ON THE REALIZATION THEORY OF IMPULSE RESPONSE SEQUENCES

In the practical physics and engineering systems, the informations that we can acquire are only the input-output data. It is an lmportant problem how obtain internal structure of system by this informations, namely, the realization problem of systems. The existing realization theory are all to construct the realization from the transfer function of systems. However, for a practical system,     

Numerical realization of the conditions of Max NSther＇s residual intersection theorem

The aim of this paper is to study numerical realization of the conditions of Max Nother＇s residual intersection theorem. The numerical realization relies on obtaining the inter- section of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determin- ing the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic, even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time.     

Numerical realization of the conditions of Max Nther's residual intersection theorem

The aim of this paper is to study numerical realization of the conditions of Max Nther's residual intersection theorem. The numerical realization relies on obtaining the intersection of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determining the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic,even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time.     

Estimating Differences in Restricted Mean Lifetime Using Additive Hazards Models under Dependent Censoring

In epidemiological and clinical studies,the restricted mean lifetime is often of direct interest quantity.The differences of this quantity can be used as a basis of comparing several treatment groups with respect to their survival times.When the factor of interest is not randomized and lifetimes are subject to both dependent and independent censoring,the imbalances in confounding factors need to be accounted.We use the mixture of additive hazards model and inverse probability of censoring weighting method to estimate the differences of restricted mean lifetime.The average causal effect is then obtained by averaging the differences in fitted values based on the additive hazards models.The asymptotic properties of the proposed method are also derived and simulation studies are conducted to demonstrate their finite-sample performance.An application to the primary biliary cirrhosis(PBC)data is illustrated.     

K-STRATUM LIMIT AND K-STRATUM INTEGRAL ON THE GENERALIZED NUMBER FIELD

The main results of the present paper are:1. It is rational to define the limit by the infinitesimal method.2. We have proved that the definitions of the limit by the infinitesimal argument and by the ε-δ arguement are quite equivalent.3. It is possible to determine the values of infinite divergent integrals.Example 1.Example 2. From the following equalities we can calculate the classical electron radius η=2.818×10~(-13) cm.(c, light velocity)     

On a Linear Equation Arising in Isometric Embedding of Torus-like Surface

The solvability of a linear equation and the regularity of the solution are discussed. The equation is arising in a geometric problem which is concerned with the realization of Alexandroff＇s positive annul in R^3.     

INFINITESIMAL DEFORMATIONS OF TIME-LIKE SURFACES IN MINKOWSKI 3-SPACE

In this paper, infinitesimal deformations of time-like surfaces are investigated in Minkowski 3-space R^2,1. It is shown that some given deformations of the time-like surface can be described by 2 1 dimensional integrable systems. Moreover spectral parameters are introduced, and it is proved that deformation families are soliton surfaces‘ families.     

On the equivalence of extremal Teichmller mapping

Let T(△) and B(△) be the Teichmuller space and the infinitesimal Teichmuller space of the unit disk △ respectively. In this paper, we show that [ν]B(△) being an infinitesimal Strebel point does not imply that [ν]T(△) is a Strebel point, vice versa. As an application of our results, problems proposed by Yao are solved.     

THE COMPACT ALGEBRA STRUCTURE OF SOLITON EQUATIONS, THEIR SPINOR AKNS SYSTEM AND REALIZATION ON SPHERE

It is shown that a great sort of soliton equations, such as sine-Grodon equation and others whose inverse scattering problem is described by the AKNS system, has both noncompact and compact algebra structures on the same footing. The spinor AKNS system and realization on sphere with respect to the compact structure of the soliton equations are given.     

ON NOETHER'S THEOREM AND CONSERVATION LAWS IN THERMO-ELASTICITY

Noether's theorem is generalized to the theory of coupled fields with parameters in this paper. Considering that many problems in continuum mechanics have Lagrange densities which are linear combinations of convolution integrals on a parameter of their arguments, the condition of stationary value of these functionals is discussed. Following the thought of Noether's theorem, the author reveals some relations among the invariants of the functionals mentioned above under a family of infinitesimal transformations, variational principles and conservation laws. In addition, two conservation laws for thermo-elasticity are established.     

算子值加权模式在Banach空间的实现理论

本文处理能在Ｂａｎａｃｈ空间中实现的线性连续时间系统．这里，输入、输出和状态空间都是无穷维Ｂａｎａｃｈ空间．我们证明：加权模式有Ｂａｎａｃｈ空间实现的充要条件是它强连续且为指数阶．对状态算子是解析半群的无穷小生成元的情况，得到了Ｂａｎａｃｈ空间实现的存在性定理．所有定理都是在时间域中给出的．     

Infinitesimal Perturbation Analysis: A Tool for Simulation

Perturbation analysis is a technique that expedites the process of performing experiments on discrete-event simulation models. This makes it possible to derive sensitivity estimates from one computer execution of a simulation model. Infinitesimal perturbation analysis (IPA) is one class of algorithms used in perturbation analysis. In this paper, the techniques and algorithms used in simulation to perform infinitesimal perturbation analysis are examined. Each algorithm is discussed in detail, with comments concerning implementation problems and examples with experimental results for serial transfer lines. The results of this paper show that for simple systems, IPA can be easily implemented in a general-purpose simulation language such as SIMAN. Unfortunately, for any given system, parameter or performance measure, the algorithm used to generate the gradient may vary. Additionally, algorithms for more complex classes of problems do not yet exist. This problem hampers the current possibility of incorporating IPA into general-purpose simulation languages.     

Robustness of perturbation analysis estimators for queueing systems with unknown distributions

Sample-path-based stochastic gradient estimators for performance measures of queueing systems rely on the assumption that a probability distribution of the random vector of interest (e.g., a service or interarrival time sequence) is given. In this paper, we address the issue of dealing with unknown probability distributions and investigate the robustness of such estimators with respect to possibly erroneous distribution choices. We show that infinitesimal perturbation analysis (IPA) can be robust in this sense and, in some cases, provides distribution-independent estimates. Comparisons with other gradient estimators are provided, including experimental results. We also show that finite perturbation analysis (FPA), though only providing gradient approximations, possesses some attractive robustness properties with respect to unknown distribution parameters. An application of FPA estimation is included for a queueing system performance optimization problem involving customers with real-time constraints.This work was supported in part by the National Science Foundation Grant ECS-88-01912 and by the Office of Naval Research Contract N00014-87-K-0304.The authors wish to thank Dr. Jack Holtzman for several useful comments and suggestions.     

Convergence of a stochastic approximation algorithm for the GI/G/1 queue using infinitesimal perturbation analysis

Discrete-event systems to which the technique of infinitesimal perturbation analysis (IPA) is applicable are natural candidates for optimization via a Robbins-Monro type stochastic approximation algorithm. We establish a simple framework for single-run optimization of systems with regenerative structure. The main idea is to convert the original problem into one in which unbiased estimators can be derived from strongly consistent IPA gradient estimators. Standard stochastic approximation results can then be applied. In particular, we consider the GI/G/1 queue, for which IPA gives strongly consistent estimators for the derivative of the mean system time. Convergence (w.p.1) proofs for the problem of minimizing the mean system time with respect to a scalar service time parameter are presented.     

Online IPA Gradient Estimators in Stochastic Continuous Fluid Models

This paper applies infinitesimal perturbation analysis (IPA) to loss-related and workload-related metrics in a class of stochastic flow models (SFM). It derives closed-form formulas for the gradient estimators of these metrics with respect to various parameters of interest, such as buffer size, service rate, and inflow rate. The IPA estimators derived are simple and fast to compute, and are further shown to be unbiased and nonparametric, in the sense that they can be computed directly from the observed data without any knowledge of the underlying probability law. These properties hold out the promise of utilizing IPA gradient estimates as ingredients of online management and control of telecommunications networks. While this paper considers single-node SFMs, the analysis method developed is amenable to extensions to networks of SFM nodes with more general topologies.     

Sensitivity estimation for Gaussian systems

In this paper we address the construction of efficient algorithms for the estimation of gradients of general performance measures of Gaussian systems. Exploiting a clever coupling between the normal and the Maxwell distribution, we present a new gradient estimator, and we show that it outperforms both the single-run based infinitesimal perturbation analysis (IPA) estimator and the score function (SF) estimator, in the one-dimensional case, for a dense class of test functions. Next, we present an example of the multi-dimensional case with a system from the area of stochastic activity networks. Our numerical experiments show that this new estimator also has significantly smaller sample variance than IPA and SF. To increase efficiency, in addition to variance reduction, we present an optimized method for generating the Maxwell distribution, which minimizes the CPU time.     

Performance optimization of queueing systems with perturbation realization

After the intensive studies of queueing theory in the past decades, many excellent results in performance analysis have been obtained, and successful examples abound. However, exploring special features of queueing systems directly in performance optimization still seems to be a territory not very well cultivated. Recent progresses of perturbation analysis (PA) and sensitivity-based optimization provide a new perspective of performance optimization of queueing systems. PA utilizes the structural information of queueing systems to efficiently extract the performance sensitivity information from a sample path of system. This paper gives a brief review of PA and performance optimization of queueing systems, focusing on a fundamental concept called perturbation realization factors, which captures the special dynamic feature of a queueing system. With the perturbation realization factors as building blocks, the performance derivative formula and performance difference formula can be obtained. With performance derivatives, gradient-based optimization can be derived, while with performance difference, policy iteration and optimality equations can be derived. These two fundamental formulas provide a foundation for performance optimization of queueing systems from a sensitivity-based point of view. We hope this survey may provide some inspirations on this promising research topic.     

Infinitesimal perturbation analysis for second derivative estimation and design of manufacturing flow controllers

A simulation-based numerical technique for the design of near-optimal manufacturing flow controllers for unreliable flexible manufacturing systems uses quadratic approximations of the value functions that characterize the optimal policy and employs stochastic optimization to design the key coefficients of the quadratic approximations. First and second derivative estimates that drive the optimization algorithm are obtained from a single sample path of the system via infinitesimal perturbation analysis (IPA). Extensive computational experience is reported for one, two, and three-part-type production systems. The relative performance of first-order and second-order stochastic optimization algorithms is investigated. The computational efficiency of these algorithms is finally compared to conventional controller design algorithms based on state-space discretization and successive approximation.This research was supported by the National Science Foundation, Grant No. DDM-89-14277 and DDM-9215368.     

On an Alternative Parameterization of the Solutions of the Partial Realization Problem

The solutions of the partial realization problem have to satisfy a finite number of interpolation conditions at . The minimal degree of an interpolating deterministic system is called the algebraic degree or McMillan degree of the partial covariance sequence and is easy to compute. The solutions of the partial stochastic realization problem have to satisfy the same interpolation conditions and have to fulfill a positive realness constraint. The minimal degree of a stochastic realization is called the positive degree. In the literature, solutions of the partial realization problem are parameterized by the Kimura–Georgiou parameterization. Solutions of the partial stochastic realization problem are then obtained by checking the positive realness constraint for the interpolating solutions of the corresponding partial realization problem. In this paper, an alternative parameterization is developed for the solutions of the partial realization problems. Both the solutions of the partial and partial stochastic realization problem are analyzed in this parameterization, while the main concerns are the minimality and the uniqueness of the solutions. Based on the structure of the parameterization, a lower bound for the positive degree is derived.     

Smoothing complements and randomized score functions

This paper establishes connections between two derivative estimation techniques:infinitesimal perturbation analysis (IPA) and thelikelihood ratio orscore function method. We introduce a systematic way of expanding the domain of the former to include that of the latter, and show that many likelihood ratio derivative estimators are IPA estimators obtained in a consistent manner through a special construction. Our extension of IPA is based onmultiplicative smoothing. A function with discontinuities is multiplied by asmoothing complement, a continuous function that takes the value zero at a jump of the first function. The product of these functions is continuous and provides an indirect derivative estimator after an appropriate normalization. We show that, in substantial generality, the derivative of a smoothing complement is a randomized score function: its conditional expectation is a derivative of a likelihood ratio. If no conditional expectation is applied, derivative estimates based on multiplicative smoothing have higher variance than corresponding estimates based on likelihood ratios.