We report fabrication of a novel microstructured optical fiber made of biodegradable and water soluble materials that features approximately 1 dB/cm transmission loss. Two cellulose butyrate tubes separated with hydroxypropyl cellulose powder were codrawn into a porous double-core fiber offering integration of optical, microfluidic, and potentially drug release functionalities.

It is well known that the Krasnosel'skii-Mann algorithm and the CQ algorithm for a split feasibility problem are not strongly convergent. In this paper, we present a KM-CQ-like algorithm with strong convergence, which combines the KM algorithm with the CQ algorithm by introducing two parameter sequences for solving the split feasibility problem. Under some parametric controlling conditions, the strong convergence of the algorithm is shown. Finally, we propose a modified KM-CQ-like algorithm and establish its strong convergence theorem.

Abstract. In this paper, we consider the least squares semidefinite programming with a large number of equality and inequality constraints. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. In this paper, we propose to overcome this difficulty by reformulating the problem as a system of semismooth equations with two level metric projection operators. We then design an inexact smoothing Newton method to solve the resulting semismooth system. At each iteration, we use the BiCGStab iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Our numerical experiments confirm the high efficiency of the proposed method.

Abstract. This paper is devoted to the discussion of extended covering rough set models. Based on the notion of neighborhood, five pairs of dual covering approximation operators were defined with their properties being discussed. The relationships among these operators were investigated. The main results are conditions with which these covering approximation operators are identical.

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