STABILITY CRITERION FOR LINEAR MULTIVARIABLE SYSTEMS

Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when this condition is also necessary. These criteria are satisfied for cycles in R3.Field and Swift, and Hofbauer, considered examples in R4 for which our sufficient condition for stability is not optimal. They obtained necessary and sufficient conditions for asymptotic stability using a transition-matrix technique.In this paper, we combine our previous methods with the transition-matrix technique and obtain necessary and sufficient conditions for asymptotic stability for a larger class of heteroclinic cycles. In particular, we obtain a complete theory for ‘simple’ heteroclinic cycles in R4 (thereby proving and extending results for homoclinic cycles that were stated without proof by Chossat, Krupa, Melbourne and Scheel). A partial classification of simple heteroclinic cycles in R4 is also given. Finally, our stability results generalize naturally to higher dimensions and many of the higher-dimensional examples in the literature are covered by this theory.

This paper presents a study of English-Indonesian translation of the humorous utterances in Walt Disney’s Donald Duck comics. Twenty one Indonesian translated comics of the 2008 issues and their original English versions were used as the source of data. A total of 480 humorous English utterances were identified and verified by 4 native English speakers. These 480 English utterances and their translations were used as the data. Analyses of the collected data were then made to see the translation techniques used by the translator in translating the humorous utterances and to see the resulted pragmatic equivalence viewed from the equivalence of pragmatic force between the source text (ST) and target text (TT), involving implicture analysis of the utterances. The findings of the research reveal that 647 uses of translation techniques are made to translate the 480 utterances, as more than one techniques are used in some of the utterances. Seventeen out of 18 translation techniques proposed by Molina & Albir (2002) are chosen by the translator. It is also found out that the translator’s choice of translation techniques has resulted in 96.87% of the translated humorous utterances being equivalent in their pragmatic force, compared to the original English utterances. The use of such translation techniques as generalization, established equivalent, linguistic compression, amplification, literal translation, compensation, linguistic amplification, variation, particularization, borrowing, transposition, description, and calque has resulted in equivalent pragmatic force between ST and TT. Only minor portion (3.13%) of the translated text is not equivalent in its pragmatic force, and this is caused by the use of amplification, discursive creation, reduction, adaptation, and modulation techniques. The high rate of pragmatic equivalence shows the translator’s success in translating the text. Key words : implicature, pragmatic force, pragmatic equivalence, translation technique

On the stability of certain systems under resonance conditions

By means of piecewise continuous functions which are modifications of classifical Lyapunov’s functions, some sufficient conditions for asymptotic stability in the large of solutions of almost periodic impulsive differential equations are presented.

In this thesis, we introduce and examine four new temporal logic formalisms that can be used as specification languages for the automated verification of the reliability of hardware and software designs with respect to a desired behavior. The work is organized in two parts. In the first one, we reason about two logics for computations, GCTL* and MCTL*, which are useful to describe a correct execution of monolithic closed systems. In the second one, instead, we focus on two logics for strategies, SL and mATL*, which are useful to formalize several interesting properties about interactive plays in multi-entities systems modeled as multi-agent games. In the “Logics for Computations” part, we first study the immersion of the idea of graded quantifications into the temporal-logic framework. In first order logic, existential and universal quantifiers express the concepts of the existence of at least one individual object satisfying a formula, or that all individual objects satisfy a formula. In other logics, these quantifiers have been generalized to express that, for a given non-negative integer n, at least n or all but n individuals satisfy a particular formula. Here, we consider GCTL, a temporal logic with graded path quantifiers, which allows to describe properties like “there exist at least n different classes of computational fluxes in which a system reaches a predetermined state”, where the classes over paths are computed by means of a predetermined equivalence relation. More precisely, we uniformly extend the classic concept of graded quantifiers from states to paths, through the use of a concept of path equivalence with respect to a given path formula. About this logic, in particular, we study the expressiveness and succinctness relationships with respect to GµCalculus and the complexity of the satisfiability problem, which results to be ExpTime-Complete. This research is partially based on the works [BMM09] “Graded Computation Tree Logic” and [BMM10] “Graded Computation Tree Logic with Binary Coding” published, respectively, in the proceedings of the “IEEE Symposium on Logic in Computer Science, 2009” and “EACSL Annual Conference on Computer Science Logic, 2010”. Preliminary results can be also found in [Mog07]. Furthermore, we consider special quantifiers over substructures, which allow to select, using parametric criteria, small critical parts of a system to be successively verified. In literature, there are some attempts to define a logic that allows to modify the underlying structure under exam and then to verify on it some assigned property. However, as far as we know, none of them is able to select minimal submodels of a given property describing the criteria on which then execute the verification process. Here, we base our work on the search of a new operator that merges the concept of quantifiers on structures with that one derived by a generalization of the concept of pruning. The results of this work, is a class of three different extensions of CTL* with minimal model quantifiers, which we name MCTL*. Regarding these logics, we study several reductions among them, as well as the satisfiability problem that we prove to be highly undecidability, i.e., Σ_1^1-Hard, for two out of the three cases. This research is partially based on the work [MM09] “Branching-Time Temporal Logics with Minimal Model Quantifiers” published in the proceedings of the “International Conference on Developments in Language Theory, 2009”. In the “Logics for Strategies” part, we first study the problem of defining a new specification language through which it is possible to express several important properties of multi-entities systems that are neither expressible using classical monolithic temporal logics, such as CTL*, nor using two-agent-teams temporal logics, such as ATL*. In literature, we can found some proposal of logics that try to achieve this goal, but unfortunately, none of them succeeds completely on all the aspects. Among them, one of the most important attempts is CHP-SL, a logics in which one can use variables over strategies. However, this logic has a deep weakness, since it does not allow to describe games with more than two players and even two-players concurrent games. Here, we introduce SL, a logic with a syntax similar in some aspects to the first order logic, in which the strategies of the agent building the game are treated as first order objects on which we can quantify. This logic generalizes CHP-SL, by allowing the specification of the correct behavior of multi-agent concurrent games. In SL, for example, we are able to express very complex but useful Nash equilibria that are not expressible with CHP-SL. We enlighten that Nash equilibrium is one of the most important concepts in game theory. For the introduced logic, we solve two problems left open in the work on CHP-SL. Precisely, we show that the related model-checking problem is 2ExpTime-Complete, thus not harder of the same problem for several subsumed logics, while we prove that its satisfiability problem is highly undecidable, i.e., Σ_1^1-Hard. This research is partially based on the work [MMV10a] “Reasoning About Strategies” published in the proceedings of the “IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 2010”. Finally, we consider the concept of relentful strategic reasoning, i.e., a formalism that expresses the ability of a strategy to be used not only to achieve a first given goal, but also to change its final goal in dependence of the history of the play. In the context of planning, memoryful quantification, i.e., quantification over computations that does not lose information about the past along the time, is one of the principal way to express the fact that a system is able to achieve a desired result, and shift to a different goal if some event happens. However, this kind of quantification was not considered before in the context of multi-agent planning. Here, we introduce mATL*, a fusion of the classic alternating temporal logic ATL* with memoryful quantification, with the aim of covering the previous idea. About this logics, we prove that, although it is equivalent to ATL*, it is exponentially more succinct. Nevertheless, we prove that both the model-checking and the satisfiability problems remain 2ExpTime-Complete, as for ATL*. This research is partially based on the work [MMV10b] “Relentful Strategic Reasoning in Alternating-Time Temporal Logic” published in the proceedings of the “International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2010”.

In this work, the asymptotic stability bounds are identified for a class of linear quasi-periodic dynamical systems with stochastic parametric excitations and nonlinear perturbations. The application of a Lyapunov–Perron (L-P) transformation converts the linear part of such systems to a linear time-invariant form. In the past, using the Infante’s approach for linear time-invariant systems, stability theorem and corollary were derived and demonstrated for time periodic systems with variation in stochastic parameters. In this study, the same approach is extended toward linear quasi-periodic with stochastic parameter variations. Furthermore, the Lyapunov’s direct approach is employed to formulate the stability conditions a for quasi-periodic system with nonlinear perturbations. If the nonlinearities satisfy a bounding condition, sufficient conditions for asymptotic stability can be derived for such systems. The applications of stability theorems are demonstrated with practical examples of commutative and noncommutative quasi-periodic systems.

Syntax and semantics are proposed for realtime (i.e., continuous-time) regular expressions, which extend and generalize existing SVA regular expressions. The extensions are motivated by practical needs for AMS circuit verification and were developed as part of the authors' contribution to analog assertions work in the Accellera committee standardizing Verilog-AMS. Given a suitable notion of sampling, we prove that the realtime semantics provided for the existing SVA clocked digital regular expressions is equivalent to the original discrete semantics. As a result, the existing digital operators can intermix freely with the new realtime operators, which is a major contribution of our framework. We also investigate the theoretical relationship between our framework and the timed regular expressions of Asarin, Caspi, and Maler. We provide a semantically faithful embedding of timed regular expressions into our realtime regular expressions, as well as a construction of timed automata recognizers for our realtime regular expressions. These constructions show that our realtime regular expressions are no less expressive than the timed regular expressions of [1] and no more expressive than the generalized timed regular expressions of [2]. The automata recognizers also provide the basis for an implementation strategy for our framework.

Certain algebraic invariants of the integral group ring ZG of a group G were introduced and investigated in relation to the problem of extending the Farrell-Tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. It turns out that the finiteness of these invariants of a group G implies the existence of a generalized Farrell-Tate cohomology for G which is computed via complete resolutions. In this article we present these algebraic invariants and their basic properties and discuss their relationship to the generalized Farrell-Tate cohomology. In addition we present the status of conjecture which claims that the finiteness of these invariants of a group G is equivalent to the existence of a finite dimensional model for EG, the classifying space for proper actions.

Aim of this thesis is that to furnish some methodologies for the accurate evaluation of the electromagnetic characteristics of a microstrip. This results particularly useful for the extraction of equivalent circuital parameters, needed from circuit simulators to study more complex structures. From an analysis of the available models in literature, it is possible to find that some approximations are usually assumed to simplify the treatment. It can be observed that it is usual to neglect the conductive losses, that nevertheless result more and more remarkable with the increase of the density of the circuits. Besides, the existing models for the analysis of microstrips don't generally take into account the thickness of the structure, if not in a perturbative way. This thesis has the objective to propose some models that try to eliminate or however to reduce the approximation around the finite conductivity and the finite thickness of a microstrip. In the first chapter, general aspects of the microstrips are introduced, shortly examining its uses and the constructive aspects. In the second chapter a lossless microstrip of infinitesimal thickness is examined. Different kinds of sources are examined. The aim of the chapter is to introduce the method that will be used in future. In the third chapter, a microstrip of infinitesimal thickness and finite conductibility is examined. Then the method is generalized to the case of an arbitrary number of coupled microstrips. In the fourth chapter, it is shortly presented a variation of the method previously exposed, studying the problem of a thick strip in the free space. Then, a microstrip of finite thickness is examined. In the thesis, also the computational aspects related to the convergence of the method and to the numerical treatment of the integrals.

In the present paper we consider initial value problems for Hilfer fractional differential equations and for system of Hilfer fractional differential equations. By using equivalent integral equations and some fixed point theorems, we study the local existence of solutions. We extend these local existence results globally with the help of continuation theorems and generalized Gronwall inequality.

On characterizing and generalizing the optional [formula omitted]-stability property for pricing set

Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper we contribute to foundations of such techniques and present a complete algorithm for synthesis of a class of recursive functions defined by structural recursion over a given algebraic data type definition. The functions we consider map an algebraic data type to a string; they are useful for, e.g., pretty printing and serialization of programs and data. We formalize our problem as learning deterministic sequential top-down tree-to-string transducers with a single state (1STS). The first problem we consider is learning a tree-to-string transducer from any set of input/output examples provided by the user. We show that, given a set of input/output examples, checking whether there exists a 1STS consistent with these examples is NP-complete in general. In contrast, the problem can be solved in polynomial time under a (practically useful) closure condition that each subtree of a tree in the input/output example set is also part of the input/output examples. Because coming up with relevant input/output examples may be difficult for the user while creating hard constraint problems for the synthesizer, we also study a more automated active learning scenario in which the algorithm chooses the inputs for which the user provides the outputs. Our algorithm asks a worst-case linear number of queries as a function of the size of the algebraic data type definition to determine a unique transducer. To construct our algorithms we present two new results on formal languages. First, we define a class of word equations, called sequential word equations, for which we prove that satisfiability can be solved in deterministic polynomial time. This is in contrast to the general word equations for which the best known complexity upper bound is in linear space. Second, we close a long-standing open problem about the asymptotic size of test sets for context-free languages. A test set of a language of words L is a subset T of L such that any two word homomorphisms equivalent on T are also equivalent on L. We prove that it is possible to build test sets of cubic size for context-free languages, matching for the first time the lower bound found 20 years ago.

In this paper we consider the asymptotic stability of linear interval time-delay systems on the base of using Lyapunov's direct method and methods of interval analysis. A sufficient condition of asymptotic stability is obtained using the concept of Lyapunov-Krasovsky functional.

The goal of this contribution is presenting a Theorem which states the asymptotic stability of a feedback controlled system with a Linear Generalized Model Predictive Control (LGMPC). Concerning the asymptotic stability, a sufficient and constructive condition on the weight matrices of the cost function used in the optimization problem in LGMPC for one step prediction horizon is demonstrated. The condition consists of a lower bound for one of these matrices. The obtained condition is explained and discussed by means of some physical considerations. The second part of this contribution is devoted to the saturation case and proves a sufficient condition for obtaining asymptotic stability and saturation avoidance.

A secondary controller which uses a number of Annular Momentum Control Devices (AMCD's) for enhancement of structural damping in large flexible space structures is investigated. The closed-loop secondary controller is shown to be equivalent to a certain closed-loop optimal linear regulator, and the necessary and sufficient conditions for asymptotic stability are obtained. Sufficient conditions for asymptotic stability are also obtained which are much less restrictive than those obtained in an earlier paper. Design of a robust stable primary controller is also discussed.