LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

In this article, we obtain the large deviations and moderate deviations for negatively dependent (ND) and non-identically distributed random variables defined on (-∞, +∞). The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.     

Single machine scheduling with total tardiness criterion and convex controllable processing times

We consider a single machine scheduling problem with total tardiness criteria and controllable job-processing times specified by a convex resource consumption function. The objective is to have the total tardiness limited into a given range, and minimize the total resource consumption. A polynomial time algorithm of O(n ²) is presented for the special case where jobs have a common due date.     

Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force

The pull-in instability and the vibration for a prestressed circular electrostatically actuated microplate are investigated in consideration of the Casimir force. Based on von Kármán’s nonlinear bending theory of thin plates, the governing equations for the whole analysis are decomposed into two two-point boundary value problems. For static deformation of the plate, the geometric nonlinearity is involved and the pull-in parameters are obtained by using the shooting method through taking the applied voltage or Casimir parameter as an unknown. This algorithm is also used to study the small amplitude free vibration about the predeformed bending configuration following an assumed harmonic time mode, and the variation of the prestress and Casimir parameters dependent fundamental natural frequency with the applied voltage is presented. Several case studies are compared with available published simulations to confirm the proposed method. The influences of various parameters, such as the initial gap-thickness ratio, Casimir effect, prestress on the pull-in instability behavior and the natural frequency are examined.     

Constructing C1 triangular patch of degree six by the Boolean sum of an approximation operator and an interpolation operator

A new method to construct C¹ triangular patches which satisfy the given boundary curves and cross-boundary slopes is presented. The Boolean sum of an approximation operator and an interpolation operator is employed to construct the triangular patch. The approximation operator is used to construct a polynomial patch of degree six. The polynomial of degree six affords more freedoms, which makes the approximation operator not only approximate the given boundary interpolation conditions but also have a better approximation precision in the interior of the triangle, so that the triangular patch has a better precision on both the boundary and the interior of the triangular domain. The interpolation operator is utilized to build an interpolation patch which satisfies the given boundary conditions. The Boolean sum of the approximation and interpolation patches forms the triangular patch. Comparison results of the new method with other three methods are given.     

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.     

博弈论在通信对抗态势预测中的应用

本文首先提出了基于博弈论预测电磁态势演变的基本构想,设置了通信对抗的场景并构建了相应的数学模型.其次,分析了通信对抗电磁态势生成流程,最后结合一定的作战背景进行了仿真实验,基于双方博弈的原则预测了通信对抗态势的演变.仿真结果与理论分析相符,该研究成果已在多个作战仿真系统中得到了成功应用.     

完全非正规Toeplitz算子

In this paper, we show that the hyponormal Toeplitz operator Tφ with trigonometric polynomial symbol φ is either normal or completely non-normal. Moreover, if Tφ is non-normal, then Tφ has a dense set of cyclic vectors. Some general conditions are also considered.     

Application of quantitative structure-activity relationship to the determination of binding constant based on fluorescence quenching

Quantitative structure-activity relationship (QSAR) model was used to predict and explain binding constant (log K) determined by fluorescence quenching. This method allowed us to predict binding constants of a variety of compounds with human serum albumin (HSA) based on their structures alone. Stepwise multiple linear regression (MLR) and nonlinear radial basis function neural network (RBFNN) were performed to build the models. The statistical parameters provided by the MLR model (R²=0.8521, RMS=0.2678) indicated satisfactory stability and predictive ability while the RBFNN predictive ability is somewhat superior (R²=0.9245, RMS=0.1736). The proposed models were used to predict the binding constants of two bioactive components in traditional Chinese medicines (isoimperatorin and chrysophanol) whose experimental results were obtained in our laboratory and the predicted results were in good agreement with the experimental results. This QSAR approach can contribute to a better understanding of structural factors of the compounds responsible for drug-protein interactions, and can be useful in predicting the binding constants of other compounds.     

Improving the visible light photocatalytic activity of mesoporous TiO2 via the synergetic effects of B doping and Ag loading

B-doped together with Ag-loaded mesoporous TiO₂ (Ag/B–TiO₂) was prepared by a two-step hydrothermal method in the presence of boric acid, triblock copolymer surfactant, and silver nitrate, followed by heat treatment. The obtained samples were characterized by X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), UV–vis diffuse reflectance spectroscopy, X-ray photoelectron spectroscopy (XPS), and nitrogen adsorption–desorption. It was revealed that all samples consist of highly crystalline anatase with mesoporous structure. For Ag/B–TiO₂, B was doped into TiO₂ matrix in the form of both interstitial B and substitutional B while Ag was deposited on the surface of B–TiO₂ in the form of metallic silver. Compared with the single B-doped or Ag-loaded TiO₂ one, mesoporous Ag/B–TiO₂ exhibits much higher visible light photocatalytic activity for the degradation of Rhodamine 6G, which can be ascribed to the synergistic effects of B doping and Ag loading by narrowing the band gap of the photocatalyst and preventing the fast recombination of the photogenerated charge carriers, respectively.     

Experimental research on an arbitrary pulse generation system for imaging VISAR

Imaging VISAR is an important diagnostic tool for a variety of shock-related phenomena in laser-driven experiments. To adapt to various types of shaped driven pulse, the imaging VISAR needs an illuminating light with good shaping capability. Here, a flexible laser probe system was experimentally studied. Being generated from a 1064-nm DFB laser, the continuous wave was modulated by a waveguide amplitude modulator driven by 10 GS/s arbitrary waveform generator. After being amplified by fiber amplifiers and Nd:YAG rod amplifiers, the signal pulse was frequency-converted to 532-nm green light by a thermally controlled LBO crystal with a final output energy larger than 10 mJ. Finally, the green light was coupled into a 1-mm core diameter, multimode fused silica optical fiber and propagated to the imaging VISAR. The probe laser could realize accurate pulse shaping with time resolution below 100 ps. Uniformity in intensity and capability of arbitrary pulse shaping provides great convenience for the analysis of experimental data.