improving newton raphson method for nonlinear equations by modified adomian decomposition method in this paper we present some efficient numerical algorithms for solving nonlinear equations based on newton raphson method the modified adomian decomposition method is applied to construct the numerical algorithms some numerical illustrations are given to show the efficiency of algorithms

a study of convergence on the newton homotopy continuation method the traditional newton method is a well known and popular method for solving non linear equation it has high efficient in the convergence speed however we always need to guess the initial value in the iteration process good initial guess value can solve the equation quickly bad initial guess value usually will yield divergence homotopy continuation method is a kind of perturbation method it can guarantee the answer by a certain path if we choose the auxiliary homotopy function or call start system well this paper presents some useful rules for the choice of the auxiliary homotopy function to avoid the problem of divergence of traditional newton method

weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions in this paper applying the theory of semigroups of operators to evolution families and banach fixed point theorem we prove the existence and uniqueness of the weighted pseudo almost periodic mild solution of the semilinear evolution equation x t a t x t f t x t with nonlocal conditions x 0 x 0 g x in banach space x under some suitable hypotheses

on a class of second order anti periodic boundary value problems of concern is the existence and uniqueness of anti periodic solutions to a class of abstract nonlinear second order differential equations the investigation relies on the theory of m accretive operators in banach or hilbert spaces examples of boundary value problems for ordinary and partial differential equations are also discussed

weighted pseudo antiperiodic solutions for fractional integro differential equations in banach spaces in this paper we prove the existence of weighted pseudo antiperiodic mild solutions for fractional integro differential equations in the form d u t au t t a t s au s ds f t u t t r where f u is stepanov like weighted pseudo antiperiodic and a generates a resolvent family of bounded and linear operators on a banach space x a l loc 1 r and 0 here the fractional derivative is considered in the sense of weyl also we give a short proof to show that the vector valued space of stepanov like weighted pseudo antiperiodic functions is a banach space

a new technique to obtain derivative free optimal iterative methods for solving nonlinear equations abstract a new technique to obtain derivative free methods with optimal order of convergence in the sense of the kung traub conjecture for solving nonlinear smooth equations is described the procedure uses steffensen like methods and pade approximants some numerical examples are provided to show the good performance of the new methods

a new method to deduce high order compact difference schemes for two dimensional poisson equation abstract this paper introduces a novel method for deducing high order compact difference schemes for the two dimensional 2d poisson equation like finite volume method a dual partition is introduced combining simpson integral formula and parabolic interpolation a family of fourth order and sixth order compact difference schemes are obtained based on three different types of dual partitions moreover several new fourth order compact schemes are gained and numerical experiments are shown two of them are much better than almost any other fourth order schemes which have been presented in others work the outline for the nonlinear poisson equation is also given numerical experiments are presented to verify the feasibility of this new method and the high accuracy of these fourth order and sixth order compact difference schemes

on some examples and constructions of contact manifolds the first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all dimensions and the fact that every closed contact 3 manifold which is not smoothly a rational homology sphere contact embeds with trivial normal bundle inside a hypertight closed contact 5 manifold this uses known construction procedures by bourgeois on products with tori and geiges on branched covering spaces we pass from these procedures to definitions this allows to prove a uniqueness statement in the case of contact branched coverings and to study the global properties such as tightness and fillability of the results of both constructions without relying on any auxiliary choice in the procedures a second goal allowed by these definitions is to study relations between these constructions and the notions of supporting open book as introduced by giroux and of contact fiber bundle as introduced by lerman for instance we give a definition of bourgeois contact structures on flat contact fiber bundles which is local strictly includes the results of the bourgeois construction and allows to recover an isotopy class of supporting open books on the fibers this last point relies on a reinterpretation inspired by an idea by giroux of supporting open books in terms of pairs of contact vector fields

stepanov like pseudo almost periodic mild solutions to perturbed nonautonomous evolution equations with infinite delay abstract in this paper we prove the invariance of stepanov like pseudo almost periodic functions under bounded linear operators furthermore we obtain existence and uniqueness theorems of pseudo almost periodic mild solutions to evolution equations u t a t u t h t and u t a t u t f t b u t t c t s u s d s f t on r assuming that a t satisfy acquistapace terreni conditions that the evolution family generated by a t has exponential dichotomy that r 0 a is almost periodic that b c t s t s are bounded linear operators that f is lipschitz with respect to the second argument uniformly in the first argument and that h f f are stepanov like pseudo almost periodic for p 1 and continuous to illustrate our abstract result a concrete example is given

computing the first eigenvalue of the p laplacian via the inverse power method abstract in this paper we discuss a new method for computing the first dirichlet eigenvalue of the p laplacian inspired by the inverse power method in finite dimensional linear algebra the iterative technique is independent of the particular method used in solving the p laplacian equation and therefore can be made as efficient as the latter the method is validated theoretically for any ball in r n if p 1 and for any bounded domain in the particular case p 2 for p 2 the method is validated numerically for the square

weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type abstract this paper studies suitable sufficient conditions to ensure the existence and uniqueness of weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type introduced by t a burton in the literature the abstract results are then utilized to characterize weighted pseudo almost periodic solutions to the well known logistic equation

tightness in contact metric 3 manifolds this paper begins the study of relations between riemannian geometry and global properties of contact structures on 3 manifolds in particular we prove an analog of the sphere theorem from riemannian geometry in the setting of contact geometry specifically if a given three dimensional contact manifold m admits a complete compatible riemannian metric of positive 4 9 pinched curvature then the underlying contact structure is tight in particular the contact structure pulled back to the universal cover is the standard contact structure on s3 we also describe geometric conditions in dimension three for to be universally tight in the nonpositive curvature setting

weighted pseudo almost automorphic solution of an integro differential equation with weighted stepanov like pseudo almost automorphic forcing term in this paper we ensure existence and uniqueness of weighted pseudo almost automorphic solution of an integrodifferential equation with weighted s p pseudo almost automorphic forcing term in a banach space x we use fractional powers of operators and the banach fixed point theorem in order to obtain our result very recently introduced concept of weighted s p pseudo almost automorphy has been used here

on a class of quadratic convergence iteration formulae without derivatives a class of iterative formulae without derivatives are proposed in this paper these methods are shown to be quadratic convergence some numerical tests are given

tight contact structures with no symplectic fillings we exhibit tight contact structures on 3 manifolds that do not admit any symplectic fillings

a massera type theorem for almost automorphic solutions of differential equations abstract in this note we present a massera type theorem for the existence of almost automorphic solutions of periodic linear evolution equations of the form x t a t x t f t where a t is unbounded linear operator depending on t periodically and generates a periodic evolutionary process f is almost automorphic the main results are stated in terms of the almost automorphy of solutions and their carleman spectra

comparison of homotopy perturbation method and homotopy analysis method comparison of homotopy perturbation method hpm and homotopy analysis method is made revealing that the former is more powerful than the later furthermore the hpm is further developed in this paper by applying the modern perturbation methods

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

a class of steffensen type methods with optimal order of convergence abstract in this paper a family of steffensen type methods of fourth order convergence for solving nonlinear smooth equations is suggested in the proposed methods a linear combination of divided differences is used to get a better approximation to the derivative of the given function each derivative free member of the family requires only three evaluations of the given function per iteration therefore this class of methods has efficiency index equal to 1 587 kung and traub conjectured that the order of convergence of any multipoint method without memory cannot exceed the bound 2 d 1 where d is the number of functional evaluations per step the new class of methods agrees with this conjecture for the case d 3 numerical examples are made to show the performance of the presented methods on smooth and nonsmooth equations and to compare with other ones

parametric iterative methods of second order for solving nonlinear equation two new three parametric methods of second order without derivatives are presented for solving the nonlinear equation the iterative formulae based on the liapunov method of dynamic system are deduced and their convergence is provided finally some numerical experiments show the feasibility of the above methods

existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations this paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations upon making some suitable assumptions the existence and uniqueness of a weighted pseudo almost periodic solution is obtained to illustrate our main result we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional differential equations with feedback control

high order iterative methods without derivatives for solving nonlinear equations the new second order and third order iterative methods without derivatives are presented for solving nonlinear equations the iterative formulae based on the homotopy perturbation method are deduced and their convergences are provided finally some numerical experiments show the efficiency of the theoretical results for the above methods

weighted pseudo almost automorphic functions and wpaa solutions to semilinear evolution equations abstract in this paper we reveal several basic properties about nonlinear vector valued weighted pseudo almost automorphic functions including equivalence completeness translation invariance composition theorem and convolution theorem of these functions we also give some concrete examples to illustrate our results finally we obtain a new existence theorem of nonlinear weighted pseudo almost automorphic solutions for semilinear evolution equations in banach spaces

weighted stepanov like pseudo almost automorphy and applications abstract in this paper we propose a new class of functions called weighted stepanov like pseudo almost automorphic functions which generalize in a natural fashion the concept of almost automorphy and its various extensions we systematically explore the properties of the weighted stepanov like pseudo almost automorphic functions in general banach space including a composition result as an application we establish some sufficient criteria for the existence uniqueness of the weighted pseudo almost automorphic solution to a class of partial neutral functional differential equations and also to a class of nonlinear volterra integral equations of convolution type with infinite delay in banach space some interesting examples are presented to illustrate the main findings

existence of weighted pseudo almost periodic solutions to some classes of differential equations with sp weighted pseudo almost periodic coefficients abstract in this paper we introduce the concept of weighted pseudo almost periodicity in the sense of stepanov also called s p weighted pseudo almost periodicity and study its properties next we present a result on the existence of weighted pseudo almost periodic solutions to the n dimensional heat equation with s p weighted pseudo almost periodic coefficients

weak and strong fillability of higher dimensional contact manifolds for contact manifolds in dimension three the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent we extend these facts to higher dimensions in particular we define a natural generalization of weak fillings and prove that it is indeed weaker at least in dimension five while also being obstructed by all known manifestations of overtwistedness we also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense these depend on a higher dimensional analogue of giroux torsion which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary

tight contact structures on some small seifert fibered 3 manifolds we classify tight contact structures on the small seifert fibered 3 manifolds m 1 r1 r2 r3 with ri 0 1 q and r1 r2 the result is obtained by combining convex surface theory with computations of contact ozsvath szabo invariants we also show that some of the tight contact structures on the manifolds considered are nonfillable justifying the use of heegaard floer theory

steffensen type methods for solving nonlinear equations in the present paper by approximating the derivatives in the well known fourth order ostrowski s method and in a sixth order improved ostrowski s method by central difference quotients we obtain new modifications of these methods free from derivatives we prove the important fact that the methods obtained preserve their convergence orders 4 and 6 respectively without calculating any derivatives finally numerical tests confirm the theoretical results and allow us to compare these variants with the corresponding methods that make use of derivatives and with the classical newton s method

on connected sums and legendrian knots abstract we study the behavior of legendrian and transverse knots under the operation of connected sums as a consequence we show that there exist legendrian knots that are not distinguished by any known invariant moreover we classify legendrian knots in some non legendrian simple knot types

the contact invariant in sutured floer homology we describe an invariant of a contact 3 manifold with convex boundary as an element of juhasz s sutured floer homology our invariant generalizes the contact invariant in heegaard floer homology in the closed case due to ozsvath and szabo

admissible transverse surgery does not preserve tightness we produce the first examples of closed tight contact 3 manifolds which become overtwisted after performing admissible transverse surgeries along the way we clarify the relationship between admissible transverse surgery and legendrian surgery we use this clarification to study a new invariant of transverse knots namely the range of slopes on which admissible transverse surgery preserves tightness and to provide some new examples of knot types which are not uniformly thick our examples also illuminate several interesting new phenomena including the existence of hyperbolic universally tight contact 3 manifolds whose heegaard floer contact invariants vanish and which are not weakly fillable and the existence of open books with arbitrarily high fractional dehn twist coefficients whose compatible contact structures are not deformations of co orientable taut foliations

contact structures on product five manifolds and fibre sums along circles two constructions of contact manifolds are presented i products of s1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and ii fibre connected sums along isotropic circles baykur has found a decomposition as required for i for all closed oriented 4 manifolds as a corollary we can show that all closed oriented 5 manifolds that are cartesian products of lower dimensional manifolds carry a contact structure for symplectic 4 manifolds we exhibit an alternative construction of such a decomposition this gives us control over the homotopy type of the corresponding contact structure in particular we prove that mathbb cp 2 times s 1 admits a contact structure in every homotopy class of almost contact structures the existence of contact structures is also established for a large class of 5 manifolds with fundamental group mathbb z 2

infinitely many universally tight torsion free contact structures with vanishing ozsvath szabo contact invariants ozsvath szabo contact invariants are a powerful way to prove tightness of contact structures but they are known to vanish in the presence of giroux torsion in this paper we construct on infinitely many manifolds infinitely many isotopy classes of universally tight torsion free contact structures whose ozsvath szabo invariant vanishes we also discuss the relation between these invariants and an invariant on t3 and construct other examples of new phenomena in heegaard floer theory along the way we prove two conjectures of k honda w kazez and g matic about their contact topological quantum field theory almost all the proofs in this paper rely on their gluing theorem for sutured contact invariants

weighted pseudo almost periodic solutions for some partial functional differential equations abstract in this work we give sufficient conditions for the existence and uniqueness of a weighted pseudo almost periodic solution for some partial functional differential equations to illustrate our main result we study the existence of a weighted pseudo almost periodic solution for some diffusion equation with delay

existence and classification of overtwisted contact structures in all dimensions we establish a parametric extension h principle for overtwisted contact structures on manifolds of all dimensions which is the direct generalization of the 3 dimensional result from 12 it implies in particular that any closed manifold admits a contact structure in any given homotopy class of almost contact structures

obstructing pseudoconvex embeddings and contractible stein fillings for brieskorn spheres abstract a question in low dimensional symplectic topology asks whether every compact contractible 4 manifold admits the structure of a stein domain a related conjecture due to gompf asserts that no nontrivial brieskorn homology sphere admits a pseudoconvex embedding in c 2 with either orientation we give the first known example of a contractible boundary irreducible 4 manifold that admits no stein structure with either orientation though its boundary has stein fillings with both orientations we also verify gompf s conjecture with one orientation for a family of brieskorn spheres of which some are known to admit a smooth embedding in c 2 a byproduct of our example is the construction of a cork that does not admit a stein structure with either orientation

antiperiodic solutions of semilinear integrodifferential equations in banach spaces abstract we are concerned in this paper with the existence of antiperiodic mild solutions of some semilinear integrodifferential equations in a banach space we study further properties of antiperiodic functions including a new composition theorem and introduce the new concept of asymptotically antiperiodic functions

on symplectic fillings of lens spaces le st be the contact structure naturally induced on the lens space l p q s 3 z pz by the standard contact structure st on the three sphere s 3 we obtain a complete classification of the symplectic fillings of l p q st up to orientation preserving diffeomorphisms in view of our results we formulate a conjecture on the diffeomorphism types of the smoothings of complex two dimensional cyclic quotient singularities

enlarging the convergence domain in local convergence studies for iterative methods in banach spaces in this work we introduce a new form of setting the general assumptions for the local convergence studies of iterative methods in banach spaces that allows us to improve the convergence domains specifically a local convergence result for a family of higher order iterative methods for solving nonlinear equations in banach spaces is established under the assumption that the frechet derivative satisfies the lipschitz continuity condition for some values of the parameter these iterative methods are of fifth order the importance of our work is that it avoids the usual practice of boundedness conditions of higher order derivatives which is a drawback for solving some practical problems the existence and uniqueness theorem that establishes the convergence balls of these methods is obtained we have considered a number of numerical examples including a nonlinear hammerstein equation and computed the radii of the convergence balls it is found that the radius of convergence ball obtained by our approach is much larger when compared with some other existing methods the global convergence properties of the family are explored by analyzing the dynamics of the corresponding operator on complex quadratic polynomials

quantitative darboux theorems in contact geometry this paper begins the study of relations between riemannian geometry and contact topology on 2n 1 manifolds and continues this study on 3 manifolds specifically we provide a lower bound for the radius of a geodesic ball in a contact 2n 1 manifold m that can be embedded in the standard contact structure on r that is on the size of a darboux ball the bound is established with respect to a riemannian metric compatible with an associated contact form for in dimension three it further leads us to an estimate of the size for a standard neighborhood of a closed reeb orbit the main tools are classical comparison theorems in riemannian geometry in the same context we also use holomorphic curves techniques to provide a lower bound for the radius of a ps tight ball

on the existence of anti periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators the existence of anti periodic solutions hence also that of periodic solutions to the nonlinear parabolic type evolution equation ddt u t u t f t u t 0 t r is shown under the assumptions that the subdifferential operator is odd and that f t t r is a family of monotone operators satisfying the anti periodicity condition f t t v f t v v d f t hence f t t v f t v v d d f t t r for a fixed t r here coerciveness of is not assumed an application to a heat equation is given without assuming boundedness of the domain of rxn

anti periodic solutions for semilinear evolution equations in this paper we use the homotopy method to establish the existence and uniqueness of anti periodic solutions for the nonlinear anti periodic problem a t x bx f t a e t r x t t x t where a t x is a nonlinear map and b is a bounded linear operator from r n to r n sufficient conditions for the existence of the solution set are presented also we consider the nonlinear evolution problems with a perturbation term which is multivalued we show that for this problem the solution set is nonempty and weakly compact in w 1 2 i r n for the case of convex valued perturbation and prove the existence theorems of anti periodic solutions for the nonconvex case all illustrative examples are provided

on the homotopy analysis method for nonlinear problems a powerful easy to use analytic tool for nonlinear problems in general namely the homotopy analysis method is further improved and systematically described through a typical nonlinear problem i e the algebraically decaying viscous boundary layer flow due to a moving sheet two rules the rule of solution expression and the rule of coefficient ergodicity are proposed which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering an explicit analytic solution is given for the first time with recursive formulas for coefficients this analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

reducibility in sasakian geometry the purpose of this paper is to study reducibility properties in sasakian geometry first we give the sasaki version of the de rham decomposition theorem however we need a mild technical assumption on the sasaki automorphism group which includes the toric case next we introduce the concept of it cone reducible and consider s 3 bundles over a smooth projective algebraic variety where we give a classification result concerning contact structures admitting the action of a 2 torus of reeb type in particular we can classify all such sasakian structures up to contact isotopy on s 3 bundles over a riemann surface of genus greater than zero finally we show that in the toric case an extremal sasaki metric on a sasaki join always splits

modified homotopy perturbation method for nonlinear equations and comparison with adomian decomposition method abstract in this paper we present some efficient numerical algorithms for solving nonlinear equations based on newton raphson method by using modified homotopy perturbation method the modified adomian decomposition method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method appl math comput 145 2003 887 893 is compared with new algorithms some numerical illustrations are given to show the efficiency of algorithms

an efficient algorithm for solving troesch s problem abstract a new algorithm is presented for solving troesch s problem the numerical scheme based on the modified homotopy perturbation technique is deduced some numerical experiments are made compared with the variational iteration method and the adomian decomposition method the scheme is shown to be highly accurate and only a few terms are required to obtain accurate computable solutions finally the algorithm is applied to other problems

computing the first eigenpair of the p laplacian in annuli abstract we propose a method for computing the first eigenpair of the dirichlet p laplacian p 1 in the annulus a b x r n a x b n 1 for each t a b we use an inverse iteration method to solve two radial eigenvalue problems one in the annulus a t with the corresponding eigenvalue t and boundary conditions u a 0 u t and the other in the annulus t b with the corresponding eigenvalue t and boundary conditions u t 0 u b next we adjust the parameter t using a matching procedure to make t coincide with t thereby obtaining the first eigenvalue p hence by a simple splicing argument we obtain the positive l normalized radial first eigenfunction u p the matching parameter is the maximum point of u p in order to apply this method we derive estimates for t and t and we prove that these functions are monotone and locally lipschitz continuous moreover we derive upper and lower estimates for the maximum point which we use in the matching procedure and we also present a direct proof that u p converges to the l normalized distance function to the boundary as p we also present some numerical results obtained using this method

an index for closed orbits in beltrami fields abstract we consider the class of beltrami fields eigenfields of the curl operator on three dimensional riemannian solid tori such vector fields arise as steady incompressible inviscid fluids and plasmas using techniques from contact geometry we construct an integer valued index for detecting closed orbits in the flow which are topologically inessential they have winding number zero with respect to the solid torus the most important feature of the index is its computability it can be rigorously determined from a c 1 approximation to the vector field on any meridional disc of the solid torus as a result we obtain a test for detecting the non existence of a global cross section to the 3d flow via purely 2d information

existence of pseudo almost automorphic solutions to some abstract differential equations with sp pseudo almost automorphic coefficients abstract this paper introduces and studies the notion of s p pseudo almost automorphy or stepanov like pseudo almost automorphy which generalizes in a natural fashion the concept of pseudo almost automorphy that was recently introduced in the literature by liang xiao and zhang we next obtain the existence of pseudo almost automorphic solutions to some differential equations with s p pseudo almost automorphic coefficients

cabling and transverse simplicity we study legendrian knots in a cabled knot type specifically given a topological knot type c we analyze the legendrian knots in knot types ob tained from k by cabling in terms of legendrian knots in the knot type k as a corollary of this analysis we show that the 2 3 cable of the 2 3 torus knot is not transversely simple and moreover classify the transverse knots in this knot type this is the first classification of transverse knots in a non transversely simple knot type we also classify legendrian knots in this knot type and exhibit the first example of a legendrian knot that does not destabi lize yet its thurston bennequin invariant is not maximal among legendrian representatives in its knot type in this paper we continue the investigation of legendrian knots in tight contact 3 manifolds using 3 dimensional contact topological methods in eh1 the authors introduced a general framework for analyzing legendrian knots in tight contact 3 manifolds there we streamlined the proof of the classification of legendrian unknots originally proved by eliashberg eraser in ef and gave a complete classification of legendrian torus knots and figure eight knots in eh2 we gave the first structure theorem for legendrian knots namely the reduction of the analysis of connected sums of legendrian knots to that of the prime summands this yielded a plethora of non legendrian simple knot types a topological knot type is legendrian simple if legendrian knots in this knot type are determined by their thurston bennequin invariant and rotation number moreover we exhibited pairs of legendrian knots in the same topological knot type with the same thurston bennequin and rotation numbers which required arbitrarily many stabilizations before they became legendrian isotopic see eh2