An inexact alternating direction method of multipliers with relative error criteria

In this paper, we study an inexact version of the alternating direction method of multipliers (ADMM) for solving two-block separable linearly constrained convex optimization problems. Specifically, the two subproblems in the classic ADMM are allowed to be solved inexactly by certain relative error criteria, in the sense that only two parameters are needed to control the inexactness. Related convergence analysis are established under the assumption that the solution set to the KKT system of the problem is not empty. Numerical results on solving a class of sparse signal recovery problems are also provided to demonstrate the efficiency of the proposed algorithm.     

Lipid Production by Culturing Oleaginous Yeast and Algae with Food Waste and Municipal Wastewater in an Integrated Process

Food waste and municipal wastewater are promising feedstocks for microbial lipid biofuel production, and corresponding production process is to be developed. In this study, different oleaginous yeast strains were tested to grow in hydrolyzed food waste, and growths of Cryptococcus curvatus, Yarrowia lipolytica, and Rhodotorula glutinis in this condition were at same level as in glucose culture as control. These strains were further tested to grow in municipal primary wastewater. C. curvatus and R. glutinis had higher production than Y. lipolytica in media made from primary wastewater, both with and without glucose supplemented. Finally, a process was tested to grow C. curvatus and R. glutinis in media made from food waste and municipal wastewater, and the effluents from these processes were further treated with yeast culture and phototrophic algae culture; 1.1 g/L C. curvatus and 1.5 g/L R. glutinis biomass were further produced in second-step yeast cultures, as well as 1.53 and 0.58 g/L Chlorella sorokiniana biomass in phototrophic cultures. The residual nitrogen concentrations in final effluents were 33 mg/L and 34 mg/L, respectively, and the residual phosphorus concentrations were 1.5 and 0.6 mg/L, respectively. The lipid contents in the produced biomass were from 18.7% to 28.6%.     

POSITIVE SOLUTIONS TO m-POINT BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH p-LAPLACIAN

In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained.     

OSCILLATION OF NONLINEAR IMPULSIVE PARABOLIC DIFFERENTIAL EQUATION WITH SEVERAL DELAYS

In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equation are investigated and a series of new sufficient conditions is established.     

EXISTENCE AND ATTRACTIVITY OF ALMOST PERIODIC SOLUTION FOR SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS AND VARIABLE COEFFICIENTS

In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system is studied. By using the Schauder's fixed point theorem and Lyapunov function, we obtain some sufficient conditions about the existence and attractivity of almost periodic solutions to the above system, and all its solutions converge to such almost periodic solution. An example is given to illustrate that the conditions of our results are feasible.     

有损耗波导中非线性TE波的数值模拟

本文发展了一种以有限元技术为基础的数值方法,用它分析有损耗波导中的非线性TE模。在这种方法中,非线性有损耗波导中TE波与功率有关的复传播常数和局城电场分布,可从这种波导直接得到,没有任何近似。作为这种方法的应用,计算了非线性有损耗波导系统中TE0模的功率色散关系和电场分布。     

On the nonlinear matrix equation

Based on fixed point theorems for monotone and mixed monotone operators in a normal cone, we prove that the nonlinear matrix equation always has a unique positive definite solution. A conjecture which is proposed in [X.G. Liu, H. Gao, On the positive definite solutions of the matrix equation X^s±A^TX^-tA=I_n, Linear Algebra Appl. 368 (2003) 83–97] is solved. Multi-step stationary iterative method is proposed to compute the unique positive definite solution. Numerical examples show that this iterative method is feasible and effective.