Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Vortex lattices in a spin-orbit coupled binary Bose-Einstein condensates with dipolar interaction

International Journal of Theoretical Physics - We consider the stationary state of a spin-orbit coupled (SOC) binary Bose-Einstein condensates with dipole-dipole interaction (DDI). Our results are...     

Trends in the detection of pharmaceuticals and endocrine-disrupting compounds by Field-Effect Transistors (FETs)

Field-effect transistors (FETs) are one of the most widely-used electronic sensors for continuous monitoring and detection of contaminants such as pharmaceuticals and endocrine-disrupting compounds at low concentrations. FETs have been successfully utilized for the rapid analysis of these environmental pollutants due to their advantageous material properties like the disposability, rapid responses and simplicity. This paper presented an up-to-date overview of applied strategies with different bio-based materials in order to enhance the analytical performances of the designed sensors. Comparison and discussion were made between characteristics of recently engineered FET bio-sensors used for the detection of famous and selected pharmaceutical compounds in the literature. The recent progress in environmental research applications, comments on interesting trends, current challenge for future research in endocrine-disrupting chemicals’ (EDCs) detection using FETs biosensors were highlighted.     

Synthesis and characterization of three co-crystals of bis(benzimidazole) derivatives with aromatic dicarboxylic acids

Research on Chemical Intermediates - Combination of three aromatic carboxylic acids (5-nitroisophthalic acid (H2nip), 2,6-naphthalenedicarboxylic acid (H2ndc), tetrabromoterephthalic acid (H2tbta))...     

Stability criterion for synchronization of linearly coupled unified chaotic systems

This paper investigates the synchronization of two linearly coupled unified chaotic systems. A new stability criterion for asymptotic synchronization is attained using the Lyapunov stability theory and linear matrix inequality (LMI) approach. A numerical example is given to illuminate the design procedure and advantage of the result derived.     

Analysis of X（1576） as a Tetraquark State with the QCD Sum Rules

We take the viewpoint that X（1576） is the tetraquark state which consists of a scalar diquark and an antiscalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mx= （1.66 =k 0.14） GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X（1576）.     

Scheduling dual gripper robotic cell: One-unit cycles

We consider the scheduling problem of cyclic production in a bufferless dual-gripper robot cell processing a family of identical parts. The objective is to find an optimal sequence of robot moves so as to maximize the long-run average throughput rate of the cell. While there has been a considerable amount of research dealing with single-gripper robot cells, there are only a few papers devoted to scheduling in dual-gripper robotic cells. From the practical point of view, the use of a dual gripper offers the attractive prospect of an increase in the cell productivity. At the same time, the increase in the combinatorial possibilities associated with a dual-gripper robot severely complicates its theoretical analysis. The purpose of this paper is to extend the existing conceptual framework to the dual-gripper situation, and to provide some insight into the problem.We provide a notational and modelling framework for cyclic production in a dual-gripper robotic cell. Focusing on the so-called active cycles, we discuss the issues of feasibility and explore the combinatorial aspects of the problem. The main attention is on 1-unit cycles, i.e., those that restore the cell to the same initial state after the production of each unit. For an m-machine robotic cell served by a dual-gripper robot, we describe a complete family of 1-unit cycles, and derive an analytical formula to estimate their total number for a given m. In the case when the gripper switching time is sufficiently small, we identify an optimal 1-unit cycle. This special case is of particular interest as it reflects the most frequently encountered situation in real-life robotic systems. Finally, we establish the connection between a dual-gripper cell and a single-gripper cell with machine output buffers of one-unit capacity and compare the cell productivity for these two models.     

Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28–30, 1990, pp. 63–78) has certain merits over the estimators derived through the estimation of the regression function. Some of the properties of the BRPA estimator have been studied in Chen et al. (J. Multivariate Anal. 57 (1996) 191) and Bai and Huang (Sankhya: Indian J. Statist. Ser. A. 61 (Pt. 2) (1999) 208–217). In this article, we further study the properties of the BRPA estimator and give its convergence rate under some quite general conditions. Simulation results are presented for the illustration of the convergence rate. Some comparisons with existing estimators such as the Müller estimator are provided.     

Positive periodic solution for a two-species ratio-dependent predator-prey system with time delay and impulse

A two-species ratio-dependent predator-prey model with time delay and impulse is investigated. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.     

基于氮化碳复合材料磁性固相萃取结合高效液相色谱法测定尿液中3种羟基多环芳烃

建立了测定尿液中3种羟基多环芳烃的氮化碳复合材料磁性固相萃取结合高效液相色谱-荧光检测法。所构筑的磁性氮化碳材料，经扫描电子显微镜、X射线衍射仪、振动样品磁强计和比表面积分析仪表征后，用于尿液中3种羟基多环芳烃的富集净化。考察了吸附剂用量、吸附时间、洗脱溶液和洗脱体积（单次洗脱体积×洗脱次数）对萃取效率的影响。结合高效液相色谱-荧光分析，在0.25~250 μg/L范围内线性关系良好（相关系数r=0.999），3种羟基多环芳烃的检出限和定量限分别为0.08和0.25 μg/L，回收率为90.1%~102%，日内和日间精密度分别为1.5%~7.7%和2.2%~8.7%。该本方法简单、快速、高效，可用于尿液中羟基多环芳烃的分析。