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).     

Schrödinger operators and unique continuation. Towards an optimal result

In this article we prove the property of unique continuation (also known for C^∞ functions as quasianalyticity) for solutions of the differential inequality |Δu|?|Vu| for V from a wide class of potentials (including class) and u in a space of solutions YV containing all eigenfunctions of the corresponding self-adjoint Schrödinger operator. Motivating question: is it true that for potentials V, for which self-adjoint Schrödinger operator is well defined, the property of unique continuation holds?     

On Wiener‐type polynomials of thorn graphs

We derive the expressions of the ordinary, the vertex‐weighted and the doubly vertex‐weighted Wiener polynomials of a type of thorn graph, for which the number of pendant edges attached to any vertex of the underlying parent graph is a linear function of its degree. We also define variable vertex‐weighted Wiener polynomials and calculate them for the same type of thorn graphs. Copyright © 2009 John Wiley & Sons, Ltd.