convergence for a class of improved sixth order chebyshev halley type methods in this paper we consider the semilocal convergence on a class of improved chebyshev halley type methods for solving f x 0 where f x y is a nonlinear operator x and y are two banach spaces is a non empty open convex subset in x to solve the problems that f x is unbounded in and it can not satisfy the whole lipschitz or h o lder continuity f x n is replaced by f x 0 n for all x where n n 0 x0 is an initial point moreover f x is assumed to be local h o lder continuous so the convergence conditions are relaxed we prove an existence uniqueness theorem for the solution which shows that the r order of these methods is at least 5 q where q 0 1 especially when f x is local lipschitz continuous the r order will become six

electrical characteristics of a class of n order triangular network abstract this paper investigates the electrical properties of a class of n order triangular resistor network model the authors establish by constructing equivalent model the second order nonlinear difference equation model we propose by using equivalent transformation method the general and specific methods of solution for the nonlinear difference equation and at once obtain an accurate equivalent resistance formula of n order triangular resistor network and a series of special conclusions are analyzed and compared finally we study the oscillation and resonance characteristics of the triangular lc network under different conditions where the method used is variable substitution by using the equivalent resistance results obtained this study reveals the electrical characteristics of triangular lc network and establishes a new theoretical foundation for related disciplines

resistance between two nodes of a ring network abstract the resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists given m positive integers m 1 m 2 m n let g m i 1 n be the resistor network with node set v v 1 v 2 v n and with a unit resistor between arbitrary two nodes u v i v v i 1 for i 1 2 n where v i v j 0 if i j and v i m i v n 1 v 1 gervacio 2016 introduces a modified method to compute the resistance between two nodes based on this method in this paper we use the elimination and substitution principles in electrical circuit to obtain the resistance between arbitrary two nodes of g m i 1 n

a note on the halley method in banach spaces abstract we provide a convergence theorem under the usual ostrowski kantorovich conditions for an equivalent form of the halley method in banach spaces the best possible upper error bound for the method is obtained some applications to the solution of quadratic operator equations are provided

on the r order of the halley method an r order bound for the halley method is obtained in this work where an analysis of the convergence of the method is also presented under mild differentiability conditions to do this a new technique is developed where the involved operator must satisfy some recurrence relations

recursive pointwise design for nonlinear systems this paper presents a recursive pointwise design rpd method for a class of nonlinear systems represented by x t f x t g x t u t a main feature of the rpd method is to recursively design a stable controller by using pointwise information of a system the design philosophy is that f x t and g x t can be approximated as constant vectors in very small local state spaces based on the design philosophy we numerically determine constant control inputs in very small local state spaces by solving linear matrix inequalities lmis derived in this paper the designed controller switches to another constant control input when the states move to another local state space although the design philosophy is simple and natural the controller does not always guarantee the stability of the original nonlinear system x t f x t g x t u t therefore this paper gives ideas of compensating the approximation caused by the design philosophy after addressing outline of the pointwise design we provide design conditions that exactly guarantee the stability of the original system the controller design conditions require to give the maximum and minimum values of elements in the functions f x t and g x t in each local state space therefore we also present design conditions for unknown cases of the maximum and minimum values furthermore we construct an effective design procedure using the pointwise design a feature of the design procedure is to subdivide only infeasible regions and to solve lmis again only for the subdivided infeasible regions the recursive procedure saves effort to design a controller a design example demonstrates the utility of the rpd method

interactive multiple objective programming subject to flexible constraints abstract an interactive decision support system is introduced which aids in solving multiple objective programming problems subject to strict and flexible constraints integral part is an extension of a well known fuzzy sets approach evaluating possible solutions by their degrees of membership to objectives and constraints this approach is linked to classical multiple objective programming models if the decision maker cannot determine membership functions a priori the system suggests functions dependent on the given information and interactive modifications are allowed

packing dimers on 2p 1 x 2q 1 lattices we use computational method to investigate the number of ways to pack dimers on m x n lattices where both m and n are odd in this case there is always a single vacancy in the lattices we show that the dimer configuration numbers on 2k 1 x 2k 1 odd square lattices have some remarkable number theoretical properties in parallel to those of close packed dimers on 2k x 2k even square lattices for which an exact solution exists furthermore we demonstrate that there is an unambiguous logarithmic term in the finite size correction of free energy of odd by odd lattice strips with any width n or 1 this logarithmic term determines the distinct behavior of the free energy of odd square lattices these findings reveal a deep and previously unexplored connection between statistical physics models and number theory and indicate the possibility that the monomer dimer problem might be solvable

two point resistances in a family of self similar x y flower networks abstract the computation of resistance between two nodes in networks is a fundamental problem in both electric theory and graph theory in this paper first a recursive algorithm for computing resistance between any two nodes in a family of self similar x y flower networks is given the x y flower networks display rich behavior as observed in a large variety of real systems then as explanations using the algorithm explicit expressions for some resistances in 1 3 flower networks and 2 2 flower networks are obtained

recursion transform method for computing resistance of the complex resistor network with three arbitrary boundaries we develop a general recursion transform r t method for a two dimensional resistor network with a zero resistor boundary as applications of the r t method we consider a significant example to illuminate the usefulness for calculating resistance of a rectangular m ifmmode times else texttimes fi n resistor network with a null resistor and three arbitrary boundaries a problem never solved before since green s function techniques and laplacian matrix approaches are invalid in this case looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of an arbitrary boundary since the boundary is like a wall or trap which affects the behavior of finite network in this paper we obtain several general formulas of resistance between any two nodes in a nonregular m ifmmode times else texttimes fi n resistor network in both finite and infinite cases in particular 12 special cases are given by reducing one of the general formulas to understand its applications and meanings and an integral identity is found when we compare the equivalent resistance of two different structures of the same problem in a resistor network

dimer model on a triangular lattice we analyze the partition function of the dimer model on an mathcal m ifmmode times else texttimes fi mathcal n triangular lattice wrapped on a torus obtained by fendley moessner and sondhi phys rev b 66 214513 2002 from a finite size analysis we have found that the dimer model on such a lattice can be described by a conformal field theory having a central charge c ensuremath 2 the shift exponent for the specific heat is found to depend on the parity of the number of lattice sites mathcal n along a given lattice axis e g for odd mathcal n we obtain the shift exponent ensuremath lambda 1 while for even mathcal n it is infinite ensuremath lambda ensuremath infty in the former case therefore the finite size specific heat pseudocritical point is size dependent while in the latter case it coincides with the critical point of the thermodynamic limit

two point resistance of a resistor network embedded on a globe we consider the problem of two point resistance in an m ensuremath 1 ifmmode times else texttimes fi n resistor network embedded on a globe a geometry topologically equivalent to an m ifmmode times else texttimes fi n cobweb with its boundary collapsed into one single point we deduce a concise formula for the resistance between any two nodes on the globe using a method of direct summation pioneered by one of us z z tan l zhou and j h yang j phys a math theor 46 195202 2013 this method is contrasted with the laplacian matrix approach formulated also by one of us f y wu j phys a math gen 37 6653 2004 which is difficult to apply to the geometry of a globe our analysis gives the result in the form of a single summation

modification of the kantorovich assumptions for semilocal convergence of the chebyshev method this study obtains two semilocal convergence results for the well known chebyshev method which is a third order iterative process the hypotheses required are modifications to the normal kantorovich ones the results obtained are applied to the reduction of nonlinear integral equations of the fredholm type and first kind

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

theory of impedance networks the two point impedance and lc resonances we present a formulation of the determination of the impedance between any two nodes in an impedance network an impedance network is described by its laplacian matrix l which has generally complex matrix elements we show that by solving the equation lu u with orthonormal vectors ua the effective impedance between nodes p and q of the network is zpq u p u q 2 where the summation is over all not identically equal to zero and u p is the pth component of u for networks consisting of inductances l and capacitances c the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of this curious result suggests the possibility of practical applications to resonant circuits our formulation is illustrated by explicit examples

the equivalent resistance of a 3 n cobweb network and its conjecture of an m n cobweb network we investigate the equivalent resistance of a 3 n cobweb network the difference equations of the model are constructed by network analysis and their general solution is obtained by matrix transformations it is found that the equivalent resistance can be expressed by the trigonometric function of k 7 which decreases with the increase of the order n by analyzing and comparing the equivalent resistances of the 1 n 2 n and 3 n cobweb networks a conjecture on the equivalent resistance of the m n cobweb network is proposed

asymptotic expansion for the resistance between two maximally separated nodes on an m by n resistor network we analyze the exact formulae for the resistance between two arbitrary notes in a rectangular network of resistors under free periodic and cylindrical boundary conditions obtained by wu j phys a 37 6653 2004 based on such expression we then apply the algorithm of ivashkevich izmailian and hu j phys a 35 5543 2002 to derive the exact asymptotic expansions of the

theory of resistor networks the two point resistance the resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the laplacian matrix associated with the network explicit formulae for two point resistances are deduced for regular lattices in one two and three dimensions under various boundary conditions including that of a mobius strip and a klein bottle the emphasis is on lattices of finite sizes we also deduce summation and product identities which can be used to analyse large size expansions in two and higher dimensions

a transfer matrix approach to random resistor networks introduces a transfer matrix formulation to compute the conductance of random resistor networks the authors apply this method to strips of width up to 40 and use finite size scaling arguments to obtain an estimate for the conductivity critical exponent in two dimensions t 1 28 or 0 03

semilocal convergence for halley s method under weak lipschitz condition the semilocal convergence properties of halley s method for nonlinear operator equations are studied under the hypothesis that the second derivative satisfies some weak lipschitz condition the method employed in the present paper is based on a family of recurrence relations which will be satisfied by the involved operator an application to a nonlinear hammerstein integral equation of the second kind is provided

recurrence relations for the super halley method in this paper we give sufficient conditions in order to assure the convergence of the super halley method in banach spaces we use a system of recurrence relations analogous to those given in the classical newton kantorovich theorem or those given for chebyshev and halley methods by different authors 1998 elsevier science ltd all rights reserved

logarithmic corrections in the free energy of monomer dimer model on plane lattices with free boundaries using exact computations we study the classical hard core monomer dimer models on m x n plane lattice strips with free boundaries for an arbitrary number v of monomers or vacancies we found a logarithmic correction term in the finite size correction of the free energy per lattice site the coefficient of the logarithmic correction term depends on the number of monomers present v and the parity of the width n of the lattice strip the coefficient equals to v when n is odd and v 2 when n is even the results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers we also study the finite size correction in the low dimer density limit where the number of dimers d is fixed in this case the coefficient of the logarithmic correction term equals to d for both odd and even n

fuzzy optimal control the problem of fuzzy optimal control of nonlinear systems is formulated and solved on the basis of fuzzy mathematical programming the fuzzy optimal control problem is extended to the case of multicriteria optimal control a particular case of fuzzy optimal control with fuzzy objective function and crisp transversality conditions is also considered

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

finite size effects for the ising model on helical tori we analyze the exact partition function of the ising model on a square lattice under helical boundary conditions obtained by liaw et al phys rev e 73 055101 r 2006 based on such an expression we then extend the algorithm of ivashkevich izmailian and hu j phys a 35 5543 2002 to derive an exact asymptotic expansion of the logarithm of the partition function and its first to fourth derivatives at the critical point from such results we find that the shift exponent for the specific heat is ensuremath lambda 1 for all values of the helicity factor d we also find that finite size corrections for the free energy the internal energy and the specific heat of the model in a crucial way depend on the helicity factor of the lattice

resistance between two nodes in general position on an m n fan network the resistance between two nodes in general position on a fan network with n radial lines and m transverse lines is determined also a similar result of izmailian kenna and wu j phys a math theor 47 035003 2014 for an m ifmmode times else texttimes fi n cobweb network is reproduced but the method used here is significantly different it avoids the use of the kirchhoff matrix requires the solution of just one instead of two eigenvalue problems and results directly in only a single summation further the current distribution is given explicitly as a byproduct of the method the method is the same as that used by tan zhou and yang j phys a math theor 46 195202 2013 to find the cobweb resistance between center and perimeter for 1 ensuremath le m ensuremath le 3 and general n proof of their conjecture for general m is discussed