Selective depiction of susceptibility transitions using Laplace-filtered phase maps

In this work, we aim to demonstrate the ability of Laplace-filtered three-dimensional (3D) phase maps to selectively depict the susceptibility transitions in an object. To realize this goal, it is first shown that both the Laplace derivative of the z component of the static magnetic field in an object and the Laplacian of the corresponding phase distribution may be expected to be zero in regions of constant or linearly varying susceptibility and to be nonzero when there is an abrupt change in susceptibility, for instance, at a single point, a ridge, an interface, an edge or a boundary. Next, a method is presented by which the Laplace derivative of a 3D phase map can be directly extracted from the complex data, without the need for phase unwrapping or subtraction of a reference image. The validity of this approach and of the theory behind it is subsequently demonstrated by simulations and phantom experiments with exactly known susceptibility distributions. Finally, the potential of the Laplace derivative analysis is illustrated by simulations with a Shepp-Logan digital brain phantom and experiments with a gel phantom containing positive and negative focal susceptibility deviations.     

Necessary and sufficient conditions for weak efficiency in non-smooth vectorial optimization problems

By using the concepts of local cone approximations and K-directional derivatives, we obtain necessary conditions of optimality for the weak efficiency of the vectorial optimization problems with the inequalities and abstract constraints. We introduce the notion of stationary point (weak and strong) and we prove that, under suitable hypotheses of K-invexity, the stationary points are weakly efficient solutions (global).     

RESULTS ON A QUESTION OF ZHANG AND YANG

Abstract For a meromorphic function f,let N(l+1(r,1/f) denote the counting function of zeros of f of order l at least.Let f be a nonconstant meromorphic function,such that (N)(r,f) =S(r,f).Denote F =f...     

Long time asymptotics of a Brownian particle coupled with a random environment with non-diffusive feedback force

We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behavior of the Brownian particle has bounded (in time) variance when the particle interacts with a subdiffusive field; when the interaction is with a superdiffusive field the variance of the limiting process grows in time as t^2γ−1, 1/2<γ<1. Two different kinds of superdiffusing (random) environments are considered: one is described through the use of the fractional Laplacian; the other via the Riemann-Liouville fractional integral. The subdiffusive field is modeled through the Riemann-Liouville fractional derivative.     

A new Jacobi operational matrix: An application for solving fractional differential equations

In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives which is applied together with spectral tau method for numerical solution of general linear multi-term fractional differential equations (FDEs). A new approach implementing shifted Jacobi operational matrix in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of nonlinear multi-term FDEs. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. The proposed methods are applied for solving linear and nonlinear multi-term FDEs subject to initial or boundary conditions, and the exact solutions are obtained for some tested problems. Special attention is given to the comparison of the numerical results obtained by the new algorithm with those found by other known methods.     

Solitary pattern solutions for fractional Zakharov-Kuznetsov equations with fully nonlinear dispersion

The fractional Zakharov-Kuznetsov equations are increasingly used in modeling various kinds of weakly nonlinear ion acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. This has led to a significant interest in the study of these equations. In this work, solitary pattern solutions of fractional Zakharov-Kuznetsov equations are investigated by means of the homotopy perturbation method with consideration of Jumarie’s derivatives. The effects of fractional derivatives for the systems under consideration are discussed. Numerical results and a comparison with exact solutions are presented.     

小檗碱衍生物合成及生理活性研究进展

小檗碱是一种季铵型异喹啉生物碱,主要存在于毛茛科、芸香科和小檗科等植物中,具有多种药理功能.近年来,大量小檗碱衍生物的合成,极大提高了小檗碱的生理活性及拓展了小檗碱的应用范围.文章重点综述了小檗碱及其衍生物的生物及化学合成,简述了其生理活性,并对新型小檗碱衍生物合成的设计方向作了展望.     

Determination of metabolic profile of anti-malarial trioxane CDRI 99/411 in rat liver microsomes using HPLC

CDRI 99/411 is a potent 1,2,4‐trioxane anti‐malarial candidate compound of the Central Drug Research Institute, India. This study aimed to conduct comprehensive in vitro metabolic investigations of CDRI 99/411 to corroborate its preclinical investigations. Preliminary in vitro metabolic investigations were performed to assess the metabolic stability [in vitro half‐life (t_1/2) and in vitro hepatic intrinsic clearance (Cl_int)] of CDRI 99/411 in male Sprague–Dawley rat and human liver microsomes using validated high‐performance liquid chromatography with photodiode array detector. The observed in vitro t_1/2 of the compound in rat and human liver microsomes was 13 min with in vitro Cl_int 130.7 ± 25.0 μL/min/mg and 19 min with in vitro Cl_int 89.3 ± 17.40 μL/min/mg. These observations suggested moderate metabolic degradation and in vitro Cl_int with insignificant difference (p > 0.05) in the metabolic stability profile in rat and human. Hence, in vitro metabolic investigations were performed with rat liver microsomes. It was observed that CDRI 99/411 exhibited sigmoidal kinetics. At nonlinear regression (r ≥ 0.99) EC₅₀ and Hill slope values were 17 µm and 1.50, respectively. The metabolism of CDRI 99/411 was primarily mediated by CYP3A2 and was inferred by CYP reaction phenotyping with known potent inhibitors. Two metabolites of CDRI 99/411 were detected which were undetectable on incubation with 1‐aminobenzotriazole and ketoconazole. Copyright © 2011 John Wiley & Sons, Ltd.