毕的斯克斯关于sin 1°数值解研究

自托勒密(Ptolemy,约90-168)时代开始,sin 1°精确值与弦表的整体精度相关,波斯数学家阿尔·卡西(Jamshīd Mas’ūd al-K shī,约1380-1429)在这一问题上首先取得突破性成就.该问题同样困扰着16世纪多位欧洲数学家,德国数学家毕的斯克斯(Bartholomaeus Pitiscus,1561-1613)最先有所建树.对毕的斯克斯求解sin 1°数值解法进行分析,并将其与卡西相关算法进行比较研究.

花烛属植物的核型分析

对花烛属植物3个栽培品种———斯克斯、亚美哥和瓦伦天奴的核型进行了分析。结果表明,斯克斯的核型为2n=2x=30=8m+18sm+4st,属2B型,亚美哥的核型为2n=2x=30=4m+20sm+6st,属3B型,瓦伦天奴的核型为2n=2x=30=8m+18sm+4st(2SAT),属3B型。

A simplified model for extreme-wave kinematics in deep sea

Based on the fifth-order Stokes regular wave theory, a simplified model for extreme-wave kinematics in deep sea was developed. In this model, from the wave records the average of two neighboring wave periods for the extreme crest or trough was defined as the period of the Stokes wave by the up and down zero-crossing methods. Then the input wave amplitude was deduced by substituting the wave period and extreme crest or trough into the expression for the fifth-order Stokes wave elevation. Thus the corresponding formula for the wave velocity can be used to describe kinematics beneath the extreme wave. By comparison with the published numerical models and experimental data, the proposed model is validated to be able to calculate the extreme wave velocity rather easily and accurately.

Nonequilibrium Statistical Physics Subject to the Anomalous Langevin Equation in Liouville Space

Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed as a fundamental equation of statistical physics. This equation reflects that the law of motion of particles obeying reversible, deterministic laws in dynamics becomes irreversible and stochastic in thermodynamics. From this the fundamental equations of nonequilibrium thermodynamics, the principle of entropy increase and the theorem of minimum entropy production have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation etc. have been derived rigorously from the kinetic kinetic equation which is reduced from the anomalous Langevin equation in Liouville space. All these are unified and self consistent. But it is difficult to prove that entropy production density σ can never be negative everywhere for all the isolated inhomogeneous systems far from equilibrium.

Observation of Excited vs（NO2） and Relaxation Process of HNS in Solution by CARS Technique

Investigation on vibrational excitation and relaxation process will provide important in- formation for a better understanding of ultrafast dynamic response of energetic materials. Using sub-ps time-resolved coherent anti-Stokes Raman scattering （CARS） experiments, we directly observe excitation of vibrational mode vs（NO2） and its relaxation process of ground state HNS （2,2＇,4,4＇,6,6＇-hexanitrostillbenein） in solution. The results show that vs（NO2） at 1385 cm-1 has been excited and relaxation time of 0.38 and 8.5 ps is obtained. The possible quantum beat frequencies are also discussed via fs-CARS experiments. The original results provide an insight into ultrafast process of energetic materials.

Polarization state measurement based on photoelastic modulation

Polarization coding is a specific encoding method by using the polarization state of optical signal carrying coded in- formation. It focuses on nonlinear effects, polarization mode dispersion and other issues in high-speed fiber-optic communi- cations. This paper presents a measurement method for polarization state based on elastic-optic modulator. This method not only retains the original advantages of elastic-optic modulator for polarization measurement, but also overcomes the defects of existing methods including high modulation frequency and invalid collection by using array detector. Matlab simulation and experimental verification scheme are given. The feasibility of this method is verified through theoretical analysis, and simulation and experimental results are carried out. The error analysis of the measurement results shows that the method can meet the measurement requirements and provide conditions for using the polarization encoding in high-speed communication.

Numerical Simulation of a Planing Vessel at High Speed

Planing vessels are applied widely in civil and military situations.Due to their high speed,the motion of planning vessels is complex.In order to predict the motion of planning vessels,it is important to analyze the hydrodynamic performance of planning vessels at high speeds.The computational fluid dynamic method（CFD） has been proposed to calculate hydrodynamic performance of planning vessels.However,in most traditional CFD approaches,model tests or empirical formulas are needed to obtain the running attitude of the planing vessels before calculation.This paper presents a new CFD method to calculate hydrodynamic forces of planing vessels.The numerical method was based on Reynolds-Averaged Navier-Stokes（RANS） equations.The volume of fluid（VOF） method and the six-degrees-of-freedom equation were applied.An effective process was introduced to solve the numerical divergence problem in numerical simulation.Compared with experimental results,numerical simulation results indicate that both the running attitude and hydrodynamic performance can be predicted well at high speeds.

Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

Traditional ligand-field theory has to be improved by taking into account both 'pure electronic' contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R1, R2, R'3, R'2, and R'1 lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG: Cr3+ as well as thermal shifts of GSZFS, R1 line and R2 line of ruby have been calculated.The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R1 line and R2 line of ruby, several conclusions have also been obtained.

Preconditioners for Incompressible Navier-Stokes Solvers

In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

Microscale deformation behavior of sandstone mineral particles based on XCT scanning

This work aimed to quantify the physical and mechanical behavior of three-dimensional microstructures in rocks under uniaxial compression.A high-precision in situ XCT(X-ray transmission computed tomography)technology was applied to investigating the behavior of mineral grains in sandstone:the movement,the rotation deformation,and the principal strains between fault zone and non-fault zone.The results indicate that after unloading,the shear strain of mineral grains is periodic in the radial direction,the strain of mineral grains in the fracture zone is about 30 times of the macro strain of the specimen,which is about 5 times in the non-fracture zone,and the shear strain near the fault zone is larger than the compressive strain,and there is the shear stress concentration feature.

The inextricable perplexity： Simple analysis on the theme of Ulysses

Joyce began his literary career with strong discontent with his social condition. Ulysses is Joyce＇s optimum work, which takes 3 Dublin characters＇ experience in one day as the main line to show the paralysation and crisis of the whole Western society, people＇s emptiness on their minds, loneliness on their feelings and labefaction on their spirits, also, it showed the inextricable perplexity. To treat the theme of inextricable perplexity, this paper is trying to set about the inextricable Catholic Church and identity problems, with the ideas of Alick West-the outstanding English Marxist literary critic of the 20th century.

General formulas for drag coefficient and settling velocity of sphere based on theoretical law

The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.

Turbulence Model Investigations on the Boundary Layer Flow with Adverse Pressure Gradients

In this paper, a numerical study of flow in the turbulence boundary layer with adverse and pressure gradients （APGs） is conducted by using Reynolds-averaged Navier-Stokes （RANS） equations. This research chooses six typical turbulence models, which are critical to the computing precision, and to evaluating the issue of APGs. Local frictional resistance coefficient is compared between numerical and experimental results. The same comparisons of dimensionless averaged velocity profiles are also performed. It is found that results generated by Wilcox （2006） k-co are most close to the experimental data. Meanwhile, turbulent quantities such as turbulent kinetic energy and Reynolds-stress are also studied.

Numerical Simulation of the Stokes Wave for the Flow around a Ship Hull Coupled with the VOF Model

The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method （FVM） is applied to solve Reynolds averaged Navier-Stokes （RANS） equation. The realizable k-e turbulence model has been implemented to capture turbulent flow around the ship hull in the free surface zone. The volume of fluid （VOF） method coupled with the Stokes wave theory has been used to determine the free surface effect of water. By using is a six degrees of freedom model, the ship hull＇s movement is numerically solved with the Stokes wave together. Under the action of Stokes waves on the sea, the interface between the air and water waves at the same regular pattem and so does the pressure and the vertical velocity. The ship hull moves in the same way as the wave. The amplitude of the ship hull＇s heave is less than the wave height because of the viscosity damping. This method could provide an important reference for the study of ships＇ movement, wave and hydrodynamics.

Femtosecond Stimulated Raman Line Shapes:Dependence on Resonance Conditions of Pump and Probe Pulses

Resonance enhancement has been increasingly employed in the emergent felntosecond stimu- lated Raman spectroscopy （FSRS） to selectively monitor molecular structure and dynamics with improved spectral and temporal resolutions and signal-to-noise ratios. Such joint eflforts by the technique- and application-oriented scientists and engineers have laid the foundation for exploiting the tunable FSRS methodology to investigate a great variety of photosensitive systems and elucidate the underlying functional mechanisms on molecular time scales. Dur- ing spectral analysis, peak line shapes remain a major concern with an intricate dependence on resonance conditions. Here, we present a comprehensive study of line shapes by tuning the Rarnan pump wavelength from red to blue side of the ground-state absorption band of the fluorescent dye rhodarnine 6G in solution. Distinct line shape patterns in Stokes and anti-Stokes FSRS as well as from the low to high-frequency modes highlight the competition between multiple third-order and higher-order nonlinear pathways, governed by difl^rent res- onance conditions achieved by Raman pump and probe pulses. In particular, the resonance condition of probe wavelength is revealed to play an important role in generating circular line shape changes through oppositely phased dispersion via hot luminescence （HL） pathways. Meanwhile, on-resonance conditions of the Rarnan pump could promote excited-state vibrational modes which are broadened and red-shifted from the coincident ground-state vibrational modes, posing challenges for spectral analysis. Certain strategies in tuning the Raman pump and probe to characteristic regions across an electronic transition band are discussed to improve the FSRS usability and versatility as a powerful structural dynamics toolset to advance chemical, physical, materials, and biological sciences.

A Note on Similarity Solutions of Navier-Stokes Equations

This note looks at the two similarity solutions of the Navier-Stokes equations in polar coordinates. In the second solution an initial value problem is reduced into generalized stationary KDV and hence integrable.

Effect of Bed Vicinity on Vortex Shedding and Force Coefficients of Fluid Flow on an Offshore Pipeline

The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×10^4.Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.

Finance Sector in Eurasian Economies During and After the Global Crisis in 2008

As in the other countries around the world, banking systems in Eurasian economies, comprised of Armenia, Azerbaijan, Georgia, Kazakhstan, the Kyrgyz Republic, Tajikistan, Turkmenistan and Uzbekistan, were adversely affected by the 2008 global crisis. A common challenge across most economies is to revive private-sector credit growth. Compared with the high increases of 80 percent in the period immediately prior to the crisis, credit growth has slowed sharply and even turned negative in real terms in a number of economies. Governments in many countries have taken measures to address banking sector stress. The measures for restoring credit growth and thus a high economic growth will be discussed in a part of our work. In the short run, such measures include aiding banks to repair balance sheets and also providing liquidity. In the medium term, measures should promote de-dollarization and the development of local debt markets.

Prediction of Transverse Permeability for Unidirectional Fiber Tows Based on the Homogenization Theory

The transverse permeability of unidirectional fiber tows is calculated using homogenization method.Each fiber tow consisting of 21 filaments is arranged in uniform square packing.Stokes governing equation is analogized with Lame equation used in the linear elasticity problem and is solved by the finite element code ANSYS.The prediction for transverse permeability of unidirectional fiber obtained by the homogenization approach is compared with other analytical methods.The result shows a good agreement with Kozeny-Carman equation and Gebart square packing model.A model for nonuniform fiber distribution and measurement technology are proposed.It can be found that the experimental result is in excellent agreement with predicted permeability in the nonuniform distribution model.

Crest-Height Distribution of Nonlinear Random Waves

The wave crest is an important factor for the design of both fixed and floating marine structures.Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage.Many empirical and theoretical distribution functions for wave crest heights have been proposed,but there is a lack of agreement between them.It is of significance to develop a better new nonlinear wave crest height distribution model.The progress in the research of wave crest heights is reviewed in this paper.Based on Stokes' wave theory,an approximate nonlinear wave crest-height distribution formula with simple parameters is derived.Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail.The new crest-height distribution model agrees well with observations.Also,the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.