Nonpolar InGaN/GaN multiple quantum wells (MQWs) grown on the {11-00} sidewalls of c-axis GaN wires have been grown by organometallic vapor phase epitaxy on c-sapphire substrates. The structural properties of single wires are studied in detail by scanning transmission electron microscopy and in a more original way by secondary ion mass spectroscopy to quantify defects, thickness (1-8 nm) and In-composition in the wells (∼16%). The core-shell MQW light emission characteristics (390-420 nm at 5 K) were investigated by cathodo- and photoluminescence demonstrating the absence of the quantum Stark effect as expected due to the nonpolar orientation. Finally, these radial nonpolar quantum wells were used in room-temperature single-wire electroluminescent devices emitting at 392 nm by exploiting sidewall emission.

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We consider a class of smoothing methods for minimization problems where the feasible set is convex but the objective function is not convex, not differentiable and perhaps not even locally Lipschitz at the solutions. Such optimization problems arise from wide applications including image restoration, signal reconstruction, variable selection, optimal control, stochastic equilibrium and spherical approximations. In this paper, we focus on smoothing methods for solving such optimization problems, which use the structure of the minimization problems and composition of smoothing functions for the plus function (x) + . Many existing optimization algorithms and codes can be used in the inner iteration of the smoothing methods. We present properties of the smoothing functions and the gradient consistency of subdifferential associated with a smoothing function. Moreover, we describe how to update the smoothing parameter in the outer iteration of the smoothing methods to guarantee convergence of the smoothing methods to a stationary point of the original minimization problem.

Abstract. This paper presents a new formulation for the stochastic linear complementarity problem (SLCP), which aims at minimizing an expected residual defined by an NCP function. We generate observations by the quasi-Monte Carlo methods and prove that every accumulation point of minimizers of discrete approximation problems is a minimum expected residual solution of the SLCP. We show that a sufficient condition for the existence of a solution to the expected residual minimization (ERM) problem and its discrete approximations is that there is an observation ω i such that the coefficient matrix M(ω i ) is an R 0 matrix. Furthermore, we show that, for a class of problems with fixed coefficient matrices, the ERM problem becomes continuously differentiable and can be solved without using discrete approximation. Preliminary numerical results on a refinery production problem indicate that a solution of the new formulation is desirable.

We consider superlinearly convergent analogues of Newton methods for nondifferentiable operator equations in function spaces. The superlinear convergence analysis of semismooth methods for nondifferentiable equations described by a locally Lipschitzian operator in R n is based on Rademacher's theorem which does not hold in function spaces. We introduce a concept of slant differentiability and use it to study superlinear convergence of smoothing methods and semismooth methods in a unified framework. We show that a function is slantly differentiable at a point if and only if it is Lipschitz continuous at that point. An application to the Dirichlet problems for a simple class of nonsmooth elliptic partial differential equations is discussed.

We consider a class of difference-of-convex (DC) optimization problems whose objective is levelbounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. While this kind of problems can be solved by the classical difference-of-convex algorithm (DCA) [26], the difficulty of the subproblems of this algorithm depends heavily on the choice of DC decomposition. Simpler subproblems can be obtained by using a specific DC decomposition described in [27]. This decomposition has been proposed in numerous work such as [18], and we refer to the resulting DCA as the proximal DCA. Although the subproblems are simpler, the proximal DCA is the same as the proximal gradient algorithm when the concave part of the objective is void, and hence is potentially slow in practice. In this paper, motivated by the extrapolation techniques for accelerating the proximal gradient algorithm in the convex settings, we consider a proximal difference-of-convex algorithm with extrapolation to possibly accelerate the proximal DCA. We show that any cluster point of the sequence generated by our algorithm is a stationary point of the DC optimization problem for a fairly general choice of extrapolation parameters: in particular, the parameters can be chosen as in FISTA with fixed restart [15]. In addition, by assuming the Kurdyka-Lojasiewicz property of the objective and the differentiability of the concave part, we establish global convergence of the sequence generated by our algorithm and analyze its convergence rate. Our numerical experiments on two difference-of-convex regularized least squares models show that our algorithm usually outperforms the proximal DCA and the general iterative shrinkage and thresholding algorithm proposed in [17].

The hedgehog (Hh) signal pathway has recently been shown to be activated in human malignancies. However, little is known about its role in the development or patient prognosis of epithelial ovarian carcinoma. In the present study, we examined in vivo and in vitro E pithelial ovarian carcinoma, which comprises the majority of malignant ovarian tumors, is the leading cause of death from gynecologic malignancy in women.(1) The survival of ovarian carcinoma patients has not improved significantly for years, indicating that further understanding of the biology of ovarian carcinoma cells is critical for the development of new treatments against this neoplasm.(2) Several studies have reported that the poor prognosis of ovarian carcinoma is related not only to the unique metastasis but also to the high proliferative activity of carcinoma cells.(3-5) However, the molecular mechanisms of the proliferation of ovarian carcinoma cells are not fully understood. Recent studies suggest that the hedgehog (Hh) signal pathway contributes to cell proliferation and differentiation in several human neoplasms, such as pancreas, prostate and skin carcinomas.

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