QSPR Modeling of Gibbs Free Energy of Organic Compounds by Weighting of Nearest Neighboring Codes

We examine the encoding of chemical structure of organic compounds by Labeled Hydrogen-Filled Graphs (LHFGs). Quantitative Structure-Property Relationships (QSPR) for a representative set of 150 organic molecules have been derived by means of the optimization of correlation weights of local invariants of the LHFGs. We have tested as local invariants Morgan extended connectivity of zero- and first order, numbers of path of length 2 (P2) and valence shells of distance of 2 (S2) associated with each atom in the molecular structure, and the Nearest Neighboring Codes (NNC). The best statistical characteristics for the Gibbs free energy has been obtained for the NNC weighting. Statistical parameters corresponding to this model are the following n = 100, r² = 0.9974, s = 5.136 kJ/mol, F = 38319 (training set); n = 50, r² = 0.9990, s = 3.405 kJ/mol, F = 48717 (test set). Some possible further developments are pointed out.     

Formation of the surface charge on silica in mixed solvents

At sufficiently high concentrations of methanol and of alkali salts in aqueous silica dispersions, the negative -potentials of the particles are decreased. This effect is more pronounced with lithium than with other alkali cations, and it is independent on the anion. The NMR spectra indicate lithium adsorption on silica from mixed solvents, but not in the absence of alcohol.Supported by a contract with the XMX Corporation, Burlington, Massachusetts, USA     

Back-and-forth shooting method for solving two-point boundary-value problems

The paper proposes a special iterative method for a nonlinear TPBVP of the form (t)=f(t, x(t),p(t)), (t)=g(t, x(t),p(t)), subject toh(x(0),p(0))=0,e(x(T),p(T))=0. Certain stability properties of the above differential equations are taken into consideration in the method, so that the integration directions associated with these equations respectively are opposite to each other, in contrast with the conventional shooting methods. Via an embedding and a Riccati-type transformation, the TPBVP is reduced to consecutive initial-value problems of ordinary differential equations. A preliminary numerical test is given by a simple example originating in an optimal control problem.     

Knockout reaction mechanism studied by ~6He projectile

Knockout reaction experiment was carried out by using the 6He beams at 61.2 MeV/u impinging on a CH2 target. The α core fragments at forward angles were detected in coincidence with the recoiled protons at larger angles. From this exclusive meas urement the valence nucleon knockout mechanism and the core knockout mechanism can be distinguished by the relation be tween the polar angles of the core fragments and the recoiled protons, respectively. It is demonstrated that the core knockout mechanism may result...     

Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

Three‐unit semicircles curve: A compact 3D graphical representation of DNA sequences based on classifications of nucleotides

A new three‐dimensional graphical representation of DNA sequences, three‐unit semicircles (TUS)‐curve, which maps a given sequence into a dot sequences embedded in three‐unit semicircles, is proposed based on three biclassifications of nucleotides. TUS‐curve has the merit of compactness and could avoid the degeneracy and loss of information. The geometrical center of the curve, which indicates the distribution of base frequencies of the corresponding DNA sequence, is extracted and applied to analyze the similarity of various species. Phylogenetic tree of 11 species based on their first exons of β‐globin genes showed that the TUS‐curve is a powerful tool to get valuable biological information. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Continuous time markov decision processes with interventions

We study Markov jump decision processes with both continuously and instantaneouslyacting decisions and with deterministic drift between jumps. Such decision processes were recentlyintroduced and studied from discrete time approximations point of view by Van der Duyn Schouten.Weobtain necessary and sufficient optimality conditions for these decision processes in terms of equations and inequalities of quasi-variational type. By means of the latter we find simple necessaryand sufficient conditions for the existence of stationary optimal policies in such processes with finite state and action spaces, both in the discounted and average per unit time reward cases.     

Generalized vector variational-like inequalities and nonsmooth vector optimization problems

In this article, we establish some relationships between a solution of generalized vector variational-like inequalities and an efficient solution or a weakly efficient solution to the nonsmooth vector optimization problem under the assumptions of pseudoinvexity or invariant pseudomonotonicity. Our results extend and improve the corresponding results in the literature.     

The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair consisting of a left‐invariant Riemannian metric g and a positive constant c such that , where is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that is solvable for some left‐invariant Riemannian metric g.