Microextraction of metal ions based on solidification of a floating drop: Basics and recent updates

This review provides a comprehensive evaluation of solidified floating organic drop microextraction (SFODME) procedures for metal ions preconcentration and their contributions to green chemistry. In this article we focused on the modifications that have been performed in the recent years to improve this environmentally friendly procedure. Among the most important of these modifications are the inclusion of ultrasonic energy, vortex and air agitation to enhance the dispersion process. The article also discussed new challenges in the procedure by using more ecofriendly solvents as extractants such as ionic liquids, deep eutectic. and supramolecular solvents. The coupling of SFODME with solid phase extraction increases selectivity and efficiency of the preconcentration procedure.     

ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

ＯＮＡＰＡＩＲＯＦＮＯＮＩＳＯＭＥＴＲＩＣＩＳＯＳＰＥＣＴＲＡＬＤＯＭＡＩＮＳＷＩＴＨＦＲＡＣＴＡＬＢＯＵＮＤＡＲＩＥＳＡＮＤＴＨＥＷＥＹＬＢＥＲＲＹＣＯＮＪＥＣＴＵＲＥＳＬＥＥＭＡＮ，Ｂ．Ｄ．ＣＨＥＮＨＵＡＭａｎｕｓｃｒｉｐｔｒｅｃ...     

Spray Freeze-drying – The Process of Choice for Low Water Soluble Drugs?

Most of the novel highly potent drugs, developed on the basis of modern molecular medicine, taking into account cell surface recognition techniques, show poor water solubility. A chemical modification of the drug substance enhancing the solubility often decreases the pharmacological activity. Thus, as an alternative an increase of the solubility can be obtained by the reduction of the size of the drug particles. Unfortunately, it is often difficult to obtain micro or nanosized drug particles by classical or more advanced crystallization using supercritical gases or by milling techniques. In addition, nanosized particles are often not physically stable and need to be stabilized in an appropriate matrix. Thus, it may be of interest to manufacture directly nanosized drug particles stabilized in an inert hydrophilic matrix, i.e. nanostructured and nanocomposite systems. Solid solutions and solid dispersions represent nanostructured and nanocomposite systems. In this context, the use of the vacuum-fluidized-bed technique for the spray-drying of a low water soluble drug cosolubilized with a hydrophilic excipient in a polar organic solvent is discussed. In order to avoid the use of organic solvents, a special spray-freeze-drying technique working at atmospheric pressure is presented. This process is very suitable for temperature and otherwise sensitive drugs such as pharmaproteins.     

Fast and efficient preparation of Baylis-Hillman-derived (E)-allylic azides and related compounds in aqueous medium

A practical access to alkyl- and aryl-substituted (E)-2-(azidomethyl)alkenoates and related azido compounds from the corresponding allylic bromides in aqueous acetone is described. An alternative method to obtain the starting bromides based on heterogeneous catalysis under mild conditions was also investigated.     

The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator

Abstract The existence of infinitely many solutions to Sturm-Liouville boundary value problem with aLaplacian-like operator is studied by applying generalized polar coordinates.     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.      

Conditional expectation of integrands and random sets

The conditional expectation of integrands and random sets is the main tool of stochastic optimization. This work wishes to make up for the lack of real synthesis about this subject. We improve the existing hypothesis and simplify the corresponding proofs. In the convex case we especially study the problem of the exchange of conditional expectation and subdifferential operators.     

A Generalized Unpaired Electron Spin Density Equation and Organic Hyperconjugation Mechanism

A large class of stereochemcial and related interactions in organic chemistry are repulsive and others are attractive, but the relative orientation of two methyl groups and the amount of energy required to twist one relative to the other (the hindered rotation energy barriers), or the alignment of such a group with respect to a conjugated ring to which it is attached (widely attributed to a mechanism called “hyperconjugation”) are estimated to be small in compared with the total energy of the molecule. We used theories of both isotropic and anisotropic proton hyperfine interactions in the π‐electron systems developed in the early sixties. They are approximated by the magnetic dipole nteractions between each proton and an electron spin magnetization that is distributed in 2s and 2p Slater atomic orbitals center on carbon atoms. We have extended these theories to the non‐planar olefinic cation radicals, which are very important in biochemistry as well as in petroleum catalysis. A three dimensional electron spin density equation has been developed in this paper to handle some Jahn‐Teller vibronic molecules. The new electron spin density equation related the observed proton hyperfine splittings to the non‐planar structures of the open‐chain alkene cation radicals generated by radiolysis and various chemical oxidation methods. The spin densities and the conformational calculations based on valence bond theory and symmetry principles are compared with some more elaborated molecular orbital calculations in the literature. The localized valence bond approaches are better in accord with our experimental results. The anomalous line‐width effect of the four methyl groups observed in the 2,3‐dimethyl‐2‐butene cation radicals also confirmed the positive sign of the electron‐proton hyperfine constant of hyper‐conjugation mechanism. A methyl substituent attached to a conjugated molecule often behaves as if it formed part of the region of conjugation; the charge appears to flow from the methyl group into the π electron system and it may also give rise to an appreciable dipole moment. Methylation also gives rise to an appreciable dipole moment, and the resultant red shift of electronic absorption bands is of some importance in the design of dye molecules.     

L p -dual Quermassintegral sums

In this paper, we first introduce a concept of L _p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L _p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L _p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

The Huber theorem for non-compact conformally flat manifolds

It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions. Received: April 14, 2000; revised version: March 20, 2001