Triangular norms which are meet-morphisms in interval-valued fuzzy set theory

In this paper we study t-norms on the lattice of closed subintervals of the unit interval. Unlike for t-norms on a product lattice for which there exists a straightforward characterization of t-norms which are join-morphisms, respectively meet-morphisms, the situation is more complicated for t-norms in interval-valued fuzzy set theory. In previous papers several characterizations were given of t-norms in interval-valued fuzzy set theory which are join-morphisms and which satisfy additional properties, but little attention has been paid to meet-morphisms. Therefore, in this paper, we focus on t-norms which are meet-morphisms. We consider a general class of t-norms and investigate under which conditions t-norms belonging to this class are meet-morphisms. We also characterize the t-norms which are both a join- and a meet-morphism and which satisfy an additional border condition.     

Two-dimensional body of maximum mean resistance

A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, [Alexander Yu. Plakhov, Paulo D.F. Gouveia, Problems of maximal mean resistance on the plane, Nonlinearity, 20 (2007), 2271-2287], shapes of nonconvex bodies were sought which would maximize the braking force of the medium on their movement. Giving continuity to this study, new investigations have been undertaken which culminate in an outcome which represents a large qualitative advance relative to that which was achieved earlier. This result, now presented, consists of a two-dimensional shape which confers on the body a resistance which is very close to its theoretical supremum value. But its interest does not lie solely in the maximization of Newtonian resistance; on regarding its characteristics, other areas of application are seen to begin to appear which are thought to be capable of having great utility. The optimal shape which has been encountered resulted from numerical studies, thus it is the object of additional study of an analytical nature, where it proves some important properties which explain in great part its effectiveness.     

Cycles of covers

We initially consider an example of Flynn and Redmond, which gives an infinite family of curves to which Chabauty’s Theorem is not applicable, and which even resist solution by one application of a certain bielliptic covering technique. In this article, we shall consider a general context, of which this family is a special case, and in this general situation we shall prove that repeated application of bielliptic covers always results in a sequence of genus 2 curves which cycle after a finite number of repetitions. We shall also give an example which is resistant to repeated applications of the technique.     

Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method

A method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear equations.     

Determination of Lagrangians from Equations of Motion and Commutator Brackets

The question as to whether a given set of equations, which govern the dynamical evolution of a system, determine a Lagrangian is considered. This problem, which has come to be known as the inverse problem of the calculus of variations, is reviewed and theorems which contain systems of partial differential equations which determine a type of self-adjointness are developed. It is shown that, given a reasonable form for the classical correspondence, the usual quantum commutator brackets can be expressed in terms of classical quantities which satisfy a particular form of these equations.     

Deficiencies in Safety Schemes which Rely on Stochastically Failing Protective Equipment

Probability theory is used to assess the deficiencies of safetyschemes which rely on devices which can fail either in an undetectedmanner only, or in both undetected and detected ways. Threequantities are used to express the deficiencies of these schemes;the mean period during which devices are ineffective, the proportionof time for which they are ineffective and the distributionof the durations of their ineffective periods. Analytical expressionsare derived for these quantities for a scheme in which onlyundetected failures occur and devices are replaced at regularintervals. Monte Carlo simulation techniques are used to estimatethe measures of deficiency for situations in which both typesof failure are possible. Consideration is given to the "cost-benefit"aspects of safety schemes in simple circumstances in which therate of occurrence of the hazards involved, and the penaltyto be paid in the event of a catastrophe, are known.     

油井分层注水倍数计算方法

运用水井纵向劈分方法,对B-Z油田3口水井对应5个小层进行劈分,将与油井连通的各水井水量劈分到连通层位上.运用水井平面劈分方法,对上述各区水井劈分到各层的产水量劈分到该层与水井连通的油井上,将各水井水量劈分到同一油井相同层位上的水量累加得到与水井连通油井的注水量.运用劈分结果计算出B-Z油田水井射开层位的累积注水倍数,对油田后续开发调整提供理论依据.     

Tests of Optimality in Constrained Optimization

Sufficiency and necessity theorems are described which testthe optimality of a vector when it is required to minimize agiven function of variables which are subject to inequalities. The paper starts with an exposition of theorems of alternatives,which are fundamental when the functions considered are linear,and proceeds to a systematic formulation of various constraintqualifications, which make it possible to extend results whichhold in linear programming to the non-linear case.     

Analysis of Venn Diagrams Using Cycles in Graphs

This paper is the last in a series by the authors on the use of graph theory to analyze Venn diagrams on few curves. We complete the construction (and hence the enumeration) of spherical Venn diagrams on five curves, which yields additional results about conjectures of Grünbaum concerning which Venn diagrams are convex, which are exposed, and which can be drawn with congruent ellipses.     

The nucleolus and kernel of veto-rich transferable utility games

The process of computing the nucleolus of arbitrary transferable utility games is notoriously hard. A number of papers have appeared in which the nucleolus is computed by an algorithm in which either one or a huge number of huge linear programs have to be solved. We show that on the class of veto-rich games, the nucleolus is the unique kernel element. Veto-rich games are games in which one of the players is needed by coalitions in order to obtain a non-zero payoff. We then provide a fast algorithm which does not use linear programming techniques to compute the nucleolus of these games. Furthermore, we provide a few examples of economic situations which belong to the class of veto-rich games and which are treated in the literature.     

Combining maintenance activities in an operational Planning Phase: a Set-Partitioning approach

Joint execution of maintenance activities can redua costs becausepreparative activities, like opening a machine, may be shared.Combining execution, however, also implies that activities arecamed out at times other than originally planned. In this paper,we analyse the problem of determining which activities shouldbe combined at which moments in time. We develop a methodologyto represent the cost-effectiveness of combining activities,and to identify an optimal combination plan. The method consistsof three phases: one in which penalty cost functions are derived,another in which combinations are evaluated, and finally onein which the optimal combination is obtained through a set-partitioningalgorithm.     

An extension of Radner's theorem

Radner's theorem states that the optimal solution for a static linear quadratic Gaussian (LQG) team is linear. In this paper, we find the optimal solution for a static LQG team in which each player knows which observations he has, but in which the observation set that a player receives (how many, which measuring device,etc.) is random before the team acts. Via the concept of nesting, the result extends to the dynamic case and includes teams in which the order of play of the team members as well as their sets of data are random. We also include random changes in the cost function which depend on the randomness of the observation system but are independent of the stochastic process that the team is observing and controlling.     

协同设计资源的两级不确定调度问题研究及其求解

针对协同设计资源调度问题中存在的设计任务不确定、资源需求模糊以及任务进行过程中可能出现变化等情况,提出一种基于不确定规划和反应式调度的两级不确定调度模型,通过根据满足系数对最好及最坏规划进行折中的方法对模型进行转化,然后采用离散的自由搜索算法进行求解.通过实例,验证了该方法的有效性.     

A Minkowskian theory of observation: Application to uncertainty and fuzziness

This paper examines various ways to introduce subjectivity in the measures of uncertainty. In the first part, by using a simple physical remark concerning discrete entropy in Shannon sense, we derive a so-called ‘complete discrete entropy’ which provides a unified approach to discrete and continuous entropy, and applies directly to variables which involves both probability and possibility.In the second part, by using three elementary axioms, we derive a Minkowskian theory of observation which holds when the observable is a pair (syntax, semantics) and which involves a parameter which is directly related to the subjectivity of the observer. This model is then applied to the observation of uncertainty, transinformation and membership, in which case it provides a new approach to fuzzy number.     

Wide area telecommunication network design: application to the Alberta SuperNet

This article proposes a solution methodology for the design of a wide area telecommunication network. This study is motivated by the Alberta SuperNet project, which provides broadband Internet access to 422 communities across Alberta. There are two components to this problem: the network design itself, consisting of selecting which links will be part of the solution and which nodes should house shelters; and the loading problem which consists of determining which signal transport technology should be installed on the selected edges of the network. Mathematical models are described for these two subproblems. A tabu search algorithm heuristic is developed and tested on randomly generated instances and on Alberta SuperNet data.     

Terminable and interminable paths and trails in infinite graphs

The paper is concerned with certain kinds of random processes in infinite graphs. A finite trail of a graph which cannot be continued from either end is called terminated, and a finite trail is called terminable of it is a segment of a finite terminated trail; analogously for 1 - ∞ trails, finite paths, and 1 - ∞ paths.For k = 1,2,3,…, there exist graphs which contain 2 - ∞ paths and have node-connectivity k and in which no finite path and no 1 - ∞ path is terminable, and also such graphs in which every finite path and every 1 - ∞ path is terminable. In any graph with infinite node-connectivity every node of valency N₀ is the end-node of terminated 1 - ∞ paths. There exist graphs with node-connectivity N₀ in which every 1 - ∞ path is terminable. For λ = 1,2,3,…, there exist graphs which contain 2 - ∞ paths and have edge-connectivity λ and in which no finite trail and no 1 - ∞ trail is terminable, and also such graphs in which every finite trail and every 1 - ∞ trail is terminable. In contrast to the situation for 1 - ∞ paths, every connected infinite graph in which every 1 - ∞ trail is terminable contains at least one node of odd edge-degree and if in addition every finite trail is terminable, then there are at least two nodes of odd edge-degree.     

A note on the finitization of Abelian and Tauberian theorems

We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem, which presents a simple condition under which the converse holds. Our approach is inspired by proof theory, and in particular Gödel's functional interpretation, which we use to establish quantitative versions of both of these results.     

Multi-frequency mode-locked lasers

A new theoretical model is constructed which describes the operation of multi-frequency, pulsed mode-locked laser cavities. The model, which is a combination of multi channel interactions in the canonical master mode-locking model subject to three different gain models which account for both self- and cross-saturation effects, results in mode-locking dynamics which qualitatively describe the observed experimental dual-frequency laser operation. Specifically, the combination of self- and cross-saturation in the gain allows for mode-locking at two frequencies simultaneously, which can be of significantly different energies and pulsewidths. The model gives a framework for understanding the operation and stability of the increasingly important and timely technology of dual- and multi-frequency mode-locked laser cavities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global stability of stationary solutions of reaction-diffusion systems

We give a condition which implies that the trivial solution, U ≡ 0, of a class of reaction-diffusion systems with homogeneous Dirichlet boundary conditions, is a global attractor for all nonnegative solutions. In certain cases, this condition, which relates the diffusion matrix and the domain to a parameter which depends on the nonlinear term, significantly improves similar conditions which can be obtained from energy estimates. Applications are given to equations arising in mathematical ecology.