(φ,ξ,η,λ)‐Structures of Parabolic Type

We consider (,,,)structures of parabolic type on hypersurfaces of dual spaces and study the rank of the affinor . We consider almost contact metric structures of parabolic type of the first kind on hypersurfaces of 4dimensional dual metric space. We study the properties of these structures and give examples of normal, integrable, and Sasakian parabolic structures.     

Start‐up class models in multiple‐class queues with N‐policy

In this paper, we consider multipleclass queueing systems with Npolicy in which the idle server starts service as soon as the number of customers in the startup class reaches threshold N. We consider the cases of FCFS and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behavior of such systems.     

Stability Tests for Two Common Classes of Linear Time‐Delay and Hybrid Systems

The stability of linear timedelay systems with point internal delays is difficult to deal with in practice because of the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. This feature usually causes the system to possess an infinite number of poles. In this paper, stability tests for this class of systems are obtained based either on extensions of classical tests applicable to delayfree systems or on approaches within the framework of twodimensional digital filters. Some of those twodimensional stability tests are also proved to be useful for stability testing of a common class of linear hybrid systems which involve coupled continuous and digital substates after a slightadhoc adaptation of the tests for that situation.     

On the Completeness and Decidability of the Horn‐Like Fragment of the First‐Order Linear Temporal Logic

We prove the completeness and decidability of the Hornlike sequents, specifically, the socalled D₂sequents (of the firstorder linear temporal logic) considered in the author's paper [Lith. Math. J., 41(3), 266–281 (2001)]. In this paper, with the help of the infinitary calculus G_L, grounded by the author in his earlier papers, for D₂sequents we construct a D₂Sat calculus of the socalled saturated type consisting of decidable deductive procedures replacing the omegarule for the always operator. In the present paper, in order to prove the completeness and decidability of the calculus D₂Sat, we construct the socalled invariant decidable calculus D₂IN. We prove the equivalence of the calculi D₂IN, D₂Sat, and G _L ^** for the socalled saturated D₂sequents. From this equivalence, by reducing an arbitrary D₂sequent to a saturated D₂sequent, and also from the completeness of the G _L ^** calculus and decidability of the invariant calculus D₂IN, we deduce the completeness and decidability of the calculus D₂Sat in the class of D₂sequents.     

Von Neumann Categories and Extended L2 Cohomology

In this paper we suggest a new general formalism for studying the L2 invariants of polyhedra and manifolds. First, we examine generality in which one may apply the construction of the extended Abelian category, which was earlier suggested by the author using the ideas of P. Freyd. This leads to the notions of a finite von Neumann category and a trace on such a category. Given a finite von Neumann category, we study the extended L2 homology and cohomology theories with values in the Abelian extension. Any trace on the initial category produces numerical invariants – the von Neumann dimension and the Novikov–Shubin numbers. Thus, we obtain the local versions of the Novikov–Shubin invariants, localized at different traces. In the Abelian case this localization can be made more geometric: we show that any torsion object determines a divisor – a closed subspace of the space of the parameters. The divisors of torsion objects together with the information produced by the local Novikov–Shubin invariants may be used to study multiplicities of intersections of algebraic and analytic varieties (we discuss here only simple examples demonstrating this possibility). We compute explicitly the divisors and the von Neumann dimensions of the extended L2 cohomology in the real analytic situation. We also give general formulae for the extended L2 cohomology of a mapping torus. Finally, we show how one can define a De Rham version of the extended cohomology and prove a De Rhamtype theorem.     

A sample path analysis of the M t /M t /c queue

The exact transient distribution of the queue length of the M _t /M _t /1 single server queue with timedependent Poisson arrival rate and timedependent exponential service rate was recently obtained by Zhang and Coyle [63] in terms of a solution to a Volterra equation. Their method involved the use of generating functions and complex analysis. In this paper, we present an approach that ties the computation of these transient distributions directly to the random sample path behavior of the M _t /M _t /1 queue. We show the versatility of this method by applying it to the M _t /M _t /c multiserver queue, and indicating how it can be applied to queues with timedependent phase arrivals or timedependent phase service.     

Spatial shape‐preserving interpolation using ν‐splines

We present a global iterative algorithm for constructing spatial G ²continuous interpolating splines, which preserve the shape of the polygonal line that interpolates the given points. Furthermore, the algorithm can handle data exhibiting two kinds of degeneracy, namely, coplanar quadruples and collinear triplets of points. The convergence of the algorithm stems from the asymptotic properties of the curvature, torsion and Frénet frame of splines for large values of the tension parameters, which are thoroughly investigated and presented. The performance of our approach is tested on two data sets, one of synthetic nature and the other of industrial interest.     

Spaces over a Category and Assembly Maps in Isomorphism Conjectures in K‐ and L‐Theory

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraicKandLtheory of integral group rings and to the Baum–Connes Conjecture on the topologicalKtheory of reducedC*algebras of groups. The approach is through spectra over the orbit category of a discrete groupG.We give several points of view on the assembly map for a family of subgroups and characterize such assembly maps by a universal property generalizing the results of Weiss and Williams to the equivariant setting. The main tools are spaces and spectra over a category and their associated generalized homology and cohomology theories, and homotopy limits.     

Resource allocation in the North Sea demersal fisheries: A goal programming approach

The management of a fishery is a complex task generally involving multiple, often conflicting, objectives. These objectives typically include economic, biological and social goals such as improving the income of fishers, reducing the catch of depleted species and maintaining employment.Multicriteria decision making (MCDM) techniques appear wellsuited to such a management problem, allowing compromises between conflicting objectives to be analysed in a structured framework. In comparison to other fields, such as water resource planning, forestry and agriculture, there have been few applications of MCDM to fisheries.In this paper, a goal programming model of the North Sea demersal fishery is presented. The model is used to demonstrate the potential applicability of this type of approach to the analysis and development of fisheries management plans with multiple objectives. Alternative scenarios are considered for the problem, and tradeoffs between given objectives are also highlighted and discussed.     

A robust decomposition method for the analysis of production lines with unreliable machines and finite buffers

We consider production lines consisting of a series of machines separated by finite buffers. The processing time of each machine is deterministic and all the machines have the same processing time. All machines are subject to failures. As is usually the case for production systems we assume that the failures are operation dependent [3,7]. Moreover, we assume that the times to failure and the repair times are exponentially distributed. To analyze such systems, a decomposition method was proposed by Gershwin [13]. The computational efficiency of this method was later significantly improved by the introduction of the socalled DDX algorithm [5,6]. In general, this method provides fairly accurate results. There are, however, cases for which the accuracy of this decomposition method may not be acceptable. This is the case when the reliability parameters (average failure time and average repair time) of the different machines have different orders of magnitude. Such a situation may be encountered in real production lines. In [8], an improvement of Gershwin's original decomposition method has been proposed that in general provides more accurate results in the above mentioned situation. This other method is referred to as the Generalized Exponential (GE) method. The basic difference between the GEmethod and that of Gershwin is that it uses a twomoment approximation instead of a singlemoment approximation of the repair time distributions of the equivalent machines. There are, however, still cases for which the accuracy of the GEmethod is not as good as expected. This is the case, for example, when the buffer sizes are too small in comparison with the average repair time. We present in this paper a new decomposition method that is based on a better approximation of the repair time distributions. This method uses a threemoment approximation of the repair time distributions of the equivalent machines. Numerical results show that the new method is very robust in the sense that it seems to provide accurate results in all situations.     

Relative E ‐Theory

The Etheory of A. Connes and N. Higson provides a new realization of Khomology based on the notion of asymptotic morphisms. In this paper we define relative Etheory, associating to a C*algebra A and an ideal I the Abelian groups Enrel(A;I). These groups are related to the Etheory groups of A and I in the familiar way by a long exact sequence and excision isomorphisms. The definition of relative Etheory is motivated by the properties of first order, elliptic differential operators on complete Riemannian manifolds. Applications will be considered in a future publication.     

On the Periodic Zeta‐Function. II

We obtain a more precise asymptotic formula than in [Lith. Math. J., 41(2), 168–177 (2001)] for the mean square of the periodic zetafunction.     

Tableaus with Invertible Rules for Many‐Valued Modal Propositional Logics

We investigate tableaubased theorem proving for some families of manyvalued modal propositional logics. We consider manyvalued counterparts of wellknown twovalued modal logics obtained from various combinations of four basic properties of the accessibility relation, i.e., reflexivity, transitivity, seriality, and Euclideaness. For each of these logics we introduce tableau systems with certain invertible rules. We prove soundness and completeness of the presented tableau systems.     

Risk programming for agricultural resource allocation: A multidimensional risk approach

This paper develops an approach to deal with risk in agricultural decisions. Although the model is in line with the Prospect ranking theory and the Partitioned multiobjective risk method, which recognise the multidimensional character of any risk measure taken in agricultural decisionmaking problems, its behavioural hypothesis and analytical development are totally different. The way in which the approach works is illustrated through a simple but wellknown example in agricultural planning.     

SHADOC: a multi‐agent model to tackle viability of irrigated systems

The viability of irrigated systems in the Senegal River Valley is being brought into question today due to their underutilization. We assume that their viability depends largely on the way their different components behave and interact. We therefore sought to examine in greater depth today's knowledge of the structure of these systems and activities performed within them. This led to the development of a multiagent system model, a kind of virtual irrigated system, with a special focus on rules in use for access to credit, water allocation and cropping season assessment as well as organization and coordination of farmers. The purpose of this paper is to show how this kind of tool is relevant to the study of irrigated systems' viability. As an example it is used to examine the influence of existing social networks on the viability of irrigated systems.     

Economic and biological risk analysis of the Norwegian spring‐spawning herring fishery

The purpose of this paper is to study the biological and economic risks involved in the management of the Norwegian springspawning herring fishery. We use a discrete time and agestructured model based on historical data. The current paper investigates, under different levels of fishing mortalities, the risk probabilities related to the time behaviour of the spawning stock and profit. We show that the exploitation of the herring stock is vulnerable to small changes in harvesting and price level.     

On a Positivity Property of the Riemann ξ‐Function

We consider a quantitative version of the positivity condition of the Riemann function. J. C. Lagarias obtained that for >10. The main aim of this paper is to prove the equality for 1.     

Modelling the trade‐offs between farm income and the reduction of erosion and nitrate pollution

Water is a very limited resource in Tunisia, both in quantity and in quality. Problems of quality are related to urban, industrial and agricultural activity. Erosion is causing dams to silt up and is leading to phosphorus accumulation in water. The use of agrochemicals, primarily nitrogen and phosphorus, is causing problems of eutrophication. This paper presents the results of a study of sediment and nitrate pollution. The methodology used is based on the EPIC simulation model and a multiobjective programming model (MOPM). The data generated by EPIC are input for the MOPM together with the economic variables. These tools are applied to a 486 ha farm located in northern Tunisia which includes an irrigated area of 300 ha. The study considers three objectives: maximization of gross margin, minimization of erosion, and minimization of nitrate losses. The noninferior set estimation method is implemented to generate the tradeoff curves between the objectives. Results show that nitrate losses are important for both rainfed and irrigated land. The same conclusion is valid for erosion. It is shown that the farmer can reduce the environmental burden without decreasing gross margin, since he is operating below the efficiency curve.     

Asymptotic Expansion of M ‐Estimator Over Wiener Space

In this paper we consider an Mestimator defined as a solution of a given estimating function. Sufficient conditions of existence of an Mestimator and its stochastic expansion are presented. In the case where the underlying probability space is a Wiener space and the leading term of the stochastic expansion is a martingale, asymptotic expansions of its distribution function are obtained with the aid of Malliavin calculus. Applications to a stationary ergodic diffusion model are also discussed.     

A Population Dynamics Model with Parental Care

A model for an agestructured unlimited population dynamics with parental care of offspring is presented (migration of individuals is not taken into account). The model consists of six partial integrodifferential equations for single males, single females, pairs with offspring under parental care, pairs without offspring under parental care, and offspring of the male and female sex. A class of separable solutions is constructed.