Self-Assembly of the Complexes of Bipodal Thiophosphorylated Thioureas

N-Thiophosphorylated thioureas, of general formula [(i-PrO) 2 P(S)NHC(S)] 2 Z (Z = f , y -diamino(oxy)alkyl or 1,10-diaza-18-crown-6), in the form of potassium salts, react with a number of soft ions (Cd 2+ , Zn 2+ , Co 2+ , Ni 2+ , Pd 2+ ) to form novel dimeric complexes. The cadmium (Z = HN(CH 2 ) 2 NH), palladium (Z = HN(CH 2 ) 2 O(CH 2 ) 2 NH), and cobalt (Z = 1,10-diaza-18-crown-6) complexes were analyzed by x-ray crystallography. In the former complex, crown cavities remain free. This fact will allow us to obtain "guest-host" complexes with alkali metal cations.     

Computational assessment of environmental hazards of nitroaromatic compounds: influence of the type and position of aromatic ring substituents on toxicity

Structural Chemistry - This study summarizes the results of our recent QSAR and QSPR investigations on prediction of numerous aspects of environmental behavior of nitro compounds. In this study, we...     

Extremal probabilities for Gaussian quadratic forms

 Denote by Q an arbitrary positive semidefinite quadratic form in centered Gaussian random variables such that E(Q)=1. We prove that for an arbitrary x>0, inf _Q P(Q≤x)=P(χ² _n /n≤x), where χ _n ² is a chi-square distributed rv with n=n(x) degrees of freedom, n(x) is a non-increasing function of x, n=1 iff x>x(1)=1.5364…, n=2 iff x[x(2),x(1)], where x(2)=1.2989…, etc., n(x)≤rank(Q). A similar statement is not true for the supremum: if 1<x<2 and Z ₁ ,Z ₂ are independent standard Gaussian rv's, then sup_0≤λ≤1/2 P{λZ ₁ ² +(1−λ)Z ₂ ² ≤x} is taken not at λ=0 or at λ=1/2 but at 0<λ=λ(x)<1/2, where λ(x) is a continuous, increasing function from λ(1)=0 to λ(2)=1/2, e.g. λ(1.5)=.15…. Applications of our theorems include asymptotic quantiles of U and V-statistics, signal detection, and stochastic orderings of integrals of squared Gaussian processes. Received: 24 June 2002 / Revised version: 26 January 2003 Published online: 15 April 2003 Research supported by NSA Grant MDA904-02-1-0091 Mathematics Subject Classification (2000): Primary 60E15, 60G15; Secondary 62G10     

Linearization of third-order ordinary differential equations by point and contact transformations

We present here the solution of the problem on linearization of third-order ordinary differential equations by means of point and contact transformations. We provide, in explicit forms, the necessary and sufficient conditions for linearization, the equations for determining the linearizing point and contact transformations as well as the coefficients of the resulting linear equations.     

Invariant Lagrangians and a new method of integration of nonlinear equations

A method for solving the inverse variational problem for differential equations admitting a Lie group is presented. The method is used for determining invariant Lagrangians and integration of second-order nonlinear differential equations admitting two-dimensional noncommutative Lie algebras. The method of integration suggested here is quite different from Lie's classical method of integration of second-order ordinary differential equations based on canonical forms of two-dimensional Lie algebras. The new method reveals existence and significance of one-parameter families of singular solutions to nonlinear equations of second order.     

A Comparative Study of the Cyclic Chlorophosphites with C2-Symmetrical Organic Fragments as the Reagents for Enantiomeric Composition Control of the Chiral Alcohols

Abstract

The ³¹P NMR method is intensively used for enantiomeric composition control during the last years [I]. Among all other derivatizing agents the C2-symmetrical ones have some advantages.     

Platinum (II) phosphine complexes with acetylene ligands containing 1,4,5,8-naphthalenediimide: Synthesis, crystal structure and electrochemistry

A new acetylene ligand modified with the electron-accepting 1,4,5,8-naphthalenediimide group and its Pt(II) phosphine complexes are reported. The Pt(II) complexes incorporate optical properties of the imide group, and display two reversible imide-centred reduction processes.