回归反射玻璃微珠折射率的测量和分析

文章分析了回归反射高折射率玻璃微珠的光学特点以及玻璃微珠回归反射特性与折射率的关系 .用微光学测量系统 ,根据几何光学近轴光线成像原理 ,给出玻璃微珠折射率的测量方法 ,分析和讨论了测量方法的误差 .

Noncommutative Differential Calculus and Its Application on the Lattice

By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.

Vortex of Fluid Field as Viewed from Curvature

The vortex is a common phenomenon in fluid field. In this paper, vortex can be represented by curvature c, which varies with arc length s. The variance of point (x, y) with arc length in stream line satisfies a 2-order variablecoefficient linear ordinary differential equation. The type vortex can be analyzed qualitatively by this ordinary differential equation.

Algebraic-Geometric Solution to (2+1)-Dimensional Sawada-Kotera Equation

Special solution of the （2＋1）-dimensional Sawada Kotera equation is decomposed into three （0＋1）- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve. Explicit algebraic-geometric solution is obtained on the basis of a deeper understanding of the KdV hierarchy.

Cylindrical KP-Burgers Equation for Two-Temperature Ions in Dusty Plasma with Dissipative Effects and Transverse Perturbations

In this paper, the cylindrical KP-Burgers equation with variable coefficient for two-temperature ions in unrsagnified dusty plasma with dissipative effects and transverse perturbations in cylindrical geometry is derived by using the standard reductive perturbation technique. With the help of variable-coeiffcient generalized projected Ricatti equation expansion method, the cylindrical KP-Burgers equation is solved and shock wave solution is obtained. The effecta of some important parameters to the shock wave solution are illustrated from the wave evolution figures. The effects caused by dissipation and transverse perturbations are also discussed.

Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory

Spaces of equivalence modulo a relation of congruence are constructed on field solutions to establish a theory of the universe that includes the theory QFT （Quantum Field theory）, the SUSY （Super-symmetry theory） and HST （heterotic string theory） using the sheaves correspondence of differential operators of the field equations and sheaves of coherent D - Modules [1]. The above mentioned correspondence use a Zuckerman functor that is a factor of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry [2, 3]. The obtained development includes complexes of D - modules of infinite dimension, generalizing for this way, the BRST-cohomology in this context. With it, the class of the integrable systems is extended in mathematical physics and the possibility of obtaining a general theory of integral transforms for the space - time （integral operator cohomology [4]）, and with it the measurement of many of their observables [5]. Also tends a bridge to complete a classification of the differential operators for the different field equations using on the base of Verma modules that are classification spaces of SO（l, n ＋ 1）, where elements of the Lie algebra al（1, n ＋ 1）, are differential operators, of the equations in mathematical physics [1]. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field （Verma modules） and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic L G - bundles category with a special connection （Deligne connection）. The corresponding D - modules may be viewed as sheaves of conformal blocks （or co-invariants） （images under a version of the Penrose transform [1, 6]） naturally arising in the framework of conformal field theory.

Multisymplectic Geometry for the Seismic Wave Equation

The multisymplectic geometry for the seismic wave equation is presented in this paper.The local energy conservation law,the local momentum evolution equations,and the multisymplectic form are derived directly from the variational principle.Based on the covariant Legendre transform,the multisymplectic Hamiltonian formulation is developed.Multisymplectic discretization and numerical experiments are also explored.

Ermakov System and Plane Curve Motions in Affine Geometries

It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.

Group—Invariant Solutions in Plane Curve Motions

Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.

Analytical geometry method of planetary gear trains

This paper presents an analytical geometry method for kinematics and efficiency of planetary gear trains (PGTs). The novel method which is capable of evolution and contrast analysis of mechanism kinematics, can be applied to any typical one-and two-degree-of-freedom plane PGTs containing any number of simple, compound or complex-compound planetary gear sets. The efficiency analysis of this method features a systematized and programmed process and its independence of the speed ratio. The primary contribution of this work lies in the integration of quantitative calculation, qualitative evolution and comparative analysis of kinematics of PGTs into one diagram, and in the integration of kinematics and efficiency analysis into a single method system. First, the analytical geometry method is defined, its basic properties are given, and the systematization procedure to perform kinematic analysis is demonstrated. As an application, analytical geometry diagrams of common PGTs are exhibited in the form of a list, whose kinematic characteristics and general evolution tendency are discussed. Then, with the mapping of PGTs onto the angular speed plane, the efficiency formula of analytical geometry, which has an extremely concise form, and a simple method for power flow estimation are put forward. Moreover, a general procedure is provided to analyze the efficiency and power flow. Finally, four numerical examples including a complicated eleven-link differential PGTs are given to illustrate the simpleness and intuitiveness of the analytical geometry method.

2-Harmonic Submanifolds in a Complex Space Form

In the present paper,the authors study totally real 2-harmonic submanifolds in a complex space form and obtain a Simons' type integral inequality of compact submanifolds as well as some relevant conclusions.

VARIABLE FEEDRATE INTERPOLATION OF NURBS TOOLPATH WITH GEOMETRIC AND KINEMATICAL CONSTRAINTS FOR FIVE-AXIS CNC MACHINING

Variable feedrate interpolation algorithms for five-axis parametric toolpath are very promising but still rather limited currently.In this paper,an off-line feedrate scheduling method of dual NURBS curve is presented with geometric and kinematical constraints.For a given dual parametric curve,the feedrates of sampling points are first scheduled sequent with confined feedrate of cutter tip and machine pivot,chord error,normal acceleration and angular feedrate.Then,the feedrate profiles of angular feed acceleration sensitive regions of the path are adjusted using a bi-directional scanning algorithm.After that,a linear programming method is used to adjust the feedrate profiles of linear feed acceleration sensitive regions and control the linear feed acceleration of both cutter tip and machine pivot within preset values.Further,a NURBS curve is used to fit the feedrates of sampling points.Finally,illustrative examples are carried out to validate the feasibility of the proposed feedrate scheduling method.The results show that the proposed method has the ability of effectively controlling the angular feed characters of cutter axis as well as the chord error and linear feed characters of cutter tip and machine pivot,and it has potential to be used in high accuracy and high quality five-axis machining.

Decay Rates of the Hyperbolic Equation in an Exterior Domain with Half-Linear and Nonlinear Boundary Dissipations

This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain.The damping is put on partly the boundary and partly on the interior of the domain.The energy decay results are established by Riemannian geometry method.

Differential geometric modeling of guidance problem for interceptors

It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry the-ory,rather than directly decomposing the motion in the Cartesian coordinates.The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper,based on the classical differential geometry curve theory.Firstly,the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS,the kinematic equations of LOS are established,and the concepts of curvature and torsion of LOS are proposed.Simultaneously,the new relative dynamic equations between interceptor and target are constructed.Secondly,it is found that there is an instan-taneous rotation plane of LOS (IRPL) in the space,in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems.The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN.In addition,the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL.After that,the dif-ferential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced,and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC.Moreover,the performance of the original guidance laws will be reduced after the differential geometric transformation.At last,an exoatmospheric intercep-tion is taken for simulation to demonstrate the differential geometric modeling proposed in this paper.

Lie Symmetry Analysis,Bcklund Transformations and Exact Solutions to (2+1)-Dimensional Burgers' Types of Equations

This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.

ELIMINATION IN WEYI ALGEBRA AND q-IDENTITIES

In this paper, the following are introduced briefly： the basic concept of q-proper-hypergeometric; an algorithmic proof theory for q-proper-hypergeometric identities; and elimination in the non- commutative Weyl algebra. We give an algorithm for proving the single-variable q-proper-hypergeometric identities that is based on Zeilberger＇s approach and the elimination in Weyl algebra. Finally, we test several examples that have been proven by D. Zeilberger and H. Will using the WZ-pair method and Gosper algorithm.

Global dynamics of hepatitis C viral infection with logistic proliferation

A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.

The Hyperbolic Darboux Image and Rectifying Gaussian Surface of Nonlightlike Curve in Minkowski 3-Space

In this paper,we give the classification of the singularities of hyperbolic Darboux image and rectifying Gaussian surface of nonlightlike curve in Minkowski 3-space.We establish the relationship between the singularities and the geometric invariants of curves which are deeply related to its order of contact with helices.