Computer Forecasting of Australian Rules Football for a Daily Newspaper

An exponential smoothing technique operating on the margins of victory was used to predict the results of Australian Rules football matches for a Melbourne daily newspaper from 1981-86 and again for a competitor in 1991-92. An initial ‘quick and dirty’ program used only a factor for team ability and a common home ground advantage to predict winning margins. Probabilities of winning were accumulated to predict a final ladder, with a simulation to predict chances of teams finishing in any position. Changes to the competition forced a more complicated approach, and the current version uses several parameters which allow for ability, team/ground interaction, team interaction, and a tendency for team ability to regress towards the mean between seasons. A power method is used to place greater weight on the errors in closer matches, and errors across the win-lose boundary. While simple methods were used originally, the Hooke and Jeeves method was used in optimizing the parameters of the current model. Both the original model and the improved version performed at the level of expert tipsters.     

推理规则的信息熵描述

根据信息理论的一些基本观点首次定义了决策逻辑系统中公式的信息熵,由此给出了知识系统中推理规则信息熵的定义。然后讨论了推理规则信息熵的某些性质。随后又建立了一些推理规则信息熵有关的若干重要概念,从而揭示了信息论与知识表达系统之间的某些联系,为信息理论应用于人工智能及数据挖掘提供了一定的理论或技术性工具。     

Suggested research topics in sensitivity and stability analysis for semi-infinite programming problems

We suggest several important research topics for semi-infinite programs whose problem functions and index sets contain parameters that are subject to perturbation. These include optimal value and optimal solution sensitivity and stability properties and penalty function approximation techniques. The approaches proposed are a natural carryover from parametric nonlinear programming, with emphasis on practical applicability and computability.Research supported by National Science Foundation Grant SES 8722504 and Grant ECS-86-19859 and Grant N00014-89-J-1537, Office of Naval Research.     

Dirichlet Problem for Degenerate Quasilinear Elliptic Equations Suggested by the Anisotropic Permeation

By Browder's pseudo-monotone operator theory and the techniques belonging to J. Leray and J. Lions, the existence theorem of the generalized solution of the Dirichlet problem for a strongly degenerate quasilincar elliptic equation has been proved in the anisotropic Sobolev space.     

A Positivity Property of a Quantum Anharmonic Oscillator Suggested by the BMV Conjecture

In this work an observation concerning a positivity property of the quantum anharmonic oscillator is made. This positivity property is suggested by the BMV conjecture.     

Branching Rules for General Linear Groups

In this article we give a branching rule for Harish–Chandra restriction from the general linear group Gl _n (q) to the Levi subgroup Gl _n?1(q) × Gl₁(q) in the case of the unipotent block.     

Calculus Rules for Derivatives of Multimaps

In this paper, by virtue of two intermediate derivative-like multifunctions, which depend on an element in the intermediate space, some exact calculus rules are obtained for calculating the derivatives of the composition of two set-valued maps. Similar rules are displayed for sums. Moreover, by using these calculus rules, the solution map of a parametrized variational inequality and the variations of the feasible set of a parametrized mathematical programming problem are studied. This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 10871216 and 60574073).     

Residual Finiteness for Admissible Inference Rules

We look into methods which make it possible to determine whether or not the modal logics under examination are residually finite w.r.t. admissible inference rules. A general condition is specified which states that modal logics over K4 are not residually finite w.r.t. admissibility. It is shown that all modal logics over K4 of width strictly more than 2 which have the co-covering property fail to be residually finite w.r.t. admissible inference rules; in particular, such are K4, GL, K4.1, K4.2, S4.1, S4.2, and GL.2. It is proved that all logics over S4 of width at most 2, which are not sublogics of three special table logics, possess the property of being residually finite w.r.t. admissibility. A number of open questions are set up.     

Quasi-Multiplier Rules for Quasidifferentiable Extremum Problems

The purpose of the present article is to contribute to clarify the role of the Lagrange multipliers within the theory of the first order necessary optimality conditions for nonsmooth constrained optimization, when the directional derivatives of functions involved in the extremum problems are not sublinear. This task is accomplished in the particular case of quasidifferentiable problems with side constraints. In such setting, making use of the image-space approach, it is possible to establish a generalized (nonlinear) separation result by means of which a new Lagrange principle is obtained. According to this principle, which seems to fit better quasidifferentiable extremum problems than the classic one, the concept of linear multiplier is to be replaced with that of quasi-multiplier, a sublinear and continuous functional whose existence can be guaranteed under mild assumptions, even when classic multipliers fail to exist. Such as extension allows to formulate in terms of Lagrange function the known optimality necessary condition for unconstrained quasidifferentiable optimization expressed in form of quasidifferential inclusion. Along with this, other multiplier rules are established.     

Different Quality Indexes for Lattice Rules

We consider lattice rules (i.e. cubature formulas with equal coefficients whose nodes lie on a lattice) which are exact for trigonometric polynomials in two variables with different spectra. Various quality indexes are characterized. Extremal properties of indexes are obtained. A new family of lattice rules of trigonometric degree is presented. Also a family of lattice rules exact on trigonometric polynomials of a hexagonal spectrum is constructed.     

Describing a Basis in Semireduced Form for Inference Rules of Intuitionistic Logic

It is shown that a set of all rules in semireduced form whose premises satisfy a collection of specific conditions form a basis for all rules admissible in IPC. The conditions specified are quite natural, and many of them show up as properties of maximal theories in the canonical Kripke model for IPC. Besides, a similar basis is constructed for rules admissible in the superintuitionistic logic KC, a logic of the weak law of the excluded middle.     

Branching Rules for Splint Root Systems

Algebras and Representation Theory - A root system is splint if it is a decomposition into a union of two disjoint root systems. Examples of such root systems arise naturally in studying embeddings...     

Some Calculus Rules for Contingent Epiderivatives

This article presents some calculus rules for contingent epiderivatives of set-valued maps. Among other results the main emphasis is focused on a formula for scalar multiplication, sum formulae and chain rules. The calculus of contingent cones and some inversion theorems are used as a tool. Some applications are also given.     

Improved Error Bounds for Lattice Rules

We establish results on the worst-case errors that can be achieved by well-chosen lattice rules for standard classes of multivariate periodic functions. These theorems improve or generalize earlier results of this type.     

A Suggested Mechanism for Nonlinear Wall Roughness Effects on High Reynolds Number Flow Stability

The interactions between an uneven wall and free stream unsteadiness and their resultant nonlinear influence on flow stability are considered by means of a related model problem concerning the nonlinear stability of streaming flow past a moving wavy wall. The particular streaming flows studied are plane Poiseuille flow and attached boundary-layer flow, and the theory is presented for the high Reynolds number regime in each case. That regime can permit inter alia much more analytical and physical understanding to be obtained than the finite Reynolds number regime; this may be at the expense of some loss of real application, but not necessarily so, as the present study shows. The fundamental differences found between the forced nonlinear stability properties of the two cases are influenced to a large extent by the surprising contrasts existing even in the unforced situations. For the high Reynolds number effects of nonlinearity alone are destabilizing for plane Poiseuille flow, in contrast with both the initial suggestion of earlier numerical work (our prediction is shown to be consistent with these results nevertheless) and the corresponding high Reynolds number effects in boundary-layer stability. A small amplitude of unevenness at the wall can still have a significant impact on the bifurcation of disturbances to finite-amplitude periodic solutions, however, producing a destabilizing influence on plane Poiseuille flow but a stabilizing influence on boundary-layer flow.