A Monotone Discretization for the Fractional Obstacle Problem

We propose a monotone discretization method for obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over a bounded Lipschitz domain. Our approach is motivated by the success of the monotone discretization of the fractional Laplacian [SIAM J. Numer. Anal. 60(6), pp. 3052-3077, 2022]. By exploiting the problem's unique structure, we establish the uniform boundedness, existence, and uniqueness of the numerical solutions. Moreover, we employ the policy iteration method to efficiently solve discrete nonlinear problems and prove its convergence after a finite number of iterations. The improved policy iteration, adapted to the regularity result, exhibits superior performance by modifying the discretization in different regions. Several numerical examples are provided to illustrate the effectiveness of our method.Comment: 18 pages, 7 figure

Abstract test case prioritization using repeated small-strength level-combination coverage

Abstract—Abstract Test Cases (ATCs) have been widely used in practice, including in combinatorial testing and in software product line testing. When constructing a set of ATCs, due to limited testing resources in practice (for example in regression testing), Test Case Prioritization (TCP) has been proposed to improve the testing quality, aiming at ordering test cases to increase the speed with which faults are detected. One intuitive and extensively studied TCP technique for ATCs is λ-wise Level-combination Coverage based Prioritization (λLCP), a static, black-box prioritization technique that only uses the ATC information to guide the prioritization process. A challenge facing λLCP, however, is the necessity for the selection of the fixed prioritization strength λ before testing — testers need to choose an appropriate λ value before testing begins. Choosing higher λ values may improve the testing effectiveness of λLCP (for example, by finding faults faster), but may reduce the testing efficiency (by incurring additional prioritization costs). Conversely, choosing lower λ values may improve the efficiency, but may also reduce the effectiveness. In this paper, we propose a new family of λLCP techniques, Repeated Small-strength Level-combination Coverage-based Prioritization (RSLCP), that repeatedly achieves the full combination coverage at lower strengths. RSLCP maintains λLCP’s advantages of being static and black box, but avoids the challenge of prioritization strength selection. We performed an empirical study involving five different versions of each of five C programs. Compared with λLCP, and Incremental strength LCP (ILCP), our results show that RSLCP could provide a good trade-off between testing effectiveness and efficiency. Our results also show that RSLCP is more effective and efficient than two popular techniques of Similarity-based Prioritization (SP). In addition, the results of empirical studies also show that RSLCP can remain robust over multiple system releases

Prioritising abstract test cases: an empirical study

Test-case prioritisation (TCP) attempts to schedule the order of test-case execution such that faults can be detected as quickly as possible. TCP has been widely applied in many testing scenarios such as regression testing and fault localisation. Abstract test cases (ATCs) are derived from models of the system under test and have been applied to many testing environments such as model-based testing and combinatorial interaction testing. Although various empirical and analytical comparisons for some ATC prioritisation (ATCP) techniques have been conducted, to the best of the authors' knowledge, no comparative study focusing on the most current techniques has yet been reported. In this study, they investigated 18 ATCP techniques, categorised into four classes. They conducted a comprehensive empirical study to compare 16 of the 18 ATCP techniques in terms of their testing effectiveness and efficiency. They found that different ATCP techniques could be cost-effective in different testing scenarios, allowing us to present recommendations and guidelines for which techniques to use under what conditions. © The Institution of Engineering and Technology 2018

On the selection of strength for fixed-strength interaction coverage based prioritization

Abstract test cases are derived by modeling the system under test, and have been widely applied in practice, such as for software product line testing and combinatorial testing. Abstract test case prioritization (ATCP) is used to prioritize abstract test cases and aims at achieving higher rates of fault detection. Many ATCP algorithms have been proposed, using different prioritization criteria and information. One ATCP approach makes use of fixed-strength level-combinations information covered by abstract test cases, and is called fixed-strength interaction coverage based prioritization (FICBP). Before using FICBP, the prioritization strength λ needs to be decided. Previous studies have generally focused on λ values ranging between 1 and 6. However, no study has investigated the appropriateness of such a range, nor how to assign the prioritization strength for FICBP. To answer these questions, this paper reports on an empirical study involving four real-life programs (each of which with six versions). The experimental results indicate that λ should be set approximately equal to a value corresponding to half of the number of parameters, when testing resources are sufficient. Our results also show that when testing resources are limited or insufficient, either small or large λ values are suggested for FICBP

Carbon dots-based dual-emission ratiometric fluorescence sensor for dopamine detection

The detection of Dopamine (DA) is significant for disease surveillance and prevention. However, the development of the precise and simple detection techniques is still at a preliminary stage due to their high tester requirements, time-consuming process, and low accuracy. In this work, we present a novel dual-emission ratiometric fluorescence sensing system based on a hybrid of carbon dots (CDs) and 7-amino-4-methylcoumarin (AMC) to quickly monitor the DA concentration. Linked via amide bonds, the CDs and AMC offered dual-emissions with peaks located at 455 and 505 nm, respectively, under a single excitation wavelength of 300 nm. Attributed to the fluorescence of the CDs and AMC in the nanohybrid system can be quenched by DA, the concentration of DA could be quantitatively detected by monitoring the ratiometric ratio change in fluorescent intensity. More importantly, the CDs-AMC-based dual-emission ratiometric fluorescence sensing system demonstrated a remarkable linear relationship in the range of 0–33.6 μM to detection of DA, and a low detection limit of 5.67 nM. Additionally, this sensor successfully applied to the detection of DA in real samples. Therefore, the ratiometric fluorescence sensing system may become promising to find potential applications in biomedical dopamine detection

Design and analysis of the porous ZrO₂/(ZrO₂+Ni) ceramic joint with load bearing-heat insulation integration

The joining of ceramics with metals is widely used in aerospace engineering where high strength and excellent heat insulation materials are desired. In this paper, a new multifunctional bolted joint with load bearing-heat insulation integration is prepared with porous ZrO2/(ZrO2+Ni) sandwich ceramics. Double-shear behavior of the bolted joint connecting C/SiC plates is-analyzed by ABAQUS codes. It is found that shearing damage occurs at shearing faces of the bolt, the shearing failure faces are layered rather than smooth. To improve its shearing strength, we introduce the shear band (ZrO2+ V%Ni of thickness h) to its shearing faces. Results show that the shear band can improve the shearing strength and slow down the attenuation of load bearing capacity after reaching the shearing strength, without obviously increasing the thermal conductivity. An optimal structural design is performed and proper shear band is defined to balance the shearing strength and heat insulation performance of the ceramic joint. (C) 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.National Natural Science Foundation of China [11102003, 11472038]SCI(E)[email protected]; [email protected]

Measuring residual stress and its influence on properties of porous ZrO₂</(ZrO₂+Ni) ceramics

Ceramic-metal functionally graded materials (FGMs) have been extensively used in aerospace engineering where high strength and excellent heat insulation materials are desired. However, their performance highly depends on the internal residual stress, which is generated inevitably due to the thermal mismatch of ceramic and metal. In this paper, based on the nanoindentation test, the field distribution of the residual stress of porous ZrO2/(ZrO2+Ni) ceramic-metal FGMs is measured. The residual stress field measured by nanoindentation agrees qualitatively with the finite element simulation results. Then a constitutive relation is established to investigate the effects of residual stress on the macroscopic deformation behavior of porous ZrO2/(ZrO2+Ni) FGMs, which agrees well with the bending and compression experiments. It is found that residual stress can improve both the flexural strength and stiffness of the porous ZrO2/(ZrO2+Ni) FGMs, by densifying and compensating the tensile stress of the porous middle layer (ZrO2) during the bending process, respectively. However, it has no obvious influence on the ultimate compressive strength of the porous ZrO2/(ZrO2+Ni) FGMs, but mainly influences its initial stage of elastic deformation in the compressive behavior. (C) 2014 Elsevier B.V. All rights reserved.Nanoscience & NanotechnologyMaterials Science, MultidisciplinaryMetallurgy & Metallurgical EngineeringSCI(E)[email protected]; [email protected]