π‐Electron currents in larger fully aromatic benzenoids

Recently, we have reported on calculation of π‐electron ring currents in several smaller fully benzenoid hydrocarbons having up to eight fused benzene rings and five Clar π‐aromatic sextets. In contrast to early HMO ring current calculations and more recent ab initio calculations of π‐electron density, our current calculations are based on a graph theoretical model in which contributions to ring currents comes from currents associated with individual conjugated circuits. In this contribution, we consider several larger fully benzenoid hydrocarbons having from 9 to 13 fused rings and from six or seven π‐aromatic sextets. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Existence of invariant manifolds for stochastic equations in infinite dimension

We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, UK, 1992). We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor (The Convenient Setting for Global Analysis, Surveys and Monographs, Vol. 53, Amer. Math. Soc., Providence, RI, 1997). Our main result is a weak version of the Frobenius theorem on Fréchet spaces. As an application, we characterize all finite-dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates.     

Regularity of finite-dimensional realizations for evolution equations

We show that a continuous local semiflow of C^k-maps on a finite-dimensional C^k-manifold M with boundary is in fact a local C^k-semiflow on M and can be embedded into a local C^k-flow around interior points of M under some weak assumption. This result is applied to an open regularity problem for finite-dimensional realizations of stochastic interest rate models.     

Synthesis, structure and properties of novel N-thiophosphorylated derivatives of 1,3-dihydro-2H-benzimidazol-2-imine and imidazolidine-2-imine

The reaction of bis-thiourea o-C₆H₄[NHC(S)NHP(S)(Oi-Pr)₂]₂ (1) with iodine, KOH and ClCH₂C(O)OCH₃ leads to O,O′-diisopropyl-1,3-dihydro-2H-benzimidazol-2-ylideneamidothiophosphate (2) formation. The complex of the potassium salt of compound 2 with 18-crown-6, having the composition [K(18-crown-6)L], has been synthesized. Bis-thiourea [CH₂NHC(S)NHP(S)(Oi-Pr)₂]₂ (6) forms a stable potassium salt, which oxidation by iodine leads to a product of heterocyclization, O,O′-diisopropyl-(1-{[(diisopropoxyphosphorothio)amino]carbonothioyl}imidazolidine-2-ylidene)amidothiophosphate (8), in which one of the thiourea fragments is kept.     

Cobalt(II) Complexes with N‐Thioacylamidophosphates and 2,2′‐Bipyridyl and 1,10‐Phenathroline. Crystal Structures,Solution 1H NMR Spectral and Magnetic Properties

Structure and magnetic properties of N‐diisopropoxyphosphorylthiobenzamide PhC(S)‐N(H)‐P(O)(OiPr)₂ ( HL^I ) and N‐diisopropoxyphosphoryl‐N′‐phenylthiocarbamide PhN(H)‐C(S)‐N(H)‐P(O)(OiPr)₂ ( HL^II ) complexes with the Co^II cation of formulas [Co{PhC(S)‐N‐P(O)(OiPr)₂}₂] ( 1 ), [Co{PhN(H)‐C(S)‐N‐P(O)(OiPr)₂}₂] ( 2 ), [Co{PhC(S)‐N(H)‐P(O)(OiPr)₂}₂{PhC(S)‐N‐P(O)(OiPr)₂}₂] ( 1a ) and [Co{PhC(S)‐N‐P(O)(OiPr)₂}₂}(2,2′‐bipy)] ( 3 ), [Co{PhC(S)‐N‐P(O)(OiPr)₂}₂(1,10‐phen)] ( 4 ), [Co{PhN(H)‐C(S)‐N‐P(O)(OiPr)₂}₂(2,2′‐bipy)] ( 5 ), [Co{PhN(H)‐C(S)‐N‐P(O)(OiPr)₂}₂(1,10‐phen)] ( 6 ) were investigated. Paramagnetic shifts in the ¹H NMR spectrum were observed for high‐spin Co^II complexes with HL^I,II , incorporating the S‐C‐N‐P‐O chelate moiety and two aromatic chelate ligands. Investigation of the thermal dependence of the magnetic susceptibility has shown that the extended materials 1‐2 and 6 show ferromagnetic exchange between distorted tetrahedral ( 1 , 2 ) or octahedral ( 1a , 6 ) metal atoms whereas 3 and 5 show antiferromagnetic properties. Compound 4 behaves as a spin‐canted ferromagnet, an antiferromagnetic ordering taking place below a critical temperature, T_c = 115 K. Complexes 1 and 1a were investigated by single crystal X‐ray diffraction. The cobalt(II) atom in complex 1 resides a distorted tetrahedral O₂S₂ environment formed by the C=S sulfur atoms and the P=O oxygen atoms of two deprotonated ligands. Complex 1a has a tetragonal‐bipyramidal structure, Co(O^ax)₂(O^eq)₂(S^eq)₂, and two neutral ligand molecules are coordinated in the axial positions through the oxygen atoms of the P=O groups. The base of the bipyramid is formed by two anionic ligands in the typical 1,5‐O,S coordination mode. The ligands are in a trans configuration.     

Dimension Functions of Orthonormal Wavelets

The article is devoted to dimension functions of orthonormal wavelets on the real line with dyadic dilations. We describe properties of dimension functions and prove several characterization theorems. In addition, we provide a method of construction of dimension functions. Various new examples of dimension functions and orthonormal wavelets are included.     

Optimization of the direct LSC method for determination of biogenic component in liquids by applying 14C

Journal of Radioanalytical and Nuclear Chemistry - Determination of fraction of biogenic component in liquid fuels by a direct radiocarbon measurement in liquid scintillation counter (direct-LSC...     

Variable neighborhood search for extremal graphs. 23. On the Randi? index and the chromatic number

Let G=(V,E) be a simple graph with vertex degrees d₁,d₂,…,d_n. The Randi? index R(G) is equal to the sum over all edges (i,j)∈E of weights . We prove several conjectures, obtained by the system AutoGraphiX, relating R(G) and the chromatic number χ(G). The main result is χ(G)≤2R(G). To prove it, we also show that if v∈V is a vertex of minimum degree δ of G, G−v the graph obtained from G by deleting v and all incident edges, and Δ the maximum degree of G, then .     

Modélisation et simulation numérique du changement de phase liquide–vapeur en cavitéModeling and numerical simulation of liquid–vapor phase change in an enclosed cavity

A model for the simulation of boiling flow with phase change in a closed cavity is presented. A front-tracking method is used to deal with the liquid–vapor interface. The liquid phase is incompressible while the vapor phase is weakly compressible and obeys to the perfect gas law. This model can deal with large density ratio (${\rho }_l/{\rho }_v?1000$) flows while accounting for the saturation curve. Computations are performed on a 1D validation case, idealizing a pressure cooker. Results are compared with a low Mach number approximation. To cite this article: V. Daru et al., C. R. Mecanique 334 (2006).