EXCALIBUR — a Monte Carlo program to evaluate all four-fermion processes at LEP 200 and beyond

A Monte Carlo program is presented that computes all four-fermion processes in e⁺e⁻ annihilation. QED initial state corrections and QCD contributions are included. Fermions are taken to be massless, allowing a very fast evaluation of the matrix element. A systematic, modular and self-optimizing strategy has been adopted for the Monte Carlo integration, which serves also as an example for further event generators in high energy particle physics.     

Lattice structure of e-implications on L

In this paper, we consider the set of all e-implications on L^∗ and define two operations on the set of all representable e-implications on L^∗, thus endowing it with monoid structure which is also a distributive complete lattice.     

An interpolation problem associated with H-optimal design in systems with distributed input lags

A variety of H^∞ optimal design problems reduce to interpolation of compressed multiplication operators, f(s) → π_k(w(s)f(s)), where w(s) is a given rational function and the subspace K is of the form K=H² φ(s)H². Here we consider φ(s) = (1-e^α-5)/(s - α), which stands for a distributed delay in a system's input. The interpolation scheme we develop, adapts to a broader class of distributed lags, namely, those determined by transfer functions of the form B(e^−s)/b(s), where B(z) and b(s) are polynomials and b(s) = 0 implies B(e^−s) = 0.     

A spectral characterization of H-optimal feedback performance and its efficient computation

We study the spectral properties of a ‘Toeplitz⁺ Hankel’ operator which arises in the context of the mixed-sensitivity H^∞-optimization problem and whose largest eigenvalue characterizes the optimal achievable performance ε₀. The existence of such an operator was first shown by Verma and Jonckheere [26], who also'noted the potential numerical advantage of computing eo through its eigenvalue characterization rather than through the ε-iteration. Here, we investigate this operator in detail, with the objective of efficiency computing its spectrum. We define an ‘adjoint’ linear-quadratic problem that involves the same ‘Toeplitz⁺ Hankel’ operator, as shown by Jonckheere and Silverman [13–16]. Consequently, a finite polynomial algorithm allows ε₀ to be characterized as simply as the largest root of a polynomial. Finally, a computationally more attractive state space algorithm emerges from the H^t8/LQ relationship. This algorithm yields a very good accuracy evaluation of the performance ε₀ by solving just one algebraic Riccati equation. Thorough exploitation of this algorithm results in a drastic computation reduction with respect to the standard e-iteration.     

参数曲面上的插值与混合

如何表示曲面上的曲线,在处理诸如数控加工中的路径设计以及CAD/CAM等领域频繁出现的曲面裁剪问题时显得日益重要.给出了数据点的切方向(切方向及曲率向量或测地曲率值)指定而G¹连续(G²连续)插值曲面上任意点列的方法.作为曲面上曲线插值问题的特例,还讨论了曲面上曲线的混合问题.基本思想是借助于微分几何的有关结论,曲面上曲线的插值问题被转化为其参数平面上类似的曲线插值问题.该方法能够用二维隐式方程来表示曲面上的插值曲线,从而把在显示该曲线时所面对的曲面求交的几何问题转化为计算隐式曲线的代数问题.实验证明该方法是可行的,而且适用于CAD/CAM及计算机图形学等领域.     

A batch arrival queue with a vacation time under single vacation policy

We consider an M^x/G/1 queueing system with a vacation time under single vacation policy, where the server takes exactly one vacation between two successive busy periods. We derive the steady state queue size distribution at different points in times, as well as the steady state distributions of busy period and unfinished work (backlog) of this model.Scope and purposeThis paper addresses issues of model building of manufacturing systems of job-shop type, where the server takes exactly one vacation after the end of each busy period. This vacation can be utilized as a post processing time after clearing the jobs in the system. To be more realistic, we further assume that the arrivals occur in batches of random size instead of single units and it covers many practical situations. For example in manufacturing systems of job-shop type, each job requires to manufacture more than one unit; in digital communication systems, messages which are transmitted could consist of a random number of packets. These manufacturing systems can be modeled by M^x/G/1 queue with a single vacation policy and this extends the results of Levy and Yechiali, Manage Sci 22 (1975) 202, and Doshi, Queueing Syst 1 (1986) 29.     

Semantics of sub-probabilistic programs

The aim of this paper is to extend the probabilistic choice in probabilistic programs to sub-probabilistic choice, i.e., of the form (p)P ^⋈(q)Q where p + q ⩽ 1. It means that program P is executed with probability p and program Q is executed with probability q. Then, starting from an initial state, the execution of a sub-probabilistic program results in a sub-probability distribution. This paper presents two equivalent semantics for a sub-probabilistic while-programming language. One of these interprets programs as sub-probabilistic distributions on state spaces via denotational semantics. The other interprets programs as bounded expectation transformers via wp-semantics. This paper proposes an axiomatic systems for total logic, and proves its soundness and completeness in a classical pattern on the structure of programs.     

Bounded size dictionary compression: SC-completeness and NC algorithms

We study the parallel complexity of a bounded size dictionary version (LRU deletion heuristic) of the LZ2 compression algorithm. The unbounded version was shown to be P-complete. When the size of the dictionary is O(log^kn), the problem of computing the LZ2 compression is shown to be hard for the class of problems solvable simultaneously in polynomial time and O(log^kn) space (that is, SC^k). We also introduce a variation of this heuristic that turns out to be an SC^k-complete problem (the original heuristic belongs to SC^k+1). In virtue of these results, we argue that there are no practical parallel algorithms for LZ2 compression with LRU deletion heuristic or any other heuristic deleting dictionary elements in a continuous way. For simpler heuristics (SWAP, RESTART, FREEZE), practical parallel algorithms are given.     

On the stability of the information state system

The purpose of this paper is to present some preliminary results on the stability of the information state system. The information state system underlies the (infinite dimensional) dynamics of an H_∞ controller for a nonlinear system. Thus it is important to understand its stability and the structure of its equilibrium points. We analyse the important case corresponding to the mixed sensitivity problem. We prove the existence of an equilibrium information state, convergence under very general conditions to such an equilibrium state p_e and uniqueness of this state (up to an irrelevant constant). In this case the equilibrium p_e is usually singular in the sense that it takes on the value − ∞ except on a low dimensional subset of its domain.This meshes with the article [9] which analysed the effect of using p_e to initialize the information state controller and gave explicit formulas which in many cases produce a dramatic reduction in the amount of computation required to implement the controller. What this article suggests is that indeed p_e is the only equilibrium initialization possible.     

On pure H reduced-order dynamic controllers: an erratum

There are at least two approaches advocated to obtain a pure H^∞ reduced-order dynamic controller for a given augmented plant. One approach is to eliminate completely the H² aspect from a standard H²/H^∞ setting. A second approach is to equate the H² aspect with the H^∞ aspect in that same setting. This paper invalidates the first approach but affirms the second approach and produces the correct equations resulting therefrom.     

On the weighted sensitivity minimization problem for delay systems

We consider the H^∞-optimal sensitivity problem for delay systems. In particular, we consider computation of μ:= inf {|W-φq|_∞ : q ε H^∞(j )} where W(s) is any function in RH^∞(j ), and φ in H^∞(j ) is any inner function. We derive a new explicit solution in the pure delay case where φ = e^−sh, h > 0.     

A new characterization of invariant subspaces of and applications to the optimal sensitivity problem

This paper gives a new equivalent characterization for invariant subspaces of H², when the underlying structure is specified by the so-called pseudorational transfer functions. This plays a fundamental role in computing the optimal sensitivity for a certain important class of infinite-dimensional systems, including delay systems. A closed formula, easier to compute than the well-known Zhou–Khargonekar formula, is given for optimal sensitivity for such systems. An example is given to illustrate the result.     

Bessel function of the first kind with complex argument

A new method of computing integral order Bessel functions of the first kind J_n(z) when either the absolute value of the real part or the imaginary part of the argument z = x + iy is small, is described. This method is based on computing the Bessel functions from asymptotic expressions when x∼ 0 (or y ∼ 0). These expansions are derived from the integral definition of Bessel functions. This method is necessary because some existing algorithms and methods fail to give correct results for small x small y. In addition, our overall method of computing Bessel functions of any order and argument is discussed and the logarithmic derivative is used in computing these functions. The starting point of the backward recurrence relations needed to evaluate the Bessel function and their logarithmic derivatives are investigated in order to obtain accurate numerical results. Our numerical method, together with established techniques of computing the Bessel functions, is easy to implement, efficient, and produces reliable results for all z.     

On the strict logic foundation of fuzzy reasoning

This paper focuses on the logic foundation of fuzzy reasoning. At first, a new complete first-order fuzzy predicate calculus system K^* corresponding to the formal system L^* is built. Based on the many-sort system K_ms^* corresponding to K^*, the triple I methods of FMP and FMT for fuzzy reasoning and their consistency are formalized, thus fuzzy reasoning is put completely and rigorously into the logic framework of fuzzy logic.The author is indebted to anonymous referee for his useful comments which have helped to improve the paper.     

L 1 Sensitivity minimization for plants with commensurate delays

In this paper we consider the problem ofL ¹ sensitivity minimization for linear plants with commensurate input delays. We describe a procedure for computing the minimum performance, and we characterize optimal solutions. The computations involve solving a one-parameter family of finite-dimensional linear programs. Explicit solutions are presented for important special cases.Notation X ^* Dual space of a normed linear spaceX - All elements inS with norm 1 - S The annihilator subspace defined as . - S The annihilator subspace defined as . - BV(X) Functions of bounded variation onX - C ₀(X) Continuous function on a locally compact spaceX such that for all > 0, {x X¦ ¦f(x)¦s is compact - C ^N (a, b) Vectors of continuous functions on (a, b) The authors acknowledge support from the Army Research Office, Center for Intelligent Control, under grant DAAL03-86-K-0171, and the National Science Foundation, under grant 8810178-ECS.     

Flow regularity and optimality conditions with controls inL p

In this paper we study theC ^p regularity of the flow of a nonlinear nonautonomous control system with respect to control maps belonging toL ^p withp≥r. The results obtained are applied to get first- and second-order optimality conditions when the control space isL ^p . The problem which we consider is in the Mayer form and includes endpoint constraints. We present first-order necessary conditions for a wide class of control systems. Moreover, we show that the usual second-order sufficient conditions are effective only if the mapf that defines the control system is a polynomial of degree two in the control variable and the controls belong toL ².     

H disturbance attenuation for state delayed systems

In this note, the differential game and dissipation inequality are applied to the disturbance attenuation or H^∞-control for linear systems with delayed state. Firstly, a simple sufficient condition on the existence of a γ-suboptimal H^∞ state feedback controller is given, which is independent of delay, and an observer-based dynamic output feedback solution is presented in terms of Riccati inequalities (or Riccati equations). Secondly, a sufficient condition on the existence of a delay-dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods.     

Reduced-order filtering design for non-linear systems with H ∞ setting

In this article, sufficient conditions are presented for the existence of an H ^∞ filter with a state dimension less than the plant. The conditions are characterised in terms of the solution to a Hamilton–Jacobi inequality, which is exactly the one used in the construction of the full-order H ^∞ filters. When these conditions hold, state-space formulae are also given for such reduced-order filters. Both affine and general non-affine non-linear systems are examined. The development uses only elementary concepts of dissipativity and differential game, thus the given proofs are simple and clear. To illustrate our result, some numerical examples are also included.     

On decoupling the H-optimal sensitivity problem for products of plants

In this note we show how to solve the H^∞-optimal sensitivity problem for a SISO plant P(s) = P₁(s)P₂(s), given the solutions for P₁(s), P₂(s). This allows us to solve the problem for systems of the form e^−hsP₀(s), where P₀(s) is the transfer function of a stable, LTI, finite dimensional system.