generating equilateral random polygons in confinement in this paper we continue an earlier study diao et al 2011 j phys a math theor 44 405202 on the generation algorithms of random equilateral polygons confined in a sphere here the equilateral random polygons are rooted at the center of the confining sphere and the confining sphere behaves like an absorbing boundary one way to generate such a random polygon is the accept reject method in which an unconditioned equilateral random polygon rooted at origin is generated the polygon is accepted if it is within the confining sphere otherwise it is rejected and the process is repeated the algorithm proposed in this paper offers an alternative to the accept reject method yielding a faster generation process when the confining sphere is small in order to use this algorithm effectively a large reusable data set needs to be pre computed only once we derive the theoretical distribution of the given random polygon model and demonstrate with strong numerical evidence that our implementation of the algorithm follows this distribution a run time analysis and a numerical error estimate are given at the end of the paper

existence and uniqueness of positive solutions to a class of singular m point boundary value problems abstract this paper investigates the existence and uniqueness of positive solutions to a class of singular m point boundary value problems of second order ordinary differential equations a sufficient condition for the existence and uniqueness of c 0 1 positive solutions as well as c 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem our nonlinearity f t u may be singular at u t 0 and or t 1

third order boundary value problems with nonlocal boundary conditions we treat the existence of multiple positive solutions for a third order boundary value problem with nonlocal boundary conditions in our work each of the three boundary conditions is a linear functional on c 0 1 that is given by a stieltjes integral but is not necessarily a positive functional

multiple solutions to a three point boundary value problem for higher order ordinary differential equations in this paper we provide sufficient conditions for the existence of at least three solutions to a three point boundary value problem for higher order ordinary differential equations the nonlinear term f in the differential equation under consideration may depend on higher order derivatives of arbitrary order and this is where the main novelty of this work lies by applying the two pairs of upper and lower solutions method of henderson and thompson as well as degree theory the existence of at least three solutions of the problem is given

multiple positive solutions for multipoint boundary value problems with one dimensional p laplacian abstract in this paper we consider the multiplicity of positive solutions for the one dimensional p laplacian differential equation p u q t f t u u 0 t 0 1 subject to some boundary conditions by means of a fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems

positive solutions of singular boundary value problems for systems of nonlinear fourth order differential equations abstract in this paper we study the singular boundary value problems for systems of nonlinear fourth order differential equations u 4 t a 1 t f 1 t u t v t u t v t b 1 t g 1 t u t v t u t v t v 4 t a 2 t f 2 t u t v t u t v t b 2 t g 2 t u t v t u t v t 0 t 1 u 0 u 1 v 0 v 1 0 1 u 0 1 u 0 0 1 u 1 1 u 1 0 2 v 0 2 v 0 0 2 v 1 2 v 1 0 under some weaker conditions we show the existence of single and multiple positive solutions of the above problem by applying the fixed point theorem of cone expansion and compression type due to krasnosel skill

existence and multiplicity of non negative solutions for systems of perturbed hammerstein integral equations abstract we study the existence of positive solutions for a system of perturbed hammerstein integral equations our setting is quite general and covers a wide class of systems of boundary value problems the main ingredient in our theory is the classical fixed point index theory for compact maps

finite size scaling in strips antiperiodic boundary conditions the exact values of the universal amplitude a relating the correlation length xi approximately l a to the strip width l at the critical point of ising and 3 state potts models are obtained for the case of antiperiodic or twisted boundary conditions predictions are also made for the finite size scaling behaviour of the interfacial tension

existence results for some n dimensional nonlocal boundary value problems abstract in this article we study an n th dimensional nonlocal boundary value problem for a second order differential equation of sturm liouville type by using the linear part of the boundary condition an equivalent integral equation is obtained and then the nonlinear alternative fixed point result is applied some special cases are also given

positive solutions of nonlinear second order m point boundary value problem abstract in this paper by using krasnoselskii s fixed point theorem of cone expansion compression type and under suitable conditions we present the existence of single and multiple positive solutions to the nonlinear second order m point boundary value problem u t a t f u t 0 0 t 1 u 0 0 u 1 i 1 m 2 a i u i where is a positive parameter a i 0 for i 1 2 m 3 and a m 2 0 i satisfy 0 1 2 m 2 1 and i 1 m 2 a i i 1 we derive an explicit interval of such that for any in this interval the existence of at least one positive solution to the boundary value problem is guaranteed and the existence of at least two solutions for in an appropriate interval is also discussed

positive solutions for one dimensional p laplacian boundary value problems with dependence on the first order derivative abstract this paper presents sufficient conditions for the existence and multiplicity of positive solutions to the one dimensional p laplacian differential equation p u a t f u u 0 subject to some boundary conditions we show that it has at least one or two or three positive solutions under some assumptions by applying the fixed point theorem

positive solutions of the three point boundary value problem for second order differential equations with an advanced argument abstract in this paper by using the fixed point index method we establish the existence of at least one or at least two positive solutions to the three point boundary value problem for a second order differential equation with an advanced argument u t a t f u h t 0 t 0 1 u 0 0 u u 1 where 0 1 0 and 1 0 as an application we also give an example to demonstrate our result

conformal theory of spin correlations in the semi infinite 3 state potts and self dual zn models in the conformal theory the magnetization operator of the critical 3 state potts or self dual z3 model is degenerate at level 6 solving a sixth order differential equation the authors calculate the bulk 4 spin correlation function and the spin spin correlation function in the half space the spin spin correlation function of the semi infinite self dual zn model is also obtained for arbitrary n both free and fixed spin boundary conditions are considered

existence of positive solutions to third order differential equations with advanced arguments and nonlocal boundary conditions abstract we use a fixed point theorem due to avery and peterson to establish the existence of at least three non negative solutions of some nonlocal boundary value problems to third order differential equations with advanced arguments an example is given to illustrate the main results

the modified xxz heisenberg chain conformal invariance and the surface exponents of c 1 systems the authors present the operator content of the xxz chain in the presence of external fields the finite size scaling spectra can be expressed in terms of irreps of shifted u 1 kac moody algebras the shift depending on the external fields using an explicit feigin fuchs construction 1982 they project out from these spectra the operator content of c 1 systems with free fixed and mixed boundary conditions they also show how this projection mechanism works for a finite number of sites

two dimensional semi infinite multicritical ising models the order parameter correlation functions of the z2 invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi infinite plane constrained to fixed or free boundary conditions these yield the corresponding universal surface exponents which distinguish the behaviour between even and odd critical models we also make explicit the interplay between duality and boundary conditions

the average crossing number of equilateral random polygons in this paper we study the average crossing number of equilateral random walks and polygons we show that the mean average crossing number acn of all equilateral random walks of length n is of the form a similar result holds for equilateral random polygons these results are confirmed by our numerical studies furthermore our numerical studies indicate that when random polygons of length n are divided into individual knot types the for each knot type can be described by a function of the form where a b and c are constants depending on and n0 is the minimal number of segments required to form the profiles diverge from each other with more complex knots showing higher than less complex knots moreover the profiles intersect with the acn profile of all closed walks these points of intersection define the equilibrium length of i e the chain length at which a statistical ensemble of configurations with given knot type upon cutting equilibration and reclosure to a new knot type does not show a tendency to increase or decrease this concept of equilibrium length seems to be universal and applies also to other length dependent observables for random knots such as the mean radius of gyration rg

positive solutions of three point boundary value problems for second order impulsive differential equations with advanced arguments in this paper we discuss three point boundary value problems for second order impulsive differential equations with advanced arguments we establish sufficient conditions under which such problems have positive solutions to obtain the results we use the fixed point index

multiple positive solutions of resonant and non resonant nonlocal boundary value problems abstract we study the existence of positive solutions for equations of the form u t f t u t a e t 0 1 when f t u 2 u 0 for u 0 for some constant 0 and for the perturbed equation u t 2 u t h t u t a e t 0 1 when h t u 0 subject to various non local boundary conditions in particular we establish existence and multiplicity of positive solutions for non perturbed boundary value problems at resonance by considering equivalent non resonant perturbed problems with the same boundary conditions

positive solutions of nonlinear singular third order two point boundary value problem abstract in this paper we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third order two point boundary value problem u t a t f u t 0 0 t 1 u 0 u 0 u 1 0 where is a positive parameter under various assumptions on a and f we establish intervals of the parameter which yield the existence of at least one at least two and infinitely many positive solutions of the boundary value problem by using krasnoselskii s fixed point theorem of cone expansion compression type

existence and multiplicity for positive solutions of a multi point boundary value problem abstract in this paper we study the existence and multiplicity of positive solutions of multi point boundary value problems for systems of nonlinear second order ordinary differential equations

the growth of the mean average crossing number of equilateral polygons in confinement the physical and biological properties of collapsed long polymer chains as well as of highly condensed biopolymers such as dna in all organisms are known to be determined at least in part by their topological and geometrical properties with this purpose of characterizing the topological properties of such condensed systems equilateral random polygons restricted to confined volumes are often used however very few analytical results are known in this paper we investigate the effect of volume confinement on the mean average crossing number acn of equilateral random polygons the mean acn of knots and links under confinement provides a simple alternative measurement for the topological complexity of knots and links in the statistical sense for an equilateral random polygon of n segments without any volume confinement constrain it is known that its mean acn acn is of the order here we model the confining volume as a simple sphere of radius r we provide an analytical argument which shows that acn of an equilateral random polygon of n segments under extreme confinement meaning r n grows as o n2 we propose to model the growth of acn as a r n2 b r nln n under a less extreme confinement condition where a r and b r are functions of r with r being the radius of the confining sphere computer simulations performed show a fairly good fit using this model

operator content of the blume capel quantum chain the authors calculated the conformal anomaly number of the blume capel quantum chain via finite size corrections to the ground state energy in addition they compute at the tricritical point the lowest excitations of the spectrum to be compared with the theoretical description in terms of the irreducible representations of the corresponding virasoro algebra

existence and iteration of positive solutions for a multipoint one dimensional p laplacian boundary value problem abstract in this paper we study the existence and iteration of positive solutions for the one dimensional p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following multipoint boundary condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i by applying a monotone iterative method we not only obtain the existence of positive solutions for the problem but also establish iterative schemes for approximating the solutions

existence of triple positive solutions for multi point boundary value problems with a one dimensional p laplacian in this paper we consider the existence of multiple positive solutions for multi point boundary value problems with a one dimensional p laplacian f p u t q t f t u t u t 0 01 a email protected email protected i email protected email protected m 2 0 i 1 m email protected i i 1 m email protected email protected 0 1 0 x 1 x 2 x m 2 1 by the fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

positive solutions for second order four point boundary value problems with alternating coefficient abstract in this paper we investigate the existence of positive solutions for a class of nonlinear second order four point boundary value problems with alternating coefficient our approach relies on the krasnosel skii fixed point theorem the result of this paper is new and extent the previously known result

positive solutions to singular system with four point coupled boundary conditions abstract existence of positive solution to a nonlinear singular system with four point coupled boundary conditions of the type x t f t x t y t t 0 1 y t g t x t y t t 0 1 x 0 0 x 1 y y 0 0 y 1 x is established the nonlinearities f g 0 1 0 0 0 are continuous and singular at t 0 t 1 while the parameters satisfy 0 1 0 1 an example is included to show the applicability of our result

on the mean and variance of the writhe of random polygons we here address two problems concerning the writhe of random polygons first we study the behavior of the mean writhe as a function length second we study the variance of the writhe suppose that we are dealing with a set of random polygons with the same length and knot type which could be the model of some circular dna with the same topological property in general a simple way of detecting chirality of this knot type is to compute the mean writhe of the polygons if the mean writhe is non zero then the knot is chiral how accurate is this method for example if for a specific knot type k the mean writhe decreased to zero as the length of the polygons increased then this method would be limited in the case of long polygons furthermore we conjecture that the sign of the mean writhe is a topological invariant of chiral knots this sign appears to be the same as that of an ideal conformation of the knot we provide numerical evidence to support these claims and we propose a new nomenclature of knots based on the sign of their expected writhes this nomenclature can be of particular interest to applied scientists the second part of our study focuses on the variance of the writhe a problem that has not received much attention in the past in this case we focused on the equilateral random polygons we give numerical as well as analytical evidence to show that the variance of the writhe of equilateral random polygons of length n behaves as a linear function of the length of the equilateral random polygon

characteristics of shape and knotting in ideal rings we present two descriptions of the local scaling and shape of ideal rings primarily featuring subsegments our focus will be the squared radius of gyration of subsegments and the squared internal end to end distance defined to be the average squared distance between vertices k edges apart we calculate the exact averages of these values over the space of all such ideal rings not just a calculation of the order of these averages and compare these to the equivalent values in open chains this comparison will show that the structure of ideal rings is similar to that of ideal chains for only exceedingly short lengths these results will be corroborated by numerical experiments they will be used to analyze the convergence of our generation method and the effect of knotting on these characteristics of shape

generating random walks and polygons with stiffness in confinement the purpose of this paper is to explore ways to generate random walks and polygons in confinement with a bias toward stiffness here the stiffness refers to the curvature angle between two consecutive edges along the random walk or polygon the stiffer the walk polygon the smaller this angle on average thus random walks and polygons with an elevated stiffness have lower than expected curvatures the authors introduced and studied several generation algorithms with a stiffness parameter that regulates the expected curvature angle at a given vertex in which the random walks and polygons are generated one edge at a time using conditional probability density functions our generating algorithms also allow the generation of unconfined random walks and polygons with any desired mean curvature angle in the case of random walks and polygons confined in a sphere of fixed radius we observe that as expected stiff random walks or polygons are more likely to be close to the confinement boundary the methods developed here require that the random walks and random polygons be rooted at the center of the confinement sphere

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian f p x t q t f t x t x t 0 t 0 1 subject to the following boundary value conditions x 0 i 1n a ix x i x 1 i 1n b ix x i where f p s s p 2 s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem

duality of ordinary and extraordinary surface critical behaviour in the two dimensional potts model the dual relationship between semi infinite two dimensional q state potts models with free and fixed spin boundary conditions is used to study the surface critical behaviour at the bulk critical temperature with fixed boundary spins i e the extraordinary transition both the magnetisation and energy densities have singularities of the same form mod t tc mod 2 alpha as the bulk free energy at t tc both the spin spin and energy energy correlations decay as r 4 parallel to the surface

scaling behavior of random knots using numerical simulations we investigate how overall dimensions of random knots scale with their length we demonstrate that when closed non self avoiding random trajectories are divided into groups consisting of individual knot types then each such group shows the scaling exponent of 0 588 that is typical for self avoiding walks however when all generated knots are grouped together their scaling exponent becomes equal to 0 5 as in non self avoiding random walks we explain here this apparent paradox we introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots we also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

critical behaviour near multiple junctions and dirty surfaces in the two dimensional ising model the authors consider m two dimensional semi infinite planes of ising spins joined together through surface spins and study the critical behaviour near to the junction the m 0 limit of the model according to the replica trick corresponds to the semi infinite ising model in the presence of a random surface field rsfi using conformal mapping second order perturbation expansion around the weak and strong coupled planes limits and a differential renormalization group they show that the surface critical behaviour of the rsfi model is described by ising critical exponents with logarithmic corrections to scaling while at multiple junctions m 2 the transition is of first order there is a spontaneous junction magnetization at the bulk critical point

triple positive solutions for boundary value problems on infinite intervals abstract this paper deals with the existence of triple positive solutions for sturm liouville boundary value problems of second order nonlinear differential equation on a half line by using a fixed point theorem in a cone due to avery peterson we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term

a note on multi point boundary value problems abstract multi point boundary value problems for a second order ordinary differential equation are considered in this note an existence result is obtained with the help of coincidence degree theory

positive solutions for singular boundary value problems of a coupled system of differential equations by using fixed point theorem of cone expansion and compression this paper investigates the existence of multiple positive solutions for singular boundary value problems of a coupled system of nonlinear ordinary differential equations

unbounded solutions of the singular boundary value problems for second order differential equations on the half line this paper presents some results on the existence of multiple unbounded solutions for the boundary value problems for second order differential equations on half line and on the uniqueness of unbounded solution

existence of positive solutions to second order four point impulsive differential problems with deviating arguments in this paper we discuss four point boundary value problems for impulsive second order differential equations with deviating arguments we investigate separately cases when arguments are of delayed or advanced types we formulate sufficient conditions under which our problems have at least one or two positive solutions to obtain our results we apply the fixed point index

existence of solutions of semilinear systems with gradient dependence via eigenvalue criteria abstract in this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient these criteria are determined by some relationships between the upper and lower bounds on suitable strips of r n of the nonlinearities of the system and the principal characteristic values of some associated linear hammerstein integral operators moreover using smoothing tools the totality of the involved cone is established

on positive solutions of boundary value problems on the half line we study the existence of positive solutions of boundary value problems on the half line for differential equations of second order the krasnoselskii fixed point theorem on cone compression and expansion is used

existence of three positive solutions for m point boundary value problems on infinite intervals abstract in this paper by using the avery peterson fixed point theorem on a cone we establish the existence of three positive solutions for m point boundary value problems on infinite intervals p x t t f t x t x t 0 0 t x 0 i 1 m 2 i x i lim t x t 0 where p s s p 2 s p 1 r r f t u v r 3 r is a continuous function r 0 i 0 and 0 1 2 m 2 are given

on existence of multiple positive solutions for ϕ laplacian multipoint boundary value abstract in this paper we consider the following multipoint boundary value problem with one dimensional laplacian x t q t f t x t x t 0 t 0 1 x 0 i 1 n 2 i x i x 1 i 1 n 2 i x i where is an odd and increasing homeomorphism i 0 1 with 0 1 2 n 2 1 i and i are nonnegative constants and f t x t x t is continuous and allowed to change sign by fixed point theorems we obtain new results on the existence of at least three positive solutions of this boundary value problem which includes and improves some related results in the relevant literature

positive solutions for three point one dimensional p laplacian boundary value problems with advanced arguments this paper considers the existence of positive solutions for advanced differential equations with one dimensional p laplacian to obtain the existence of at least three positive solutions we use a fixed point theorem due to avery and peterson

curvature of random walks and random polygons in confinement the purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere curvature is one of several basic geometric properties that can be used to describe random walks and polygons we show that confinement affects curvature quite strongly and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from 2 to to study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced for this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions these expressions are functions that depend only on the radius r of the confinement sphere we then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks finally we compare the confinement effect on curvature of random walks with random polygons

multiple positive solutions for boundary value problems of second order delay differential equations with one dimensional p laplacian abstract we consider the boundary value problems p x t q t f t x t x t 1 x t 0 p s s p 2 s p 1 t 0 1 subject to some boundary conditions by using a generalization of the leggett williams fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of at least three positive solutions to the above problems

three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we consider the existence of at least three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second order ordinary differential equations the associated green s function for the boundary value problems is first given the proofs of our main results are based upon the leggett williams fixed point theorem finally we give an example to demonstrate our result

a fast ergodic algorithm for generating ensembles of equilateral random polygons knotted structures are commonly found in circular dna and along the backbone of certain proteins in order to properly estimate properties of these three dimensional structures it is often necessary to generate large ensembles of simulated closed chains i e polygons of equal edge lengths such polygons are called equilateral random polygons however finding efficient algorithms that properly sample the space of equilateral random polygons is a difficult problem currently there are no proven algorithms that generate equilateral random polygons with its theoretical distribution in this paper we propose a method that generates equilateral random polygons in a step wise uniform way we prove that this method is ergodic in the sense that any given equilateral random polygon can be generated by this method and we show that the time needed to generate an equilateral random polygon of length n is linear in terms of n these two properties make this algorithm a big improvement over the existing generating methods detailed numerical comparisons of our algorithm with other widely used algorithms are provided

multiplicity results for second order m point boundary value problem by using fixed point theorems some new results for multiplicity of positive solutions for a class of second order m point boundary value problem are obtained the associated green s function of the problem is also given

on positive solutions of boundary value problems for second order functional differential equations on infinite intervals we study the existence of positive solutions for the following boundary value problem on infinite interval for second order functional differential equations x t px t qx t f t xt 0 t 0 x t x t t t 0 limt x t 0 and x t px t qx t f t xt x t 0 t 0 x t x t t t 0 limt x t 0 where p 0 2 2 0 and q 0 the fixed point theorem on cone is used

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

positive solution for m point boundary value problems in this paper we investigate an m point boundary value problem with sign changing nonlinearity the existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree moreover the associated green s function for the above problem is also given