Theoretical analysis and numerical solution of laser pulse transformation for satellite laser ranging

The processes of the pulse transformation in satellite laser ranging (SLR) are analyzed, the analytical expressions of the transformation are deduced, and the effects of the transformation on Center-of-Mass corrections of satellite and ranging precision are discussed. The numerical solution of the transformation and its effects are also given. The results reveal the rules of pulse transformation affected by different kinds of factors. These are significant for designing the SLR system with millimeter accuracy.     

An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series

We derive the I transformation, an iterative sequence transformation that is useful for the convergence acceleration of certain Fourier series. The derivation is based on the concept of hierarchical consistency in the asymptotic regime. We show that this sequence transformation is a special case of the J transformation. Thus, many properties of the I transformation can be deduced from the known properties of the J transformation (like the kernel, determinantal representations, and theorems on convergence behavior and stability). Besides explicit formulas for the kernel, some basic convergence theorems for the I transformation are given here. Further, numerical results are presented that show that suitable variants of the I transformation are powerful nonlinear convergence accelerators for Fourier series with coefficients of monotonic behavior. This revised version was published online in August 2006 with corrections to the Cover Date.     

基于生存数据的半参数变换的删失回归估计

生存数据经过未知的单调变换后等于协变量的线性函数加上随机误差, 随机误差的分布函数已知或是带未知参数的已知函数\bd 本文先给出未知单调变换的一个相合估计, 再对删失数据做变换, 在此基础上给出了协变量系数的最小二乘估计, 并讨论它的大样本性质.     

广义耦合KdV孤子方程的达布变换及其奇孤子解

借助谱问题的规范变换, 给出广义耦合KdV孤子方程的达布变换,利用达布变换来产生广义耦合KdV孤子方程的奇孤子解,并且用行列式的形式来表达广义耦合KdV孤子方程的奇孤子解．作为应用,广义耦合KdV孤子方程奇孤子解的前两个例子被给出．     

广义耦合KdV孤子方程的达布变换及其偶孤子解

根据广义耦合KdV孤子方程的Lax对, 借助谱问题的规范变换, 一个包含多参数的达布变换被构造出来. 利用达布变换来产生广义耦合KdV孤子方程的偶孤子解, 并且用行列式的形式来表达广义耦合KdV孤子方程的偶孤子解. 作为应用, 广义耦合KdV孤子方程的偶孤子解的前两个例子被给出.     

基于函数arccos(px+q)变换的灰色预测模型研究

借助于函数变换理论和灰色系统建模理论,并结合反余弦函数和线性函数的特点,提出了反余弦函数和线性函数相结合的变换方法并建立了一个改进的GM(1,1)模型.证明了这种变换一方面能提高序列的光滑比并压缩序列的级比;另一方面可以使还原误差减小.具体算例结果表明,经过反余弦函数和线性函数相结合建立的改进GM(1,1)模型的拟合精度优于传统GM(1,1)模型和基于反余弦函数变换的GM(1,1)模型的拟合精度.     

直觉模糊变换半群的积与覆盖关系

提出了直觉模糊变换半群的(全)直积,圈积,直觉模糊变换半群的覆盖的定义,利用代数的手段讨论了直觉模糊变换半群的积的结合性质,研究了直觉模糊变换半群的积的覆盖关系.     

Quadratic Transformations of Triangular Finite Elements in Two Dimensions

The general quadratic isoparametric transformation of a triangleresults in an element with three parabolic curved sides. Thevertices are assumed fixed and the transformation is completelydetermined by the image positions of the non-vertex nodes. Inorder to study the bijectivity of this transformation, simplifiedsufficient conditions for the bijectivity of quadratic transformationsof any convex masterelement are derived. Properties of imageelements that result from the quadratic transformation of atriangle when the transformation Jacobians are linear are consideredin detail. Present address: Computer Research Laboratory, MS 50-662, Tektronix,Inc., PO Box 500, AFQ1, Beaverton, OR 97077, U.S.A.     

OSCILLATION CRITERIA FOR SECOND ORDER NEUTRAL DIFFERENCE EQUATION WITH CONTINUOUS VARIABLE

In this paper, we are concerned with the second order neutral difference equation with continuous variable. Using the integral transformation and generalized Riccati transformation, we obtain some oscillation criteria.     

Darboux transformation and explicit solutions for two integrable equations

A new N-fold Darboux transformation for two integrable equations is constructed with the help of a gauge transformation for the spectral problem proposed by Qiao [Z.J. Qiao, Phys. Lett. A 192 (1994) 316-322]. By the Darboux transformation, explicit soliton and multi-soliton solutions for the two equations are obtained. In particular, soliton and complexiton solutions are shown through some figures.     

On the refinement of bounds of heuristic algorithms for the traveling salesman problem

A number of heuristics for the traveling salesman problem (TSP) rely on the assumption that the triangle inequality (TI) is satisfied. When TI does not hold, the paper proposes a transformation such that for the transformed problem the TI holds. Consequently, the bounds obtained for heuristics are valid with appropriate modification. Moreover, for a TSP satisfying TI the same transformation strengthens such bounds. The transformation essentially maps the problem into one that is minimal with respect to the property that TI holds. For the symmetric TSP the transformation is particularly simple. For an application of the transformation in the asymmetric case we need the dual solution of an assignment problem.     

Application of the differential transformation method to the free vibrations of strongly non-linear oscillators

This paper adopts the differential transformation method to obtain the free vibration behavior of an oscillator with fifth-order non-linearities. The principle of differential transformation is briefly introduced, and is then applied in the derivation of a set of difference equations for the free vibration oscillator problem. The solutions are subsequently solved by a process of inverse transformation. The time responses of the oscillator are presented under different parameter conditions, and the current results are then compared with those derived from the established Runge–Kutta method in order to verify the accuracy of the proposed method. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the proposed differential transformation method is a powerful and efficient tool for solving non-linear problems.     

The practical use of the Euler transformation

The generalised Euler transformation is a powerful transformation of infinite series which can be used, in theory, for the acceleration of convergence and for analytic continuation. When the transformation is applied to a series with rounded coefficients, its behaviour can differ substantially from that predicted theoretically. In general, analytic continuation is impossible in this case. It is still possible, however, to use the transformation for acceleration of convergence, but some changes are necessary in the method of choosing the optimum parameter value.     

Geometrical correspondence of the Miura transformation induced from affine Kac–Moody algebras

The Miura transformation plays a crucial role in the study of integrable systems. There have been various extensions of the Miura transformation, which have been used to relate different kinds of integrable equations and to classify the bi-Hamiltonian structures. In this paper, we are mainly concerned with the geometric aspects of the Miura transformation. The generalized Miura transformations from the mKdV-type hierarchies to the KdV-type hierarchies are constructed under both algebraic and geometric settings. It is shown that the Miura transformations not only relate integrable curve flows in different geometries but also induce the transition between different moving frames. Moreover, the Miura transformation gives the factorization of generating operators of constraint Gelfand–Dickey hierarchy. Other geometric formulations are also investigated.     

Some transformations and reduction formulas for multipleq-hypergeometric series

Summary Some simple ideas of G. E. Andrews ([2], [3]) are used here to derive a transformation formula for a general multiple q-series with essentially arbitrary terms. As applications of (or motivated by) this q-series transformation, several transformation and reduction formulas for q-hypergeometric series in two and more variables are presented. Relevant connections of the various q-identities considered here with a number of known results are also indicated.Supported, in part, by N.S.E.R.C. (Canada) Grant A-7353.     

On the plausibility transformation method for translating belief function models to probability models

In this paper, we propose the plausibility transformation method for translating Dempster–Shafer (D–S) belief function models to probability models, and describe some of its properties. There are many other transformation methods used in the literature for translating belief function models to probability models. We argue that the plausibility transformation method produces probability models that are consistent with D–S semantics of belief function models, and that, in some examples, the pignistic transformation method produces results that appear to be inconsistent with Dempster’s rule of combination.     

Eine Approximation der Binomialverteilung durch die Normalverteilung der Ordnung 1/n

Summary The class (1) of transformations of a binomial variablek is studied. The famous De Moivre-Laplace local and integral limit theorems are generalized for the asymptotically standardized transformations (2). The transformation (4) respectively (3) is singled out as the only one with an error of order 1/n. Besides it is shown, that the error term of ordern ^–1/2 of the identical transformation, the angular transformation, and the logarithmic transformation are in proportion to 1/6, –1/12, and –1/3. Results on the influence of a correction of unbiasedness are mentioned in the last section. Such corrections allow a slight improvement of our new transformation.     

THE CALCULUS OF GENERATING FUNCTIONS AND THE FORMAL ENERGY FOR HAMILTONIAN ALGORITHMS

1.DarbouxTransformationConsidercotangentbundleT*R"acRZnwithnaturalsymplecticstructureandtheproductofcotangentbundles(T*R")x(T*R")=R4nwithnaturalproductsymplecticstructureCorrespondingly,weconsidertheproductspaceR"xR"rsRZn.ItscotangentbunT*(R"xR")=T*Rzn=R'nhasnaturalsymplecticstructure')PreparedbyQinMengzhaoChoosesymplecticcoordinatesz~(p,q)onthesymplecticmanifold,thenforsymplectictransformationg:T*R"~T*R",wehaveitisaLagrangiansubmanifoldofT*R"xT*RninR4n~(R'",J4.).NotethatonR4nth…     

An Extended Multistep Shanks Transformation and Convergence Acceleration Algorithm with Their Convergence and Stability Analysis

The molecule solution of an extended discrete Lotka–Volterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is shown that our new sequence transformation accelerates some kinds of linearly convergent sequences and factorially convergent sequences with good numerical stability. Some numerical examples are also presented.