Achromatic waveguide coupling with a hybrid grating-mirror

A new grating coupler that incorporates a hybrid grating-mirror is proposed. An analysis of the device indicates that it has a much larger achromatic range than that of conventional grating couplers, as well as a relaxed fabrication requirement for the grating.     

Some notes on Zadeh’s extensions

This paper shows that the Zadeh’s extensions of sendograph-metric-continuous fuzzy-valued functions are sendograph-metric-continuous fuzzy functions.     

Minimax mean-variance models for fuzzy portfolio selection

This paper discusses fuzzy portfolio selection problem in the situation where each security return belongs to a certain class of fuzzy variables but the exact fuzzy variable cannot be given. Two credibility-based minimax mean-variance models are proposed. The crisp equivalents of the models to linear programming ones are given in three special cases. In addition, a general solution algorithm is also provided. To help understand the modeling idea and to illustrate the effectiveness of the proposed algorithm, one example is presented.     

The DCT-based oscillation detection method for a single time series

This paper proposes a new method based on the discrete cosine transform (DCT), named as the DCT-based method, to detect oscillations for a single time series. The main idea is to isolate different frequency components of the time series via the DCT, and to detect oscillations by checking the regularity of zero-crossings of these isolated components. This method has the following features: (i) usage of only time series information of process variables without additional process knowledge, (ii) ability to deal with slowly varying trends, (iii) robustness to both white and colored noises, (iv) capability to handle the presence of multiple oscillations, and (v) amenability to complete automation without human intervention. Simulation examples and industrial case studies are presented to demonstrate the effectiveness and the above features of the DCT-based method.     

Development of a diagnostic system using a testing-based approach for strengthening student prior knowledge

Students learn new instructions well by building on relevant prior knowledge, as it affects how instructors and students interact with the learning materials. Moreover, studies have found that good prior knowledge can enable students to attain better learning motivation, comprehension, and performance. This suggests it is important to assist students in obtaining the relevant prior knowledge, as this can enable them to engage meaningfully with the learning materials. Tests are often used to help instructors assess students’ prior knowledge. Nevertheless, conventional testing approaches usually assign only a score to each student, and this may mean that students are unable to realize their own individual weaknesses. To address this problem, instructors can diagnose the test results to provide more detailed information to each student, but this is obviously a time-consuming process. Therefore, this study proposes a testing-based diagnosis system to assist instructors and students in diagnosing and strengthening prior knowledge before new instruction is undertaken. Furthermore, an experiment was conducted to evaluate the effectiveness of the proposed approach in an interdisciplinary course, since several studies have indicated that students learn more and better in such courses when applying relevant prior knowledge to what they are learning. The experimental results show that the developed system is able to effectively diagnose students’ prior knowledge and enhance their learning motivation and performance on an interdisciplinary course. In addition, two diagnostic evaluations were also conducted to assess whether the diagnoses given by the system were consistent with the decisions of experts. The results demonstrate that the proposed system can effectively assist instructors and students in diagnosing and strengthening prior knowledge before new instruction is undertaken, since the diagnoses produced by the system were broadly consistent with those of experts.     

An inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities

In this paper, we investigate an inexact hybrid projection-proximal method for solving a class of generalized mixed variational inequalities in Hilbert spaces. We construct a general inexact hybrid projection-proximal point algorithm, in which an inexact relaxed proximal point step is followed by a suitable orthogonal projection onto a hyperplane. Under some suitable conditions concerned with the pseudomonotone set-valued mapping T, the nonsmooth convex function f and the step size λ_k, we prove the convergence of the inexact hybrid projection-proximal point algorithm for solving generalized mixed variational inequalities in Hilbert spaces.