing hybrid and M06 functionals in combination with three different basis sets is used to calculate the ground state of a cage like (ZnO)₁₂ nanocluster which has been consistently reported as the more stable cluster for its particular size. B3LYP and B3PW91 hybrid functionals combined with 6‐31+G*, Lanl2dz and SDD basis sets are employed to treat the ZnO molecular system. Alternatively, three M06 functionals in combination with three basis sets are employed in the nanostructure calculations. Results obtained by treating ZnO sodalite cage nanocluster with M06 functionals demonstrated comparable quality to results obtained with hybrid functionals. Within this study, efficient theoretical DFT methods with the widely known hybrid and the recently created M06 meta‐hybrid functionals are employed to study nanostructured ZnO. Our resulting parameters provide a fresh approach performance wise on the different theoretical methods to treat transition metal nanostructures, particularly, ZnO nanoclusters geometry and electronic structure.     

Synthesis of Some C‐3,4,5‐Substituted 2,6‐Dimethyl‐1,4‐dihydropyridines (4‐DHPs)

A series of C‐3,4,5‐substituted 2,6‐dimethyl‐1,4‐dihydropyridines (1,4‐DHPs) with pharmacological properties were prepared by a variation from the classical Hantzsch synthesis. The procedure involves treatment of the respective aldehyde with either ethyl‐3‐aminocrotonate or 3‐aminocrotonitrile in anhydrous acetic acid at temperatures not exceeding 60°C, thus minimizing by‐product formation. The structures of title compounds were elucidated by ¹H NMR, ¹³C NMR, FTIR, and elemental analysis.     

Drug-dendrimer supramolecular complexation studied from molecular dynamics simulations and NMR spectroscopy

Fully atomistic molecular dynamics (MD) simulations and NMR spectroscopy were employed to get insights about the molecular details of drug-dendrimer supramolecular association phenomena, using piroxicam (PRX) and the third generation poly(amido amine) (PAMAM-G3) dendrimer as model systems. Theoretical results concerning the complex stoichiometry suggest that PRX forms drug-dendrimer complexes of the type 24:1 at pH 7.0. This result was validated with the experimental quantities obtained from aqueous solubility profiles, which led to an empiric stoichiometry of 23:1 for the PRX:PAMAM-G3 system. The predicted binding mode between PRX and PAMAM-G3 accounts for the preferred encapsulation of the drug inside dendrimer cavities, which is mainly driven by van der Waals and hydrogen bonding interactions, and to a lesser extent, for the external association of the guest through electrostatic contacts with the positively charged amino groups of PAMAM periphery. The binding mode obtained from MD simulations was confirmed with 2D-NOESY experiments, which evidence the preferred internal complexation of PRX with PAMAM-G3. The predominance of internal encapsulation over external contacts in the PRX:PAMAM-G3 system differs from the general behaviour expected for acidic anionic guests, for which external electrostatic interactions with the positively charged PAMAM surface have been postulated as the most relevant factor for drug association.     

Topological representation for monadic implication algebras

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.