on efficient weighted newton methods for solving systems of nonlinear equations in this study we present iterative methods of convergence order four and six for solving systems of nonlinear equations the fourth order scheme is composed of two steps namely newton iteration as the first step and weighted newton iteration as the second step the sixth order scheme is composed of three steps the first two steps are same as that of fourth order scheme whereas the third step is again based on weighted newton iteration computational efficiency in its general form is discussed comparison between the efficiencies of proposed techniques and existing techniques is made it is proved that for large systems the new methods are more efficient numerical tests are performed which confirm the theoretical results moreover theoretical order of convergence is verified in the examples

variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

nondeterministic space is closed under complementation in this paper we show that nondeterministic space s n is closed under complementation for s n greater than or equal to log n it immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by kuroda inform and control 7 1964 pp 207 233

on the local convergence of a fifth order iterative method in banach spaces a new predictor corrector iterative procedure that combines newton s method as predictor scheme and a fifth order iterative method as a corrector is designed for solving nonlinear equations in banach spaces we analyze the local order of convergence and the regions of accessibility of the new method comparing it with newton s method both theoretical and numerically

efficient high order methods based on golden ratio for nonlinear systems abstract we derive new iterative methods with order of convergence four or higher for solving nonlinear systems by composing iteratively golden ratio methods with a modified newton s method we use different efficiency indices in order to compare the new methods with other ones and present several numerical tests which confirm the theoretical results

analysis of two chebyshev like third order methods free from second derivatives for solving systems of nonlinear equations in this paper two chebyshev like third order methods free from second derivatives are considered and analyzed for systems of nonlinear equations the methods can be obtained by having different approximations to the second derivatives present in the chebyshev method we study the local and third order convergence of the methods using the point of attraction theory the computational aspects of the methods are also studied using some numerical experiments including an application to the chandrasekhar integral equations in radiative transfer

representations of hermitian kernels by means of krein spaces ii invariant kernels in this paper we study hermitian kernels invariant under the action of a semigroup with involution we characterize those hermitian kernels that realize the given action by bounded operators on a krein space this is motivated by the gns representation of algebras associated to hermitian functionals the dilation theory of hermitian maps on c algebras as well as others we explain the key role played by the technique of induced krein spaces and a lifting property associated to them

a family of multi point iterative methods for solving systems of nonlinear equations we extend to n dimensional case a known multi point family of iterative methods for solving nonlinear equations this family includes as particular cases some well known and also some new methods the main advantage of these methods is they have order three or four and they do not require the evaluation of any second or higher order frechet derivatives a local convergence analysis and numerical examples are provided

a modified chebyshev s iterative method with at least sixth order of convergence this paper is devoted to the construction and analysis of a high order variant of the classical chebyshev method the method has order of convergence at least six for simple roots the extension to system of equations and its semilocal convergence for nonlinear equations are presented finally an application to well known algebraic riccati equation is considered

increasing the order of convergence of iterative schemes for solving nonlinear systems a set of multistep iterative methods with increasing order of convergence is presented for solving systems of nonlinear equations one of the main advantages of these schemes is to achieve high order of convergence with few jacobian and functional evaluations joint with the use of the same matrix of coefficients in the most of the linear systems involved in the process indeed the application of the pseudocomposition technique on these proposed schemes allows us to increase their order of convergence obtaining new high order efficient methods finally some numerical tests are performed in order to check their practical behavior

minimal irreversible quantum mechanics the decay of unstable states abstract brownian motion is modelled by a harmonic oscillator brownian particle interacting with a continuous set of uncoupled harmonic oscillators the interaction is linear in the coordinates and the momenta the model has an analytical solution that is used to study the time evolution of the reduced density operator it is derived in a closed form in the one particle sector of the model the irreversible behavior of the brownian particle is described by a reduced density matrix

hyperfunction quantum field theory basic structural results the choice of the class e of generalized functions on space time in which to formulate general relativistic quantum field theory qft is discussed a first step is to isolate a set of conditions on e that allows a formulation of qft in otherwise the same way as the original proposal by wightman ark fys 28 129 1965 where e is the class of tempered distributions it is stressed that the formulation of qft in which e equals the class of fourier hyperfunctions on space time meets the following requirements a fourier hyperfunctions generalize tempered distributions thus allowing more singular fields as suggested by concrete models b fourier hyperfunction quantum fields are localizable both in space time and in energy momentum space thus allowing the physically indispensable standard interpretation of poincare covariance local commutativity and localization of energy momentum spectrum and c in fourier hyperfunction quantum field theory almost all the basic structural results of standar

representations of semigroups associated to invariant kernels with values adjointable operators abstract we consider positive semidefinite kernels valued in the algebra of adjointable operators on a ve space vector euclidean space and that are invariant under actions of semigroups a rather general dilation theorem is stated and proved for these kind of kernels representations of the semigroup on either the ve spaces of linearisation of the kernels or on their reproducing kernel ve spaces are obtainable we point out the reproducing kernel fabric of dilation theory and we show that the general theorem unifies many dilation results at the non topological level

geometric representation theory for unitary groups of operator algebras geometric realizations for the restrictions of gns representations to unitary groups of c algebras are constructed these geometric realizations use an appropriate concept of reproducing kernels on vector bundles to build such realizations in spaces of holomorphic sections a class of complex coadjoint orbits of the corresponding real banach lie groups are described and some homogeneous holomorphic hermitian vector bundles that are naturally associated with the coadjoint orbits are constructed

some remarks on the gelfand naimark segal representations of topological algebras after an appropriate restatement of the gelfand naimark segal construction for topological algebras we prove that there exists an isomorphism among the set cycl a of weakly continuous strongly cyclic representations of a barreled dual separable algebra with unit a the space hilba a of the hilbert spaces that are continuously embedded in a and are invariant under the dual left regular action of a and the set of the corresponding reproducing kernels we show that these isomorphisms are cone morphisms and we prove many interesting results that follow from this fact we discuss how these results can be used to describe cyclic representations on more general inner product spaces

probabilistic ω automata probabilistic automata are variants of nondeterministic automata over infinite words where all choices are resolved by probabilistic distributions acceptance of a run for an infinite input word can be defined using traditional acceptance criteria for automata such as buchi rabin or streett conditions the accepted language of a probabilistic automata is then defined by imposing a constraint on the probability measure of the accepting runs in this paper we study a series of fundamental properties of probabilistic automata with three different language semantics 1 the probable semantics that requires positive acceptance probability 2 the almost sure semantics that requires acceptance with probability 1 and 3 the threshold semantics that relies on an additional parameter i r0 1l that specifies a lower probability bound for the acceptance probability we provide a comparison of probabilistic automata under these three semantics and nondeterministic automata concerning expressiveness and efficiency furthermore we address closure properties under the boolean operators union intersection and complementation and algorithmic aspects such as checking emptiness or language containment

on gns representations on inner product spaces a generalization of the gns construction to hermitian linear functionals w defined on a unital algebra is considered along these lines a continuity condition h upon w is introduced such that h proves to be necessary and sufficient for the existence of a j representation on a krein space the property whether or not the gram operator j leaves the common and invariant domain of the representation invariant is characterized as well by properties of the functional w as by those of furthermore the interesting class of positively dominated functionals is introduced and investigated some applications to tensor algebras are finally discussed

a numerical approach to nonlinear two point boundary value problems for odes in this paper we propose a numerical approach to solve some problems connected with the implementation of the newton type methods for the resolution of the nonlinear system of equations related to the discretization of a nonlinear two point bvps for odes with mixed linear boundary conditions by using the finite difference method

irreducible representations of the heisenberg algebra in krein spaces the representations of the heisenberg algebra in krein spaces more generally in weakly complete inner product spaces are classified under general regularity and irreducibility conditions besides the fock representation two other types appear one with negative the other with a two sided discrete spectrum of the number operator

towards a definition of the quantum ergodic hierarchy ergodicity and mixing abstract in a previous paper we have given a general framework for addressing the definition of quantum chaos by identifying the conditions that a quantum system must satisfy to lead to non integrability in its classical limit in this paper we will generalize those results with the purpose of defining the two lower levels of the quantum ergodic hierarchy ergodicity and mixing we will also argue for the physical relevance of this approach by considering a particular example where our formalism has been successfully applied

some variant of newton s method with third order convergence we present a new modification of the newton s method which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given and the best efficiency in term of function evaluations of two of this new methods is provided

third order methods from quadrature formulae for solving systems of nonlinear equations we extend to p dimensional problems a modification of the newton method based on quadrature formulas of order at least one which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given these new methods may be more efficient then other third order methods as they do not require the use of the second order frechet derivative

applications of topological algebras of unbounded operators in this paper we discuss some physical applications of topological algebras of unbounded operators the first example is a simple system of free bosons then we consider other models related to this one finally we discuss the time evolution of two interacting models of matter and bosons we show that for all these systems it is possible to build up a common mathematical framework where the existence of the thermodynamical limit of the algebraic dynamics can be conveniently analyzed

closely embedded kreĭn spaces and applications to dirac operators abstract motivated by energy space representation of dirac operators in the sense of k friedrichs we recently introduced the notion of closely embedded kre n spaces these spaces are associated to unbounded selfadjoint operators that play the role of kernel operators in the sense of l schwartz and they are special representations of induced kre n spaces in this article we present a canonical representation of closely embedded kre n spaces in terms of a generalization of the notion of operator range and obtain a characterization of uniqueness when applied to dirac operators the results differ according to a mass or a massless particle in a dramatic way in the case of a particle with a nontrivial mass we obtain a dual of a sobolev type space and we have uniqueness while in the case of a massless particle we obtain a dual of a homogenous sobolev type space and we lose uniqueness

infinite infrared regularization and a state space for the heisenberg algebra we present a method for the construction of a krein space completion for spaces of test functions equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order this generalizes a regularization method for infrared singularities in quantum field theory introduced by morchio and strocchi to the case of singularities of infinite order we give conditions for the possibility of this procedure in terms of local differential operators and the gelfand shilov test function spaces as well as an abstract sufficient condition as a model case we construct a maximally positive definite state space for the heisenberg algebra in the presence of an infinite infrared singularity

complex velocity transformations and the bisognano wichmann theorem for quantum fields acting on krein spaces it is proven that in indefinite metric quantum field theory there exists a dense set of analytic vectors for the generator of the one parameter group of x0 x1 velocity transformations this makes it possible to define complex velocity transformations also for the indefinite metric case in combination with the results of bros epstein and moschella commun math phys 196 535 570 1998 proving bisognano wichmann bw analyticity within the linear program one then obtains a suitable generalization of the bw theorem for local relativistic quantum fields acting on krein spaces quantum fields with indefinite metric

the jarratt method in banach space setting abstract in this note we extend the jarratt method of order four into banach spaces we also establish a kantorovich type convergence theorem see the references and give an explicit expression for the error bound of the method jarratt 1966 1969

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

a fourth order method from quadrature formulae to solve systems of nonlinear equations in this paper we obtain a fourth order convergence method to solve systems of nonlinear equations this method is based on a quadrature formulae a general error analysis providing the fourth order of convergence is given numerical examples show the fourth order convergence this method does not use the second order frechet derivative

on the expressiveness and complexity of randomization in finite state monitors in this article we introduce the model of finite state probabilistic monitors fpm which are finite state automata on infinite strings that have probabilistic transitions and an absorbing reject state fpms are a natural automata model that can be seen as either randomized run time monitoring algorithms or as models of open probabilistic reactive systems that can fail we give a number of results that characterize topologically as well as with respect to their computational power the sets of languages recognized by fpms we also study the emptiness and universality problems for such automata and give exact complexity bounds for these problems

covariant representations on krein c modules associated to pairs of two maps abstract in this paper we construct a ksgns type covariant representation on a krein c module for a covariant completely positive map and the result is applied to construct a ksgns type covariant representation associated with a pair of two maps where is a covariant completely positive map on a c algebra and is a covariant map on a krein c module the ksgns type covariant representation for a pair is applied to give a new covariant j representation of a crossed product of a c algebra and a new covariant map of a crossed product of a hilbert c module by a discrete group

a steffensen s type method in banach spaces with applications on boundary value problems in this paper a modified steffensen s type iterative scheme for the numerical solution of a system of nonlinear equations is studied two convergence theorems are presented the numerical solution of boundary value problems by the multiple shooting method using the proposed iterative scheme is analyzed

accelerated methods of order 2p for systems of nonlinear equations we present a new iterative method of order of convergence 5 for solving nonlinear systems by composing the midpoint method with newton s method and using an approximation for the jacobian matrix in order to reduce the required number of functional evaluations per iteration in addition we compare the efficiency index of these methods with that of newton s method and present several numerical tests which confirm the theoretical results and allow us to compare these variants with newton s method

models of local relativistic quantum fields with indefinite metric in all dimensions a condition on a set of truncated wightman functions is formulated and shown to permit the construction of the hilbert space structure included in the morchio strocchi modified wightman axioms the truncated wightman functions which are obtained by analytic continuation of the truncated schwinger functions of euclidean scalar random fields and covariant vector quaternionic random fields constructed via convoluted generalized white noise are then shown to satisfy this condition as a consequence such random fields provide relativistic models for indefinite metric quantum field theory in dimension 4 vector case respectively in all dimensions scalar case

indecomposable representations with invariant inner product consequences of the existence of an invariant necessarily indefinite non degenerate inner product for an indecomposable representation of a group g on a space are studied if has an irreducible subrepresentation 1 on a subspace 1 it is shown that there exists an invariant subspace 2 of containing 1and satisfying the following conditions 1 the representation 1 mod 2 on mod 2 is conjugate to the representation 1 1 2 1 is a null space for the inner product and 3 the induced inner product on 2mod 1 is non degenerate and invariant for the representation pi 2 left pi left mathfrak h 2 right right bmod mathfrak h 2 a special example being the gupta bleuler triplet for the one particle space of the free classical electromagnetic field with 1 space of longitudinal photons and 2 the space defined by the subsidiary condition

ein operatorwertiger hahn banach satz abstract we generalize arveson s extension theorem for completely positive mappings 1 to a hahn banach principle for matricial sublinear functionals with values in an injective c algebra or an ideal in b h we characterize injective w algebras by a matricial order condition we illustrate the matricial hahn banach principle by three applications 1 let a b b be unital c algebras b a subalgebra of a and b b injective if a b is a completely bounded self adjoint b bihomomorphism then it can be expressed as the difference of two completely positive b bihomomorphism 2 let m be a w algebra containing 1 h on a hilbert space h if m is finite and hyperfinite there exists an invariant expectation mapping p of b h onto m p is an extension of the center trace 3 combes 7 proved that a lower semicontinuous scalar weight on a c algebra is the upper envelope of bounded positive functionals we generalize this result to unbounded completely positive mappings with values in an injective w algebra

the gauss seidelization of iterative methods for solving nonlinear equations in the complex plane abstract in this paper we introduce a process we have called gauss seidelization for solving nonlinear equations we have used this name because the process is inspired by the well known gauss seidel method to numerically solve a system of linear equations together with some convergence results we present several numerical experiments in order to emphasize how the gauss seidelization process influences on the dynamical behavior of an iterative method for solving nonlinear equations

general efficient class of steffensen type methods with memory for solving systems of nonlinear equations abstract there are a very small number of high quality derivative free methods with memory for solving a system of nonlinear equations numerically motivated and inspired by the fact we propose a more efficient general class of steffensen type multipoint methods with memory this proposed class requires one divided difference and inverse of only one matrix per full iteration we also demonstrate their applicability and illustrate that these methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations numerically for quantitative comparison we have also computed total number of convergent points and convergent percentage along with basins of attractions on a number of test problems to recommend the best quality algorithm

non unitary representations of nilpotent groups i cohomologies extensions and neutral cocycles let be a finite dimensional representation of a connected nilpotent group g and u be a unitary representation of g we investigate the structure of the extensions of by u and correspondingly the group h1 u of 1 cohomologies a spectral criterion of triviality of h1 u is proved and systematically used in the study of various types of decomposition of the extensions we consider a special type of u cocycles neutral cocycles which play a crucial role in the theory of j unitary representations of groups on pontryagin k spaces