A formula of two-partition Hodge integrals

Motivated by the Mariño-Vafa formula of Hodge integrals and physicists' predictions on local Gromov-Witten invariants of toric Fano surfaces in a Calabi-Yau threefold, the third author conjectured a formula of certain Hodge integrals in terms of certain Chern-Simons invariants of the Hopf link. We prove this formula by virtual localization on moduli spaces of relative stable morphisms.

     

Integrating streaming and file-transfer Internet traffic: fluid and diffusion approximations

We study the behavior of a communication link that divides its capacity fairly among file transfers and streaming flows. We identify appropriate asymptotic regimes and obtain fluid and diffusion limits. The non-trivial, yet tractable, limits can be used for performance analysis and policy design. Furthermore, the scalings used to obtain these limits are themselves of interest and help explain phenomena observed in previous simulation studies.      

Dynamic model of a flying manipulator with two highly flexible links

Nonlinear dynamic model of a flying manipulator with two revolute joints and two highly flexible links is obtained using Hamilton’s principle. Flying base of the manipulator is a rigid body. Stress is treated three dimensionally in the isotropic linearly-elastic links, but the in-plane and out-of-plane warpings of the links’ cross-sections are neglected. Although the links’ cross-sections undergo negligible elastic orientation, their models are more accurate than a nonlinear 3D Euler–Bernoulli beam. Tension, compression, twisting and spatial deflections of each link are coupled to each other by some nonlinear terms including two new ones. In the issue of flying flexible-link manipulators new terminologies, namely forward/inverse kinetics instead of forward/inverse kinematics are suggested, since determination of position and orientation of the end-effector is coupled to the partial differential motion equations.     

Estimation of trace elements in water matrix from photon attenuation coefficients

The method of elemental analysis based on the measurement of attenuation coefficient has been used to estimate the impurity introduced in a water matrix using a scintillation detector with a single channel analyser. For a 2% change in the mass attenuation coefficient the minimum detectable fractions of impurities were estimated to be of the order of 625–1250 μg/g for uranium and thorium compounds at photon energies 32.1 and 59.5 keV.     

利用TOF的Q值进行粒子鉴别的研究

飞行时间计数器(TOF)是北京谱仪(BESⅡ)中用于粒子鉴别的重要子探测器. 当带电粒子击中TOF时，闪烁计数器同时测量粒子的飞行时间T和脉冲幅度Q. 本文利用BESⅡ采集的双m事例，对脉冲幅度Q进行了研究. 利用J/ψ强子事例样本，给出了脉冲幅度最可几值Qmp随粒子bg值的变化关系. 这表明可以利用TOF测量的脉冲幅度Q值实现对粒子的鉴别. 最后给出用脉冲幅度Q进行粒子鉴别的效率和误判率.     

Numerical solution of boundary integral equations by means of attenuation factors

We consider first-kind boundary integral equations with logarithmickernel such as those arising from solving Dirichlet problemsfor the Laplace equation by means of single-layer potentials.The first-kind equations are transformed into equivalent equationsof the second kind which contain the conjugation operator andwhich are then solved with a degenerate-kernel method basedon Fourier analysis and attenuation factors. The approximationswe consider, among them spline interpolants, are linear andtranslation invariant. In view of the particularly small kernel,the linear systems resulting from the discretization can besolved directly by fixed-point iteration.     

Analysis of π-mode Stopband in an Asymmetric Millimeter-Wave Helical Slow-Wave Structure

A simple closed form formula for the estimation of π-mode stopband in an azimuthally asymmetric helical slow-wave structure (SWS) was developed following coupled-mode analysis of multiple reflections of the degenerate space-harmonic modes from the support rod discontinuities. The method incorporates the effects of circuit loss, and accrues the accuracy of 3D electromagnetic analysis by allowing the use of dispersion characteristics obtainable from any standard electromagnetic modeling. The formula is simple and amenable to easy computation, even using a scientific calculator, and without resorting to exhaustive and time-intensive numerical computation, and at the same time, without sacrificing the accuracy in results. The analysis was benchmarked against published results and excellent agreement observed. The analysis was further used for demonstrating the stopband phenomenon for a typical millimeter-wave helical slow-wave structure. Compared to low frequency structures, the stopband phenomenon for a millimeter-wave structure was found to be more pronounced, and an interesting inference was drawn as to how asymmetry induced stopband might be made to advantage in combating π-mode instabilities in a millimeter-wave traveling-wave tube.     

Mathematical simulation of a seven link biped robot on various surfaces and ZMP considerations

In recent years, numerous researches have been done based on simulation of legged mechanism, especially on biped robots simulation and control. The following article focuses on the biped robot simulation and control over various manners such as horizontal, ascending and descending surfaces with the aid of mathematical modeling methods (in MATLAB/SIMULINK environment). Similar parameters to human walking process will be obtained such as ZMP and joint’s actuator torques. The mathematical simulation has been used to interpolate trajectory of the robot path with the given break points. Of course, after the robot’s path determination, third-order spline method will be used because of the very high precision and ability to calculate the kinematic and dynamic parameters. With the aid of this program, common parameters such as linear and angular velocity and acceleration, joint’s angles and inertial forces for the given specifications and conditions (Nominal, no disturbances) will be calculated and simulated. Also, the two types of ZMP (Fixed and moving) have been considered and calculated with the aid of the software.     

Formulation of spectra-based attenuation coefficients in water as a function of depth and off-axis distance for 4, 10 and 15 MV X-ray beams

On the basis of X-ray spectra information for 4, 10 and 15 MV X-rays from a linear accelerator, we propose a method for formulating the attenuation coefficient in water as a function of depth and off-axis distance. It was confirmed by transmission measurement that the formulation provides a good estimation of the attenuation coefficient in water. Using the formulation, we further assessed the effective attenuation coefficient in water as a function of off-axis distance.     

LaCoO3中自旋态转变现象的超声研究

测量了LaCoO₃单相多晶样品的纵波与横波超声声速和衰减随温度的变化关系, 在材料的自 旋态转变温度附近（≈90K），纵波声速出现明显的软化并伴随一个尖锐的衰减峰，但是在 横波的测量中却没有出现类似的超声异常，分析认为LaCoO₃在90K附近的自旋态 转变是由于Co³⁺离子是从低自旋态(LS,t⁶_2ge⁰ _g)转变到中等自旋态(IS,t⁵ _2ge¹_g )，而不是高等自旋态(HS,t⁴_2ge²_g).随着温度的升高，在 200K附近纵波和横波测量上都观察到一个伴随着微小声速软化的宽大的衰减峰，这可能是随 机分布的IS态Co³⁺离子的Jahn-Teller效应导致的局域晶格扭曲所造成的. 关键词： 超声声速与衰减 自旋态转变 Jahn-Teller效应