The fastest,simplified method of Lyapunov exponents spectrum estimation for continuous-time dynamical systems

Nonlinear Dynamics - Classical method of Lyapunov exponents spectrum estimation for a n-th-order continuous-time, smooth dynamical system involves Gram–Schmidt orthonormalization and...     

Cyclocondensation of Thioamides and Haloacetic Acid Derivatives Provides Only 4-Thiazolidinones; Isomeric 5-Thiazolidinones Were Not observed

Cycloaddition of intermediates formed from the nucleophilic addition of aryl isothiocyanate to acidic cyanomethylenes and α-halocarbonyl compounds gave only 4-thiazolidinones. 5-Thiazolidinones were not observed. Cyano-(4-oxo-3-phenylthiazolidin-2-ylidene)-acetic acid ethyl ester (1) and cyano-[5-(4-methoxybenzylidene)-4-oxo-3-phenylthiazolidin-2-ylidene]-acetic acid ethyl ester (2a) also were shown to exhibit moderate antiviral activity.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

An efficient method for the transformation of 5-ylidenerhodanines into 2,3,5-trisubstituted-4-thiazolidinones

The use of 3-substituted-2-mercaptoacrylic acids, synthesized via hydrolysis of 5-ylidenerhodanines for the preparation of 2,3,5-trisubstituted-4-thiazolidinones via a new variant of the one-pot, three-component reaction has been studied.     

Dissecting a brick into bars

Consider the set of all lengths of sides of an N-dimensional parallelepiped. If this set has no more than k elements, the parallelepiped will be called a bar (the definition of a bar depends on k). We prove that a parallelepiped can be dissected into a finite number of bars if and only if the lengths of its sides span a linear space of dimension at most k over \mathbb Q{{\mathbb Q}} . This extends and generalizes a well-known theorem of Max Dehn about the splitting of rectangles into squares. Several other results about dissections of parallelepipeds are obtained.     

Application of centrifugation to the large-scale purification of electric arc-produced single-walled carbon nanotubes

We report a further advance in the bulk purification of nitric acid-treated single-walled carbon nanotubes (SWNTs) by use of high-speed centrifugation. We have already shown that low-speed centrifugation is effective in removing amorphous carbon (AC). In these earlier experiments, the AC preferentially suspends in aqueous dispersions on low-speed centrifugation (2000g), leaving the SWNTs in the sediment. In a surprising reversal, we now show that high-speed centrifugation (20000g) of well-dispersed preparations is effective in sedimenting carbon nanoparticles (CNP), while leaving the SWNTs suspended in aqueous media. Taken together, these two techniques allow the bulk scale (10 g) purification of SWNTs by efficiently separating the two main contaminants, in an industrially viable process. We show that the mechanism of these separations is based on the differential charging (zeta-potential) of the AC, CNPs, and SWNTs that comes about during the chemical processing. Due to their more robust structure, nitric acid oxidation leaves the CNPs with a surface charge density lower than that of the SWNTs, and thus the CNPs do not form stable dispersions in aqueous media during high-speed centrifugation. The efficiency of the process was confirmed by the high purification recovery factor (PRF = 90%), which is a measure of the fractional quantity of the product recovered after the purification. We demonstrate that the purity of SWNTs significantly affects their mechanical and electrical properties.     

Transition strengths and first-order properties of excited states from local coupled cluster CC2 response theory with density fitting

A new ab initio method for calculating transition strengths and orbital-unrelaxed first-order properties of singlet ground and excited states of extended molecular systems is presented. It is based on coupled cluster response theory at the level of the CC2 model with local approximations introduced to the doubles-excitation part of the wave function. Density fitting is employed for the calculation of the electron repulsion integrals, so that--with the exception of doubles amplitudes--only three-indexed objects do occur in the formalism. The new method was tested by performing calculations for a set of various molecules and excited states and by comparing the results with corresponding canonical (nonlocal) calculations. It turned out that for calculating transition strengths and properties of excited states the ordinary Boughton-Pulay domains are insufficient in numerous cases. To circumvent this problem a new scheme for extending domains is proposed, which is based on the solution of the coupled perturbed localization and Hartree-Fock equations. When such extended domains are used, a satisfactory agreement between canonical and local results is achieved.     

Effect of gem-Difluorination on the Key Physicochemical Properties Relevant to Medicinal Chemistry: The Case of Functionalized Cycloalkanes

Physico-chemical properties important to drug discovery (pK_a, LogP, and aqueous solubility), as well as metabolic stability, were studied for a series of functionalized gem-difluorinated cycloalkanes and compared to those of non-fluorinated and acyclic counterparts to evaluate the impact of the fluorination. It was found that the influence of the CF₂ moiety on the acidity/basicity of the corresponding carboxylic acids and amines was defined by inductive the effect of the fluorine atoms and was nearly the same for acyclic and cyclic aliphatic compounds. Lipophilicity and aqueous solubility followed more complex trends and were affected by the position of the fluorine atoms, ring size, and even the nature of the functional group present; also, significant differences were found for the acyclic and cyclic series. Also, gem-difluorination either did not affect or slightly improved the metabolic stability of the corresponding model derivatives. The presented results can be used as a guide for rational drug design employing fluorine and establish the first chapter in a catalog of the key in vitro properties of fluorinated cycloalkanes.     

Improving efficiency of the largest Lyapunov exponent’s estimation by its determination from the vector field properties

Nonlinear Dynamics - Controlling dynamics of nonlinear systems is one of the most important issues in science and engineering. Thus, there is continuous need to study and develop numerical...