on linear volterra equations in banach spaces abstract in this paper we present the basic theory for a class of volterra differential integral equations of convolution type in banach spaces we show that existence of resolvent operator for such an equation is equivalent to its wellposedness and we obtain a hille yosida theorem unfortunately this result is not easy to apply and therefore it is important to have peturbation theorems available we present a result of this type which also contains an existence theorem and show by means of several examples that it cannot be improved

differentiability of solutions with respect to parameters in neutral differential equations with state dependent delays in this paper we consider a class of nonlinear neutral differential equations with state dependent delays in both the neutral and the retarded terms we study well posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the c norm

analysis of a model of stage structured population dynamics growth with time state dependent time delay the main purpose of this paper is to analyze a model of stage structured population growth where age to maturity is state dependent we found that a positive equilibrium always exists criteria for stability is obtained

linearized stability in periodic functional differential equations with state dependent delays in this paper we study stability of periodic solutions of a class of nonlinear functional differential equations fdes with state dependent delays using the method of linearization we show that a periodic solution of the nonlinear fde is exponentially stable if the zero solution of an associated linear periodic linear homogeneous fde is exponentially stable

on differentiability of solutions with respect to parameters in state dependent delay equations in this paper we study differentiability of solutions with respect to parameters in state dependent delay equations in particular we give sufficient conditions for differentiability of solutions in thew1 pnorm 1 p in establishing our main results we make use of a version of the uniform contraction principle for quasi banach spaces

local analysis of co dimension one and co dimension two grazing bifurcations in impact microactuators impact microactuators rely on repeated collisions to generate gross displacements of a microelectromechanical machine element without the need for large applied forces their design and control rely on an understanding of the critical transition between non impacting and impacting long term system dynamics and the associated changes in system behavior in this paper we present three co dimension one characteristically distinct transition scenarios associated with grazing conditions for a periodic response of an impact microactuator a discontinuous jump to an impacting periodic response associated with parameter hysteresis a continuous transition to an impacting chaotic attractor and a discontinuous jump to an impacting chaotic attractor using the concept of discontinuity mappings a theoretical analysis is presented that predicts the character of each transition from a set of quantities that are computable in terms of system properties at grazing specifically we show how this analysis can be applied to predict the bifurcation behavior on neighborhoods of two co dimension two bifurcation points that separate the co dimension one bifurcation scenarios the predictions are validated against results from numerical simulations of a model impact microactuator

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

concurrent forward bounding for distributed constraint optimization problems a distributed search algorithm for solving distributed constraints optimization problems dcops is presented the new algorithm scans the search space by using multiple search processes sps that run on all agents concurrently sps search in non intersecting parts of the global search space and perform branch bound search each search process sp uses the mechanism of forward bounding fb to prune efficiently its part of the global search space the concurrent forward bounding concfb algorithm enables all sps to share their upper bound across all parts of the global search space the number of concurrent sps is controlled dynamically by the concfb algorithm by performing dynamic splitting within each sp a dynamic variable ordering is employed in order to help control the balance of computational load among all agents and across different sps the concfb algorithm is evaluated experimentally and compared to all state of the art dcop algorithms the number of non concurrent logical operations non concurrent steps the total number of messages sent and cpu time are used as performance metrics the evaluation procedure considers different dcop problem types with a varying number of agents and different constraint graphs as problems become larger and denser concfb is shown to outperform all other evaluated algorithms by 2 3 orders of magnitude in all performance measures further evaluations comparing different variants of concfb provide important insights into the working of the algorithm and reveals the contribution of its different components

periodicity in a food limited population model with toxicants and state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

existence of periodic solutions of partial neutral functional differential equations with unbounded delay abstract in this article we establish a result of existence of periodic solutions for the class of quasi linear partial neutral functional differential equations with unbounded delay that can be described as the abstract functional differential equation d dt x t f t x t ax t g t x t where a is the infinitesimal generator of a strongly continuous semigroup of linear operators on a banach space and f and g are appropriate functions defined on a phase space

approximating probabilistic inference in bayesian belief networks is np hard abstract it is known that exact computation of conditional probabilities in belief networks is np hard many investigators in the ai community have tacitly assumed that algorithms for performing approximate inference with belief networks are of polynomial complexity indeed special cases of approximate inference can be performed in time polynomial in the input size however we have discovered that the general problem of approximating conditional probabilities with belief networks like exact inference resides in the np hard complexity class we develop a complexity analysis to elucidate the difficulty of approximate probabilistic inference more specifically we show that the existence of a polynomial time relative approximation algorithm for major classes of problem instances implies that np p we present our proof and explore the implications of the result

solving weighted csp by maintaining arc consistency recently a general definition of arc consistency ac for soft constraint frameworks has been proposed by t schiex proc cp 2000 singapore 2000 pp 411 424 in this paper we specialize this definition to weighted csp and introduce two o ed3 enforcing algorithms then we refine the definition and introduce a stronger form of arc consistency ac along with two o n2d2 ed3 algorithms as in the csp case an important application of ac is to combine it with search we empirically demonstrate that a branch and bound algorithm that maintains either ac or ac is a state of the art general solver for weighted csp our experiments cover binary max csp and max sat problems

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

existence of periodic solutions in neutral state dependent delays equations and models sufficient conditions are obtained for the existence of positive periodic solutions of neutral equations with state dependent delays the proof is based on the theory of coincidence degree the existence results are applied to equations of population dynamics

border collisions inside the stability domain of a fixed point abstract recent studies on a power electronic dc ac converter inverter have demonstrated that such systems may undergo a transition from regular dynamics associated with a globally attracting fixed point of a suitable stroboscopic map to chaos through an irregular sequence of border collision events chaotic dynamics of an inverter is not suitable for practical purposes however the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use in the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions we describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map

and or branch and bound search for combinatorial optimization in graphical models this is the first of two papers presenting and evaluating the power of a new framework for combinatorial optimization in graphical models based on and or search spaces we introduce a new generation of depth first branch and bound algorithms that explore the and or search tree using static and dynamic variable orderings the virtue of the and or representation of the search space is that its size may be far smaller than that of a traditional or representation which can translate into significant time savings for search algorithms the focus of this paper is on linear space search which explores the and or search tree in the second paper we explore memory intensive and or search algorithms in conjunction with the and or search space we investigate the power of the mini bucket heuristics in both static and dynamic setups we focus on two most common optimization problems in graphical models finding the most probable explanation in bayesian networks and solving weighted csps in extensive empirical evaluations we demonstrate that the new and or branch and bound approach improves considerably over the traditional or search strategy and show how various variable ordering schemes impact the performance of the and or search scheme

border collision bifurcations including period two to period three for piecewise smooth systems abstract we examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter in the simplest case there is a surface in phase space along which the map has no derivative or has two one sided derivatives is the border of two regions in which the map is smooth as the parameter is varied a fixed point e may collide with the border and we may assume that this collision occurs at 0 a variety of bifurcations occur frequently in such situations but never or almost never occur in smooth systems in particular e may cross the border and so will exist for 0 but it may be a saddle in one case say 0 for 0 there may be a stable period 3 orbit which similarly shrinks to e0 as 0 hence one observes the following stable periodic orbits a stable period 2 orbit collapses to a point and is reborn as a stable period 3 orbit we also see analogously stable period 2 to stable period p orbit bifurcations with p 5 11 52 or period 2 to quasi periodic or even to a chaotic attractor we believe this phenomenon will be seen in many applications

a non local pde model for population dynamics with state selective delay local theory and global attractors we propose a non local pde model for the evolution of a single species population that involves delayed feedback where the delay such as the maturation time in the delayed birth rate is selective and the selection depends on the status of the system this delay selection in contrast with the usual state dependent delay widely used in ordinary delay differential equation ensures the lipschitz continuity of the nonlinear functional in the classical phase space we also develop the local theory and the existence and upper semi continuity of the global attractor with respect to parameters

unifying tree decompositions for reasoning in graphical models the paper provides a unifying perspective of tree decomposition algorithms appearing in various automated reasoning areas such as join tree clustering for constraint satisfaction and the clique tree algorithm for probabilistic reasoning within this framework we introduce a new algorithm called bucket tree elimination bte that extends bucket elimination be to trees and show that it can provide a speed up of n over be for various reasoning tasks time space tradeoffs of tree decomposition processing are analyzed

phase synchronized quasiperiodicity in power electronic inverter systems abstract the development of switch mode operated power electronic converter systems has provided a broad range of new effective approaches to the conversion of electric power in this paper we describe the transitions from regular periodic operation to quasiperiodicity and high periodic resonance behavior that can be observed in a pulse width modulated dc ac converter operating with high feedback gain we demonstrate the occurrence of two different types of torus birth bifurcations and present a series of phase portraits illustrating the appearance of phase synchronized quasiperiodicity our numerical findings are verified through comparison with an experimental inverter system the results shed light on the transitions to quasiperiodicity and to various forms of three frequency dynamics in non smooth systems

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

enhancement schemes for constraint processing backjumping learning and cutset decomposition abstract researchers in the areas of constraint satisfaction problems logic programming and truth maintenance systems have suggested various schemes for enhancing the performance of the backtracking algorithm this paper defines and compares the performance of three such schemes backjumping learning and cycle cutset the backjumping and the cycle cutset methods work best when the constraint graph is sparse while the learning scheme mostly benefits problem instances with dense constraint graphs an integrated strategy is described which utilizes the distinct advantages of each scheme experiments show that in hard problems the average improvement realized by the integrated scheme is 20 25 higher than any of the individual schemes

adopt asynchronous distributed constraint optimization with quality guarantees the distributed constraint optimization problem dcop is a promising approach for modeling distributed reasoning tasks that arise in multiagent systems unfortunately existing methods for dcop are not able to provide theoretical guarantees on global solution quality while allowing agents to operate asynchronously we show how this failure can be remedied by allowing agents to make local decisions based on conservative cost estimates rather than relying on global certainty as previous approaches have done this novel approach results in a polynomial space algorithm for dcop named adopt that is guaranteed to find the globally optimal solution while allowing agents to execute asynchronously and in parallel detailed experimental results show that on benchmark problems adopt obtains speedups of several orders of magnitude over other approaches adopt can also perform bounded error approximation it has the ability to quickly find approximate solutions and unlike heuristic search methods still maintain a theoretical guarantee on solution quality

self sustained oscillations in a ring array of coupled lossless transmission lines abstract in this paper we derive a neutral difference differential system with diffusion which arises from a ring array of coupled lossless transmission lines we investigate the problem of self sustained oscillations of the considered transmission lines and apply a global hopf bifurcation theorem to establish the existence of multiple large amplitude phase locked periodic solutions in the corresponding neutral system

memory intensive and or search for combinatorial optimization in graphical models in this paper we explore the impact of caching during search in the context of the recent framework of and or search in graphical models specifically we extend the depth first and or branch and bound tree search algorithm to explore an and or search graph by equipping it with an adaptive caching scheme similar to good and no good recording furthermore we present best first search algorithms for traversing the same underlying and or search graph and compare both algorithms empirically we focus on two common optimization problems in graphical models finding the most probable explanation mpe in belief networks and solving weighted csps wcsp in an extensive empirical evaluation we demonstrate conclusively the superiority of the memory intensive and or search algorithms on a variety of benchmarks

winding number locking on a two dimensional torus synchronization of quasiperiodic motions we propose a new autonomous dynamical system of dimension n 4 that demonstrates the regime of stable two frequency motions and period doubling bifurcations of a two dimensional torus it is shown that the period doubling bifurcation of the two dimensional torus is not followed by the resonance phenomenon and the two dimensional ergodic torus undergoes a period doubling bifurcation the interaction of two generators is also analyzed the phenomenon of external and mutual synchronization of two frequency oscillations is observed for which winding number locking on a two dimensional torus takes place

slowly oscillating periodic solutions of autonomous state dependent delay equations more than a dozen years since the peak of activity on the question of the existence of periodic slowly oscillating solutions of autonomous delay differential equations following the early work of jones l wright 2 and grafton 3 the work of nussbaum 4 51 is to be specially noted for providing several new fixed point results and a global bifurcation theorem which are particularly useful for proving the existence of periodic solutions other important works include those of hadeler and tomiuk 6 kaplan and yorke 7 chow 8 chow and hale 9 alt lo 111 and walther 12 131 see hale s book 14 for an overview to the best of our knowledge only nussbaum 5 and alt 1 l considered the question of the existence of periodic solutions of autonomous state dependent delay differential equations nussbaum considered a special equation 0 3 below in 5 but did not prove a general result alt 1 l considered more complicated integral threshold type state dependent delays which have arisen in various models in epidemiology and structured population models alt obtained a theorem for a general class of state dependent equations on which we comment below the lack of results on periodic solutions for state dependent equations is probably explained by the fact that it is not clear what kinds of state dependent delays are interesting or natural and on a lack of compelling examples of such equations arising from plausible mathematical models however some recent papers of belair and mackey 15 and belair 16 contain some interesting state dependent delay equations arising in economics and population biology state dependent delays of threshold type arise naturally in structured population models see lo 111 the motivation for this paper stems from consideration of the innocent looking equation x t kx t r x t 0 1 where r x is bell shaped e g r x 01 emxz 1 01 0 i 01 5 1 if k 7r 2 and r o 1 then the zero solution of 0 1 is unstable a formal linearization would yield z t kz t 1 which is known to be unstable for

periodic solutions for differential equations with state dependent delay and positive feedback existence of a nontrivial periodic orbit and a homoclinic orbit connecting 0 to the periodic orbit is shown for the differential equation x t x t f x t r r r x t with state dependent delay and positive feedback here 0 f and r are smooth real functions with r 0 1 and f 0

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

equilibrium torus bifurcation in nonsmooth systems abstract considering a set of two coupled nonautonomous differential equations with discontinuous right hand sides describing the behavior of a dc dc power converter we discuss a border collision bifurcation that can lead to the birth of a two dimensional invariant torus from a stable node equilibrium point we obtain the chart of dynamic modes and show that there is a region of parameter space in which the system has a single stable node equilibrium point under variation of the parameters this equilibrium may disappear as it collides with a discontinuity boundary between two smooth regions in the phase space the disappearance of the equilibrium point is accompanied by the soft appearance of an unstable focus period 1 orbit surrounded by a resonant or ergodic torus detailed numerical calculations are supported by a theoretical investigation of the normal form map that represents the piecewise linear approximation to our system in the neighbourhood of the border we determine the functional relationships between the parameters of the normal form map and the actual system and illustrate how the normal form theory can predict the bifurcation behaviour along the border collision equilibrium torus bifurcation curve

bifurcations in nonsmooth dynamical systems a review is presented of the one parameter nonsmooth bifurcations that occur in a variety of continuous time piecewise smooth dynamical systems motivated by applications a pragmatic approach is taken to defining a discontinuity induced bifurcation dib as a nontrivial interaction of a limit set with respect to a codimension one discontinuity boundary in phase space only dibs that are local are considered that is bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows three classes of systems are considered involving either state jumps jumps in the vector field or jumps in some derivative of the vector field a rich array of dynamics are revealed involving the sudden creation or disappearance of attractors jumps to chaos bifurcation diagrams with sharp corners and cascades of period adding for each kind of bifurcation identified where possible a kind of normal form or discontinuity mapping dm is given together with a canonical example and an application the goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators impact oscillators dc dc converters and problems in control theory

coexisting tori and torus bubbling in non smooth systems abstract pulse modulated power electronic converters represent an important class of piecewise smooth dynamical systems with a broad range of applications in modern power supply systems the paper presents a detailed investigation of a number of unusual bifurcation phenomena that can occur in power converters with multilevel control in the first example a closed invariant curve arises in a border collision bifurcation as a period 6 saddle cycle collides with a stable fixed point of focus type and transforms it into an unstable focus point the second example involves the formation of a structure of coexisting tori through the interplay between border collision and global bifurcations we examine the behavior of the system in the presence of two coexisting stable resonance tori and finally show how an existing torus can develop heteroclinic bubbles that connect the points of a stable resonance cycle with an external pair of saddle and focus cycles the appearance of these structures is explained in terms of a sequence torus birth bifurcations with pairs of stable and unstable tori folding one over the other

controllability of impulsive neutral functional differential inclusions with infinite delay abstract the paper is concerned with the controllability of the first order impulsive neutral functional differential inclusions with infinite delay in a banach space sufficient conditions for controllability are obtained by using a fixed point theorem for condensing maps due to martelli as an application we also consider an impulsive neutral partial functional differential equation

semiring based constraint satisfaction and optimization we introduce a general framework for constraint satisfaction and optimization where classical csps fuzzy csps weighted csps partial constraint satisfaction and others can be easily cast the framework is based on a semiring structure where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain and the two semiring operations and x model constraint projection and combination respectively local consistency algorithms as usually used for classical csps can be exploited in this general framework as well provided that certain conditions on the semiring operations are satisfied we then show how this framework can be used to model both old and new constraint solving and optimization schemes thus allowing one to both formally justify many informally taken choices in existing schemes and to prove that local consistency techniques can be used also in newly defined schemes

existence results for an impulsive abstract partial differential equation with state dependent delay in this paper we establish the existence of mild solutions for a class of impulsive abstract partial functional differential equation with state dependent delay

controllability results for functional semilinear differential inclusions in frechet spaces abstract in this paper a recent nonlinear alternative for multivalued admissible contractions in frechet spaces due to frigon combined with semigroups theory is used to investigate the controllability of some classes of semilinear functional and neutral functional differential inclusions in frechet spaces

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

cascades of alternating pitchfork and flip bifurcations in h bridge inverters abstract power electronic dc ac converters inverters play an important role in modern power engineering these systems are also of considerable theoretical interest because their dynamics is influenced by the presence of two vastly different forcing frequencies as a consequence inverter systems may be modeled in terms of piecewise smooth maps with an extremely high number of switching manifolds we have recently shown that models of this type can demonstrate a complicated bifurcation structure associated with the occurrence of border collisions considering the example of a pwm h bridge single phase inverter the present paper discusses a number of unusual phenomena that can occur in piecewise smooth maps with a very large number of switching manifolds we show in particular how smooth pitchfork and flip bifurcations may form a macroscopic pattern that stretches across the overall bifurcation structure we explain the observed bifurcation phenomena show under which conditions they occur and describe them quantitatively by means of an analytic approximation

arc consistency for soft constraints the notion of arc consistency plays a central role in constraint satisfaction r dechter constraint processing morgan kaufmann san mateo ca 2003 it is known since the introduction of valued and semi ring constraint networks in 1995 that the notion of local consistency can be extended to constraint optimisation problems defined by soft constraint frameworks based on an idempotent cost combination operator this excludes non idempotent operators such as which define problems which are very important in practical applications such as max csp where the aim is to minimise the number of violated constraints in this paper we show that using a weak additional axiom satisfied by most existing soft constraints proposals it is possible to define a notion of soft arc consistency that extends the classical notion of arc consistency and this even in the case of non idempotent cost combination operators a polynomial time algorithm for enforcing this soft arc consistency exists and its space and time complexities are identical to that of enforcing arc consistency in csps when the cost combination operator is strictly monotonic for example max csp a directional version of arc consistency first introduced by m c cooper reduction operations in fuzzy or valued constraint satisfaction fuzzy sets and systems 134 3 2003 311 342 is potentially even stronger than the non directional version since it allows non local propagation of penalties we demonstrate the utility of directional arc consistency by showing that it not only solves soft constraint problems on trees but that it also implies a form of local optimality which we call arc irreducibility

periodic solutions for delay lotka volterra competition systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for the periodic distributed delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t 0 t ij k ij s u j t s ds i 1 2 n and the periodic state dependent delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t u j t j t u 1 t u n t i 1 2 n where ri aii 0 aij 0 j i i j 1 2 n are continuous periodic functions tij 0 j i i j 1 2 n kij c tij 0 0 0 tijkij s ds 1 j i i j 1 2 n i c rn 1 r and i i 1 2 n are periodic with respect to their first arguments respectively

mini buckets a general scheme for bounded inference this article presents a class of approximation algorithms that extend the idea of bounded complexity inference inspired by successful constraint propagation algorithms to probabilistic inference and combinatorial optimization the idea is to bound the dimensionality of dependencies created by inference algorithms this yields a parameterized scheme called mini buckets that offers adjustable trade off between accuracy and efficiency the mini bucket approach to optimization problems such as finding the most probable explanation mpe in bayesian networks generates both an approximate solution and bounds on the solution quality we present empirical results demonstrating successful performance of the proposed approximation scheme for the mpe task both on randomly generated problems and on realistic domains such as medical diagnosis and probabilistic decoding

and or search spaces for graphical models the paper introduces an and or search space perspective for graphical models that include probabilistic networks directed or undirected and constraint networks in contrast to the traditional or search space view the and or search tree displays some of the independencies present in the graphical model explicitly and may sometimes reduce the search space exponentially indeed most algorithmic advances in search based constraint processing and probabilistic inference can be viewed as searching an and or search tree or graph familiar parameters such as the depth of a spanning tree treewidth and pathwidth are shown to play a key role in characterizing the effect of and or search graphs vs the traditional or search graphs we compare memory intensive and or graph search with inference methods and place various existing algorithms within the and or search space

generalized best first search strategies and the optimality of a this paper reports several properties of heuristic best first search strategies whose scoring functions depend on all the information available from each candidate path not merely on the current cost g and the estimated completion cost h it is shown that several known properties of a retain their form with the minmax of f playing the role of the optimal cost which helps establish general tests of admissibility and general conditions for node expansion for these strategies on the basis of this framework the computational optimality of a in the sense of never expanding a node that can be skipped by some other algorithm having access to the same heuristic information that a uses is examined a hierarchy of four optimality types is defined and three classes of algorithms and four domains of problem instances are considered computational performances relative to these algorithms and domains are appraised for each class domain combination we then identify the strongest type of optimality that exists and the algorithm for achieving it the main results of this paper relate to the class of algorithms that like a return optimal solutions i e admissible when all cost estimates are optimistic i e h h on this class a is shown to be not optimal and it is also shown that no optimal algorithm exists but if the performance tests are confirmed to cases in which the estimates are also consistent then a is indeed optimal additionally a is also shown to be optimal over a subset of the latter class containing all best first algorithms that are guided by path dependent evaluation functions

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

existence results for fractional neutral integro differential equations with state dependent delay in this paper we study the existence of mild solutions for a class of abstract fractional neutral integro differential equations with state dependent delay the results are obtained by using the leray schauder alternative fixed point theorem an example is provided to illustrate the main results

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative

partial constraint satisfaction abstract a constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed in some cases it may be impossible or impractical to solve these problems completely we may seek to partially solve the problem in particular by satisfying a maximal number of constraints standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with and take advantage of the differences between partial and complete constraint satisfaction extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods a general model of partial constraint satisfaction is proposed

positive periodic solutions for a class of higher dimensional state dependent delay functional differential equations with feedback control we use the krasnosel skii s fixed point theorem for cones to study the existence of positive periodic solutions of the following a class of higher dimensional state dependent delay functional differential equations with feedback controlx t a t x t f t x t x t t t x t u t a t u t b t u t c t x h t x t moreover we apply our results obtained in this paper to some population model