on the depth of the tangent cone and the growth of the hilbert function for a d dimensional cohen macaulay local ring r mn we study the depth of the associated graded ring of r with respect to an rm primary ideal i in terms of the vallabrega valla conditions and the length of it jit where j is a j minimal reduction of i and t 1 as a corollary we generalize sally s conjecture on the depth of the associated graded ring with respect to a maximal ideal to rm primary ideals we also study the growth of the hilbert function

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

a new iteration method for solving algebraic equations in this paper a nonlinear algebraic equation f x 0 by applying taylor s theorem is converted into a coupled iteration systeml x n 1 g x n 0andg x n f x n l x n wherel x ax 2 bx c the formula is of high convergence some examples are given

a new iteration method with cubic convergence to solve nonlinear algebraic equations abstract in this paper a new iteration scheme is proposed to solve the roots of an algebraic equation f x 0 given an initial guess x0 the roots of the equation can be obtained using the following iteration scheme x n 1 x n f x n f 2 x n 2 f x n f x n f x n this iteration scheme has unique convergence characteristics different from the well known newton s method it is shown that this iteration method has cubic local convergence in the neighborhood of the root using this scheme real or complex roots for specific algebraic equations can be found because there are two iteration directions for a given initial guess two solutions can be found for certain algebraic equations with multiple roots examples are presented and compared with other methods

non monotonic fuzzy measures and the choquet integral abstract this paper discusses non monotonic fuzzy measures which are set functions without monotonicity and the choquet integral with respect to non monotonic fuzzy measures a concrete example shows that the choquet integral is meaningful in the case of non monotonic fuzzy measures as well as in the case of ordinary fuzzy measures every comonotonically additive positively homogeneous functional of bounded variation can be represented as a choquet integral with respect to a non monotonic fuzzy measure of bounded variation the space of such functionals is a real banach space isometrically isomorphic to the space of non monotonic fuzzy measures of bounded variation

on the continuity of the concave integral whenever a functional is concave it is natural to ask whether its sendograph is a closed convex set if so the hahn banach theory implies that the functional can be represented as the infimum of all continuous linear functionals greater than or equal to it we refer to such representation as a dual representation dominated convergence of the concave integral for capacities is characterized in terms of dual representation whenever sequences of functions converge pointwise outside a set of zero capacity

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

some numerical methods for solving nonlinear equations by using decomposition technique in this paper we use the system of coupled equations involving an auxiliary function together with decomposition technique to suggest and analyze some new classes of iterative methods for solving nonlinear equations these new methods include the halley method and its variant forms as special cases various numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

depth of fiber cones of ideals with almost minimal mixed multiplicity let r m be a cohen macaulay local ring of dimension d 0 i an m primary ideal with almost minimal mixed multiplicity such that depth g i d 1 we show that fm i has almost maximal depth i e depth fm i d 1

a third order newton type method for nonlinear equations based on modified homotopy perturbation method in this paper we present a new iterative method for solving nonlinear algebric equations by using modified homotopy perturbation method we also discuss the convergence criteria of the present method to assess its validity and accuracy the method is applied to solve several test problems

iterative methods with fourth order convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 m aslam noor new iterative schemes for nonlinear equations appl math comput in press and noor and noor m aslam noor k inayat noor some iterative schemes for nonlinear equations appl math comput in press we show that this new iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

a new family of iterative methods for solving system of nonlinear algebric equations abstract homotopy perturbation method hpm is applied to construct a new iterative method for solving system of nonlinear algebric equations comparison of the result obtained by the present method with that obtained by revised adomian decomposition method hossein jafari varsha daftardar gejji appl math comput 175 2006 1 7 reveals that the accuracy and fast convergence of the new method

on modified newton methods for solving a non linear algebraic equations abstract in this paper we present a new modified newton method for solving a non linear algebraic equation by using the well known nedzhibov s method d k r babajee m z dauhoo an analysis of the properties of the variants of newton s method with third order convergence applied mathematics and computation 183 1 2006 659 684 we proposed a new iteration method and we show by one equation that this new iteration method is more quickly convergence than newton s method

fifth order iterative methods for solving nonlinear equations abstract in this paper we suggest and analyze a new two step iterative method for solving nonlinear equation f x 0 by rewriting the given nonlinear equation as a coupled system of equations and using the taylor series it is shown that this new iterative method is of fifth order several examples are given to illustrate its performance and efficiency comparison with other methods is also given this method can be viewed as an improvement of the halley s method

j multiplicity and depth of associated graded modules abstract let r be a noetherian local ring we define the minimal j multiplicity and almost minimal j multiplicity of an arbitrary r ideal on any finite r module for any ideal i with minimal j multiplicity or almost minimal j multiplicity on a cohen macaulay module m we prove that under some residual conditions the associated graded module gr i m is cohen macaulay or almost cohen macaulay respectively our work generalizes the results for minimal multiplicity and almost minimal multiplicity obtained by sally rossi valla wang huckaba elias corso polini and vaz pinto

a discrete choquet integral for ordered systems a model for a choquet integral for arbitrary finite set systems is presented the model includes in particular the classical model on the system of all subsets of a finite set the general model associates canonical non negative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system which are then extended to arbitrary valuations on the set system it is shown that the general choquet integral can be computed by a simple monge type algorithm for so called intersection systems which include as a special case weakly union closed families generalizing lovasz classical characterization we give a characterization of the superadditivity of the choquet integral relative to a capacity on a union closed system in terms of an appropriate model of supermodularity of such capacities

artin nagata properties minimal multiplicities and depth of fiber cones abstract minimal values of multiplicities of ideals have a strong relation with the depth of blowup algebras in this paper we introduce the notion of goto minimal j multiplicity for ideals of maximal analytic spread in a cohen macaulay ring inspired by the work of s goto a jayanthan t puthenpurakal and j verma we study the interplay among this new notion the notion of minimal j multiplicity introduced by c polini and y xie and the cohen macaulayness of the fiber cone of ideals satisfying certain residual assumptions we are also able to provide a bound on the reduction number of ideals of goto minimal j multiplicity having either cohen macaulay associated graded algebra or linear decay in the depth of their powers

the concave integral over large spaces this paper investigates the concave integral for capacities defined over large spaces we characterize when the integral with respect to capacity v can be represented as the infimum over all integrals with respect to additive measures that are greater than or equal to v we introduce the notion of loose extendability and study its relation to the concave integral a non additive version for the levi theorem and the fatou lemma are proven finally we provide several convergence theorems for capacities with large cores

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

bipolarization of posets and natural interpolation the choquet integral w r t a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of 0 1 n we take this basic fact as a starting point to define the choquet integral in a very general way using the geometric realization of lattices and their natural triangulation as in the work of koshevoy a second aim of the paper is to define a general mechanism for the bipolarization of ordered structures bisets or signed sets as well as bisubmodular functions bicapacities bicooperative games as well as the choquet integral defined for them can be seen as particular instances of this scheme lastly an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper

a theory of fuzzy measures representations the choquet integral and null sets abstract some theorems of t murofushi and m sugeno fuzzy sets and systems 29 1989 201 227 concerning representation of fuzzy measures and the choquet integral are generalized it is shown that if there is a certain relation between two measurable functions then the choquet integral is additive for these two functions in addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a algebra