Scheduling a system of nonsingular affine recurrence equations onto a processor array

Most work on the problem of scheduling computations onto a systolic array is restricted to systems of uniform recurrence equations. In this paper, this restriction is relaxed to include systems of affine recurrence equations. In this broader class, a sufficient condition is given for the system to be computable. Necessary and sufficient conditions are given for the existence of an affine schedule, along with a procedure that constructs the schedule vector, when one exists. This material is based upon work supported by the Office of Naval Research under contract nos. N00014-84-K-0664 and N00014-85-K-0553.     

New optical orthogonal codes by using diophantine equations

Two families of optical orthogonal codes (OOC's) are algebraically designed by using the parametric binary quartic and quadratic forms. The first family of codes has ideal auto and cross-correlation properties and the second family has nonideal cross-correlation properties. The performance of these codes is presented as function of the number of simultaneous OCDMA system users. We present examples of the constructed codes for illustration purposes. The algebraic OOC's being proposed in this paper find applications in asynchronous optical code division multiple access (OCDMA) systems.     

Improving the performance of linear inverse solutions by inverting the resolution matrix

This paper proposes a new strategy for improving the localization capabilities of linear inverse solutions, based on the relationship between the real solution and the estimated solution as described by the resolution matrix equation. Specifically, we present two alternatives based on either the partial or total inversion of the resolution matrix and applied them to the minimum norm solution, which is known for its poor performance in three-dimensional (3-D) localization problems. The minimum norm transformed inverse showed a clear improvement in 3-D localization. The strong dependence of localization errors with the eccentricity of the sources, characteristic of this solution, disappears after the proposed transformation. A similar effect is illustrated, using a realistic example where multiple generators at striate areas are active. While the original minimum norm incorrectly places the generators at extrastriate cortex, the transformed minimum norm localizes, for the example considered, the sources at their correct eccentricity with very low spatial blurring.     

Solving the Maxwell equations by the Chebyshev method: a one-step finite-difference time-domain algorithm

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than current finite-difference time-domain (FDTD) algorithms.     

On a linear diophantine problem of Frobenius

In this paper, linear diophantine problem of Frobenius is discussed. A theorem concerning the largest integer _m (a₁,a₂) and the smallest integer G (a₁,a₂) with m different representations with a₁,a₂ as basis is proved.     

Computational improvement in the calculation of the natural log of a square matrix

A computational improvement on an algorithm previously derived for the calculation of the natural log of a square matrix is presented, allowing a more general use of the algorithm. This algorithm is useful in estimating the state-space model of a continuous-time multivariable system from data obtained with a discrete-time model.<>     

Selective screening of waveguide modes by a system of two grids with square cells

The problem of selective screening of waveguide modes with the help of a filter consisting of two metal grids with square cells is analyzed. The filter has perfect contacts at conductors’ crosses. The investigation is performed by means of the method of averaged boundary conditions. The general expressions are obtained for the mode reflection and transmission coefficients. Examples of filtering of various modes are presented for the case of a circular waveguide. The method is shown to be especially efficient for extraction of higher order modes. It is noted that, in such filters, grids with very thin conductors are the most promising.     

Rate equations for a three-level system

Time-dependent rate equations for the populations of a three-level molecular system are derived from the density matrix in the limit, in which the dephasing time is shorter than any relevant time scale, and the cross relaxation (dephasing) times are faster than the time scale characterizing changes in the envelope of the pumping field. These equations reduce to results obtained by other authors when non-linear two photon effects and power broadening are neglected.     

Transfer matrix of a linear dynamic system

A formula is given which relates a transfer matrix to the differential equations of the underlying system.     

布里渊传感系统中超高速方波脉冲源的设计

为了解决布里渊传感器技术中缺少超高速方波脉冲源的实际情况,实现总线较小的码间串扰及高速发送器通道较好的信号完整性,采用对系统中的敏感信号线进行串扰分析、建模及电磁场仿真分析并在此基础上进行制版测试的方法,提出了一种基于现场可编程门阵列器件的超高速脉冲源的设计方案,并进行了理论分析和实验验证。通过宽带示波器对实际板路的测量,取得了脉冲信号不同脉宽的时域波形及眼图数据。结果表明,输出脉冲的最小脉宽1ns,最大幅度1.0V,上升/下降时间均小于300ps,脉冲宽度在1ns~5ns间可调,重复频率在1kHz~10kHz间可调。这一结果对超高速脉冲源的设计理论的完善是有帮助的。     

Error-free solution to a Toeplitz system of equations

A numerical method which allows error-free computation of the solution to a Toeplitz system of equations is developed. The method requires that the system of equations have rational entries. To avoid error that is inherent in floating-point arithmetic, multiple-modulus residue arithmetic is applied to a modified version of the Levinson algorithm and to an algorithm presented by S.Y. Kung and Y.H. Hu (1983). The error-free method has a highly parallel structure and can be implemented with existing software and hardware. The exact method presented here serves as an outline for the general approach to the development of error-free solution methods     

利用均方稳定方法对网络控制系统的分析及优化

网络控制系统(NCS)具有成本低、创建和维护比较简易、灵活性强、系统故障诊断方便等优点,近几年被广泛应用于设备制造、工业自动化以及航空航天等领域。在以上所提到的诸多领域中,利用网络控制系统保持网络的稳定性非常重要,但是在实际应用时网络的使用过程中不可避免地带来了时滞、数据丢包、数据包时序错乱等问题,这些可能出现的情况使得NCS的分析和设计非常复杂。研究了NCS的模型建立、稳定性分析以及控制器设计问题。通过仿真实验对所得到的理论结果的可行性和有效性进行了验证。     

Formulation of multiport equations via block matrix elimination

Algorithms for formulating the hybrid equations of linear multiports are derived by means of block matrix elimination. The algorithms can be implemented using sparse matrix techniques. The computational requirements of each algorithm are determined, and rules on how to choose the most efficient algorithm for solving a given problem are obtained.     

Strip and line path integrals with a square pixel matrix: a unified theory for computational CT projections

Calculated forward projection techniques have been used for various purposes in computerized tomography applications, and several models have been proposed to simulate the tomography projection process. Since the area weighted strip integral is one of the best models, methods to facilitate the computation of strip integrals would be very useful. In particular, a triangular subtraction technique with a reduced number of weighting factors is proposed for the calculation of the strip integral. A unified path integral theory is also proposed to bridge various models and to clarify the integral interaction when a line or a strip passes through a square pixel matrix.     

Expansions for the capacitance of a square in a square with acomparison

Expansions are given for the capacitance per unit length for the geometry in which two infinite square cylinders are placed concentric with each other with their sides parallel to each other. A comparison is made with an expansion for the capacitance of the Bowman squares     

Solution of large dense complex matrix equations utilizingwavelet-like transforms

This paper presents the wavelet-like transforms, which are quite different from the wavelet transform for the solution of large dense complex matrix equations. From a purely numerical standpoint, these wavelet-like transforms are not true orthogonal transforms as the condition number of the resulting matrix changes after the thresholding. These effects are illustrated through examples     

三面角反射器的高频电磁散射分析

几何光学/区域投影(Geometrical Optics/Area Projection, GO/AP)法是一种综合利用GO和AP进行电大尺寸目标单站雷达散射截面积(Radar Cross Section, RCS)预估的高频混合算法.文章推导建立了利用GO/AP法进行RCS预估的通用流程, 计算出不同入射方向下三角形三面角反射RCS的完整表达式; 将其与RCS最大值的经验公式以及FEKO软件的仿真结果进行对比, 验证了GO/AP法的可行性; 在边界入射方向对GO/AP算法进行改进, 进一步拓宽了GO/AP法对观察角的适应范围.     

Measurement of the resistivity of a thin square sample with a square four-probe array

Geometrical correction factors are evaluated for the measurement of the resistivity of a square conducting sample whose thickness is small compared to the probe spacing of a square four-probe array. The correction factors allow the computation of the resistivity when the probes are not on the periphery of the square sample. The solution is based on the method of images and is written in a compact, easily-evaluated form. The resistivity measurement error encountered with the square sample is presented in graphical form for use in test structure design.     

Solution of large dense complex matrix equations utilizing wavelet-like transforms

The objective of this paper is to explore the validity of various mathematical properties of the wavelet-like transforms for the solution from thin wire structures utilizing the conventional integral equation technique based on the method of moments. It is illustrated through numerical experimentation that the conventional mathematical bounds existing for the classical wavelet transform do not apply to the wavelet-like transforms. Also the classical wavelet transform is really not applicable for the solution of the matrix equations. These statements will be illustrated through examples.