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.     

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.     

Movement Problems in Comprehensive Schools

The project which is described here was based on schools in which the main movement problem was one of minimizing the time spent in journeys between activities in the school day. A mathematical model was developed which provides estimates of these times. This was used to investigate the effects of varying the layout of the school buildings and layouts which would reduce the movement times were obtained. Possible timetable and organizational changes which could reduce movement were also suggested.     

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.     

Breakdown of a 2D Heteroclinic Connection in the Hopf-Zero Singularity (II): The Generic Case

In this paper, we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singularity. The method consists in obtaining an asymptotic formula for the difference between these manifolds which turns to be exponentially small respect to the unfolding parameter. The formula obtained is explicit but depends on the so-called Stokes constants, which arise in the study of the original vector field and which corresponds to the so-called inner equation in singular perturbation theory.     

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.     

Dynamic and static loss in stability of flexible spherical shells made out of a composite material

The dynamic and static stability of shallow spherical shells which are rectangular in a plane are investigated. It is assumed that the shell is made out of a composite material which is weakly shear resistant and hence the refined theories which allow for transverse shear deformations and rotational inertia are applied. The solutions which were obtained are compared with solutions founded on the basis of the Kirchhoff-Love theory. It is shown that the results which are obtained on the basis of the classical theory are high for both the static and dynamic loss in stability, and are qualitatively different from the results obtained using the refined theory. The solutions were obtained using the Bubnov-Galerkin method in the higher approximations.     

An index notation for multivariate statistical analysis

This paper presents a simple account of an index notation which is useful in multivariate statistical analysis and which serves to clarify some of the matrix identities which arise in matrix differential calculus.     

Spatial Environment in Comprehensive Schools

This paper describes a mechanism for aiding the designer in generating an efficient and flexible provision of teaching space to match the complex and varying needs in comprehensive schools. The mechanism is a computer program package which comprises three parts: SECS A which outputs schedules of accommodation for any given set of group activity data: SECS B which appraises any existing schedule of accommodation in relation to the minimum; and SES C which identifies the minimum physical flexibility necessary to achieve any set of alternative future accommodation schedules.     

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.     

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.     

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)     

Terrorists’ Eradication Versus Perpetual Terror War

We study an infinite-horizon sequential dynamic game where the players are a government and an international terrorist organization. We provide conditions for the existence of equilibria in which the terrorists’ resources are totally destroyed by a government’s strike. Specifically, we study strong eradication equilibria in which the government’s strike annihilates the terrorists’ resources, preventing the terrorists from acting. We also pay attention to weak eradication equilibria in which the terrorists’ resources are destroyed but in which the initial value of the terrorists’ strike is nevertheless positive. We also show the existence of an equilibrium in which war is perpetual between the government and the terrorists. Perpetual war can only coexist with weak eradication equilibria. For these cases, we provide conditions under which the government would be better off in a weak eradication equilibrium.     

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.     

Steepest-descent failure analysis

An extensive failure analysis of the steepest-descent optimization algorithm has been made. Each of the ways in which the algorithm can fail is discussed in terms of both the mathematical and numerical manifestations of a failure and the information which each type of failure provides about the formulation of the physical problem. Numerical tests for each of the various types of failure are described; several faulty problem formulations are presented, each of which illustrates a particular type of failure. A table is presented in which all failure modes are summarized and the corresponding numerical tests are exhibited.     

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.     

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.     

A Cardinal Pattern Inspired by AD

Assuming Con(AD), a model in which there are unboundedly many regular cardinals below Θ and in which the only regular cardinals below Θ are limit cardinals was previously constructed. Using a large cardinal hypothesis far beyond Con(AD), we construct in this paper a model in which there is a proper class of regular cardinals and in which the only regular cardinals in the universe are limit cardinals. Mathematics Subject Classification: 03E55, 03E60.     

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.     

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.