具有种内互惠作用的Lotka-Volterra互惠共存模型

对具有种内互惠作用的Lotka-Volterra互惠共存模型进行了完整的全局分析，得到了一些新的结果。     

Integral Method o Reciprocity in the Spectroscopy of Laser Crystals with Impurity Centers

A new method of determining the stimulated emission cross-section spectra from the absorption cross-section spectra, which we call the integral method of reciprocity, is suggested it does not require knowledge of the structure of the impurity-center electron levels. Based on this method, formulas for calculating the radiation lifetime of impurity centers in crystals have been derived. The effectiveness of the integral method of reciprocity was demonstrated in determining the stimulated emission cross sections and radiation lifetime of an ytterbium ion in the laser crystals Yb³⁺:KYW and Yb³⁺:KGW.     

两个相邻目标对平面波、高斯波束的光散射

基于等效原理和互易性定理研究了两个靠近目标对平面波、高斯波束的光散射问题,给出了这一复合光散射模型的二阶散射结果。通常一阶散射结果容易求解,但由于耦合效应的复杂性,很难给出二阶散射结果的解析形式。为了解决这一问题,应用互易性定理给出了求解任意相邻介质目标二阶散射场的公式,同时借助等效原理将求解散射场公式中的体积分简化为面积分的形式,从而降低了求解难度。求解了两相邻球形粒子的复合散射场,并将求解结果与应用时域积分方程法求得的结果进行了比较。同时,还讨论了束腰半径、目标位置对散射截面及偏振度的影响。     

平行柱体对平面波/高斯波束电磁散射

基于等效原理和互易性定理，研究了N个相互平行二维柱体对平面波/高斯波束的电磁散射特性，给出了求解N阶散射场公式.一阶散射可通过求解单个柱体的散射场得到，但对于高阶散射场而言，由于耦合散射的复杂性，很难给出精确的解析解.为了解决这一问题，借助等效原理和互易性定理给出了求解N阶散射场的面积分公式.只要给出柱体的i-1阶散射场及相关目标表面上的等效电流和(或)等效磁流，就可应用此公式求解i阶散射场.应用该近似方法计算了相互平行非均匀等离子体涂层导体圆柱的单/双站散射宽度，讨论了束腰半径、等离子体涂层厚度、电子密度、碰撞频率及雷达频率等对散射结果的影响.     

格林互易定理在求解均匀带电圆环的静电势分布中的应用

对于静电场,由普遍的格林互易定理得出特殊情形下的格林互易定理.应用该定理推导出均匀带电圆环的数种在形式上互不相同的静电势分布解式.     

Sur l'' application de réciprocité pour une surface fibrée en coniques définie sur un corps local

For a proper smooth variety X defined over a local field k, unramified class field theory investigates the reciprocity map _X: SK₁(X) ^ab ₁(X) as introduced by S. Saito. We study this map in the case when X is a surface admitting a proper surjection onto a smooth geometrically connected curve C with a smooth conic as generic fibre. Without any assumption on the reduction of C, we prove that _X is injective modulo n for all n invertible in k and its cokernel is the same as that of _C.     

Elliptic Apostol sums and their reciprocity laws

We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).

     

The identification of tyre induced vehicle interior noise

Sound transmission into a vehicle is classified as either airborne or structure borne sound. From the point view of noise control, the reduction of noise transferred by different paths requires different solutions. Coherence function analysis is often used to identify transmission paths. However it can be difficult to separate the airborne from structure borne components. The principle of acoustic reciprocity offers a convenient method for overcoming this difficulty. The principal states that the transfer function between an acoustic volume velocity source and an acoustic receiver is independent of a reversal of the position of source and receiver. The work done on this study involves exciting a stationary tyre and measuring the surface velocity of the tyre at a number of discrete points. The acoustic transfer functions between each point on the tyre and a receiver point are measured reciprocally. Two sets of measurements are then combined to yield a measure of the sound pressure due to a point force on the tyre via the acoustic transmission path only. This technique also provides information on the relative contributions of various regions of the tyre wall to the resultant noise. Also the sound radiation characteristics, the horn effect, and resonance at the wheel housing are identified through the reciprocal measurement.     

Reconstruction of the shape of object with near field measurements in a half-plane

We consider a mathematical problem modelling some characteristics of near field optical microscope.We take a monofrequency line source to illuminate a sample with constant index of refraction and use the scattered field data measured near the sample to reconstruct the shape of it. Mixed reciprocity relation and factorization method are applied to solve our problem.Some numerical examples to show the feasibility of the method are presented.     

Bi-velocity transport processes. Single-component liquid and gaseous continua

The present contribution supplements the previous findings regarding the need for two independent velocities rather than one when quantifying mass, momentum and energy transport phenomena in fluid continua. Explicitly, for the case of single-component fluids the present paper furnishes detailed expressions for the phenomenological coefficients appearing in the constitutive equations governing these bi-velocity transport processes. Whereas prior analyses furnished coefficient values only for the case of dilute monatomic gases using data from Burnett’s solution of the Boltzmann equation, the present study furnishes values applicable to all fluids, liquids as well as dense gases. Moreover, whereas prior coefficient calculations derived these values (for dilute monatomic gases) from Burnett’s solution of Boltzmann’s gas-kinetic equation, the latter a molecular theory, the present analysis derives the liquid- and gas-phase values from purely macroscopic data requiring knowledge only of the fluid’s coefficients of thermal expansion, isothermal compressibility, and thermometric diffusivity. In the dilute monatomic gas case common to both levels of analysis, the respective molecularly and macroscopically derived phenomenological coefficients are found to be in excellent agreement, confirming the credibility of both bi-velocity theory and the theory establishing the values of the phenomenological coefficients appearing in the constitutive relations derived therefrom. Whereas the preceding macroscopic calculations invoked Onsager’s reciprocal theorem relating coupled phenomenological coefficients, an alternative scheme is presented at the conclusion of the paper, one that reverses the usual order of things, at least in the present single-component fluid case. This alternate scheme enables Onsager’s nonequilibrium reciprocal relation, originally derived by him using molecular arguments, to be derived using purely macroscopic arguments originating from knowledge of Maxwell’s equilibrium reciprocal relations, the latter fundamental to equilibrium thermodynamics.