二元函数极限的求法

二元函数极限的存在性及其求法是高等数学的重点内容之一.相对于一元函数的极限,二元函数的极限存在性的判定以及求解具有一定的难度,通过典型例题总结归纳计算二元函数极限常用的方法以及易犯的错误.     

静态场边界条件有间断时边值问题的解法

静态场边值问题的解法可以分为解析法和数值法两大类.在解析法中,分离变量法是广泛应用的一种方法.当边界条件有间断时,在应用分离变量法过程中如何适当处理问题是值得注意的.本文讨论了在直角坐标和球坐标中边界存在跃变时静态场计算的两个问题,说明利用间断边界条件确定系数与单纯的傅里叶级数展开的区别,以免得出矛盾的结论.本文就此提出的一点见解,对正确应用分离变量法具有一定参考价值.     

A Note on the Generation of Phase Plane Plots on a Digital Computer

A technique is presented for generating phase plane plots on a digital computer which circumvents the difficulties associated with more traditional methods of numerical solving nonlinear differential equations. In particular, the nonlinear differential equation of operation is formulated as a pair of coupled differential equations with phase error and phase error derivative as dependent variables and arc length as the independent variable, which is uniformly distributed along the phase plane trajectory. The sinusoidal phase-locked loop and polarity-type Costas loop are used as illustrations of the proposed method of solution.     

The Cutoff Wavelengths of Composite Waveguides (Correspondence)

When electromagnetic waves propagate in waveguides of nonsimple cross section, no exact solution can be obtained by the conventional method of solving the wave equation by separation of variables. In such cases approximations are available such as perturbation methods, variational methods, etc.     

Generation of design verification tests from behavioral VHDLprograms using path enumeration and constraint programming

A method for generation of design verification tests from behavior-level VHDL programs is presented. The method generates stimuli to execute desired control-flow paths in the given VHDL program. This method is based on path enumeration, constraint generation and constraint solving techniques that have been traditionally used for software testing. Behavioral VHDL programs contain multiple communicating processes, signal assignment statements, and wait statements which are not found in traditional software programming languages. Our model of constraint generation is specifically developed for VHDL programs with such constructs. Control-flow paths for which design verification tests are desired are specified through certain annotations attached to the control statements in the VHDL programs. These annotations are used to enumerate the desired paths. Each enumerated path is translated into a set of mathematical constraints corresponding to the statements in the path. Methods for generating constraint variables corresponding to various types of carriers in VHDL and for mapping various VHDL statements into mathematical relationships among these constraint variables are developed. These methods treat spatial and temporal incarnations of VHDL carriers as unique constraint variables thereby preserving the semantics of the behavioral VHDL programs. Constraints are generated in the constraint programming language CLP(R) and are solved using the CLP(R) system. A solution to the set of constraints so generated yields a design verification test sequence which can be applied for executing the corresponding control path when the design is simulated. If no solution exists, then it implies that the corresponding path can never be executed. Experimental studies pertaining to the quality of path coverage and fault coverage of the verification tests are presented     

逐步缩小搜索域的全局优化法在微波CAD中的应用

本文描述了一种逐步缩小搜索域的全局优化法,利用此方法在全域随机投点进行判断,可以确定全局最小点所在的邻域,并给出该域中近似最小点值及其函数估值。在此邻域中再用局部优化梯度法,即可得到全局最小点。此法收敛迅速。使用方便,已用于微波电路最优化通用设计程序。最后给出验算结果和应用实例。     

Interior-point methodology for 3-D PET reconstruction

Interior-point methods have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on path-following interior-point methodology, for performing regularized maximum-likelihood (ML) reconstructions on three-dimensional (3-D) emission tomography data. The algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region (the nonnegative orthant). We propose two methods, a primal method which updates only the primal image variables and a primal-dual method which simultaneously updates the primal variables and the Lagrange multipliers. A parallel implementation permits the interior-point methods to scale to very large reconstruction problems. Termination is based on well-defined convergence measures, namely, the Karush-Kuhn-Tucker first-order necessary conditions for optimality. We demonstrate the rapid convergence of the path-following interior-point methods using both data from a small animal scanner and Monte Carlo simulated data. The proposed methods can readily be applied to solve the regularized, weighted least squares reconstruction problem.     

The equivalence of the scalar one-dimensional and vector electrodynamic approaches to the problem on the wave incidence on a slab: Solution by the direct and averaging methods

The direct and averaging methods are applied to analyze the propagation of 1D and electromagnetic waves through three different media separated by plane-parallel interfaces. It is shown that application of the direct method for calculation of the amplitudes of propagating waves is ideologically simpler but the averaging method yields simpler final expressions. Universal boundary conditions are obtained for the averaging method. These conditions are suitable for the solution of problems on the normal and oblique incidence of vertically and horizontally polarized electromagnetic waves. It is demonstrated that vector electrodynamic problems and the corresponding scalar 1D problems have the same mathematical contents and that a solution to an electrodynamic problem can be obtained from a solution to a 1D problem with the help of certain changes of coefficients and variables.     

Optimal design of electronic system utilizing an integrated multidisciplinary process

An investigation is conducted to develop an integrated model for electronic equipment design and to propose a solution method for the generated multi-attribute optimization problem. An integrated system model that incorporates all domain specific knowledge is developed that can track dependencies among the domains under study here. The overall multidisciplinary optimization problem as defined by the objective function, constraint set and design variables are formulated, and nonlinear solution methods are employed. To present the optimal solution for the electronic equipment design, the influence of several design-related functions on the objective function is examined. Additionally, the influence of weighting functions on the value of each individual function is determined. Finally, a multiattribute analysis is performed and the influence of each domain on the overall system is studied. First order and detailed optimization analysis are conducted to understand the sensitivity of each engineering field on the overall design. It is evident that not all the engineering fields are equally important in the design optimization. An amplifier, located on a shelf in a frame, used in the industry was utilized for a case study.     

FDTD Modeling for Dispersive Media Using Matrix Exponential Method

This letter presents a finite-difference time-domain formulation to model electromagnetic wave propagation in dispersive media using matrix exponential method. The Maxwell's curl equations and the time domain relations between electric fields and auxiliary variables are formulated as a first order differential matrix system. The fundamental solution to such a system is derived in terms of matrix exponential and the update equations can be extracted conveniently from the solution. Numerical results show that this formulation yields higher accuracy compared to many other previous methods, without incurring additional auxiliary variable and complexity.      

Analysis methods for optical heterodyne DPSK receivers corrupted bylaser phase noise

Two methods are presented for analyzing the effects of phase noise on the performance of an optical heterodyne binary differential-(DPSK) system. The first method utilizes a perturbation solution for filtered phase noise. By comparing the results of this analysis with simulated results, it is shown that the perturbation solution is accurate for laser linewidths up to at least 10% of the bit rate. Using this analysis, the accuracy of the widely used approximation, whereby the effects of filtering on the magnitude of the phase-noise corrupted signal are neglected, is verified. The author's second method is based on moments of random variables. As the level of phase noise in a practical DPSK system must be small, an improved formulation for the moments of the filtered phase noise is derived. It removes the major cause of this numerical instability. A maximum-entropy probability density function estimation technique is applied to the problem of analyzing the performance of a DPSK receiver. By comparing results with those obtained using the perturbation analysis, it is found that the moment-based method is effectively limited to relatively large error probabilities     

Identification of Continuous-Time Systems Using Instrumental Variables with Application to an Industrial Robot

A new method of constructing instrumental variables for identification is introduced. Its usefulness in the identification of continuous-time systems is investigated. The technique is then applied for modeling the arm of an industrial robot used for welding purposes. Results showed that the proposed method of using instrumental variables is computationally simple and at the same time gives better performance in the presence of measurement noise as compared to existing methods.     

Power estimation methods for sequential logic circuits

Recently developed methods for power estimation have primarily focused on combinational logic. We present a framework for the efficient and accurate estimation of average power dissipation in sequential circuits. Switching activity is the primary cause of power dissipation in CMOS circuits. Accurate switching activity estimation for sequential circuits is considerably more difficult than that for combinational circuits, because the probability of the circuit being in each of its possible states has to be calculated. The Chapman-Kolmogorov equations can be used to compute the exact state probabilities in steady state. However, this method requires the solution of a linear system of equations of size 2^N where N is the number of flip-flops in the machine. We describe a comprehensive framework for exact and approximate switching activity estimation in a sequential circuit. The basic computation step is the solution of a nonlinear system of equations which is derived directly from a logic realization of the sequential machine. Increasing the number of variables or the number of equations in the system results in increased accuracy. For a wide variety of examples, we show that the approximation scheme is within 1-3% of the exact method, but is orders of magnitude faster for large circuits. Previous sequential switching activity estimation methods can have significantly greater inaccuracies     

电力系统静态电压稳定裕度评估方法

基于大数据集中隐含关系探索方法和电力系统大量的不同运行状态下的潮流数据,探寻出系统中与静态电压稳定相对裕度有最强的关系的变量,并基于这些变量构建相对裕度评估方法.该方法选取一定数量的关系性较强的变量作为相对稳定裕度的最优输入变量,所使用的探索统计工具是最大互信息系数MIC （Maximal Information Coefficient）和皮尔逊相关系数PCC （Pearson Correlation Coefficient）.当所选的最优输入变量的值能从广域量测系统中获得,电力系统的静态电压稳定相对裕度便能够通过所探索出的关系实时地评估出来.结合PSS/E中39节点算例的仿真测试结果,验证了所提方法的有效性.     

Reduced base model construction methods for stochastic activitynetworks

Reduced base model construction methods for stochastic activity networks are discussed. The basic definitions concerning stochastic networks are reviewed and the types of variables used in the construction process are defined. These variables can be used to estimate both transient and steady-state system characteristics. The construction operations used and theorems stating the validity of the method are presented. A procedure for generating the reduced base model stochastic process for a given stochastic activity network and performance variable is presented. Some examples which illustrate the method and demonstrate its effectiveness in reducing the size of a state space are presented     

Blind estimation of a fractionally sampled FIR channel for OFDM transmission using residue polynomials

This paper introduces blind-channel estimation methods using residue polynomials for orthogonal-frequency-division-multiplexing (OFDM) transmission under the assumption that the channel is finite-impulse response (FIR). In terms of z transform, if the received signal is multiplied by the inverse of the transmitted signal, the resulting z transform renders the channel transfer function when additive noise is absent in the channel. For an FIR channel, samples of the recovered impulse response must be zero in the region of zeros of the channel impulse response. Based on this observation, the blind estimation problem is formulated as a solution of linear equations, treating the transmitted symbols as unknown variables. Polynomial residue arithmetic turns out to be very useful for deriving the linear equations. The proposed method is computationally more efficient than subspace methods that are applied for OFDM transmission systems. In addition, unlike subspace methods, the proposed method is deterministic and does not require estimation of the autocorrelation matrix of received signals, which is required in subspace methods.     

Finite element computation of electromagnetic fields [hyperthermiatreatment]

A three dimensional finite element solution scheme is developed for numerically computing electromagnetically induced power depositions. The solution method is applicable to those problems for which it can be reasonably assumed that the magnetic permeability is homogeneous. The method employs an incident field/scattered field approach where the incident field is precalculated and used as the forcing function for the computation of the scattered field. A physically logical condition is used for the numerical boundary conditions to overcome the fact that electromagnetic problems are generally unbounded (i.e., the boundary condition is applied at infinity) but numerical models must have a boundary condition applied to some finite location. At that numerical boundary, an outgoing spherical wave is simulated. Finally, an alternate to a direct solution scheme is described. This alternate method, a preconditioned conjugate gradient solver, provides both a storage and CPU time advantage over direct solution methods. For example, a one-thousand fold decrease in CPU time was achieved for simple test cases. Unlike most iterative methods, the preconditioned conjugate gradient technique used has the important property of guaranteed convergence. Solutions obtained from this finite element method are compared to analytic solutions demonstrating that the solution method is second-order accurate     

Planar Diffraction Analysis of Homogeneous and Longitudinally Inhomogeneous Gratings Based on Legendre Expansion of Electromagnetic Fields

Planar grating diffraction analysis based on Legendre expansion of electromagnetic fields is reported. In contrast to conventional RCWA in which the solution is obtained using state variables representation of the coupled wave amplitudes; here, the solution is expanded in terms of Legendre polynomials. This approach, without facing the problem of numerical instability and inevitable round off errors, yields well-behaved algebraic equations for deriving diffraction efficiencies, and can be employed for analysis of different types of gratings. Thanks to the recursive properties of Legendre polynomials, for longitudinally inhomogeneous gratings, wherein differential equations with non-constant coefficients are encountered, it can also be used to analyze the whole structure at one stroke. Although this is the only case for which the presented approach is efficient from both aspects of stability and computation load, the presented approach is applied to different test cases, and justified by comparison of the results to those obtained using previously reported methods. The method is general, and can handle many different cases like thick gratings, non-Bragg incidence, and cases in which higher diffracted orders or evanescent orders corresponding to real eigenvalues, have to be included in the solution of the Maxwell's equations. In deriving the formulation, a rigorous approach is followed     

Simultaneous routing and resource allocation via dual decomposition

In wireless data networks, the optimal routing of data depends on the link capacities which, in turn, are determined by the allocation of communications resources (such as transmit powers and bandwidths) to the links. The optimal performance of the network can only be achieved by simultaneous optimization of routing and resource allocation. In this paper, we formulate the simultaneous routing and resource allocation (SRRA) problem, and exploit problem structure to derive efficient solution methods. We use a capacitated multicommodity flow model to describe the data flows in the network. We assume that the capacity of a wireless link is a concave and increasing function of the communications resources allocated to the link, and the communications resources for groups of links are limited. These assumptions allow us to formulate the SRRA problem as a convex optimization problem over the network flow variables and the communications variables. These two sets of variables are coupled only through the link capacity constraints. We exploit this separable structure by dual decomposition. The resulting solution method attains the optimal coordination of data routing in the network layer and resource allocation in the radio control layer via pricing on the link capacities.     

基于遗传算法的RBF-PLS方法在辐射源识别中的应用

RBF-PLS是一种有效的径向基网络构造方法,较好地解决了隐单元数和各中心的取值问题,但宽度系数和PLS成分数难以选定。为此,该文提出采用混合编码遗传算法,以径向基网络的拟合性能和泛化能力为目标,优选宽度系数和PLS成分数,以此建立RBF-PLS-GA模型。将该方法用于雷达辐射源识别,效果良好,明显优于其他网络模型。