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.     

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.     

A minimal model for two-component FIMP dark matter:A basic search

In the multi-component configurations of dark matter phenomenology,we propose a minimal twocomponent configuration which is an extension of the Standard Model with only three new fields;one scalar and one fermion interact with the thermal soup through Higgs portal,mediated by the other scalar in such a way that the stabilities of dark matter candidates are made simultaneously by an explicit Z2 symmetry.Against the most common freeze-out framework,we look for dark matter particle signatures in the freeze-in scenario by evaluating the relic density and detection signals.A simple distinguishing feature of the model is the lack of dark matter conversion,so the dark matter components act individually and the model can be adapted entirely to both singlet scalar and singlet fermionic models,separately.We find dark matter self-interaction as the most promising approach to probe such feeble models.Although the scalar component satisfies this constraint,the fermionic one refuses it even in the resonant region.     

A signal subspace approach for modeling the hemodynamic response function in fMRI

Many fMRI analysis methods use a model for the hemodynamic response function (HRF). Common models of the HRF, such as the Gaussian or Gamma functions, have parameters that are usually selected a priori by the data analyst. A new method is presented that characterizes the HRF over a wide range of parameters via three basis signals derived using principal component analysis (PCA). Covering the HRF variability, these three basis signals together with the stimulation pattern define signal subspaces which are applicable to both linear and nonlinear modeling and identification of the HRF and for various activation detection strategies. Analysis of simulated fMRI data using the proposed signal subspace showed increased detection sensitivity compared to the case of using a previously proposed trigonometric subspace. The methodology was also applied to activation detection in both event-related and block design experimental fMRI data using both linear and nonlinear modeling of the HRF. The activated regions were consistent with previous studies, indicating the ability of the proposed approach in detecting brain activation without a priori assumptions about the shape parameters of the HRF. The utility of the proposed basis functions in identifying the HRF is demonstrated by estimating the HRF in different activated regions.     

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