Wigner Function：from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States

We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

Effects of rare earth element lanthanum on the microstructure of copper matrix diamond tool materials

Effects of rare earth element La on the microstructure of Cumatrix diamond tools were researched under the conditions of variousmaterials components and the process parameters in order to improvematerials properties. SEM, XPS and X-ray were used to investigate thefracture section, microstructure and the element valence inmaterials. The Results shown that the combination of rare earthelement La and transition element Ti is advantageous to the bondingstate Between diamond particles and matrix, so it can improve thematerials properties. Suitable sintering temperature is 790 deg. C.

Analytical Expressions of Matrix Elements of Physical Quantities for Dirac Oscillator

The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case, of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.

Finite Element Analysis of Push-Out Test of SiC Fiber Reinforced Titanium Matrix Composites

Based on the interphase layer model and the spring layer model, an improved interface model was developed to evaluate the interfacial shear strength of Titanium matrix composites(TMCs) and to analyze the effects of various parameters on the interfacial properties. The results showed that the improved interface model is more suitable for calculating the interfacial properties of SiC fiber reinforced titanium matrix composites. The interfacial shear strength of SiC/Timetal-834 predicted is 500 MPa. In addition, in order to better understand the interfacial properties of composites, some push out phenomenon were analyzed.

THE GENERATION OF NON－LINEAR STIFFNESS MATRIX OF TRIANGLE ELEMENT WHENCONSIDERING BOTH THE BENDING AND IN－PLANEME MBRANE FORCES

Using Stricklin Melhod￣[5],we have this paper has derived the formulas for the ge-neration of non-linear element stiffness matrix of a triangle element when considering both the bending and the in-plane membrane forces. A computer programme for the calculation of large deflection and inner forces of shallow shells is designed on theseformulas. The central deflection curve computed by this programme is compared with other pertaining results.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

NORMALIZED ELEMENT NODE TOPOLOGICAL MATRIX OF FINITE ELEMENT MESHES

On the basis of concept of element node topological analysis, the normalized element node topological matrices for finite element meshes are presented in the paper, including 3-node and 6-node triangular element, 4-node and 8-node quadrilateral element, 8-node and 20-node hexahedral element. It is beneficial to further analyzing topological characteristics of finite element models and automatic generation of meshes

基于声学黑洞的声学迷宫结构的优化设计

结合理论计算、有限元仿真和试验测量,研究了基于声学黑洞的声学迷宫结构的优化设计方法,给出了具有5.01和7.75个倍频程的小尺寸、宽频吸声结构。首先,基于传递矩阵法,建立声学黑洞的数学模型,计算声学黑洞的反射系数,并将理论计算结果与有限元仿真结果进行对比。然后,基于声学黑洞的导纳变化规律,设计单、双旁支管声学迷宫结构,通过优化设计,实现迷宫结构和声学黑洞导纳的匹配。最后,基于声学迷宫结构导纳的匹配结果,应用模拟退火算法构造优化模型,获得了宽频吸声的小尺寸声学迷宫结构,并打印3D样件进行试验验证。研究结果表明:应用双旁支管声学迷宫代替声学黑洞管道中的环腔,经优化设计,旁支管迷宫和声学黑洞的导纳可以实现完美匹配,并可以在保持吸声性能不变的前提下,实现结构的小尺寸设计,优化后的结构有效吸声带宽是优化前的13.36倍,倍频程是优化前的3.64倍。

柔性装配模式下飞机薄壁件装配偏差分析

针对柔性装配模式下飞机薄壁件的装配特点,综合考虑薄壁件的制造偏差、柔性工装的定位偏差及柔性件在装配力作用下的变形误差,提出一种基于柔性装配的飞机薄壁件装配偏差模型。首先,结合柔性工装定位偏差,通过确定性定位法对薄壁件发生转动和平动产生的刚性偏差进行分析,并利用影响系数法和超元刚度矩阵理论对薄壁件因夹紧和铆接装配而产生的柔性变形进行分析。其次,针对薄壁件偏差传递规律建立了装配偏差模型,利用MATLAB求解可得到薄壁件上各关键特性点的法向偏差,对装配体最终偏差进行了有效预测。最后,通过某型飞机薄壁件进行实例验证,并借助有限元分析软件ABAQUS对薄壁件装配过程进行仿真。通过对关键测点装配偏差的计算结果和仿真结果对比,验证了文中提出的飞机薄壁件装配偏差模型的可行性。

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Dual androgen-response elements mediate androgen regulation of MMP-2 expression in prostate cancer cells

Aim： To characterize the matrix metalloproteinases （MMP）-2 promoter and to identify androgen response elements （AREs） involved in androgen-induced MMP-2 expression. Methods： MMP-2 mRNA levels was determined by reverse transcription-polymerase chain reaction （RT-PCR）. MMP-2 promoter-driven luciferase assays were used to determine the fragments responsible for androgen-induced activity. Chromatin-immunoprecipitation assay and electrophoretic mobility shift assays （EMSA） were used to verify the identified AREs in the MMP-2 promoter. Results： Androgen significantly induced MMP-2 expression at the mRNA level, which was blocked by the androgen antagonist bicalutamide. Deletion of a region encompassing base pairs -1591 to -1259 （relative to the start codon） of the MMP-2 promoter led to a significant loss of androgen-induced reporter activity. Additional deletion of the 5＇-region up to -562 bp further reduced the androgen-induced MMP-2 promoter activity. Sequence analysis of these two regions revealed two putative ARE motifs. Introducing mutations in the putative ARE motifs by site-directed mutagenesis approach resulted in a dramatic loss of androgen-induced MMP-2 promoter activity, indicating that the putative ARE motifs are required for androgen-stimulated MMP-2 expression. Most importantly, the androgen receptor （AR） interacted with both motif-containing promoter regions in vivo in a chromatin immunoprecipitation assay after androgen treatment. Furthermore, the AR specifically bound to the wild-type but not mutated ARE motifs-containing probes in an in vitro EMSA assay. Conclusion： Two ARE motifs were identified to be responsible for androgen-induced MMP-2 expression in prostate cancer cells.

基体匹配-电感耦合等离子体原子发射光谱(ICP-AES)法测定砂岩型铀矿中的铀硅等主量元素

砂岩型铀矿样品按传统石墨坩埚碱熔方法,受坩埚和熔剂的影响,熔融物容易在坩埚内壁粘附,很难完全将熔融物导出溶解定容,致使检测结果偏低,且过程复杂冗长。选择无水偏硼酸锂为熔剂,石墨坩埚内铺垫石墨粉于马弗炉内1000℃熔融样品20 min,超声溶解制备砂岩型铀矿样品溶液,采用三通进样,并对标准溶液系列进行基体匹配绘制校准曲线,测定了样品中U、Si等主量元素。优化了样品熔融时间、温度、偏硼酸锂用量等条件,三通进样考察了共存待测主量元素硅对其他元素的影响,采用基体匹配法消除基体影响,确定元素分析谱线,对砂岩型铀矿国家标准物质及实际样品进行测定,各元素测定结果与标准值相符,相对偏差RE在-3.0%~2.8%,方法精密度RSD在1.2%~3.2%,样品加标回收率在97.3%~104%,方法检出限为0.60~51.69μg/g,满足分析测试要求,为砂岩型铀矿元素的分析检测提供了测量范围宽、快速、准确的检测方法。

Novel high-performance element in the electromagnetic finite-element method——node-edge element

It is known in the computational electromagnetics （CEM） that the node element has a relative wellconditioned matrix, but suffers from the spurious solution problem; whereas the edge element has no spurious solutions, but usually produces an ill-conditioned matrix. Particularly, when the mesh is over dense, the iterative solution of the matrix equation from edge element converges very slowly. Based on the node element and edge element, a node-edge element is presented, which has no spurious solutions and better-conditioned matrix. Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.

A New Classification Method of Stress Modes in Hybrid Stress Finite Element

The paper presents a new method for classifying the stress modes in hybrid stress finite element in terms of natural stress modes in finite element and the rank analysis of matrix G in forming element It reveals the relation among the different assumed stress field, and gives the general method in forming stress field Comparing with the method of eigenvalue analysis, the new method is more efficient

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.

A NEW HIGH PERFORMANCE SPARSE STATIC SOLVER IN FINITE ELEMENT ANALYSIS WITH LOOP-UNROLLING

In the previous papers, a high performance sparse static solver with two-level unrolling based on a cell-sparse storage scheme was reported. Although the solver reaches quite a high efficiency for a big percentage of finite element analysis benchmark tests, the MFLOPS （million floating operations per second） of LDL^T factorization of benchmark tests vary on a Dell Pentium IV 850 MHz machine from 100 to 456 depending on the average size of the super-equations, i.e., on the average depth of unrolling. In this paper, a new sparse static solver with two-level unrolling that employs the concept of master-equations and searches for an appropriate depths of unrolling is proposed. The new solver provides higher MFLOPS for LDL^T factorization of benchmark tests, and therefore speeds up the solution process.