Rapid and Efficient Synthesis of Imidazolines and Bisimidazolines Under Microwave and Ultrasonic Irradiation

Summary. Small assemblies of 2-imidazolines and bisimidazolines from appropriate nitriles and ethylenediamine with catalytic amounts of P₂S₅ employing a microwave assisted protocol were prepared. Sonication of this system also led to successful synthesis of 2-imidazolines and bisimidazolines. Another advantage of these systems is the ability to carry out large scale reactions.     

Combinatorial Algorithms for Some Variants of Inverse Obnoxious Median Location Problem on Tree Networks

This paper concerns with some variants of the inverse obnoxious median location problem on tree networks, where the aim is either to augment or to reduce the edge lengths at the minimum total cost such that a prespecified subset of vertices becomes an obnoxious multi-facility median location with respect to the perturbed edge lengths. For both augmentation and reduction models, under the rectilinear norm and the sum-type Hamming distance, we develop novel combinatorial algorithms with polynomial time complexities. Particularly, if the underlying tree is an extended star graph, then the problems can be solved in linear time.     

Hopf bifurcation analysis on an Internet congestion control system of arbitrary dimension with communication delay

This paper carries out a Hopf bifurcation analysis on a model of Internet congestion control system for a network with arbitrary topology. The general form of the rate-based Kelly model for a multi-source multi-link network with a communication delay is considered. Assuming the communication delay as a bifurcation parameter, we find that when the delay parameter passes a critical value, a periodic solution bifurcates from the equilibrium point. The stability and direction of bifurcating periodic solutions are studied by using the center manifold theorem and the normal form theory. We simulate our model for a typical example to show the applicability of the approach.     

Spectrophotometric determination of aqueous acidity constants of three azo dyes

The two successive steps acidity constants of three azo dye derivatives D1–D3, were determined by a spectrophotometric method using 0.10 M KNO₃ as supporting electrolyte in water solvent. The electronic spectra of the compounds were recorded in the course of their pH-metric titration with a standard base solution. The protolytic equilibrium constants can be solved very satisfactorily from absorbance data, by combining the data obtained in the spectrometric determinations with graphic methods as the absorbance diagrams. An A-diagram shows the relative absorbance changes at two wavelengths as a function of the pH. For a one-step system, the absorbance at any wavelength must be proportional to the absorbance at any other wavelength, so an A-diagram for all wavelength combinations for such a system must be linear (rank, s=1). However, if a system is governed by two or more equilibria, the A-diagrams corresponding to multi-step titrations will change direction every time a new equilibrium becomes dominant in the system. Analysis of the each uniform sub-region can then be used in evaluating of the corresponding equilibrium. A-diagrams for all wavelength combinations suggest that these systems have the rank two(s=2). The results revealed that the K_a(1) and K_a(2) values of different azo dyes follow the order D3>D2>D1.      

An exact analytical solution for creeping Dean flow of Bingham plastics through curved rectangular ducts

In this paper, an exact analytical solution for creeping flow of Bingham plastic fluid passing through curved rectangular ducts is presented for the first time. The closed form of axial velocity distribution, flow resistance ratio, and wall shear stress are derived using bounded Fourier transformation. An extensive investigation on mutual effects of Hedstrom number, curvature ratio, and aspect ratio is conducted. The results indicate that a drag reduction is caused in the flow field by increasing the Hedstrom number. It is shown that unlike the Newtonian creeping Dean flow, the critical aspect ratio (an aspect ratio in which the flow resistance ratio is independent from curvature ratio) does not exist at large enough Hedstrom numbers. Analytical solution also indicated that as Hedstrom number is increased, the value of Poiseuille number is enhanced, and unlike the Newtonian flows, the value of Poiseuille number is not zero at edges of cross section.     

Computational study of conformations and of sulfinyl oxygen-induced pentacoordination at silicon in 4-chloro-4-silathiacyclohexane 1-oxide and 4,4-dichloro-4-silathiacyclohexane 1-oxide

Second-order Møller-Plesset theory (MP2) and density functional theory (B3LYP) with the 6-311G(d,p) and 6-311+G(d,p) basis sets have been used to calculate the equilibrium geometries and relative energies of the chair, twist, and boat conformations of 4-chloro-4-silathiacyclohexane 1-oxide and 4,4-dichloro-4-silathiacyclohexane 1-oxide. The chair conformers of the axial sulfoxides are lower in energy than the chair conformers of the corresponding equatorial sulfoxides. MP2/6-311+G(d,p) predicted the chair conformer of axial trans-4-chloro-4-silathiacyclohexane 1-oxide (4a) to be 6.12, 0.44, and 0.45 kcal/mol, respectively, more stable than the corresponding 1,4-twist (4b), 2,5-twist (4c) and 1,4-boat (4d) conformers and 6.93 kcal/mol more stable than the 2,5-boat transition state ([4e]^‡). Structures 4c and 4d are stabilized by intramolecular coordination of the sulfinyl oxygen with silicon that results in trigonal bipyramidal geometry at silicon. The 1,4-boat conformer (7d) of axial 4,4-dichloro-4-silathiacyclohexane 1-oxide is also stabilized by transannular coordination of the sulfinyl oxygen with silicon. The energy difference (E_rel = 4.23 kcal/mol) between the chair conformer (7a) and 7d is larger than that between 4a and 4d. The relatively lower stability of the 1,4-boat conformer (7d) of axial 4,4-dichloro-4-silathiacyclohexane 1-oxide (7a) may be due to repulsive interactions of the axial halogen and sulfinyl oxygen atoms. The relative energies and structures of the conformers and transition states of cis- and trans-4-chloro-4-silathiacyclohexane 1-oxide and 4,4-dichloro-4-silathiacyclohexane 1-oxide are discussed in terms of hyperconjugative interactions, orbital interactions, nonbonded interactions, and intramolecular sulfinyl oxygen-silicon coordination.     

Efficient Synthesis of 3-Pyrrolin-2-one Derivatives in Aqueous Media

An efficient one-pot, three-component synthesis of 3-pyrrolin-2-ones in aqueous media at room temperature is reported. This reaction provides a green and catalyst-free method for generation of 3-pyrrolin-2-one derivatives in good yields.     

Facile and Convenient Synthesis of 5-Arylalkylidenerhodanines by Electrocatalytic Crossed Aldol Condensation

Abstract

An electrochemically induced catalytic crossed Aldol condensation of one equivalent of rhodanine with various aromatic aldehydes and ketones in ethanol in an undivided cell in the presence of sodium bromide as an electrolyte results in the formation of the corresponding 5-arylalkylidenerhodanines in 80–96% yield with reactions in 40 min.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.