PEG–SO3H as a mild, efficient and green catalytic system for the synthesis of pyrazole derivatives in aqueous medium

A versatile, alternative and environmentally benign strategy for the synthesis of a series of pyrazoles has been successfully performed in water using PEG–SO₃H as an acidic catalyst. The products are obtained in high yield from the one-pot reaction procedure involving dicarbonyl compounds and hydrazines/hydrazides. This new method totally avoids the use of organic acids and toxic or expensive solvents in this reaction. The catalyst is waste-free, easily prepared, and efficiently re-used.     

Dynamic modeling of submerged nanoparticle pushing based on atomic force microscopy in liquid medium

This article introduces a theoretical analysis of submerged nanoparticle manipulation in liquid medium using the atomic force microscopy, and gives a review of the major differences between dry and submerged manipulation processes. In this regard, the manipulation is modeled by adding the influences of the hydrodynamic forces surface forces to the manipulation model in dry air. Then, the pushing of a gold nanoparticle of 50-nm radius on a silicon substrate at a velocity of 100 nm/s is simulated, and the dynamic behaviors of the tip and nanoparticle are investigated. The results show that, in water (as compared to air), the required manipulation force and time for nanoparticle sliding and rolling increase by 3.5 and 6.5%, for sliding and 2 and 4.3% for rolling, respectively. Also, in liquids with different viscosities, the critical values related to sliding and rolling have a maximum variation of 17 and 32% for the manipulation time, and 6 and 22% for the manipulation force, respectively, as compared to the critical values related to particle manipulation in air. Moreover, for various submerged lengths of the cantilever in water, the critical values related to sliding and rolling show a maximum time variation of 9 and 10.5%, and 7 and 7.2% (for the manipulation force), respectively. Qualitative comparisons between the obtained results and those of the existing experimental investigations show the advantages of the liquid medium for the manipulation purposes.     

Cyclometalated organoplatinum(II) complexes: first example of a monodentate benzo[h]quinolyl ligand and a complex with bridging bis(diphenylphosphino)ethane

The cyclometalated complexes [Pt(ppy)R(SMe(2))] or [Pt(bhq)R(SMe(2))], where ppyH = 2-phenylpyridine, bhqH = benzo[h]quinoline and R = methyl or p-tolyl, react with bis(diphenylphosphino)ethane, dppe, in a 1:1 ratio to give the corresponding complexes [Pt(κ(1)-C-ppy)R(dppe)] or [Pt(κ(1)-C-bhq)R(dppe)], in which the ppy or bhq ligands are monodentate and dppe is chelating. The similar reaction in a 2:1 ratio gives the binuclear complexes [{Pt(ppy)R}(2)(μ-dppe)] or [{Pt(bhq)R}(2)(μ-dppe)], in which the dppe ligands are in the unusual bridging bidentate bonding mode.     

On biaccessible points in the Julia set of a Cremer quadratic polynomial

We prove that the only possible biaccessible points in the Julia set of a Cremer quadratic polynomial are the Cremer fixed point and its preimages. This gives a partial answer to a question posed by C. McMullen on whether such a Julia set can contain any biaccessible point at all.

     

Synthesis of pyrano[2,3-<Emphasis Type="Italic">c</Emphasis>]pyrazoles by ionic liquids under green and eco-safe conditions

Optimization of a green approach to the synthesis of pyrano[2,3-c]pyrazoles based on the one-pot, four-component condensation via a domino Knoevenagel/Michael/cyclization sequence was investigated. This method involved the evaluation of the activity of several ionic liquids (ILs) in various solvents. This one-pot, four-component reaction revealed simplicity, higher yield and lower toxicity advantages over a corresponding three-component method. The effect of reaction parameters including the type and amount of catalyst, type of solvent, reaction temperature and time were studied with respect to yield of pyrano[2,3-c]pyrazoles. Catalyst recyclability and time-saving aspects of the reaction suggest that this method presents real alternatives over conventional reaction protocols.     

Analysis of ray tube area in geometrical shock dynamics

We provide a rigorous analysis of structure of a ray tube in geometrical shock dynamics. Our aim is to shed more lights on the cross-sectional area function of a ray tube. We have shown that for a given ray tube and a given initial value of cross-sectional area, then its cross-sectional area can be determined uniquely everywhere. We give a definition of cross-sectional area of a ray tube in precise mathematical terms and from that we derive a set of relations, each describing the cross-sectional area for an arbitrary ray tube in geometrical shock dynamics. We have shown that from our results one can deduce Whitham’s area function relation as a partial differential equation from our general formulations. Some applications are discussed.     

Solitons in a generalized space- and time-variable coefficients nonlinear Schrödinger equation with higher-order terms

We introduce an approach that combines a similarity method with several transformations to find analytical solitary wave solutions for a generalized space- and time-variable coefficients of nonlinear Schrödinger equation with higher-order terms with consideration of varying dispersion, higher nonlinearities, gain/loss and external potential. One of these transformations is constructed in such a way that allows study of the width of localized solutions. Solitary-like wave solutions for front, bright and dark are given. The precise expressions of the soliton?s width, peak, and the trajectory of its mass center and the external potential which are symbol of dynamic behavior of these solutions, are investigated analytically. In addition, the dynamical behavior of moving, periodic, quasi-periodic of breathing, and resonant are discussed. Stability of the obtained solutions is analyzed both analytically and numerically.     

Upper bounds for Gaussian stochastic programs

We present a construction which gives deterministic upper bounds for stochastic programs in which the randomness appears on the right–hand–side and has a multivariate Gaussian distribution. Computation of these bounds requires the solution of only as many linear programs as the problem has variables. Received December 2, 1997 / Revised version received January 5, 1999? Published online May 12, 1999     

Dynamics of Cubic Siegel Polynomials

We study the one-dimensional parameter space of cubic polynomials in the complex plane which have a fixed Siegel disk of rotation number θ, where θ is a given irrational number of Brjuno type. The main result of this work is that when θ is of bounded type, the boundary of the Siegel disk is a quasicircle which contains one or both critical points of the cubic polynomial. We also show that these boundaries vary continuously as one moves in the parameter space. This is most nontrivial near the set of cubics with both critical points on the boundary of their Siegel disk. We prove that this locus is a Jordan curve in the parameter space. Most of the techniques and results can be generalized to polynomials of higher degrees. Received: 29 August 1998 / Accepted: 19 March 1999