hascasl integrated higher order specification and program development we lay out the design of hascasl a higher order extension of the algebraic specification language casl that serves both as a wide spectrum language for the rigorous specification and development of software in particular but not exclusively in modern functional programming languages and as an expressive standard language for higher order logic distinctive features of hascasl include partial higher order functions higher order subtyping shallow polymorphism and an extensive type class mechanism moreover hascasl provides dedicated specification support for monad based functional imperative programming with generic side effects including a monad based generic hoare logic

closed action calculi action calculi provide a framework for capturing many kinds of interactive behaviour by focussing on the primitive notion of names we introduce a name free account of action calculi called the closed action calculi and show that there is a strong correspondence between the original presentation and the name free presentation we also add free names plus natural axioms to the closed world and show that the abstraction operator can be constructed as a derived operator our results show that in some sense names are inessential however the purpose of action calculi is to understand formalisms which mimic the behaviour of interactive systems perhaps more significantly therefore these results highlight the important presentational role that names play

coalgebras in functional programming and type theory this is a survey article on the use of coalgebras in functional programming and type theory it presents the basic theory underlying the implementation of coinductive types families and predicates it gives an overview of the application of corecursive methods to the study of general recursion formal power series tabulations of functions on inductive data it also sketches some advanced topics in the study of the solutions to non guarded corecursive equations and the design of non standard type theory

a theory of binding structures and applications to rewriting abstract in this paper we present a theory of binding structures and give examples of its application to rewriting we define the set of binding structures as an abstract algebra and define a general notion of parameterized homomorphism a variety of operations on binding structures are presented as homomorphisms and a collection of properties useful for developing applications is given three applications are presented a generalized notion of term rewriting a theory of unification for binding structures and a set of structures and primitive rules intended to serve as a basis for design of rewriting components for quantified first order reasoning systems

boolean restriction categories and taut monads a boolean category is a restriction category if and only if it has one exception and all morphisms are deterministic in the category of sets taut monads are precisely the boolean ones it follows that collection monad types in haskell inherit an assertion calculus based on dynamic logic

on chebyshev halley methods with sixth order convergence for solving non linear equations abstract in this paper we present a family of new variants of chebyshev halley methods the new methods have sixth order convergence although they only add one evaluation of the function at the point iterated by chebyshev halley methods the numerical results presented show that the new methods work better not only in order but in efficiency

monad transformers as monoid transformers the incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a pre existing monad a complication of this approach is that the operations associated to the pre existing monad need to be lifted to the new monad in a companion paper by jaskelioff the lifting problem has been addressed in the setting of system email protected here we recast and extend those results in a category theoretic setting we abstract and generalize from monads to monoids in a monoidal category and from monad transformers to monoid transformers the generalization brings more simplicity and clarity and opens the way for lifting of operations with applicability beyond monads

a new family of optimal eighth order methods with dynamics for nonlinear equations we propose a simple yet efficient family of three point iterative methods for solving nonlinear equations each method of the family requires four evaluations namely three functions and one derivative per full iteration and possesses eighth order of convergence thus the family is optimal in the sense of kung traub conjecture and has the efficiency index 1 682 which is better than that of newton s and many other higher order methods various numerical examples are considered to check the performance and to verify the theoretical results computational results including the elapsed cpu time confirm the efficient and robust character of proposed technique moreover the presented basins of attraction also confirm better performance of the methods as compared to other established methods in literature

a first order logic of effects abstract in this paper we describe some of our progress towards an operational implementation of a modern programming logic the logic is inspired by the variable type systems of feferman and is designed for reasoning about imperative functional programs the logic goes well beyond traditional programming logics such as hoare s logic and dynamic logic in its expressibility yet is less problematic to encode into higher order logics the main focus of the paper is to present an axiomatization of the base first order theory

monad as modality abstract in 1989 eugenio moggi proposed a categorical framework for program semantics based on the notion of a strong monad he showed that various kinds of computation can be modeled in his framework on the other hand strong monads are not suited for the categorical semantics of traditional modal logics according to these observations moggi thought that the curryhoward correspondence would not hold between programs and constructive proofs in modal logics however contrary to his view we can show that proofs in a certain kind of modal logics are actually considered as programs in this paper first we shall introduce the notion of an l strong monad which is a generalization of strong monads using this new notion we can generalize moggi s semantics preserving soundness and completeness with respect to his equational logic next we shall show that l strong monads give a sound and complete semantics of a constructive version of s4 modal logic finally we present a method to extract a monad based imperative functional program from a proof in the modal logic interestingly this method can also be understood in terms of l strong monads

constructive linear time temporal logic proof systems and kripke semantics in this paper we study a version of constructive linear time temporal logic ltl with the next temporal operator the logic is originally due to davies who has shown that the proof system of the logic corresponds to a type system for binding time analysis via the curry howard isomorphism however he did not investigate the logic itself in detail he has proved only that the logic augmented with negation and classical reasoning is equivalent to the next fragment of the standard formulation of classical linear time temporal logic we give natural deduction sequent calculus and hilbert style proof systems for constructive ltl with conjunction disjunction and falsehood and show that the sequent calculus enjoys cut elimination moreover we also consider kripke semantics and prove soundness and completeness one distinguishing feature of this logic is that distributivity of the next operator over disjunction a b a b is rejected in view of a type theoretic interpretation

a family of three point methods of optimal order for solving nonlinear equations a family of three point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters it is proved that these methods have the convergence order eight requiring only four function evaluations per iteration in this way it is demonstrated that the proposed class of methods supports the kung traub hypothesis 1974 3 on the upper bound 2 n of the order of multipoint methods based on n 1 function evaluations consequently this class of root solvers possesses very high computational efficiency numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations

normalized sph with stress points smoothed particle hydrodynamics is extended to a normalized staggered particle formulation with boundary conditions a companion set of interpolation points is introduced that carry the stress velocity gradient and other derived field variables the method is stable linearly consistent and has an explicit treatment of boundary conditions also a new method for finding neighbours is introduced which selects a minimal and robust set and is insensitive to anisotropy in the particle arrangement test problems show that these improvements lead to increased accuracy and stability published in 2000 by john wiley sons ltd

a coinductive calculus for asynchronous side effecting processes we present an abstract framework for concurrent processes in which atomic steps have generic side effects handled according to the principle of monadic encapsulation of effects processes in this framework are potentially infinite resumptions modelled using final coalgebras over the monadic base as a calculus for such processes we introduce a concurrent extension of moggi s monadic meta language of effects we establish soundness and completeness of a natural equational axiomatization of this calculus our main result is a corecursion scheme that is explicitly definable over the base language and provides flexible expressive means for the definition of new operators on processes such as parallel composition moreover we present initial results on verification methods for generic side effecting processes

a bisimulation for type abstraction and recursion we present a bisimulation method for proving the contextual equivalence of packages in calculus with full existential and recursive types unlike traditional logical relations either semantic or syntactic our development is elementary using only sets and relations and avoiding advanced machinery such as domain theory admissibility and tt closure unlike other bisimulations ours is complete even for existential types the key idea is to consider sets of relations instead of just relations as bisimulations

a non iterative method for solving non linear equations abstract in this paper using a hyperbolic tangent function tanh x 0 we develop a non iterative method to estimate a root of an equation f x 0 the problem of finding root is transformed to evaluating an integral and thus we need not take account of choosing initial guess the larger the value of the better the approximation to the root alternatively we employ the signum function sgn x instead of the hyperbolic tangent function which results in an exact formula for the root availability of the present method is shown by some numerical examples for which the traditional newton s method is not appropriate

combining effects sum and tensor we seek a unified account of modularity for computational effects we begin by reformulating moggi s monadic paradigm for modelling computational effects using the notion of enriched lawvere theory together with its relationship with strong monads this emphasises the importance of the operations that produce the effects effects qua theories are then combined by appropriate bifunctors on the category of theories we give a theory for the sum of computational effects which in particular yields moggi s exceptions monad transformer and an interactive input output monad transformer we further give a theory of the commutative combination of effects their tensor which yields moggi s side effects monad transformer finally we give a theory of operation transformers for redefining operations when adding new effects we derive explicit forms for the operation transformers associated to the above monad transformers

a generalization of nash s theorem with higher order functionals the recent theory of sequential games and selection functions by escardo oliva is extended to games in which players move simultaneously the nash existence theorem for mixed strategy equilibria of finite games is generalized to games defined by selection functions a normal form construction is given which generalizes the game theoretic normal form and its soundness is proved minimax strategies also generalize to the new class of games and are computed by the berardi bezem coquand functional studied in proof theory as an interpretation of the axiom of countable choice

combining algebraic effects with continuations we consider the natural combinations of algebraic computational effects such as side effects exceptions interactive input output and nondeterminism with continuations continuations are not an algebraic effect but previously developed combinations of algebraic effects given by sum and tensor extend with effort to include commonly used combinations of the various algebraic effects with continuations continuations also give rise to a third sort of combination that given by applying the continuations monad transformer to an algebraic effect we investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads and the extent to which felleisen et al s c operator extends from continuations to its combination with algebraic effects to do all this we use dubuc s characterisation of strong monads in terms of enriched large lawvere theories

a new eighth order iterative method for solving nonlinear equations abstract in this paper we present an improvement of the fourth order newton type method for solving a nonlinear equation the new newton type method is shown to converge of the order eight per iteration the new method requires three evaluations of the function and one evaluation of its first derivative and therefore the new method has the efficiency index of 8 4 which is better than the well known newton type methods of lower order we shall examine the effectiveness of the new eighth order newton type method by approximating the simple root of a given nonlinear equation numerical comparisons are made with several other existing methods to show the performance of the presented method

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

sequential games and optimal strategies this article gives an overview of recent work on the theory of selection functions we explain the intuition behind these higher type objects and define a general notion of sequential game whose optimal strategies can be computed via a certain product of selection functions several instances of this game are considered in a variety of areas such as fixed point theory topology game theory higher type computability and proof theory these examples are intended to illustrate how the fundamental construction of optimal strategies based on products of selection functions permeates several research areas

some novel and optimal families of king s method with eighth and sixteenth order of convergence in this study our principle aim is to provide some novel eighth and sixteenth order families of king s method for solving nonlinear equations which should be superior than the existing schemes of same order the relevant optimal orders of the proposed families satisfy the classical kung traub conjecture which was made in 1974 the derivations of the proposed schemes are based on the weight function and rational approximation approaches respectively in addition convergence properties of the proposed families are fully investigated along with one lemma and two main theorems describing their order of convergence we consider a concrete variety of real life problems e g the trajectory of an electron in the air gap between two parallel plates chemical engineering problem van der waal s equation which explains the behavior of a real gas by introducing in the ideal gas equations and fractional conversion in a chemical reactor in order to check the validity applicability and effectiveness of our proposed methods further it is found from the numerical results that our proposed methods perform better than the existing ones of the same order when the accuracy is checked in the multi precision digits

on newton type methods with cubic convergence recently there has been some progress on newton type methods with cubic convergence that do not require the computation of second derivatives weerakoon and fernando appl math lett 13 2000 87 derived the newton method and a cubically convergent variant by rectangular and trapezoidal approximations to newton s theorem while frontini and sormani j comput appl math 156 2003 345 140 2003 419 derived further cubically convergent variants by using different approximations to newton s theorem homeier j comput appl math 157 2003 227 169 2004 161 independently derived one of the latter variants and extended it to the multivariate case here we show that one can modify the werrakoon fernando approach by using newton s theorem for the inverse function and derive a new class of cubically convergent newton type methods

generic weakest precondition semantics from monads enriched with order we devise a generic framework where a weakest precondition semantics in the form of indexed posets is derived from a monad whose kleisli category is enriched by posets it is inspired by jacobs recent identification of a categorical structure that is common in various predicate transformers but adds generality in the following aspects 1 different notions of modality such as may vs must are captured by eilenberg moore algebras 2 nested alternating branching like in games and in probabilistic systems with nondeterministic environments is modularly modeled by a monad on the eilenberg moore category of another

a unified stability analysis of meshless particle methods a uni ed stability analysis of meshless methods with eulerian and lagrangian kernels is presented three types of instabilities were identi ed in one dimension an instability due to rank de ciency a tensile instability and a material instability which is also found in continua the stability of particle methods with eulerian and lagrangian kernels is markedly di erent lagrangian kernels do not exhibit the tensile instability in both kernels the instability due to rank de ciency can be suppressed by stress points in two dimensions the stabilizing e ect of stress points is dependent on their locations it was found that the best approach to stable particle discretizations is to use lagrangian kernels with stress points the stability of the least squares stabilization was also studied copyright 2000 john wiley sons ltd

on a general class of multipoint root finding methods of high computational efficiency a general class of n point iterative methods for solving nonlinear equations is constructed by combining methods of newton s type and an arbitrary two point method of the fourth order of convergence it is proved that these methods have the convergence order 2 n requiring only n 1 function evaluations per iteration in this way it is demonstrated that the proposed class of methods supports the kung traub hypothesis 1974 on the upper bound 2 n of the order of multipoint methods based on n 1 function evaluations consequently this class possess as high as possible computational efficiency in the sense of the kung traub hypothesis numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations

a taylor galerkin algorithm for shock wave propagation and strain localization failure of viscoplastic continua abstract this paper presents a taylor galerkin algorithm formulated in terms of velocities and stresses which can be applied to solid dynamics problems requiring good resolution of small wavelengths such as propagation of shocks the proposed model is both fast as it uses simple linear elements triangles in 2d and tetrahedra in 3d and accurate it mitigates locking and mesh alignment problems and therefore can be applied to localized failure computations without the limitations exhibited by the classical displacement formulations

continuity spaces reconciling domains and metric spaces abstract we use continuity spaces a common refinement of posets and metric spaces to develop a general theory of semantic domains which includes metric spaces and domains of cpo s as special cases and provides the appropriate tools for producing new examples which may be suitable for modeling language constructs that occur in concurrent and probabilistic programming our proposal for a general notion of semantic domain is a symmetrically compact continuity space where is a value quantale we show that the category of symmetrically compact continuity spaces with continuous maps has many of the key properties required of a category of domains and that it captures in a natural way the traditional examples in general the category will not be cartesian closed however powerdomains do exist and by adapting a construction of suenderhauf to continuity spaces we show that they define a computational monad in the sense of moggi

means based modifications of newton s method for solving nonlinear equations in this paper we consider a family of six sets of means based modifications of newton s method for solving nonlinear equations each set is a parametric class of methods some well known methods belong to our family for example the arithmetic mean newton s method s weerakoon t g i fernando a variant of newton s method with accelerated third order convergence appl math lett 13 2000 87 93 the harmonic mean newton s method a y ozban some new variants of newton s method appl math lett 17 2004 677 682 the geometric mean newton s method t lukic n m ralevic geometric mean newton s method for simple and multiple roots appl math lett 21 2008 30 36 the power mean newton s method x zhou a class of newton s methods with third order convergence appl math lett 20 2007 1026 1030 the convergence analysis shows third order of our family comparison of the family members shows that there are no big differences between them twelve numerical examples were tested and two characteristic ones are presented

consistent pseudo derivatives in meshless methods a meshless petrov galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of shepard functions a key contribution is the development of conditions on test functions and trial functions for nonintegrable pseudo derivatives for petrov galerkin method which pass the patch test numerical results show that the resulting method is substantially more accurate than the galerkin method with shepard approximants and exceeds the rate of convergence of linear finite elements

stable power domains abstract in the category of stable dcpo s free constructions w r t algebraic theories exist from this we obtain various stable power domain constructions after handling their properties in general we concentrate on the stable plotkin power construction for continuous ground domains it is explicitly described in terms of saturated compact sets in case of algebraic ground domains this description is isomorphic to buneman s lossless power domains

a syntactic theory of sequential state abstract the assignment statement is a ubiquitous building block of programming languages in functionally oriented programming languages the assignment is the facility for modeling and expressing state changes given that functional languages are directly associated with the equational calculus theory it is natural to wonder whether this syntactic proof system is extensible to imperative variants of functional languages including state variables and side effects in this paper we show that such an extension exists and that it satisfies variants of the conventional consistency and standardization theorems with a series of examples we also demonstrate the system s capabilities for reasoning about imperative functional programs and illustrate some of its advantages over alternative models

formal security proofs with minimal fuss we show how implicit computational complexity can be used in order to increase confidence in game based security proofs in cryptography for this purpose we extend cslr a probabilistic lambda calculus with a type system that guarantees the existence of a probabilistic polynomial time bound on computations this allows us to define cryptographic constructions feasible adversaries security notions computational assumptions game transformations and game based security proofs in a unified framework we also show that the standard practice of cryptographers ignoring that polynomial time turing machines cannot generate all uniform distributions is actually sound we illustrate our calculus on cryptographic constructions for public key encryption and pseudorandom bit generation

full abstractness for a functional concurrent language with higher order value passing we study an applied typed call by value calculus which in addition to the usual types for higher order functions contains an extra type called proc for processes the constructors for terms of this type are similar to those found in standard process calculi such as ccs we first give an operational semantics for this language in terms of a labelled transition system which is then used to give a behavioural preorderbased on contexts the expression n dominates m if in every appropriate context if m can produce a boolean value then so can n

strong normalization from weak normalization in typedλ calculi for some typed calculi it is easier to prove weak normalization than strong normalization techniques to infer the latter from the former have been invented over the last twenty years by nederpelt klop khasidashvili karr de groote and kfoury and wells however these techniques infer strong normalization of one notion of reduction from weak normalization of amore complicatednotion of reduction this paper presents a new technique to infer strong normalization of a notion of reduction in a typed calculus from weak normalization of thesamenotion of reduction the technique is demonstrated to work on some well known systems including second order calculus and the system of positive recursive types it gives hope for a positive answer to the barendregt geuvers conjecture stating that every pure type system which is weakly normalizing is also strongly normalizing the paper also analyzes the relationship between the techniques mentioned above and reviews in less detail other techniques for proving strong normalization

a theory of bisimulation for a fragment of concurrent ml with local names concurrent ml is an extension of standard ml with calculus like primitives for multithreaded programming cml has a reduction semantics but to date there has been no labelled transition system semantics provided for the entire language in this paper we present a labelled transition semantics for a fragment of cml called vcml which includes features not covered before dynamically generated local channels and thread identifiers we show that weak bisimilarity for vcml is a congruence and coincides with barbed bisimulation congruence we also provide a variant of sangiorgi s normal bisimulation for vcml and show that this too coincides with bisimilarity

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

comparing logics for rewriting the large diffusion of concurrent and distributed systems has spawned in recent years a variety of new formalisms equipped with features for supporting an easy specification of such systems the aim of our paper is to analyze three proposals namely rewriting logic action calculi and tile logic chosen among those formalisms designed for the description of rule based systems for each of these logics we first try to understand their foundations then we briefly sketch some applications the overall goal of our work is to find out a common layout where these logics can be recast thus allowing for a comparison and an evaluation of their specific features

an equational notion of lifting monad we introduce the notion of an equational lifting monad a commutative strong monad satisfying one additional equation valid for monads arising from partial map classifiers we prove that any equational lifting monad has a representation by a partial map classifier such that the kleisli category of the former fully embeds in the partial category of the latter thus equational lifting monads precisely capture the equational properties of partial maps as induced by partial map classifiers the representation theorem also provides a tool for transferring nonequational properties of partial map classifiers to equational lifting monads it is proved using a direct axiomatization of kleisli categories of equational lifting monads this axiomatization is of interest in its own right

eighth order family of iterative methods for nonlinear equations and their basins of attraction abstract we present a new family of eighth order methods for solving nonlinear equations the order of convergence of the considered methods is proved and corresponding asymptotic error constants are expressed in terms of four parameters numerical examples obtained using mathematica with high precision arithmetic demonstrate convergence and efficacy of our family of methods for some combinations of parameter values the new eighth order methods produce very good results on tested examples compared to the results produced by some of the eighth order methods existing in the related literature an exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various polynomials

a formal abstract framework for modelling and testing complex software systems the contribution of this paper is twofold first it defines a unified framework for modelling abstract components as well as a formalization of integration rules to combine their behaviour this is based on a coalgebraic definition of components which is a categorical representation allowing the unification of a large family of formalisms for specifying state based systems second it studies compositional conformance testing i e checking whether an implementation made of correct interacting components combined with integration operators conforms to its specification

combining a monad and a comonad we give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics and in giving an intensional denotational semantics we do this axiomatically in terms of a monad and a comonad in a 2 category giving accounts of the eilenberg moore and kleisli constructions we analyse the eight possible relationships deducing that two pairs are isomorphic but that the other pairs are all distinct we develop those 2 categorical definitions necessary to support this analysis

cut free gentzen calculus for multimodal ck this paper extends previous work on the modal logic ck as a reference system both proof theoretically and model theoretically for a correspondence theory of constructive modal logics first the fundamental nature of ck is discussed and compared with the intuitionistic modal logic ik which is traditionally taken to be the base line then it is shown that ck admits of a cut free gentzen sequent calculus g ck which has i a local interpretation in constructive kripke models and ii does not require explicit world labels finally the paper demonstrates how non classical modal logics such as ik cs4 cl or email protected s deontic system of 2 sequents arise as theories of ck presented both as special rules and as frame classes

lifting results for categories of algebras in this paper we present results that provide an abstract setting for the construction and interpretation of categories of algebras appearing in various semantic examples including those related to scott domains and cartesian closed categories a methodology is introduced that lifts adjoint pairs on categories with monads to categories whose objects are algebras for these monads results are achieved by exploiting prior work on kleisli liftings and the existence of key isomorphisms while applicable to domain theory and the semantics of partiality the construction at work is considerably more general and is applicable to other settings as well

a family of methods for solving nonlinear equations we present a family of methods for solving nonlinear equations some well known classical methods and their modifications belong to our family for example newton potra ptak chebyshev halley and ostrowski s methods convergence analysis shows that our family contains methods of convergence order from 2 to 4 all our fourth order methods are optimal in terms of the kung and traub conjecture several examples are presented and compared

connectionist computations of intuitionistic reasoning the construction of computational models with provision for effective learning and added reasoning is a fundamental problem in computer science in this paper we present a new computational model for integrated reasoning and learning that combines intuitionistic reasoning and neural networks we use ensembles of neural networks to represent intuitionistic theories and show that for each intuitionistic theory and intuitionistic modal theory there exists a corresponding neural network ensemble that computes a fixed point semantics of the theory this provides a massively parallel model for intuitionistic reasoning in our model the neural networks can be trained from examples to adapt to new situations using standard neural learning algorithms thus providing a unifying foundation for intuitionistic reasoning knowledge representation and learning

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

a new family of eighth order iterative methods for solving nonlinear equations a family of eighth order iterative methods with four evaluations for the solution of nonlinear equations is presented kung and traub conjectured that an iteration method without memory based on n evaluations could achieve optimal convergence order 2 n 1 the new family of eighth order methods agrees with the conjecture of kung traub for the case n 4 therefore this family of methods has efficiency index equal to 1 682 numerical comparisons are made with several other existing methods to show the performance of the presented methods

new modifications of potra ptak s method with optimal fourth and eighth orders of convergence in this paper we present two new iterative methods for solving nonlinear equations by using suitable taylor and divided difference approximations both methods are obtained by modifying potra ptak s method trying to get optimal order we prove that the new methods reach orders of convergence four and eight with three and four functional evaluations respectively so kung and traub s conjecture kung and traub 1974 2 that establishes for an iterative method based on n evaluations an optimal order p 2 n 1 is fulfilled getting the highest efficiency indices for orders p 4 and p 8 which are 1 587 and 1 682 we also perform different numerical tests that confirm the theoretical results and allow us to compare these methods with potra ptak s method from which they have been derived and with other recently published eighth order methods

modelling environments in call by value programming languages in categorical semantics there have traditionally been two approaches to modelling environments one by use of finite products in cartesian closed categories the other by use of the base categories of indexed categories with structure each requires modifications in order to account for environments in call by value programming languages there have been two more general definitions along both of these lines the first generalising from cartesian to symmetric premonoidal categories the second generalising from indexed categories with specified structure to categories in this paper we investigate environments in call by value languages by analysing a fine grain variant of moggi s computational calculus giving two equivalent sound and complete classes of models one given by closed freyd categories which are based on symmetric premonoidal categories the other given by closed categories

on the algebraic structure of declarative programming languages we develop an algebraic framework logic programming doctrines for the syntax proof theory operational semantics and model theory of horn clause logic programming based on indexed premonoidal categories our aim is to provide a uniform framework for logic programming and its extensions capable of incorporating constraints abstract data types features imported from other programming language paradigms and a mathematical description of the state space in a declarative manner we define a new way to embed information about data into logic programming derivations by building a sketch like description of data structures directly into an indexed category of proofs we give an algebraic axiomatization of bottom up semantics in this general setting describing categorical models as fixed points of a continuous operator

some improvements of jarratt s method with sixth order convergence abstract in this paper we present a one parameter family of variants of jarratt s fourth order method for solving nonlinear equations it is shown that the order of convergence of each family member is improved from four to six even though it adds one evaluation of the function at the point iterated by jarratt s method per iteration several numerical examples are given to illustrate the performance of the presented methods

powersets of terms and composite monads composing various powerset functors with the term monad gives rise to the concept of generalized terms this in turn provides a technique for handling many valued sets of terms in a framework of variable substitutions thus being the prerequisite for categorical unification in many valued logic programming using an extended notion of terms as constructions of monads involve complicated calculations with natural transformations proofs are supported by a graphical approach that provides a useful tool for handling various conditions such as those well known for distributive laws

the lambda context calculus extended version we present the lambda context calculus this simple lambda calculus features variables arranged in a hierarchy of strengths such that substitution of a strong variable does not avoid capture with respect to abstraction by a weaker variable this allows the calculus to express both capture avoiding and capturing substitution instantiation the reduction rules extend the vanilla lambda calculus in a simple and modular way and preserve the look and feel of a standard lambda calculus with explicit substitutions good properties of the lambda calculus are preserved the lamcc is confluent and a natural injection into the lamcc of the untyped lambda calculus exists and preserves strong normalisation we discuss the calculus and its design with full proofs in the presence of the hierarchy of variables functional binding splits into a functional abstraction l lambda and a name binder new we investigate how the components of this calculus interact with each other and with the reduction rules with examples in two more extended case studies we demonstrate how global state can be expressed and how contexts and contextual equivalence can be naturally internalised using function application

a fully abstract denotational semantics for the π calculus this paper describes the construction of two set theoretic denotational models for the p calculus the models are obtained as initial solutions to domain equations in a functor category by associating with each syntactic construct of the p calculus a natural transformation over these models we obtain two interpretations for the language we also show that these models are fully abstract with respect to natural behavioural preorders over terms in the language by this we mean that two terms are related behaviourally if and only if their interpretations in the model are related the behavioural preorders are the standard versions of may and must testing adapted to the p calculus

on the call by value cps transform and its semantics we investigate continuations in the context of idealized call by value programming languages on the semantic side we analyze the categorical structures that arise from continuation models of call by value languages on the syntactic side we study the call by value continuation passing transformation as a translation between equational theories among the novelties are an unusually simple axiomatization of control operators and a strengthened completeness result with a proof based on a delaying transform

premonoidal categories as categories with algebraic structure we develop the study of premonoidal categories specifically we reconcile premonoidal categories with the usual study of categories with algebraic structure by adding a little extra structure we further give a notion of closedness for a premonoidal category with such extra structure and show that every premonoidal category fully embeds into a closed one

a new optimal eighth order family of iterative methods for the solution of nonlinear equations in this paper a new optimal family of methods for solving nonlinear equations is presented it is proved by analysis of convergence that each member of the family which requires three evaluations of the function and one evaluation of its first derivative per iteration is of optimal order eight numerical comparisons are made with several other existing eighth order methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the presented methods

normalized smoothing functions for sph impact computations this paper presents a normalized smoothing function nsf algorithm that can improve the accuracy of smooth particle hydrodynamics sph impact computations it is presented specifically for axisymmetric geometry but the principles also apply to plane strain and three dimensional geometry the approach consists of adjusting the standard smoothing functions for every node and every cycle such that the normal strain rates are computed exactly for conditions of constant strain rates linear velocity distributions this in turn generally improves accuracy for non uniform strain rates this can significantly improve the accuracy for free boundaries for non uniform arrangements of sph nodes and for small smoothing distances a new smoothing function is also introduced the nsf algorithm is shown to provide improved accuracy for a series of cylinder impact examples that includes two different smoothing functions and two different smoothing distances

notions of computation and monads abstract the calculus is considered a useful mathematical tool in the study of programming languages since programs can be identified with terms however if one goes further and uses conversion to prove equivalence of programs then a gross simplification is introduced programs are identified with total functions from values to values that may jeopardise the applicability of theoretical results in this paper we introduce calculi based on a categorical semantics for computations that provide a correct basis for proving equivalence of programs for a wide range of notions of computation

eilenberg moore algebras for stochastic relations we investigate the category of eilenberg moore algebras for the giry monad associated with stochastic relations over polish spaces with continuous maps as morphisms the algebras are identified as the positive convex structures on the base space the forgetful functor assigning a positive convex structure the underlying polish space has the stochastic powerdomain as its left adjoint

a variationally consistent streamline upwind petrov galerkin smooth particle hydrodynamics algorithm for large strain solid dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for explicit fast solid dynamics the proposed methodology explores the use of the streamline upwind petrov galerkin supg stabilisation methodology as an alternative to the jameson schmidt turkel jst stabilisation recently presented by the authors in lee et al 2016 in the context of a conservation law formulation of fast solid dynamics the work introduced in this paper puts forward three advantageous features over the recent jst sph framework first the variationally consistent nature of the supg stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations this differs from the jst sph framework where an a posteriori projection procedure was required to ensure global angular momentum preservation second evaluation of expensive harmonic and bi harmonic operators necessary for the jst stabilisation is circumvented in the new supg sph framework third the supg sph framework is more accurate for the same number of degrees of freedom than its jst sph counterpart and its accuracy is comparable to that of the robust but computationally more demanding petrov galerkin finite element method pg fem technique explored by the authors in lee et al 2014 gil et al 2014 2016 bonet et al 2015 as shown in the numerical examples included a series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm the resulting supg sph framework is therefore accurate robust and computationally efficient three key desired features that will allow the authors in forthcoming publications to explore its applicability in large scale simulations

a new jameson schmidt turkel smooth particle hydrodynamics algorithm for large strain explicit fast dynamics this paper presents a new smooth particle hydrodynamics sph computational framework for large strain explicit solid dynamics a mixed based set of total lagrangian conservation laws bonet et al 2015 gil et al 2016 is presented in terms of the linear momentum and an extended set of geometric strain measures comprised of the deformation gradient its co factor and the jacobian taking advantage of this representation the main aim of this paper is the adaptation of the very efficient jameson schmidt turkel jst algorithm jameson et al 1981 extensively used in computational fluid dynamics to a sph based discretisation of the mixed based set of conservation laws with three key distinct novelties first a conservative jst based sph computational framework is presented with emphasis in nearly incompressible materials second the suppression of numerical instabilities associated with the non physical zero energy modes is addressed through a well established stabilisation procedure third the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic total variation diminishing runge kutta time integrator in order to guarantee the global conservation of angular momentum for completeness exact enforcement of essential boundary conditions is incorporated through the use of a lagrange multiplier projection technique a series of challenging numerical examples e g in the near incompressibility regime are examined in order to assess the robustness and accuracy of the proposed algorithm the obtained results are benchmarked against a wide spectrum of alternative numerical strategies

application of level set approach to moving interfaces and free surface problems in flow through porous media abstract the level set technique introduced by osher and sethian has been widely used in computational fluid dynamics problems involving two or more immiscible fluids with sharp interfaces this paper presents an application of the level set to unconfined seepage problems where a free surface or a sharp interface exists it is based on considering the movement of both fluids introducing a smooth indicator function with a level set describing the interface position the proposed method can be applied to other flow in porous media problems involving immiscible fluids such as oil recovery applications

arbitrary discontinuities in space time finite elements by level sets and x fem an enriched finite element method with arbitrary discontinuities in space time is presented the discontinuities are treated by the extended finite element method x fem which uses a local partition of unity enrichment to introduce discontinuities along a moving hyper surface which is described by level sets a space time weak form for conservation laws is developed where the rankine hugoniot jump conditions are natural conditions of the weak form the method is illustrated in the solution of first order hyperbolic equations and applied to linear first order wave and non linear burgers equations by capturing the discontinuity in time as well as space results are improved over capturing the discontinuity in space alone and the method is remarkably accurate implications to standard semi discretization x fem formulations are also discussed copyright 2004 john wiley sons ltd

three step iterative methods with eighth order convergence for solving nonlinear equations a family of eighth order iterative methods for the solution of nonlinear equations is presented the new family of eighth order methods is based on king s fourth order methods and the family of sixth order iteration methods developed by chun et al per iteration the new methods require three evaluations of the function and one evaluation of its first derivative therefore this family of methods has the efficiency index which equals 1 682 kung and traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2 n 1 thus we provide a new example which agrees with the conjecture of kung traub for n 4 numerical comparisons are made to show the performance of the presented methods

stable particle methods based on lagrangian kernels abstract a large deformation particle method based on the krongauz belytschko corrected gradient meshfree method with lagrangian kernels is developed in this form the gradient is corrected by a linear transformation so that linear completeness is satisfied for the test functions shepard functions are used this guarantees that the patch test is met lagrangian kernels are introduced to eliminate spurious distortions of the domain of material stability a mass allocation scheme is developed that captures correct reflection of waves without any explicit application of traction boundary conditions in addition the lagrangian kernel versions of various forms of smooth particle methods sph including the standard forms and the randles libersky modification are presented and studied results are obtained for a variety of problems that compare this method to standard forms of sph the randles libersky correction and large deformation versions of the element free galerkin method

a two steps time discretization scheme using the sph method for shock wave propagation the smoothed particle hydrodynamics sph is a meshfree method which has been applied to a wide range of problems in the present work a new time integration algorithm using a corrected sph spatial discretization for small deformations is applied to solve the propagation of shock waves in viscoplastic continua in the method presented herein the equations are formulated in terms of stress and velocity a corrected lagrangian kernel is employed and two different sets of particles are used for the time discretization numerical instabilities are not present when using this new sph formulation the method proposed here has been proved to be efficient and it provides solutions of good accuracy

third order modifications of newton s method based on stolarsky and gini means in this paper we consider third order modifications of newton s method for solving nonlinear equations considered methods are based on stolarsky and gini means stolarsky 1975 13 stolarsky 1980 14 chen 2008 12 and depend on two parameters some known methods are special cases of our methods for example the power mean newton s method zhou 2007 10 the arithmetic mean newton s method weerakoon and fernando 2000 5 the harmonic mean newton s method ozban 2004 8 and the geometric mean newton s method lukic and ralevic 2008 9 third order convergence of the considered methods is proved and corresponding asymptotic error constants are expressed in terms of two parameters numerical examples obtained using mathematica with high precision arithmetic support the theoretical results some numerical tests were performed and it was shown that our methods yield better numerical results i e a smaller error x email protected when compared to halley euler hansen patrick ostrowski and inverse interpolation methods

a fully abstract semantics for a higher order functional language with nondeterministic computation abstract this paper presents a functional programming language based on moggi s monadic metalanguage in the first part of this paper we show how the language can be regarded as a monad on a category of signatures and that the resulting category of algebras is equivalent to the category of computationally cartesian closed categories in the second part we extend the language to include a nondeterministic operational semantics and show that the lower powerdomain semantics is fully abstract for may testing

a sixth order method for nonlinear equations abstract in this paper a sixth order method is developed by extending a third order method of weerakoon and fernando s weerakoon t g i fernando a variant of newton s method with accelerated third order convergence appl math lett 13 2000 87 93 for finding the real roots of nonlinear equations in r starting with a suitably chosen x 0 the method generates a sequence of iterates converging to the root the convergence analysis is provided to establish its sixth order of convergence in terms of computational cost it requires evaluations of only two functions and two first derivatives per iteration this implies that efficiency index of our method is 1 565 our method is comparable with the methods of neta b neta a sixth order family of methods for nonlinear equations intern j computer math 7 1979 157 161 and that of kou and li jisheng kou yitian li an improvement of jarratt method appl math comput 189 2007 1816 1821 it does not require the evaluation of the second order derivative of the given function as required in the family of chebyshev halley type methods jisheng kou xiuhua wang sixth order variants of chebyshev halley methods for solving non linear equations appl math comput 190 2007 1839 1843 jisheng kou on chebyshev halley methods with sixth order convergence for solving non linear equations appl math comput 190 2007 126 131 the efficacy of the method is tested on a number of numerical examples it is observed that our method takes less number of iterations than newton s method and the method of weerakoon and fernando on comparison with the other sixth order methods it behaves either similarly or better for the examples considered