Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived. Dedicated to the 80th birthday of Klaus Krickeberg     

On global stability of an HIV pathogenesis model with cure rate

In this paper, applying both Lyapunov function techniques and monotone iterative techniques, we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4⁺ T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12 : 2947–2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4⁺ T cells. Copyright © 2014 John Wiley & Sons, Ltd.     

A new subspace iteration method for the algebraic Riccati equation

We consider the numerical solution of the continuous algebraic Riccati equation A*X + XA ? XFX + G = 0, with F = F*,G = G* of low rank and A large and sparse. We develop an algorithm for the low‐rank approximation of X by means of an invariant subspace iteration on a function of the associated Hamiltonian matrix. We show that the sought‐after approximation can be obtained by a low‐rank update, in the style of the well known Alternating Direction Implicit (ADI) iteration for the linear equation, from which the new method inherits many algebraic properties. Moreover, we establish new insightful matrix relations with emerging projection‐type methods, which will help increase our understanding of this latter class of solution strategies. Copyright © 2014 John Wiley & Sons, Ltd.     

Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces

In recent years, Landweber iteration has been extended to solve linear inverse problems in Banach spaces by incorporating non-smooth convex penalty functionals to capture features of solutions. This method is known to be slowly convergent. However, because it is simple to implement, it still receives a lot of attention. By making use of the subspace optimization technique, we propose an accelerated version of Landweber iteration with non-smooth convex penalty which significantly speeds up the method. Numerical simulations are given to test the efficiency.     

浅谈制药工程专业有机化学实验教学的心得和体会——以三苯甲醇的制备和重结晶实验为例

有机化学实验是制药工程专业的一门必修课,旨在训练学生有机合成基本实验技能。本文以三苯甲醇的制备和重结晶实验为例,讲述了笔者在多年教学中获得的一点感悟和经验:1)将实验步骤分解成片断讲解可以使学生更好地理解和记忆实验过程和操作目的;2)重要的基本操作应反复练习,即"学习、复习、提高",通过三次重复练习来实现巩固和熟练掌握该操作的目的。     

Visible light irradiation promoted catalyst-free and solvent-free synthesis of pyrano[2,3-d]pyrimidine scaffolds at room temperature

A catalyst-free and solvent-free synthetic route for convenient one-pot synthesizing pyrano[2,3-d] pyrimidine scaffolds through Knoevenagel-Michael cyclocondensation is reported using visible light irradiation as a green promoter at room temperature based on green chemistry principles. Completing the reactions takes thoroughly less time while obtaining the products in outstanding yields. This green method includes the application of non-hazardous reaction circumstances, direct work-up without column chromatographic separation, catalyst-free, solvent-free, cost effective, simple synthesis, one-pot procedure, and high atom-economy.     

Properties of High-Swelling Native Starch Treated by Heat–Moisture Treatment with Different Holding Times and Iterations

Tapioca and potato starches were used to investigate the effect of heat–moisture treatment (HMT; 95–96 °C, 0–60 min, 1–6 iterations) on gelatinization properties, swelling power (SP), solubility and pasting properties. Tapioca starch had similar content and degree of polymerization of amylose, but a higher amylopectin short/long chain ratio, to potato starch. After HMT, the gelatinization temperature range was narrowed for tapioca starch, but was widened for potato starch. Decreases in SP and solubility were less for tapioca than potato starches, coinciding with a progressive shift to the moderate-swelling pasting profile for tapioca but a drastic change to the restricted-swelling profile for potato. Moreover, decreasing extents of SP and maximum viscosity for HMT tapioca starch were, respectively, in the range of 47–63% and 0–36%, and those of HMT potato starch were 89–92% and 63–94%. These findings indicate that the granule expansion and viscosity change of starch during gelatinization can be tailored stepwise by altering the HMT holding time and iteration.     

APPROXIMATING COMMON FIXED POINTS OF NEARLY ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings.We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.     

The asymptotic iteration method applied to certain quasinormal modes and non Hermitian systems

We study the Schrödinger equation with potentials admitting quasinormal modes using the asymptotic iteration method (AIM). We also study non-Hermitian PT symmetric potentials using AIM. The spectra, in all cases, are found to be in excellent agreement with exact results.