Irregular Isomonodromic Deformations for Garnier Systems and Okamoto's Canonical Transformations

The paper describes the Garnier systems as isomonodromic deformationequations of a linear system with a simple pole at 0 and a Poincarérank 1 singularity at infinity. The extension of Okamoto's birationalcanonical transformations to the Garnier systems in more thanone variable and to the Schlesinger systems is discussed.     

The planar discontinuous piecewise linear refracting systems have at most one limit cycle

In this paper we investigate the limit cycles of planar piecewise linear differential systems with two zones separated by a straight line. It is well known that when these systems are continuous they can exhibit at most one limit cycle, while when they are discontinuous the question about maximum number of limit cycles that they can exhibit is still open. For these last systems there are examples exhibiting three limit cycles.The aim of this paper is to study the number of limit cycles for a special kind of planar discontinuous piecewise linear differential systems with two zones separated by a straight line which are known as refracting systems. First we obtain the existence and uniqueness of limit cycles for refracting systems of focus-node type. Second we prove that refracting systems of focus–focus type have at most one limit cycle, thus we give a positive answer to a conjecture on the uniqueness of limit cycle stated by Freire, Ponce and Torres in Freire et al. (2013). These two results complete the proof that any refracting system has at most one limit cycle.     

On the Representation Theory of Lie Triple Systems

In this paper, we take a new look at the representation theory of Lie triple systems. We consider both ordinary Lie triple systems and restricted Lie triple systems in the sense of [14]. In a final section, we begin a study of the cohomology of Lie triple systems.

     

Repairable failure-delay systems with elementary structure

This paper defines repairable failure-delay systems, and gives explicit formulae for their availability. It presents models for single-component, series and parallel systems with delay at system level, and a ‘rare event’ approximation for availability and reliability of series systems with delay at component level. Finally, it uses a renewal terminating process for deriving the limiting distribution of the lifetime of failure-delay systems.     

Rotation number quantization effect

We study a class of dynamical systems on a torus that includes dynamical systems modeling the dynamics of the Josephson transition. For systems in this class, we introduce certain characteristics including a sequence of functions depending on the system parameters. We prove that if this sequence converges at a given point in the parameter space, then its limit is equal to the classical rotation number, and we then call this point a quantization point for the rotation number. We prove that the rotation number of such a system takes only integer values at a quantization point. Quantization areas are thus defined in the parameter space, and the problem of effectively describing them becomes an important part of characterizing the systems under study. We present graphs of the rotation number at quantization points and under conditions when it is not quantized (an example of a half-integer rotation number) and diagrams for quantization areas.     

Nilpotent centers of cubic systems

We present an explicit form of cubic systems with a nilpotent singular point of the focus or center type at the origin. A method for finding the focus quantities of such systems is indicated. Sufficient conditions for the existence of a nilpotent center for cubic systems are given. Cubic systems reducible to the Li´enard system are studied in detail.     

Critical systems thinking and practice

Critical systems thinking and the methodologies associated with it were developed precisely to allow analysis of complex societal problems and intervention to resolve such problems. Early approaches employing systems ideas, such as operational research, systems analysis and systems engineering, were suitable for tackling certain well-defined problems, but were found to have limitations when faced with complex problems involving people with a variety of viewpoints and frequently at odds with one another. Systems thinkers responded with approaches such as system dynamics and organisational cybernetics to tackle complexity; soft systems methodology (SSM) and interactive planning to handle subjectivity; and critical systems heuristics to help the disadvantaged in situations involving conflict. There was a corresponding enlargement of the range of problem contexts in which they felt competent to intervene. It has been critical systems thinking, however, which has supplied the bigger picture, has allowed systems thinking to mature as a discipline and has set out how the variety of methodologies now available can be used together in a coherent manner to promote successful intervention in complex societal problem situations. This paper outlines, at the request of the editor of this special issue, my involvement in developing critical systems thinking and practice, describes its origins, nature and use, and sets out a programme for future research in the area.     

Survey of research in the design and control of automated guided vehicle systems

Automated guided vehicles (AGVs) are used for the internal and external transport of materials. Traditionally, AGVs were mostly used at manufacturing systems. Currently, AGVs are also used for repeating transportation tasks in other areas, such as warehouses, container terminals and external (underground) transportation systems. This paper discusses literature related to design and control issues of AGV systems at manufacturing, distribution, transshipment and transportation systems. It is concluded that most models can be applied for design problems at manufacturing centres. Some of these models and new models already proved to be successful in large AGV systems. In fact, new analytical and simulation models need to be developed for large AGV systems to overcome large computation times, NP-completeness, congestion, deadlocks and delays in the system and finite planning horizons. We specify more specific research perspectives in the design and control of AGV systems in distribution, transshipment and transportation systems.     

Polling systems with multiple coupled servers

We consider polling systems with multiple coupled servers. We explore the class of systems that allow an exact analysis. For these systems we present distributional results for the waiting time, the marginal queue length, and the joint queue length at polling epochs. The class in question includes several single-queue systems with a varying number of servers, two-queue two-server systems with exhaustive service and exponential service times, as well as infinite-server systems with an arbitrary number of queues, exhaustive or gated service, and deterministic service times.     

RISK-BASED MULTIATTRIBUTE DECISION-MAKING IN PROPERTY AND WATERSHED MANAGEMENT

ABSTRACT. Determining best management systems for properties and evaluating their sustainability at the watershed scale are useful and important aspects of integrated watershed management. Multiattribute decision-making (MADM) is very useful for modeling the selection of best management systems for properties in a watershed. This paper reviews four MADM approaches including utility theory, surrogate worth tradeoff, free iterative search and stochastic dominance with respect to a function (SDWF). Emphasis is on determining how the first three methods could be used to determine the best (most preferred) combinations of attributes and associated management systems for a property. An application of the expected utility method with risk neutral preferences is presented in which farmer's preferences for five attributes are used to rank five farming systems for an agricultural watershed in Missouri. A framework is presented for assessing the sustainability of the best management systems for all properties in a watershed and the cost-effectiveness of policies for enhancing sustainable resource management at the watershed scale.     

Introduction to normative multiagent systems

This article introduces the research issues related to and definition of normative multiagent systems. It also describes the papers selected from NorMAS05 that are part of this double special issue and relates the papers to each other. Guido Boella received the PhD degree at the University of Torino in 2000.He is currently professor at the Department of Computer Science of the University of Torino. His research interests include multi-agent systems, in particular, normative systems, institutions and roles using qualitative decision theory.He is the co-chair of the firstworkshops on normative multi-agent systems (NorMas05), on coordination and organization (CoOrg05), and the AAAI Fall Symposium on roles (Roles05). Leendert van der Torre received the Ph.D. degree in computer science fromErasmus University Rotterdam, The Netherlands, in 1997. He is currently a Full Professor at the University of Luxembourg. He has developed the so-called input/output logics and the BOID agent architecture. His current research interests include deontic logic, qualitative game theory, and security and coordination in normative multiagent systems. Harko Verhagen received his Ph.D. degree in computer and systems sciences from Stockholm University (Sweden) in 2000 and is currently an associate professor at the department. His research has focussed on simulation of organizational behaviour, simulation as a scientific method, the use of sociological theories in multiagent systems research and more in particular theories on norms and autonomy.     

Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems

In this paper we introduce the theory of dominant solutions at infinity for nonoscillatory discrete symplectic systems without any controllability assumption. Such solutions represent an opposite concept to recessive solutions at infinity, which were recently developed for such systems by the authors. Our main results include: (i) the existence of dominant solutions at infinity for all ranks in a given range depending on the order of abnormality of the system, (ii) construction of dominant solutions at infinity with eventually the same image, (iii) classification of dominant and recessive solutions at infinity with eventually the same image, (iv) limit characterization of recessive solutions at infinity in terms of dominant solutions at infinity and vice versa, and (v) Reid’s construction of the minimal recessive solution at infinity. These results are based on a new theory of genera of conjoined bases for symplectic systems developed for this purpose in this paper.     

On the Properties of Rings of Integro-Differential Operators and Their Corresponding Equations

Mathematical Notes - The paper deals with systems of linear integro-differential equations, including systems with a matrix identically degenerate in the domain at the highest derivative of the...     

Spectral properties of Hamiltonians with a magnetic field at a fixed pseudomomentum. III

The general results (see previous Part II) on the structure of the discrete spectra of energy operators of neutral systems in a homogeneous magnetic field at a fixed pseudomomentum are proved to be applicable to Hamiltonians of arbitrary atoms. Asymptotic expressions for the discrete spectra of Hamiltonians in the presence of a homogeneous magnetic field are found for arbitrary atoms. This paper completes the investigation of the spectral properties of Hamiltonians of neutral systems in a homogeneous magnetic field at a fixed pseudomomentum. The essential and discrete parts of the spectrum for such systems were found previously; however, whether the theorems in Part II were valid for actual n-particle systems remained an open question for the case n>3. Translated from Teoreticheskaya i Mathematicheskaya Fizika, Vol. 120, No. 2, pp. 291–308, August, 1999.     

Rate-monotonic scheduling for hard-real-time systems

Hard-real-time computing systems are widely used in our society, for example, in nuclear and industrial plants, telecommunications, avionics and robotics. In such systems, almost all tasks occur infinitely often and have time deadlines, namely, their correctness relies not only on their logical results, but also on the time at which the results are available. A scheduling algorithm specifies an order in which all the tasks are to be executed, in a way that all the time deadlines are met. This paper provides a review on deterministic scheduling algorithms for hard-real-time systems, focusing mainly on fixed priority, preemptive scheduling of periodic tasks on a single processor and, in particular, on the Rate-Monotonic algorithm. After presenting some basic results, several generalisations, aimed at relaxing some constraints and facing more realistic cases, are described. Issues covered include uniprocessor and multiprocessor systems, periodic and non-periodic tasks, restricted and arbitrary deadlines, fixed and dynamic priorities, independent and synchronised tasks, as well as fault-free and fault-tolerant systems.     

Some remarks on the concept of proportionality

Proportionality plays a role in many principles of fairness or justice. In particular, it is often invoked in electoral systems aiming at a similarity of opinion distributions in the parliament and in the electorate at large. The proportional systems of representation (PR systems, for short) strive for maximal similarity between these two distributions. Unfortunately, the concept of proportionality is imprecise in two senses: it is vague and ambiguous. In other words, once a clear criterion of what we mean by proportionality is given, different PR systems may differ in the degree of proportionality achieved in any given election. This is what will be referred to as the vagueness of proportionality (of election outcomes). Proportionality is, however, also ambiguous in that it refers to different things depending on how the voters are expected to signal their opinions and on what is it that one wishes to distribute proportionally.     

Optimal arrangements of queuing systems with FIFO service discipline

The paper studies a class of queuing systems with calls occurring in a certain space. Most frequently, a flow of homogeneous requests that differ only in the moments of their arrival at the system are considered. A specific feature of the class of systems under consideration is the necessity of using the information on the positions of serving devices as well as on the positions of the entering calls and their density distribution. Such models of the queuing systems are used for studying real systems in which the service is made by the objects placed over a territory.     

Sampling of vector-valued transforms associated with Green's matrix of Dirac systems

Recently a sampling theorem associated with regular one-dimensional Dirac systems has been developed. Integral transforms whose kernels are solutions of the systems have been reconstructed from their values at the eigenvalues. In the present article the situation is considered where the kernels are replaced by Green's matrix of the problem. Thus a vector-valued sampling theorem is established for vector-valued transforms. A family of examples where the systems have variable coefficients and a vector-valued Kramer-type sampling lemma are given at the end of the paper.     

The number and stability of limit cycles for planar piecewise linear systems of node–saddle type

The objective of this paper is to study the number and stability of limit cycles for planar piecewise linear (PWL) systems of node–saddle type with two linear regions. Firstly, we give a thorough analysis of limit cycles for Liénard PWL systems of this type, proving one is the maximum number of limit cycles and obtaining necessary and sufficient conditions for the existence and stability of a unique limit cycle. These conditions can be easily verified directly according to the parameters in the systems, and play an important role in giving birth to two limit cycles for general PWL systems. In this step, the tool of a Bendixon-like theorem is successfully employed to derive the existence of a limit cycle. Secondly, making use of the results gained in the first step, we obtain parameter regions where the general PWL systems have at least one, at least two and no limit cycles respectively. In addition for the general PWL systems, some sufficient conditions are presented for the existence and stability of a unique one and exactly two limit cycles respectively. Finally, some numerical examples are given to illustrate the results and especially to show the existence and stability of two nested limit cycles.