a series solution of the cauchy problem for the generalized d dimensional schrodinger equation with a power law nonlinearity in this paper the cauchy problem for generalized d dimensional schrodinger equation with a power law nonlinearity is studied three methods homotopy analysis method ham homotopy perturbation method hpm and adomian decomposition method adm are applied to obtain series pattern solutions of the mentioned cauchy problem the recurrent relations for solving the mentioned cauchy problem is introduced for some cases of given initial conditions we obtain the closed form of the exact solutions

correlation structure of the landscape of the graph bipartitioning problem the relaxation of random walks and the autocorrelation function on the landscape of the graph bipartitioning problem are calculated

approximate analytical solutions of systems of pdes by homotopy analysis method in this paper the homotopy analysis method ham is applied to obtain series solutions to linear and nonlinear systems of first and second order partial differential equations pdes the ham solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions it is shown in particular that the solutions obtained by the variational iteration method vim are only special cases of the ham solutions

analytical methods for solving the time fractional swift hohenberg s h equation in this paper the most effective methods the homotopy perturbation method hpm and the differential transform method dtm are applied to obtain the approximate solutions of the nonlinear time fractional swift hohenberg s h equation the basic philosophy of these methods does not involve linearization weak nonlinearity assumptions or perturbation theory numerical solutions for various combinations of the parameters a eigenvalue parameter l length and a fractional index are obtained the solutions of the s h equation are useful for studies of shear thinning effects in non newtonian fluid flows at the end the solutions obtained are also presented graphically

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

imposing boundary conditions in sinc method using highest derivative approximation sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities a recent implementation of the sinc method li c and wu x numerical solution of differential equations using sinc method based on the interpolation of the highest derivatives applied mathematical modeling 31 1 2007 1 9 in which sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired we suggest an alternative approach for specifying the boundary conditions and we compare the numerical results for analysis of a laminated composite timoshenko beam implementing both li and wu s approach and our alternative approach for applying the boundary conditions for the timoshenko beam problem we obtain accurate results using both approaches including transverse shear stress by integration of the 3d equilibrium equations of elasticity the beam results indicate our approach is less dependent on the selection of the sinc mesh size than li and wu s sihd we also apply sihd to analyze a classical laminated composite plate for the plate example we experience difficulty in obtaining a complete system of equations using li and wu s approach for our approach we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge using this technique we obtain accurate results for deflection and stresses including interlaminar stresses by integration of the 3d equilibrium equations of elasticity our results for both the beam and the plate problems indicate that this approach is easily implemented has a high level of accuracy and good convergence properties

exact solutions of the generalized 2 1 dimensional nonlinear evolution equations via the modified simple equation method in this paper the modified simple equation method msem is applied to construct exact solutions of the generalized 2 1 dimensional nonlinear evolution equations nlees involving parameters via the 2 1 dimensional calogero bogoyavlenskii schiff cbs equation the 2 1 dimensional breaking soliton equation and the 2 1 dimensional bogoyavlenskii s breaking soliton equation the solitary wave solutions are derived from the exact solutions by assigning special values of the parameters

integrated local petrov galerkin sinc method for structural mechanics problems an integrated local petrov galerkin sinc method is introduced and applied to static structural mechanics problems the method approximates the highest derivative in the local weak form of the governing equation on a rectangular grid and the lower derivatives and unknown function are found by numerical indenite integration we suggest that the essential boundary conditions may be applied by the traditional penalty method or by a method in which the stiness matrix is reduced to eliminate dependent degrees of freedom we propose and compare the performance of three basis functions in terms of their accuracy and convergence properties for two problems a one dimensional tapered bar and a two dimensional plane stress elasticity problem our results indicate that the present method can provide greater accuracy than the sinc method based on interpolation of highest derivative an integration based collocation method suggested by li and wu li c and wu x numerical solution of dierential equations using sinc method based on

amplitude frequency relationship obtained using hamiltonian approach for oscillators with sum of non integer order nonlinearities in this paper the hamiltonian approximate analytical approach is extended for solving vibrations of conservative oscillators with the sum of integer and or non integer order strong nonlinearities solution of the nonlinear differential equation is assumed in the form of a trigonometric function with unknown frequency the frequency equation is obtained based on the hypothesis that the derivative of the hamiltonian in amplitude of vibration is zero the accuracy of the approximate solution is treated with two different approaches comparing the analytical value for period of vibration with the period obtained numerically and developing an error estimation method based on the ratio between the averaged residual function and the total constant energy of system the procedures given in the paper are applied for two types of examples an oscillator with a strong nonlinear term and an oscillator where the nonlinearity is of polynomial type

application of homotopy perturbation methods for solving systems of linear equations abstract in this paper homotopy perturbation methods hpms are applied to obtain the solution of linear systems and conditions are deduced to check the convergence of the homotopy series moreover we have adapted the richardson method the jacobi method and the gauss seidel method to choose the splitting matrix the numerical results indicate that the homotopy series converges much more rapidly than the direct methods for large sparse linear systems with a small spectrum radius

on the landscape ruggedness of the quadratic assignment problem local search based heuristics have been demonstrated to give very good results to approximately solve the quadratic assignment problem qap in this paper following the works of weinberger and stadler we introduce a parameter called the ruggedness coeffcient which measures the ruggedness of the qap landscape which is the union of a cost function and a neighborhood we give an exact expression and a sharp lower bound for this parameter we are able toderive from it that the landscape of the qap is rather flat and so it gives a theoretical justification of the effectiveness of local search based heuristics for this problem experimental results with simulated annealing are presented which con8rm this conclusion and also the influence of the ruggedness coe5cient on the quality of results obtained

a q operator identity for the correlation functions of the infinite xxz spin chain an explicit construction for q operators of the finite xxz spin chain with twisted boundary conditions is presented the massless and the massive regimes are considered as well as the root of unity case it is explained how these results yield an alternative expression for the trace function employed in the description of the correlation functions of the inhomogeneous xxz model on the infinite lattice by boos jimbo miwa smirnov and takeyama

poisson co homology of polynomial poisson algebras in dimension four sklyanin s case abstract in this paper we compute the poisson co homology of a polynomial poisson structure given by two casimir polynomial functions which define a complete intersection with an isolated singularity

some techniques for solving absolute value equations in this paper we introduce and analyze two new methods for solving the np hard absolute value equations ave a x x b where a is an arbitrary n n real matrix and b rn in the case singular value of a exceeds 1 the comparison with other known methods is carried to show the effectiveness of the proposed methods for a variety of randomly generated problems the ideas and techniques of this paper may stimulate further research

traces on the sklyanin algebra and correlation functions of the eight vertex model we propose a conjectural formula for correlation functions of the z invariant inhomogeneous eight vertex model we refer to this conjecture as ansatz it states that correlation functions are linear combinations of products of three transcendental functions with theta functions and derivatives as coefficients the transcendental functions are essentially logarithmic derivatives of the partition function per site the coefficients are given in terms of a linear functional tr on the sklyanin algebra which interpolates the usual trace on finite dimensional representations we establish the existence of tr and discuss the connection to the geometry of the classical limit we also conjecture that the ansatz satisfies the reduced qkz equation as a non trivial example of the ansatz we present a new formula for the next nearest neighbour correlation functions

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

density matrix elements and entanglement entropy for the spin 1 2 xxz chain at δ 1 2 we have analytically obtained all the density matrix elements up to six lattice sites for the spin 1 2 heisenberg xxz chain at 1 2 we use the multiple integral formula of the correlation function for the massless xxz chain derived by jimbo and miwa as for the spin spin correlation functions we have newly obtained the fourth and fifth neighbour transverse correlation functions we have calculated all the eigenvalues of the density matrix and analyse the eigenvalue distribution using these results the exact values of the entanglement entropy for the reduced density matrix up to six lattice sites have been obtained we observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory

homotopy perturbation method for solving hyperbolic partial differential equations this paper applies the homotopy perturbation method proposed by ji huan he to obtain approximate analytic solutions of hyperbolic partial differential equations the procedure of the method is systematically illustrated to give an extensive account of the method some examples are provided the results derived by this method will be compared with the results of characteristics method the results of homotopy perturbation method are of high accuracy verifying that the method is very effective and promising

auxiliary matrices on both sides of the equator the spectra of previously constructed auxiliary matrices for the six vertex model at roots of unity are investigated for spin chains of even and odd length the two cases show remarkable differences in particular it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to baxter s tq equation corresponding to the bethe ansatz equations above and below the equator in contrast one finds for even spin chains only one linear independent solution and complete strings the other main result is the proof of a previous conjecture on the degeneracies of the six vertex model at roots of unity the proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight vertex model conjectured by fabricius and mccoy

comparison between adomian s method and he s homotopy perturbation method in this paper it is revealed that modified form of he s homotopy perturbation method corresponds to adomian s decomposition method for certain nonlinear problems

a spectral element approach for the stability of delay systems we describe a spectral element approach to study the stability and equilibria solutions of delay differential equations ddes in contrast to the prototypical temporal finite element analysis tfea the described spectral element approach admits spectral rates of convergence and allows exploiting hp convergence schemes the described approach also avoids the limitations of analytical integrations in tfea by using highly accurate numerical quadratures enabling the study of more complicated ddes the effectiveness of this new approach is compared with well established methods in the literature using various case studies specifically the stability results are compared with the conventional tfea and legendre collocation methods whereas the equilibria solutions are compared with the numerical simulations and the homotopy perturbation method hpm solutions our results reveal that the presented approach can have higher rates of convergence than both collocation methods and the hpm copyright 2011 john wiley sons ltd

linearized galerkin and artificial parameter techniques for the determination of periodic solutions of nonlinear oscillators abstract linearized harmonic balance galerkin methods for the determination of the periodic solutions of nonlinear oscillators are presented and the results are compared with those of an artificial parameter method based on the introduction of a linear stiffness term and the linstedt poincare technique the linearized harmonic balance methods presented in this paper are not iterative and are based on taylor series expansions the neglect of nonlinear terms in the resulting series a fourier approximation to the solution and orthogonality conditions it is shown that the first approximation provided by the linearized harmonic balance technique is identical to that of the artificial parameter method whereas the second one depends on how the equation is linearized and written and the discrepancies have been found to be caused by the neglect of the nonlinear terms in the taylor series expansion because a fourier series expansion of these terms introduces harmonics which are not accounted for in the linearization procedure it is also shown that the first approximation of the artificial parameter method and the linearized harmonic balance procedure are asymptotically equivalent to that derived from a modified linstedt poincare method when the nonlinearities are small and that these techniques may not be applicable to some oscillators

homotopy perturbation reproducing kernel method for nonlinear systems of second order boundary value problems in this paper based on homotopy perturbation method hpm and reproducing kernel method rkm a new method is presented for solving nonlinear systems of second order boundary value problems bvps hpm is based on the use of traditional perturbation method and homotopy technique the hpm can reduce a nonlinear problem to a sequence of linear problems and generate a rapid convergent series solution in most cases rkm is also an analytical technique which can solve powerfully linear bvps homotopy perturbation reproducing kernel method hp rkm combines advantages of these two methods and therefore can be used to solve efficiently systems of nonlinear bvps three numerical examples are presented to illustrate the strength of the method

a q operator for the twisted xxx model taking the isotropic limit 1 in a recent representation theoretic construction of baxter s q operators for the xxz model with quasi periodic boundary conditions we obtain new results for the xxx model we show that quasi periodic boundary conditions are needed to ensure convergence of the q operator construction and derive a quantum wronskian relation which implies two different sets of bethe ansatz equations one above the other below the equator of total spin sz 0 we discuss the limit to periodic boundary conditions at the end and explain how this construction relates to the trace functional introduced by boos et al in the context of correlation functions on the infinite lattice we also identify a special subclass of solutions to the quantum wronskian and numerically verify them up to spin chains of ten sites this special type of solutions might persist for longer chains

neutrality in fitness landscapes the interplay of ruggedness and neutrality in fitness landscapes plays an important role in explaining the dynamics of evolutionary adaptation while various measures of ruggedness correlation functions adaptive walks or the density of local optima are reasonably well understood and models for constructing landscapes with a desired degree of ruggedness are readily available very little is known about neutrality we introduce the notion of additive random landscapes as a framework for tuning both neutrality and ruggedness at once and we develop a formalism that allows the explicit computation of the most salient parameters that are associated with neutrality in landscapes of this type

new exact traveling wave solutions of the 4 1 dimensional fokas equation abstract in this paper two distinct methods are applied to look for exact traveling wave solutions of the 4 1 dimensional nonlinear fokas equation namely the modified simple equation method msem and the extended simplest equation method esem some new exact traveling wave solutions involving some parameters are obtained the solitary wave solutions can be extracted by assigning special values of these parameters the obtained solutions show the simplicity and efficiency of the used approaches that can be applied for nonlinear equations as well as linear ones

performance prediction and preselection for optimization and heuristic solution procedures the operations research literature contains numerous studies on the design and application of optimization and heuristic solution procedures these studies identify a particular optimization problem suggest a general solution procedure and then customize that procedure to improve its efficiency and or accuracy in contrast this paper shows how to use existing solution procedures more effectively we develop a methodology for predicting the relative performance of alternative procedures using easily computed problem characteristics this methodology enables us for any given data set to preselect a solution procedure we apply this preselection methodology to the 0 1 knapsack problem for which two successful optimization procedures dynamic programming and branch and search are available extensive computational testing indicates that substantial savings in average computation time are achieved the benefits of our work include faster and cheaper identification of effective solution procedures as well as an improved understanding of the relationship between problem characteristics and the performance of various procedures our methodology can be applied to many optimization problems to develop easily implemented guidelines for selecting appropriate solution procedures

applications of quintic hermite collocation with time discretization to singularly perturbed problems abstract singular perturbation problems have been discussed using collocation technique with quintic hermite interpolating polynomials as base functions these polynomials have the property to interpolate the function as well as its tangent at node points to discretize the problem in temporal direction forward difference operator has been applied the given technique is a combination of collocation and difference scheme parameter uniform convergence has been studied using the method given by farrell and hegarty 1991 rate of convergence of quintic hermite difference scheme has been found to depend upon node points applicability and computational effect of the scheme has been examined through numerical examples results have been presented graphically through surface plots as well as in tabular form

a modified homotopy perturbation method for solving the nonlinear mixed volterra fredholm integral equation the purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed volterra fredholm integral equation vfie for some strongly nonlinear problems the traditional homotopy perturbation method is divergent so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed vfie by means of this method an algorithm is successfully established for solving the strongly nonlinear mixed vfie and the convergence of the algorithm is proved strictly finally several examples are presented to illustrate the application of the algorithm

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

investigating the correlation between indicators of predictive diagnostic optimisation and search result quality combinatorially complex problems are often optimised with heuristic solvers which generally provide acceptable results but no indication as to how the quality achieved compares to the best possible in previous work we have introduced predictive diagnostic optimisation pdo a heuristic based on local search that provides information about the search space structure through a set of indicators whilst searching for the optimal solution pdo can collect useful information about the search process such as the variation in the number of steps needed to locally optimise a random solution and the error between the expected and actual qualities of the local optimum known as the prediction error given previous experimental results on the quadratic assignment problem it appears that a high prediction error coincides with lower search quality and vice versa this work confirms this assumption with the help of two additional problems but also shows that the reliability of the prediction error is challenged by structural properties that lead to a homogeneity of the optima basins conversely a high variation in the number of steps that lead to the local optima increases the reliability of the prediction error as an indicator of search quality

difference equations for the correlation functions of the eight vertex model the authors propose that the correlation functions of the inhomogeneous eight vertex model in the anti ferroelectric regime satisfy a system of difference equations with respect to the spectral parameters solving the simplest difference equation they obtain the expression for the spontaneous staggered polarization conjectured by baxter and kelland 1974 they also discuss a related construction of vertex operators on the lattice

new developments in the eight vertex model ii chains of odd length we study the transfer matrix of the 8 vertex model with an odd number of lattice sites n for systems at the root of unity points mk l with m odd the transfer matrix is known to satisfy the famous tq equation where q is a specifically known matrix we demonstrate that the location of the zeroes of this q matrix is qualitatively different from the case of evenn and in particular they satisfy a previously unknown equation which is more general than what is often called bethe s equation for the case of even m where no q matrix is known we demonstrate that there are many states which are not obtained from the formalism of the sos model but which do satisfy the tq equation the ground state for the particular case of 2k 3 and n odd is investigated in detail

first order analytic difference equations and integrable quantum systems we present a new solution method for a class of first order analytic difference equations the method yields explicit minimal solutions that are essentially unique special difference equations give rise to minimal solutions that may be viewed as generalized gamma functions of hyperbolic trigonometric and elliptic type euler s gamma function being of rational type we study these generalized gamma functions in considerable detail the scattering and weight functions u and w functions associated to various integrable quantum systems can be expressed in terms of our generalized gamma functions we obtain detailed information on these u and w functions exploiting the difference equations they satisfy

the homotopy perturbation method applied for solving complex valued differential equations with strong cubic nonlinearity abstract in this paper the homotopy perturbation method is adopted for solving a complex valued second order strongly nonlinear differential equation homotopy with an imbedding parameter p 0 1 is constructed the perturbation procedure with parameter p transforms the strongly nonlinear differential equation into a system of linear complex valued differential equations whose solutions give the approximate solution of the initial differential equation to illustrate the effectiveness and convenience of the suggested procedure a duffing equation with strong cubic nonlinearity is considered the periodic solution in the first approximation is obtained the solution is compared with the exact one and shows good agreement

an improvement to homotopy perturbation method for solving system of linear equations in this paper we present an efficient numerical algorithm to find exact solutions for the system of linear equations based on homotopy perturbation method hpm a reliable modification is proposed and the modified method is employed to solve the system of linear equations the results are compared with those obtained by the original homotopy perturbation method two examples are given to illustrate the ability and reliability of the modified method the results reveal that the modified method is very simple and effective

an efficient algorithm for solving generalized pantograph equations with linear functional argument abstract a numerical method for solving the generalized retarded or advanced pantograph equation under initial value conditions is presented to display the validity and applicability of the numerical method four illustrative examples are presented the results reveal that this method is very effective and highly promising when compared with other numerical methods such as adomian decomposition method spline methods and taylor method

picard s iterative method for nonlinear advection reaction diffusion equations picard s iterative method for the solution of nonlinear advection reaction diffusion equations is formulated and its convergence proved the method is based on the introduction of a complete metric space and makes uses of a contractive mapping and banach s fixed point theory from picard s iterative method the variational iteration method is derived without making any use at all of lagrange multipliers and constrained variations some examples that illustrate the advantages and shortcomings of the iterative procedure presented here are shown

residue harmonic balance for two degree of freedom airfoils with cubic structural nonlinearity a residue harmonic balance method is extended to determine the approximations and bifurcations for a coupled airfoil systemwith cubic structural nonlinearity analytically the approximate solutions to any desired accuracy can be obtained easily by solving a set of linear algebraic equations in each step the strongly cubic nonlinear pitching and plunging stiffness terms in the two degree of freedom self excited equations of airfoil motions are considered the approximations to the angular frequency and limit cycle are analytically found the results show that the secondorder approximations obtained by the proposed technique are in excellent agreement with the numerical integration results the existence of cubic nonlinearity in the stiffness termdoes not affect the linearflutter speed of airfoilmotion a great deal however the responses are different not only after supercritical bifurcation flutter but also before the linear flutter speed in the subcritical bifurcation furthermore the supercritical and subcritical hopf bifurcations of three nonlinear cases of airfoil motions are analyzed taking the flow speed as the bifurcation parameter

bethe equations on the wrong side of the equator we analyse baxter s famous t q equations for the xxx xxz spin chain and show that apart from its usual polynomial trigonometric solution which provides the solution of bethe ansatz equations there also exists a second solution which should correspond to the bethe ansatz beyond this second solution of baxter s equation plays an essential role and together with the first one gives rise to all fusion relations

application of he s semi inverse method to the nonlinear schrodinger equation a variational theory is established for the nonlinear schrodinger equation using he s semi inverse method on the basis of the variational principle obtained a solitary solution is obtained which is the same as debnath s result l debnath nonlinear partial differential equations for scientists and engineers birkhauser boston 1997 confirming the validity of our analysis the method is straightforward and concise

autocorrelation coefficient for the graph bipartitioning problem abstract local search and its variants simulated annealing and tabu search are widely used heuristics to approximately solve np hard optimization problems to use local search one simply has to specify a neighborhood structure and a cost function which has to be optimized however from a theoretical point of view many questions remain unanswered and one of the most important is which neighborhood structure will provide the best quality solutions the aim of this paper is to theoretically justify some results previously reported by johnson et al 1989 1991 in their extended empirical study concerning simulated annealing and the graph bipartitioning problem and to sharply tune the best landscape among the two reported in that study experimental results perfectly agree with the theoretical predictions

numerical simulation of the generalized huxley equation by he s homotopy perturbation method abstract in this paper the solution of the generalized huxley equation is obtained by means of homotopy perturbation method and adomian decomposition method the comparison reveals that the former method is more effective than the later in this method a homotopy is constructed for the equation the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions moreover we will show that he s homotopy perturbation method overcome the difficulties arising in calculating adomian polynomials it is predicted that the hpm can be found wide application in engineering problems

optimization by simulated annealing an experimental evaluation part ii graph coloring and number partitioning this is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well studied domains of combinatorial optimization simulated annealing is a randomized technique proposed by s kirkpatrick c d gelatt and m p vecchi for improving local optimization algorithms here we report on experiments at adapting simulated annealing to graph coloring and number partitioning two problems for which local optimization had not previously been thought suitable for graph coloring we report on three simulated annealing schemes all of which can dominate traditional techniques for certain types of graphs at least when large amounts of computing time are available for number partitioning simulated annealing is not competitive with the differencing algorithm of n karmarkar and r m karp except on relatively small instances moreover if running time is taken into account natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based in sharp contrast to the observed performance of annealing on other problems

reduced qkz equation and correlation functions of the xxz model correlation functions of the xxz model in the massive and massless regimes are known to satisfy a system of linear equations the main relations among them are the difference equations obtained from the qkz equation by specializing the variables 1 2n as 1 n n 1 1 1 we call it the reduced qkz equation in this article we construct a special family of solutions to this system they can be written as linear combinations of products of two transcendental functions open image in new window with coefficients being rational functions we show that correlation functions of the xxz model in the massive regime are given by these formulas with an appropriate choice of open image in new window we also present a conjectural formula in the massless regime

quantum spin chains and riemann zeta function with odd arguments the riemann zeta function is an important object of number theory we argue that it is related to the heisenberg spin 1 2 anti ferromagnet in the xxx spin chain we study the probability of formation of a ferromagnetic string in the anti ferromagnetic ground state in the thermodynamics limit we prove that for short strings the probability can be expressed in terms of the riemann zeta function with odd arguments

derivation of the adomian decomposition method using the homotopy analysis method abstract adomian decomposition method has been used intensively to solve nonlinear boundary and initial value problems it has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits however very little has been done to address the mathematical foundation of the method and its error analysis in this article the mathematical derivation of the method using the homotopy analysis method is presented in addition an error analysis is addressed as well as the convergence criteria

numerical approximations for highly oscillatory bessel transforms and applications abstract this paper presents an efficient numerical method for approximating highly oscillatory bessel transforms based on analytic continuation we transform the integrals into the problems of integrating the forms on 0 with the integrand that does not oscillate and decays exponentially fast which can be efficiently computed by using gauss laguerre quadrature rule we then derive the error of the method depending on the frequency and the node number moreover we apply the scheme for studying the approximations of the solutions of two kinds of highly oscillatory integral equations preliminary numerical results show the efficiency and accuracy of numerical approximations

numerical solution of two dimensional nonlinear differential equation by homotopy perturbation method abstract in this paper an application of homotopy perturbation method is applied to solve the nonlinear two dimensional wave equation the analytic solution of the nonlinear wave equation is calculated in the form of a series with easily computable components the non homogenous equation is effectively solved by employing the phenomena of the self canceling noise terms where sum of components vanishes in the limit comparing the methodology with some known techniques shows that the present approach is powerful and reliable its remarkable accuracy properties are finally demonstrated by an example

modified laplace variational iteration method for solving fourth order parabolic partial differential equation with variable coefficients abstract in the present study a new amendment in laplace variational iteration method for the solution of fourth order parabolic partial differential equations with variable coefficients is revealed i e modified laplace variational iteration method ml vim the proposed modification is made by coupling of two methods one of them is variational iteration method vim and the other one is laplace transformation lt our modification has an important beauty that one has no need to compute lagrange multiplier via integration nor by taking convolution theorem and has a simple way to use in the implementation of our proposed scheme moreover homotopy perturbation method hpm with he s polynomials is employed for the computation of nonlinear terms the main improvement of our proposed scheme is the reduction of the problem to a simple one which also embraces for solving a nonlinear term some illustrated examples are interpreted which unveil the robustness and accuracy of the newly developed scheme

delay asymptotic solutions for the time fractional delay type wave equation abstract a new version of the wave equation endowed with time fractional derivative and multiple time delays is considered a new form of the generalized maclaurin fractional series is suggested to extract analytical solution of the model graphical investigations on the relation between the fractional derivative and the time delay are established finally we reported some remarks regarding the new model

the travelling wave solutions for non linear initial value problems using the homotopy perturbation method in this article we have used the homotopy perturbation method hpm to find the travelling wave solutions for some non linear initial value problems in the mathematical physics these problems consist of the burgers fisher equation the kuramoto sivashinsky equation the coupled schordinger kdv equations and the long short wave resonance equations together with initial conditions the results of these problems reveal that the hpm is very powerful effective convenient and quite accurate to the systems of non linear equations it is predicted that this method can be found widely applicable in engineering and physics

hidden grassmann structure in the xxz model for the critical xxz model we consider the space mathcal w alpha of operators which are products of local operators with a disorder operator we introduce two anti commutative families of operators bf b zeta bf c zeta which act on mathcal w alpha these operators are constructed as traces over representations of the q oscillator algebra in close analogy with baxter s q operators we show that the vacuum expectation values of operators in mathcal w alpha can be expressed in terms of an exponential of a quadratic form of bf b zeta bf c zeta

elementary landscape decomposition of the frequency assignment problem the frequency assignment problem fap is an important problem that arises in the design of radio networks when a channel has to be assigned to each transceiver of the network this problem is a generalization of the graph coloring problem in this paper we study a general version of the fap that can include adjacent frequency constraints using concepts from landscapes theory we prove that this general fap can be expressed as a sum of two elementary landscapes further analysis also shows that some subclasses of the problem correspond to a single elementary landscape this allows us to compute the kind of neighborhood information that is normally associated with elementary landscapes we also provide a closed form formula for computing the autocorrelation coefficient for the general fap which can be useful as an a priori indicator of the performance of a local search method

quantum kz equation with q 1 and correlation functions of the xxz model in the gapless regime an integral solution to the quantum knizhnik zamolodchikov qkz equation with q 1 is presented upon specialization it leads to a conjectural formula for correlation functions of the xxz model in the gapless regime the validity of this conjecture is verified in special cases including the nearest neighbour correlator with an arbitrary coupling constant and general correlators in the xxx and xy limits

third neighbour and other four point correlation functions of spin 1 2 xxz chain the correlation functions of the spin 1 2 xxz chain in the ground state were expressed in the form of multiple integrals for 1 1 and 1 in particular adjacent four point correlation functions were given as certain four dimensional integrals we show that these integrals can be reduced to polynomials with respect to specific one dimensional integrals the results give the polynomial representation of the third neighbour correlation functions

new formulae for solutions of quantum knizhnik zamolodchikov equations on level 4 we present a new form of solution to the quantum knizhnik zamolodchikov equation qkz on level 4 in a special case corresponding to the heisenberg xxx spin chain our form is equivalent to the integral representation obtained by jimbo and miwa in 1996 7 an advantage of our form is that it is reduced to the product of single integrals this fact is deeply related to a cohomological nature of our formulae our approach is also based on the deformation of hyper elliptic integrals and their main property deformed riemann bilinear relation jimbo and miwa also suggested a nice conjecture which relates solution of the qkz on level 4 to any correlation function of the xxx model this conjecture together with our form of solution to the qkz makes it possible to prove a conjecture that any correlation function of the xxx model can be expressed in terms of the riemann function at odd arguments and rational coefficients suggested in 8 9 this issue will be discussed in our next publication

on the existence of solutions for strongly nonlinear differential equations the objectives of this paper are twofold firstly to prove the existence of an approximate solution in the mean for some nonlinear differential equations we also investigate the behavior of the class of solutions which may be associated with the differential equation secondly we aim to implement the homotopy perturbation method hpm to find analytic solutions for strongly nonlinear differential equations

one step recursive method for solving systems of differential equations in this work an iteration one step method to integrate systems of nonlinear ordinary differential equations with initial values is presented

a modified spectral method for solving operator equations in this paper we introduce a modified spectral method for solving the linear operator equation l u f l d l h 1 h 2 where h 1 and h 2 are normed vector spaces with norms 1 and respectively and d l is the domain of l also for each h h 2 h 2 h h where is an inner product on h 2 in this method we make a new set n n 0 for h 1 using l and two sets in h 1 and h 2 then using the new set n n 0 we solve this linear operator equation we show that this method does not have some shortcomings of spectral method also we prove the stability and convergence of the new method after introducing the method we give some conditions that under them the nonlinear operator equation l u n u f can be solved some examples are considered to show the efficiency of method

analysis of regularized long wave equation associated with a new fractional operator with mittag leffler type kernel abstract in this work we aim to present a new fractional extension of regularized long wave equation the regularized long wave equation is a very important mathematical model in physical sciences which unfolds the nature of shallow water waves and ion acoustic plasma waves the existence and uniqueness of the solution of the regularized long wave equation associated with atangana baleanu fractional derivative having mittag leffler type kernel is verified by implementing the fixed point theorem the numerical results are derived with the help of an iterative algorithm in order to show the effects of various parameters and variables on the displacement the numerical results are presented in graphical and tabular form

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

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

application of he s methods to nonlinear chemistry problems in this paper he s variational iteration method vim and homotopy perturbation method hpm are implemented for solving analytically two systems of ordinary differential equations that often appear in chemical applications in both methods the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions the solution procedure is of utter simplicity and the obtained solution is of high accuracy

integral representation of the density matrix of the xxz chain at finite temperatures we present an integral formula for the density matrix of a finite segment of the infinitely long spin xxz chain this formula is valid for any temperature and any longitudinal magnetic field

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method