Fluorous Synthesis of Biaryl-Substituted Proline Analogs by 1,3-Dipolar Cycloaddition and Suzuki Coupling Reactions

A solution-phase synthesis of bicyclic prolines containing four points of diversity has been developed by a two-step synthesis involving 1,3-dipolar cycloaddition of perfluoroalkylsulfonyl-protected hydroxybenzaldehydes followed by Pd-catalyzed Suzuki coupling reaction of fluorous sulfonates with boronic acids. Both reactions are conducted under microwave irradiation and reaction mixtures are purified by solid-phase extractions without performing chromatography.     

Application of a novel micro-injector in the determination of indole derivatives in the rat pineal gland by capillary electrophoresis with electrochemical detection

A novel micro-injector has been fabricated for capillary electrophoresis (CE). It was successfully used for the determination of some indole derivatives for example melatonin (MT), serotonin (5-HT), tryptophan (Trp), and 5-hydroxy-tryptophane (5-HTrp) in the rat pineal gland by capillary electrophoresis with electrochemical detection (CE-EC). CE was performed in 0.20 mol L(-1) phosphate buffer (pH 8.0). The compounds investigated can be well separated and detected within 15 min. The working electrode used was a 300-microm diameter carbon electrode positioned opposite the outlet of the capillary. The relationship between peak current and analyte concentration was highly linear in the range from 0.10 to 500 micromol L(-1); detection limits (S/N = 3) were 0.03-0.13 micromol L(-1). The proposed method has been successfully used to analyze real biological samples.     

On a Damped Vibration Problem Involving p-Laplacian Operator: Fast Homoclinic Orbits

In this paper, we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator. Of particular interest is the resolution of an open problem. An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space. To our knowledge, our theorems appear to be the first such result about damped vibration problem with p-Laplacian operator.     

A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy

Methodology and Computing in Applied Probability - Risk measures for tail risk have an important application in the dynamic portfolio insurance strategies. We propose a new risk measure called...     

Global well-posedness for the 3-D MHD equations with partial diffusion in the periodic domain

In this paper, we prove the global well-posedness of the 3-D magnetohydrodynamics(MHD) equations with partial diffusion in the periodic domain when the initial velocity is small and the initial magnetic field is close to a background magnetic field satisfying the Diophantine condition.     

Compound Poisson approximation for unbounded functions on a group,with application to large deviations

Summary A second order error bound is obtained for approximating h d by h d , where is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to . The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.Research of the second author was supported by Schweizerischer Nationalfonds     

Differential operator Lie algebras on the ring of Laurent polynomials

A class of differential operator Lie algebras on the unit circle is introduced and discussed. They are the natural generalizations of the Witt algebra and the Virasoro algebra. Among them are the higher-spin algebrasW ₁₊ andW which occur in the physics literature.     

Analogues of hadwiger's theorem in space ℝ n —Sufficient conditions for a convex domain to enclose another

We estimate the kinematic measure of one convex domain moving to another under the groupG of rigid motions in ⁿ . We first estimate the kinematic formula for the total scalar curvature D ₀gD ₁ Rdv of then–2 dimensional intersection submanifold D ₀gD ₁. Then we use Chern and Yen's kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in ⁿ (4). Forn=4, we directly obtain another sufficient condition in ⁴.