transformation coefficients of permutation groups the eigenfunction method is used to calculate the transformation coefficients m 1 2 m1 m2 from the yamanouchi basis of the permutation group sf1 f2 to the sf1 f2 sf1 sf2 irreducible basis a program in fortran is written and tables of the transformation coefficients for the permutation group sf up to f 6 are given possible applications of the transformation coefficients are sketched

on the linear equation method for the subduction problem in symmetric groups we focus on the transformation matrices between the standard young yamanouchi basis of an irreducible representation for the symmetric group sn and the split basis adapted to the direct product subgroups we introduce the concept of subduction graph and show that it conveniently describes the combinatorial structure of the equation system arisen from the linear equation method thus we can outline an improved algorithm to solve the subduction problem in symmetric groups by a graph searching process we conclude by observing that the general matrix form for multiplicity separations resulting from orthonormalization can be expressed in terms of sylvester matrices relative to a suitable inner product in the multiplicity space

momentum classification of su n spin chains using extended young tableaux obtaining eigenvalues of permutations acting on the product space of n representations of su n usually involves either diagonalizing their representation matrices on total weight subspaces or decomposing their characters which can be obtained from frobenius formula or via graphical methods using young tableaux yt for products of fundamental representations of su n schuricht and one of us proposed the method of extended yt eyt which allows reading the eigenvalues of the cyclic permutation cn directly off the slightly modified standard yt labelling an irreducible su n representation here we generalize the method to all symmetric representations of su n and show that cn eigenvalue computation based on eyt is at least linearly faster than the standard methods mentioned

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

split standard transformation coefficients the block selective conjecture the split basis for the symmetric group sn is adapted to sn and to the product subgroup sn a sa we consider matrices transforming between split bases and the standard young yamanouchi basis of the symmetric group sn we present a conjecture for directly relating those transformation matrices to a representation matrix in the young yamanouchi basis of a cycle permutation this block selective conjecture agrees with previously obtained solutions for the transformation matrices up to and including s6 in particular the conjecture provides a correct solution for the early occurrences of multiplicities in the product sn a sa to motivate the main result of this paper we first present transformations between permuted symmetric groups

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

invariant measures on multi valued functions abstract in this paper we consider the question of under which conditions multi valued dynamical systems admit invariant measures we give results on the existence of invariant measures with full support on orbit spaces of multi valued dynamical systems we use these measures on the orbit space to induce measures on the original dynamical system we focus on the question of when a non atomic invariant measure on the orbit space induces an atomic invariant measure on the multi valued dynamical system this phenomenon is an indicator of complicated multi periodic behaviour

a study of dynamics via mobius conjugacy map on a family of sixth order modified newton like multiple zero finders with bivariate polynomial weight functions abstract a generic family of sixth order modified newton like multiple zero finders have been proposed in geum et al 2016 among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight functions and study their dynamics by investigating the relevant parameter spaces and dynamical planes via mobius conjugacy map applied to a prototype polynomial of the form z a m z b m the resulting dynamics is best illustrated through a variety of parameter spaces as well as dynamical planes

on the convergence of an optimal fourth order family of methods and its dynamics in this paper we present the study of the semilocal and local convergence of an optimal fourth order family of methods moreover the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied some anomalies are found in this family be means of studying the dynamical behavior parameter spaces are shown and the study of the stability of all the fixed points is presented

split bases and multiplicity separations in symmetric group transformation coefficients we consider matrices transforming between the standard young yamanouchi basis of the symmetric group and bases adapted to the product subgroups the split basis we derive closed formulae for transformation coefficients for b 3 which includes the first cases when a choice of multiplicity separation is required we discuss considerations which can be applied to obtain a simple form for the multiplicity separation we show that the combinatorial and algebraic structure of the littlewood richardson rule also known as the biedenharn louck pattern calculus does not assist with finding a simple multiplicity separation

fixed points imply chaos for a class of differential inclusions that arise in economic models we consider multi valued dynamical systems with continuous time of the form f x where f x is a set valued function such models have been studied recently in mathematical economics we provide a definition for chaos chaos and topological entropy for these differential inclusions that is in terms of the natural r action on the space of all solutions of the model by considering this more complicated topological space and its r action we show that chaos is the typical behavior in these models by showing that near any hyperbolic fixed point there is a region where the system is chaotic chaotic and has infinite topological entropy

enhanced group analysis and conservation laws of variable coefficient reaction diffusion equations with power nonlinearities a class of variable coefficient 1 1 dimensional nonlinear reaction diffusion equations of the general form f x ut g x unux x h x um is investigated different kinds of equivalence groups are constructed including ones with transformations which are nonlocal with respect to arbitrary elements for the class under consideration the complete group classification is performed with respect to convenient equivalence groups generalized extended and conditional ones and with respect to the set of all local transformations usage of different equivalences and coefficient gauges plays the major role for simple and clear formulation of the final results the corresponding set of admissible transformations is described exhaustively then using the most direct method we classify local conservation laws some exact solutions are constructed by the classical lie method

a third order newton type method to solve systems of nonlinear equations in this paper we present a third order newton type method to solve systems of nonlinear equations in the first we present theoretical preliminaries of the method secondly we solve some systems of nonlinear equations all test problems show the third order convergence of our method

numerical investigation of the nonlinear heat diffusion equation with high nonlinearity on the boundary a nonlinear heat diffusion problem is considered when the thermal conductivity and heat capacity are nonlinear functions of the temperature at one of the boundaries a highly nonlinear condition is imposed involving both the flux and the temperature we apply equivalence transformation which allows to reformulate the problem as an equation with linear diffusion for the transformed function this gives a unique opportunity to create a specialized implicit finite difference scheme with internal iterations that faithfully represents the energy balance for the system the equivalence transformation allows one to treat problems with plane cylindrical and spherical symmetry in an unified fashion as a featuring example we consider two versions of the nonlinear boundary condition energy absorption and energy input we show that the latter leads to blow up of the solution at the boundary and identify the profile of the blowing up solution

a reduced subduction graph and higher multiplicity in sn transformation coefficients transformation coefficients between standard bases for irreducible representations of the symmetric group sn and split bases adapted to the subgroup n1 n2 n are considered we first provide a selection rule and an identity rule for the subduction coefficients which allow us to decrease the number of unknowns and equations arising from the linear method by pan and chen then using the reduced subduction graph approach we may look at higher multiplicity instances as a significant example an orthonormalized solution for the first multiplicity three case which occurs in the decomposition of the irreducible representation 4 3 2 1 of s10 into 3 2 1 3 1 of s6 s4 is presented and discussed

a note on the transformation coefficients between the standard and non standard representations in a physically significant case closed formulae for the transformation coefficients between the standard and non standard representations of the symmetric group sn are obtained and the results are explicitly exhibited

an efficient high order iterative scheme for large nonlinear systems with dynamics abstract this study suggests a new general scheme of high convergence order for approximating the solutions of nonlinear systems the proposed scheme is the extension of an earlier study of parhi and gupta this method requires two vector function two jacobian matrices two inverse matrices and one frozen inverse matrix per iteration convergence error computational efficiency and numerical experiments are performed to verify the applicability and validity of the proposed methods compared with existing methods finally we discuss the strange fixed points and conjugacy functions on a particular case of our scheme the basins of attractions also demonstrate the dynamical behavior of this special case in the neighborhood of required roots and also assert the theoretical outcomes

an efficient algorithm for evaluating the standard young yamanouchi orthogonal representation with two column young tableaux for symmetric groups an efficient algorithm for evaluating the standard young yamanouchi orthogonal representation with two column young tableaux for symmetric groups is presented the representation matrix is given as the product of three matrices where two of them are in triangular form and are determined by an irreducible representation of the symmetric group and the other is made up of the elements which equal 1 0 or 1 according to some simple rules

calculating symmetric group split standard transformation coefficients using the block selective method a proof the split basis for the symmetric group sn is adapted to sn and to the product subgroup sn a sa the entries in the matrix that transforms between the split basis representation and the standard young yamanouchi yy basis the split standard transformation coefficients are closely related to a particle coefficients of fractional parentage recently the block selective conjecture was proposed for calculating the coefficients the conjecture implies that the transformation matrix is directly related to the representation matrix in the yy basis of a cycle permutation we present a proof of this conjecture

transformation between the young yamanouchi basis and its dual motivated by the aim of finding generalized transformation coefficients for the symmetric group we calculate the matrix which transforms the basis functions of the young yamanouchi basis into the basis functions of its dual our approach is to derive the representation matrices for both bases and then determine the transformation matrix the dual basis is associated with the subgroup chain whereas the usual yy basis is associated with the subgroup chain a combinatorial technique jeu de taquin is used to define the basis via the young yamanouchi symbols and young tableaux with which the basis functions can be indexed

the identification of young tableaux with angular momentum states young tableaux are used to label the basis vectors of the standard or young yamanouchi basis of the symmetric group despite being used for this purpose for some time a physical interpretation of what they mean has not been given weyl tableaux however which label the basis vectors of the standard or gelfand basis of the unitary group do have a physical interpretation weyl tableaux correspond to antisymmetrized states with definite total spin definite spin projection and definite total angular momentum projection we discuss how a previously well established link between young and weyl tableaux may imply young tableaux are similarly associated with such states if such an association could be made calculations using symmetric group bases could be reduced to simple angular momentum manipulations in particular this would greatly increase the efficiency of calculating the coefficients of fractional parentage of sn which can in turn be used to calculate unitary recoupling coefficients we present a methodology for determining whether such an association exists

convergence efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems in this work we present a new family of iterative methods for solving nonlinear systems that are optimal in the sense of kung and traub s conjecture for the unidimensional case we generalize this family by performing a new step in the iterative method getting a new family with order of convergence six we study the efficiency of these families for the multidimensional case by introducing a new term in the computational cost defined by grau sanchez et al a comparison with already known methods is done by studying the dynamics of these methods in an example system

an analysis of the properties of the variants of newton s method with third order convergence for the last five years the variants of the newton s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non linear equations these methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives in this paper we investigate about the relationship between these methods which are in fact based on the approximation of the second order derivative present in the third order limited taylor expansion we also prove that they are different forms of the halley method and are all contractive iterative methods in a common neighbourhood we extend some of these variants to multivariate cases and prove their respective local cubic convergence from their corresponding linear models

selection and identity rules for subductions of type a quantum iwahori hecke algebras this paper is concerned with the subduction problem of type a quantum iwahori hecke algebras ch sf q2 with a real deformation parameter q i e the problem of decomposing irreducible representations of such algebras as direct sum of irreducible representations of the subalgebras ch sf1 q2 ch sf2 q2 with f1 f2 f after giving a suitable combinatorial description for the subduction issue we provide a selection rule based on the richardson littlewood criterion which allows to determine the vanishing coupling coefficients between standard basis vectors for such representations and we also present an equivariance condition for the subduction coefficients such results extend those ones corresponding to the subduction problem in symmetric group algebras csf csf1 csf2 which are obtained by q approaching the value of 1

on subgroup adapted bases for representations of the symmetric group the split basis of an irreducible representation of the symmetric group sn m is the basis which is adapted to direct product subgroups of the form sn sm in this paper we have calculated symmetric group subduction coefficients relating the standard young yamanouchi basis for the symmetric group to the split basis by means of a novel version of the schur weyl duality we have also directly obtained matrix representations in the split basis using these techniques the advantages of this approach are that we obtain analytical expressions for the subduction coefficients and matrix representations and directly resolve issues of multiplicity in the subduction of sn sm irreducible representations from sn m irreducible representations our method is applicable to sn m irreducible representations labelled by young diagrams with large row length differences we provide evidence for a systematic expansion in the inverse row length difference and tools to compute the leading contribution which is exact when row length differences are infinite

a new approach to permutation group representations ii the formula for the yamanouchi matrix elements is rederived by the eigenfunction method in a simple fashion

a new approach based on the newton s method to solve systems of nonlinear equations an alternative strategy for solving systems of nonlinear equations when the classical newton s method fails is presented the proposed strategy is an extension for systems based on the idea presented in the article ramos and vigo aguiar 2015 it relies in obtaining the approximate solutions of a given system of equations through solving an associated system obtained through the theory underlying the newton s method in this way the solutions of the associated system that are not 2 cycles of the newton iteration function provide solutions of the original system as it is usual in most cases the associated system cannot be solved exactly and some iterative procedure must be used for particular starting values solving the associated system with the newton s method results to be more efficient than the application of the newton s method to the original system some examples are given to illustrate the performance of the proposed strategy performance profiles are evaluated in terms of number of iterations error and cpu time

irreducible representations of hecke algebras in the nonstandard basis and subduction coefficients irreducible representations of hecke algebras of the type an 1 hn q are discussed in the nonstandard basis some subduction coefficients i e the transformation coefficients between the standard and nonstandard base of hn q are derived by using the linear equation method

weak specification and baire space abstract in this paper we compute the topological entropy and we consider the question of chaos for shift spaces over countable alphabets we show that if a shift space has the weak specification property then it has chaos and we show that if in addition it has a countably infinite alphabet then it has infinite topological entropy

on form preserving point transformations of partial differential equations new identities are presented relating arbitrary order partial derivatives of and for the general point transformation these identities are used to study the nature of those point transformations which preserve the general form of a wide class of 1 1 partial differential equations these results facilitate the search for point symmetries both discrete and continuous lie and assist the search for point transformations which reduce equations to canonical but similar form a simple test for the existence of hodograph type transformations between equations of similar form is given

different anomalies in a jarratt family of iterative root finding methods abstract in this paper the behavior of a jarratt family of iterative methods applied to quadratic polynomials is studied some anomalies are found in this family be means of studying the dynamical behavior of this fourth order family of methods parameter spaces are shown and the study of the stability of all the fixed points is presented dynamical planes for members with good and bad dynamical behavior are also provided

new results on group classification of nonlinear diffusion convection equations using a new method and additional conditional and partial equivalence transformations we performed group classification in a class of variable coefficient 1 1 dimensional nonlinear diffusion convection equations of the general form f x ut d u ux x k u ux we obtain new interesting cases of such equations with the density f localized in space which have non trivial invariance algebra exact solutions of these equations are constructed we also consider the problem of investigation of the possible local transformations for an arbitrary pair of equations from the class under consideration i e of describing all the possible partial equivalence transformations in this class

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