Fujita type exponent for fully nonlinear parabolic equations and existence results

In this paper, we prove that a class of parabolic equations involving a second order fully nonlinear uniformly elliptic operator has a Fujita type exponent. These exponents are related with an eigenvalue problem in all RN and play the same role in blow-up theorems as the classical p^?=1+2/N introduced by Fujita for the Laplacian. We also obtain some associated existence results.     

A new method for solving a system of generalized nonlinear variational inequalities in Banach spaces

The purpose of this paper is by using the generalized projection approach to introduce an iterative scheme for finding a solution to a system of generalized nonlinear variational inequality problem. Under suitable conditions, some existence and strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces. The results presented in the paper improve and extend some recent results.     

Schiff bases derived from p-aminobenzyl alcohol as trigger groups for pH-dependent prodrug activation

A number of novel acid-sensitive Schiff bases derived from p-aminobenzyl alcohol and various benzaldehyde derivatives were synthesized and were subsequently shown to trigger benzyl elimination reactions. The kinetics of acid-catalyzed hydrolysis at pH 5.0 as well as stability at pH 7.4 were studied using fluorogenic model compounds. Two fluoro-substituted Schiff bases showed efficient hydrolysis at pH 5.0 combined with a long-term stability at pH 7.4 and are considered suitable candidates for the development of anticancer prodrugs.     

高斯光束在对数型非线性介质中的传输特性

根据对数型非线性介质中高斯光束的束宽和波阵面曲率变化所满足的耦合方程,采用数值计算对高斯光束的传输特性进行了详细的分析。结合相图分析了高斯光束在不同初始条件下束宽与波阵面的变化情况。利用力学类比,讨论了高斯光束在传输过程中形成的对称呼吸模式与不对称呼吸模式的空间孤子。     

直线加速器中的非线性空间电荷效应和发射度增长

直线加速器中束团的非线性空间电荷效应是引起发射度增长的重要原因之一．根据计算在屏蔽筒中非均匀分布京团的空间电荷效应的普遍方法，推导了直线加速器圆波导中几种非均匀分布束团的非线性场能公式，并给出数值计算结果．讨论了由非线性所引起发射度增长．     

Optimization and analysis of the profitability of tariff structures with two-part tariffs

Service providers often offer tariff structures with several two-part tariffs that consist of a fixed fee and a usage price, such that consumers may pick the tariff they prefer. Prices of tariffs have significant impacts on service providers’ profit, because they simultaneously influence consumers’ tariff choices and their usage. The number of tariffs also plays an important role, because more tariffs segment the market better but also increase the administrative burden and require more marketing effort. This article presents a mixed-integer nonlinear programming optimization problem to determine profit-maximizing tariffs; compares several heuristic search methods, in particular, the gradient method, stochastic search, and simulated annealing, to solve this problem; analyses the profitability of different tariff structures; and outlines the factors that drive differences in profitability across various tariff structures. The results show that especially for large samples of more than 100 consumers, simulated annealing performs best and deviates only 0.2% from the optimum. Structures with fewer two-part tariffs are generally sufficient, because additional two-part tariffs only negligibly increase service providers’ profit.     

On Liouville type theorems for fully nonlinear elliptic equations with gradient term

In this paper, we prove a Hadamard property and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with a gradient term, both in the whole space and in an exterior domain.     

Confidence Judgments for Discriminations in Nonlinear Psychophysics

Psychophysical tasks requiring stimulus discrimination frequently report underconfidence; subjects think they are doing less accurately at discrimination or identification than is the case, measured in terms of probabilities of correct performance. An investigation to see if underconfidence is predictable from the intrinsic nonlinearities of the psychophysics, without assuming that confidence itself is a subjective analogue of a frequentist probability of correct identification, is explored using the algebra of cascaded nonlinear psychophysics previously developed.     

Two Interior-Point Methods for Nonlinear P *(τ)-Complementarity Problems

Two interior-point algorithms using a wide neighborhood of the central path are proposed to solve nonlinear P _*-complementarity problems. The proof of the polynomial complexity of the first method requires the problem to satisfy a scaled Lipschitz condition. When specialized to monotone complementarity problems, the results of the first method are similar to those in Ref. 1. The second method is quite different from the first in that the global convergence proof does not require the scaled Lipschitz assumption. However, at each step of this algorithm, one has to compute an approximate solution of a nonlinear system such that a certain accuracy requirement is satisfied.