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.     

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.     

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.     

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.     

A finite‐capacity queue with exhaustive vacation/close‐down/setup times and Markovian arrival processes

We consider a finitecapacity singleserver vacation model with closedown/setup times and Markovian arrival processes (MAP). The queueing model has potential applications in classical IP over ATM or IP switching systems, where the closedown time corresponds to an inactive timer and the setup time to the time delay to set up a switched virtual connection (SVC) by the signaling protocol. The vacation time may be considered as the time period required to release an SVC or as the time during which the server goes to set up other SVCs. By using the supplementary variable technique, we obtain the queue length distribution at an arbitrary instant, the loss probability, the setup rate, as well as the Laplace–Stieltjes transforms of both the virtual and actual waiting time distributions.     

(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.     

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.     

Simulation optimization of buffer allocations in production lines with unreliable machines

We use a recent simulationbased optimization method, sample path optimization, to find optimal buffer allocations in tandem production lines where machines are subject to random breakdowns and repairs, and the product is fluidtype. We explore some of the functional properties of throughput of such systems and exploit these properties to prove the almost sure convergence of our optimization technique, under a regularity condition on the steady state. Utilizing a generalized semiMarkov process (GSMP) representation of the system, we derive recursive expressions to compute onesided directional derivatives of throughput, from a single simulation run. Finally, we give computational results for lines with up to 50 machines. We also compare results for smaller lines with the results from a more conventional method, stochastic approximation, whenever applicable. In these numerical studies, our method performed quite well on problems that are considered difficult by current computational standards.     

On K‐Theory of Simplicial Rings and Degreewise Constructions

We give a measure of the difference between Waldhausen's definition of the Ktheory of a simplicial ring and the definition we obtain by extending Quillen's definition degreewise. This has computational advantages as the degreewise Ktheory sometimes is simpler to work with.     

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.     

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.     

Equivariant Riemann–Roch for G ‐Quasi‐Projective Varieties‐I

Let G denote a complex linear algebraic group. In this paper we establish several forms of equivariant Riemann–Roch valid for the category of Gquasiprojective complex varieties. The main application is to the operation of convolution that appears in the construction of modules over convolution algebras, for example the Hecke algebras associated to a complex reductive group as well as in the representation theory of quantum groups. The paper concludes with a discussion of some of these applications. The results in this paper hold mostly at the level of Grothendieck groups. The second part of this paper will discuss the extension to higher Ktheory in detail.     

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.     

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.     

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.     

A unified framework for pull control mechanisms in multi‐stage manufacturing systems

This paper presents a unified framework for pull production control mechanisms in multistage manufacturing systems. A pull production control mechanism in a multistage manufacturing system is a mechanism that coordinates the release of parts into each stage of the system with the arrival of customer demands for final products. Four basic pull production control mechanisms are presented: Base Stock, Kanban, Generalized Kanban, and Extended Kanban. It is argued that on top of any of these basic coordination mechanisms, a local mechanism to control the workinprocess in each stage may be superimposed. Several cases of basic stage coordination mechanisms with stage workinprocess control are presented, and several production control systems that have appeared in the literature are shown to be equivalent to some of these cases.     

Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces

In this paper, we introduce two classes of variational-like inequalities with generalized monotone mappings in Banach spaces. Using the KKM technique, we obtain the existence of solutions for variational-like inequalities with relaxed – monotone mappings in reflexive Banach spaces. We present also the solvability of variational-like inequalities with relaxed – semimonotone mappings in arbitrary Banach spaces by means of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve the corresponding results of Refs. 1–6.     

An empirical bioeconomic investigation of efficiency in the insecticide regulatory process

This paper presents an interdisciplinary approach to estimating the relative efficiency of static, myopic, and dynamic insecticide regulatory decision making when there are potential impacts associated with pest resistance. A theoretical control model was developed using expected total economic surplus as the objective function, with an empirical solution to the maximization problem attained by imposing a heuristic search procedure on a bioeconomic simulation model. Although the impact of nondynamic decision making was the most severe, in percentage terms, for shortrun planning horizons, the magnitude of the longrun losses associated with nondynamic decision making could serve as a rationale for modifying the regulatory process to include dynamic considerations. The static analyses usually used in the benefits assessment procedure may severely underestimate the actual benefits of continued chemical registration, and the efficiency gains to society have the potential to offset the increased costs of regulation that would occur under a revised process.