finite

摘要： Arriving at the Seismo Lab in 1981,1 first worked with Hiroo Kanamori on the seismotectonics of the New Hebrides(Vidale and Kanamori,1983)(I don’t remember why).Then with Rob Clayton I worked on finite-difference methods of modeling seismic waves,specifically how to bump second-order methods to fourth-order and encode the inner loop in assembly language to make it run twice as fast(Vidale,1990).

摘要： Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied sciences. This review article will reveal some of these applications and will reflect the beauty behind their uses in calculating roots of real numbers, getting solutions of algebraic Equations of the second degree, and their uses in solving special ordinary differential Equations such as Legendre, Hermite, and Laguerre Equations;moreover and most important, their use in physics in solving Schrodinger Equation for a certain potential. A comparison will also be given between the results obtained via continued fractions and those obtained through the use of well-known numerical methods. Advances in the subject will be discussed at the end of this review article.

摘要： Considered here is a plasma grating generated by two counterpropagating short laser pulses. Because of the shortness of the laser pulses, theplasma dynamics are determined by only electrons, which respond to the ponderomotive pressure generated by the interacting laser fields.An electron grating cannot exist for longer than the inverse ion plasma frequency, and so because of the limited time of the ponderomotivepressure, both the life time and spatial extent of an electron grating are finite. When one of the short laser pulses is circularly polarized(propagating in the x direction with electric field vectors in the yz plane) and the other is linearly y-polarized, the electron grating is producedby the y components. Meanwhile, the z component is partially reflected, and only a fraction of it is transmitted. Thus, the finite plasmagrating can either alter the polarization of the yz-polarized pulse or act as a pulse splitter. The present paper is focused on the reflection andtransmission rates. The action of the density grating on the z component cannot be explained by the Bloch wave theory for infinite crystals,and instead a theory is developed based on four-wave mixing, which explains the transmission and reflection of the z component wheninteracting with a grating of finite extent.

摘要： Dear editor,This letter identifies two weaknesses of state-of-the-art k-winnerstake-all(k-WTA)models based on recurrent neural networks(RNNs)when considering time-dependent inputs,i.e.,the lagging error and the infeasibility in finite-time convergence based on the Lipschitz continuity.

摘要： Dear editor,Recently, finite-time consensus of multi-agent systems has attracted extensive attention of many researchers due to its wide application in physics, biology, and control engineering.Cortés [1] provided a signed gradient descent algorithm that can be used to solve the consensus of multi-agent systems with undirected connected topology in finite time.

摘要： A finite dimensional proof of the Verlinde formula Xiaotao Sun Mingshuo & Zhou Abstract We prove two recurrence relations among dimensions。

摘要： The presented article shows an estimation method of optimum autofrettage pressure taking into consideration subsequent cyclic loading. An autofrettage process is used in pressure vessel applications for strength improvement. The process relies on applying massive pressure that causes internal portions of the part to yield plastically, resulting in internal compressive residual stresses when pressure is released. Later applied working pressure (much lower than autofrettage pressure) creates stress reduced by the residual compressive stress improving the structural performance of the pressure vessels. The optimum autofrettage pressure is a load that maximizes the fatigue life of the structure at the working load. The estimation method of that pressure of a hydrogen valve is the subject of the presented work. Finite element and fatigue analyses were employed to investigate the presented problem. An automated model was developed to analyze the design for various autofrettage pressures. As the results of the procedure, the optimum autofrettage pressure is determined. The research has shown that the developed method can profitably investigate the complex parts giving the autofrettage load that maximizes the fatigue life. The findings suggest that the technique can be applied to a large group of products subjected to the autofrettage process.

摘要： The objective of this research is to study the dynamic response characteristics of a three-beam system with intermediate elastic connections under a moving load/mass-spring.In this study,the finite Sine-Fourier transform was performed for the dynamic partial differential equations of a simply supported three-beam system(SSTBS)under a moving load and a moving mass-spring,respectively.The dynamic partial differential equations were transformed into dynamic ordinary differential equations relative to the time coordinates,and the equations were solved and the displacement Fourier amplitude spectral expressions were obtained.Finally,based on finite Sine-Fourier inverse transform,the expressions for dynamic response of SSTBS under the moving load and moving mass-spring were obtained.The proposed method,along with ANSYS,was used to calculate the dynamic response of the SSTBS under a moving load/mass-spring at different speeds.The results obtained herein were consistent with the ANSYS numerical calculation results,verifying the accuracy of the proposed method.The influence of the load/mass-spring’s moving speed on the dynamic deflections of SSTBS were analyzed.SSTBS has several critical speeds under a moving load/mass-spring.The vertical acceleration incurred by a change in the vertical speed of SSTBS due to the movement of mass-spring and the centrifugal acceleration produced by the movement of massspring on the vertical curve generated by SSTBS vibration could not be neglected.

摘要： A finite element method(FEM) is proposed to solve second elliptic problems posted in domains with rough boundaries. We also present an FEM for elliptic problems as an extension of the original method. The optimal error estimates in the energy norm are also proved. Numerical results for second elliptic equations in regular and rough domains are presented to illustrate the efficiency of our method, respectively, which is consistent with theoretical analysis.