用反正切函数的级数计算圆周率π的研究

从arctanc=arctana+arctanb和arctanx的级数展开式出发,对圆周率π可以推导出许多计算公式,并可设计出计算软件.基于此软件,可验证现有公式的正确性,找出现有公式的失误,并推导出收敛效率更高的计算公式.

多组份稀土体系串级萃取分离理论级数计算公式

对多组份串级萃取理论级数计算公式进行了研究,并推导出多组份串级萃取理论级数计算公式。在多组份的组份数减少到两组份时,级数计算公式可还原成两组份级数计算公式,说明本文推导出的多组份串级萃取理论级数计算公式是正确的。

迷宫式蒸汽调节阀的级数计算方法研究

结合流体力学和热力学理论分析了蒸汽通过迷宫式调节阀的节流过程,推导出了适用于蒸汽工况的级数理论计算公式,并采用数值模拟方法分析了扩张系数和串并联结构对迷宫流道的级数计算及内部流动的影响规律。研究结果表明:在相同工况下,扩张系数越小,需要的级数越多;级数越多,压降曲线越平稳、平均流速越小、过热度越高,即节流过程越安全;在级数满足降压需要的条件下,串并联结构能有效降低迷宫流道的出口动能和马赫数。采用本文推导的理论公式计算得到的级数与实际值接近,且该公式对串联和串并联结构的迷宫流道均适用,可为迷宫式蒸汽调节阀设计过程中的级数计算提供参考。

关于一个函数级数计算的优化

本文对于高等数学中一个级数计算中的收敛速度进行讨论 ,采用了优化计算方法 ,并给出计算机程序。

两种修正的Gauss级数序列及其它的收敛性

文章先构造级数计算的两种修正的G auss序列,并研究了修正格式的收敛性及应用等问题。

小学音乐教师专业素质现状分析与思考

随着基础教育课程改革的不断深入,各地的基础音乐教学也取得了显著的成绩,但由于学科的特殊性,还有不少地区,甚至有些经济比较发达的地区,仍存在音乐教师师资配备不足的情况,这是违背教育行政部门规定的课程计划和课程标准的。教师是实施课改的关键,若按一所小学20个班级数计算,此校每周的音乐课应在40节以上,再按一名音乐教师周任课节数14-16节计算,那么这所小学应配置3名或以上的音乐教师。但是由于种种原因,师资配备严重不足。

关于经济指标术语的运用

关于经济指标术语的运用仉立位数字是经济分析的一个重要依据，它对记载历史的一个阶段、反映客观现实、预测未来等方面起着重要的作用。表达经济现象或经济实质要靠正确的数字来说话。这就要求在把好数字来源关的同时，还应把好数字的正确运用。任何一个数字都不是孤立的...

Electronic States of a Shallow Hydrogenic Donor Impurity in Different Shaped Semiconductor Quantum Wells

The shallow hydrogenic donor impurity states in square, V-shaped, and parabolic quantum wells are studied in the framework of effective-mass envelope-function theory using the plane wave basis. The first four impurity energy levels and binding energy of the ground state are more easily calculated than with the variation method. The calculation results indicate that impurity energy levels decrease with the increase of the well width and decrease quickly when the well width is small. The binding energy of the ground state increases until it reaches a maximum value, and then decreases as the well width increases. The results are meaningful and can be widely applied in the design of various optoelectronie devices.

Numerical assessment on improving multistage centrifugal impeller performance by changing inlet skew angle at impeller inlet

Multistage centrifugal impellers with four different skew angles were investigated by using computational fluid dynamics.The purpose of this work is to investigate the influences of lean angle at the blade tip of the impeller inlet.Four variations of lean angles,that is,8°,10°,15° and 20°,were made at first stage impeller.Reynolds Average Navier Stokes equation was used in simulation together with a shear?stress transport(SST) k-w turbulence model and mixing-plane approach,respectively.Three dimensional fluid flows were simplified using periodic model to reduce the computational cost and time required.A good performance was expected that the secondary flow can be effectively reduced in the flow passage of the impeller without excessive increase in manufacturing cost caused by the secondary flow.The results show that secondary flow affects the main flow intricately to form vortices or having non-uniform velocity in the flow passage,which in turn results in substantial fluid energy loss not only in the impeller but also in the guide vane downstream of impeller.The numerical solutions were performed and allowed the optimum design and operating conditions to be obtained.

Design of a continuously variable Mach-number nozzle

A design method was developed to specify the profile of the continuously variable Mach-number nozzle for the supersonic wind tunnel. The controllable contour design technique was applied to obtaining the original nozzle profile, while other Machnumbers were derived from the transformation of the original profile. A design scheme, covering a Mach-number range of3.0<Ma<4.0, was shown to illustrate the present design technique. To fully validate the present design method, computational fluid dynamics(CFD) analyses were carried out to study the flow quality in the test area of the nozzle. The computed results indicate that exit uniform flow is obtained with 1.19% of the maximal Mach-number deviation at the nozzle exit. The present design method achieves the continuously variable Mach-number flow during a wind tunnel running.

Calculation of Infinite Series Through Polygamma Functions＇ Algorithms and Laplace Transforms

Here is introduced some novel algorithms which made use of polygarnma functions to get the exact limits of a broad class of infinite series. Moreover, Laplace transform is used to find the sum of many convergent infinite series. These exact limits are found in different branches of physics for some special cases series and are in complete agreement with the values found by other authors. Moreover, the methods presented here are generalized and applied to other wide variety of sums, including alternating series. Finally, these methods are simple and quite powerful to calculate the limits of many convergent series as you can see from the examples included.

Fast Multilevel CVT-Based Adaptive Data Visualization Algorithm

Efficient data visualization techniques are critical for many scientific applications. Centroidal Voronoi tessellation(CVT) based algorithms offer a convenient vehicle for performing image analysis,segmentation and compression while allowing to optimize retained image quality with respect to a given metric.In experimental science with data counts following Poisson distributions,several CVT-based data tessellation algorithms have been recently developed.Although they surpass their predecessors in robustness and quality of reconstructed data,time consumption remains to be an issue due to heavy utilization of the slowly converging Lloyd iteration.This paper discusses one possible approach to accelerating data visualization algorithms.It relies on a multidimensional generalization of the optimization based multilevel algorithm for the numerical computation of the CVTs introduced in[1],where a rigorous proof of its uniform convergence has been presented in 1-dimensional setting.The multidimensional implementation employs barycentric coordinate based interpolation and maximal independent set coarsening procedures.It is shown that when coupled with bin accretion algorithm accounting for the discrete nature of the data,the algorithm outperforms Lloyd-based schemes and preserves uniform convergence with respect to the problem size.Although numerical demonstrations provided are limited to spectroscopy data analysis,the method has a context-independent setup and can potentially deliver significant speedup to other scientific and engineering applications.

On Computation Formula for a Series

It is one of the most interesting problems in number theory to compute someespecial series by using Zeta and Gamma functions, and results have been obtained for someespecial series. In this paper, we give an important formula which is proved also by usingZeta and Gamma functions.

Active earth pressure acting on retaining wall considering anisotropic seepage effect

This paper presents a general solution for active earth pressure acting on a vertical retaining wall with a drainage system along the soil-structure interface. The backfill has a horizontal surface and is composed of cohesionless and fully saturated sand with anisotropic permeability along the vertical and horizontal directions. The extremely unfavourable seepage flow on the back of the retaining wall due to heavy rainfall or other causes will dramatically increase the active earth pressure acting on the retaining walls, increasing the probability of instability. In this paper, an analytical solution to the Laplace differential governing equation is presented for seepage problems considering anisotropic permeability based on Fourier series expansion method. A good correlation is observed between this and the seepage forces along a planar surface generated via finite element analysis. The active earth pressure is calculated using Coulomb's earth pressure theory based on the calculated pore water pressures. The obtained solutions can be degenerated into Coulomb's formula when no seepage exists in the backfill. A parametric study on the influence of the degree of anisotropy in seepage flow on the distribution of active earth pressure behind the wall is conducted by varying ratios of permeability coefficients in the vertical and horizontal directions,showing that anisotropic seepage flow has a prominent impact on active earth pressure distribution. Other factors such as effective internal friction angle of soils and soil/wall friction conditions are also considered.

On the Gibbs Phenomenon of Fourier Series of a Classical Function

In this paper,we point out that the Fourier series of a classical function∑^∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of zero.Furthermore,we estimate the upper bound of its partial sum and get：sup n≥1｜｜∑^n k=1sin kx/k｜｜=∫^x 0sin x/x dx=1.85194, which is better than that in[1].

High performance computing of DGDFT for tens of thousands of atoms using millions of cores on Sunway TaihuLight

High performance computing(HPC)is a powerful tool to accelerate the Kohn–Sham density functional theory(KS-DFT)calculations on modern heterogeneous supercomputers.Here,we describe a massively parallel implementation of discontinuous Galerkin density functional theory(DGDFT)method on the Sunway Taihu Light supercomputer.The DGDFT method uses the adaptive local basis(ALB)functions generated on-the-fly during the self-consistent field(SCF)iteration to solve the KS equations with high precision comparable to plane-wave basis set.In particular,the DGDFT method adopts a two-level parallelization strategy that deals with various types of data distribution,task scheduling,and data communication schemes,and combines with the master–slave multi-thread heterogeneous parallelism of SW26010 processor,resulting in large-scale HPC KS-DFT calculations on the Sunway Taihu Light supercomputer.We show that the DGDFT method can scale up to 8,519,680 processing cores(131,072 core groups)on the Sunway Taihu Light supercomputer for studying the electronic structures of twodimensional(2 D)metallic graphene systems that contain tens of thousands of carbon atoms.

A Barban-Davenport-Halberstam theorem for integers with fixed number of prime divisors

The purpose of this paper is to study the distribution of integers with a given number prime divisors over arithmetic progressions,via using the large-sieve inequality,Huxley-Hooley contour and the zero-density estimate,and present a Barban-Davenport-Halberstam type theorem for it.

Numerical simulation of leading edge cavitation within the whole flow passage of a centrifugal pump

In this paper, the periodically unsteady pressure field and head-drop phenomenon caused by leading edge cavitation have been investigated numerically by computational fluid dynamics （CFD） in a single stage centrifugal pump. A CFD model for cavita- tion steady and unsteady simulation has been calculated using the κ-ω SST turbulence model combining with a multiphase ap- proach, based on a homogeneous model assumption. A truncated form of Rayleigh-Plesset equation is used as a source term for the inter-phase mass transfer. The CFD computational region includes the suction cone, impeller, side chambers and volute, as well as suction and pressure pipes. The results were compared with experimental data under non-cavitation and cavitation conditions and a good agreement was obtained for the global performance, the experimental data of the head and the efficiency are 34.04 m and 74.42% at BEP, respectively, the predicted head is 34.31 m and the predicted efficiency is 73.75%. The analy- sis of inner flow pattern shows that the vortex flow generation in the rear of cavity region is the main reason of the head-drop. Obvious increasing can be observed for the amplitude of the pressure fluctuation at the blade passing frequency with different cavitation situations, and subpeak can be found. Besides, the effects of unsteady flow in the side chambers cannot be neglected for accurately predicting the inner flow of the pump. These results imply that this numerical method is suitable for the cavitat- ing flow in the pump.

Positron Characteristics in Cadmium and Zinc Chalcogenides

Electron energy levels and positron states have been calculated for cadmium and zinc chalcogenide compounds within the pseudo-potential approach and the independent particle model.Furthermore,the present contribution deals with the electron and positron chemical potentials allowing the calculation of the positron affinity to different materials of interest and hetero-structures formed by these materials.Besides,we here determine the positron diffusion constant by means of the positron deformation potential.An attempt has been made to scale positron affinity and diffusion constant with the lattice constant and the band gap energy,respectively.Such scaling is found to be not possible.The information gathered by the present study is of prime importance for a better understanding of positron trapping at interfaces and precipitates and should be useful in slow positron beam experiments.