FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.

Secondary Nonlinear Stability of General Linear Methods for Stiff Initial Value Problems

In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.

General displacement arch-cantilever element method for stress analysis of arch dam

Based on the general displacement method and the basic hypothesis of the trial load method, a new advanced trial load method, the general displacement arch-cantilever element method, was proposed to derive the transformation relation of displacements and loads between the surface nodes and middle plane nodes. This method considers the nodes on upstream and downstream surfaces of the arch dam to be exit nodes （master nodes）, and the middle plane nodes to be slave nodes. According to the derived displacement and load transformation matrices, the equilibrium equation treating the displacement of middle plane nodes as a basic unknown variable is transformed into one that treats the displacement of upstream and downstream nodes as a basic unknown variable. Because the surface nodes have only three degrees of freedom （DOF）, this method can be directly coupled with the finite element method （FEM）, which is used for foundation simulation to analyze the stress of the arch dam with consideration of dam-foundation interaction. Moreover, using the FEM, the nodal load of the arch dam can be easily obtained. Case studies of a typical cylindrical arch dam and the Wudongde arch dam demonstrate the robustness and feasibility of the proposed method.

APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.

Application Research of Sonar Detection Method in Melting Exploration at the Bottom of Piles

Karst landforms are widely distributed in China,and are most common in Yunnan,Guizhou and Guangxi.If the development of karst caves at the bottom of the piles cannot be accurately ascertained before the construction of bridge pile foundations,accidents such as hole collapse,slurry leakage,and drill sticking will easily occur.In this paper,the principle and method of sonar detection for detecting karst caves at the bottom of bridge piles was introduced,and the sonar detection data and the cave situation at the bottom of the pile during the construction process in combination with the case of Yunnan Zhenguo Highway Project was analyzed,which verifies the practicability and reliability of sonar detection method reliability.

Strong Stability Preserving IMEX Methods for Partitioned Systems of Differential Equations

We investigate strong stability preserving(SSP)implicit-explicit(IMEX)methods for partitioned systems of differential equations with stiff and nonstiff subsystems.Conditions for order p and stage order q=p are derived,and characterization of SSP IMEX methods is provided following the recent work by Spijker.Stability properties of these methods with respect to the decoupled linear system with a complex parameter,and a coupled linear system with real parameters are also investigated.Examples of methods up to the order p=4 and stage order q—p are provided.Numerical examples on six partitioned test systems confirm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration,and they are also suitable for preserving the accuracy in the stiff limit or preserving the positivity of the numerical solution for large stepsizes.

The correlations among variability,optical peak time and spectral time lag of long gamma-ray bursts

Statistical relations are useful tools to comprehend the intrinsic physics processes of gamma-ray bursts(GRBs). In this work we collect spectral lag(τ), variability(V) and optical peak time(tp,o). We find that there is a correlation between variabilities and spectral lags, reading as V =-0.0075(±0.0007) ×log10τ +0.0351(±0.0024). There may also exist a relatively weak positive tendency between GRBs optical band peak times and their spectral time lags. Its Pearson coefficient is 0.398, which indicates a weak linear correlation. If we contain some "negative spectral lag" samples, then the latter relation would be worse due to two outlying points. The τ-V relation is consistent with previous studies, and the positive trend betweenτ and tp,oindicates the spectral lag of GRB might be caused by the curvature effect, but this conclusion is not significant.

Discussing Professor Zhang Xiaofeng’s clinical experience in the diagnosis and treatment of menorrhagia by “Tongfa”

Through the understanding,identification and treatment of menorrhagia,summarizing professor Zhang Xiaofeng’s clinical experience in the treatment of menorrhagia,focusing on the identification of evidence,using“Tong”as the application,and treating in stages,he prepared Tongjing and Blood Regulating Soup and Tiaoping Tang as the basis for addition and subtraction,to harmonize the organs,qi and blood,Chong Ren and Uterus,in order to restore the balance of yin and yang and the function of Uterus in hiding and diarrhea.

匈牙利方法在运输问题初始优化解上的推广

介绍了一种将求解指派问题的匈牙利法推广到求解一般运输问题的方法 。

ON THE SOLVABILITY OF GENERAL LINEAR METHODS FOR DISSIPATIVE DYNAMICAL SYSTEMS

The main purpose of the present paper is to examine the existence and local uniqueness of solutions of the implicit equations arising in the application of a weakly algebraically stable general linear methods to dissipative dynamical systems, and to extend the existing relevant results of Runge-Kutta methods by Humphries and Stuart(1994). [ABSTRACT FROM AUTHOR]

Extension of the rotating dipole model with oblateness of both primaries

A rotating mass dipole can be used to understand the dynamical behaviors around elongated asteroids as well as binary asteroids. In this paper an improved dipole model with oblateness in both primaries is investigated. The dynamical equations of a particle around the improved model are first derived by introducing the oblateness coefficients. The characteristic equations of equilibrium points are obtained, resulting in the emergence of new equilibria in the equatorial plane and the plane xoz de- pending on the shape of the spheroid. Numerical simulations are performed to illustrate the distribution of these equilibrium points. Significant influence from the oblateness of the primaries on the topological structure is also analyzed via zero-velocity curves.

Two Novel Approaches for Photometric Redshift Estimation based on SDSS and 2MASS

We investigate two training-set methods; support vector machines （SVMs） and Kernel Regression （KR） for photometric redshift estimation with the data from the databases of Sloan Digital Sky Survey Data Release 5 and Two Micron All Sky Survey. We probe the performances of SVMs and KR for different input patterns. Our experiments show that with more parameters considered, the accuracy does not always increase, and only when appropriate parameters are chosen, the accuracy can improve. For different approaches, the best input pattern is different. With different parameters as input, the optimal bandwidth is dissimilar for KR. The rms errors of photometric redshifts based on SVM and KR methods are less than 0.03 and 0.02, respectively. Strengths and weaknesses of the two approaches are summarized. Compared to other methods of estimating photometric redshifts, they show their superiorities, especially KR, in terms of accuracy.

Discovery of Three Large HII Regions in the Galactic Plane

We discovered three large HⅡ regions： G148.8＋2.3, G149.5＋0.0 and G169.9＋2.0 in the Sino-German A6 cm polarization survey of the Galactic plane. They have been identified based on the flat spectral indexes and the strong infrared emission properties.

Trailing (L5) Neptune Trojans: 2004 KV18 and 2008 LC18

The population of Neptune Trojans is believed to be bigger than that of Jupiter Trojans and that of asteroids in the main belt, although only eight members of this distant asteroid swarm have been observed up to now. Six leading Neptune Trojans around the Lagrange point L4 discovered earlier have been studied in detail, but two trailing ones found recently around the L5 point, 2004 KV18 and 2008 LC18, have not yet been investigated. We report our investigations on the dynamical behaviors of these two new Neptune Trojans. Our calculations show that the asteroid 2004 KV18 is a temporary Neptune Trojan. Most probably, it was captured into the trailing Trojan cloud no earlier than 2.03 ×105 yr ago, and it will not maintain this position later than 1.65 × 105 yr in the future. Based on the statistics from our orbital simulations, we ar- gue that this object is more like a scattered Kuiper belt object. By contrast, the orbit of 2008 LC18 is much more stable. Among the clone orbits spreading within the orbital uncertainties, a considerable portion of clones may survive on the L5 tadpole orbits for 4 Gyr. The strong dependence of the stability on the semimajor axis and resonant angle suggests that further observations are badly required to constrain the orbit in the stable region. We also discuss the implications of the existence and dynamics of these two trailing Trojans over the history of the solar system.

A Statistical Analysis of Radio Pulsar Timing Noise

We present an analysis of the timing observations on 27 radio pulsars, collected at Hartebeesthoek Radio Astronomy Observatory （HartRAO）, with time spans ranging between - 9 and 14yr. Our results show that the measured pulsar frequency second derivatives are non-stationary. Both the magnitude and the sign of the v values depend upon the choice of epoch and data span. A simple statistical analysis of the observed second time derivative of the pulse frequency （v obs） of a large sample of 391 （25 HartRAO and 366 Jodrell Bank Observatory）. pulsars reveals that v is only marginally correlated with both the pulsar spindown rate （P） and the characteristic age （τc）. We find correlation coefficients of ,- 0.20 and -0.30 between the measured braking indices and, respectively,P and τc. This result reaffirms earlier conclusions that the braking indices of most radio pulsars, obtained through the standard timing technique, are strongly dominated by sustained random fluctuations in the observed pulse phase.

Not enough evidence to support the correlation between gamma-ray bursts and foreground galaxy clusters in the Swift Era

The correlation between distant Gamma-Ray Bursts （GRBs） and foreground galaxy clusters is re-examined by using the well localized （with an accuracy down to a few arcsec） Swift/XRT GRBs. The galaxy clusters are compiled from both the X-ray selected ROSAT brightest cluster sample （BCS） and the BCS extension by requiring δ ≥ 0° and b ≥ 20°. The Swift/XRT GRBs fulfilling the above selection criteria are cross-correlated with the clusters. Both Nearest-Neighbor analysis and the angular two-point cross-correlation function show that there is not enough evidence supporting the correlation between the GRBs and foreground clusters. We suggest that the non-correlation is probably related to the GRB number-flux relation slope.

QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS

Focuses on a study which presented some invariants and conservation laws of general linear methods applied to differential equation systems. Information on the quadratic invariants; Conservation of symplectic structure; Details on the multiple Runge-Kutta methods; Equations of the one-leg methods.

Fe Kα line profile in AGNs: average shape and redshift dependence

We collect a sample of 381 （271 type Ⅰ） active galactic nuclei （AGNs） with XMM-Newton observations for an analysis of the dependence of Fe Kα profiles on redshifts to test the potential cosmological evolution of spins of supermassive black holes （SMBHs）. The sample spans a redshift range of z = 0.0008 - 4.76, which allows us to rebin the sample into 7 redshift groups. Phenomenological analysis of the Fe profile suggested that the line width （δ） of the narrow or broad Fe line does not show significant changes in redshift range z 〈 0.3. Using a physical model, we significantly detect a narrow Fe Kα line at 6.4 keV with an average equivalent width （EW） = 160 eV except for the two largest redshift bins. The EW of the Fe line does not show significant changes. We also find a relativistic broad line in three redshift bins （z 〈 0.116, 0.056 〈 z 〈 0.12 and 0.12 〈 z 〈 0.3）with an average EW = 522eV.

Well-posedness of two-phase local/nonlocal integral polar models for consistent axisymmetric bending of circular microplates

Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.

On the consistency of two-phase local/nonlocal piezoelectric integral model

In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.