a new auxiliary function method for solving the generalized coupled hirota satsuma kdv system abstract in this letter a new auxiliary function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations the main idea of this method is to take full advantage of the solutions of the elliptic equation to construct exact travelling wave solutions of nonlinear partial differential equations more new exact travelling wave solutions are obtained for the generalized coupled hirota satsuma kdv system

patterns on liquid surfaces cnoidal waves compactons and scaling abstract localized patterns and nonlinear oscillation formations on the bounded free surface of an ideal incompressible liquid are investigated cnoidal modes solitons and compactons as traveling non axially symmetric shapes are discussed a finite difference differential generalized korteweg de vries kdv equation is shown to describe the three dimensional motion of the fluid surface and in the limit of long and shallow channels one recovers the well known kdv equation a tentative expansion formula for the representation of the general solution of a nonlinear equation for given initial conditions is introduced the model is useful in multilayer fluid dynamics cluster formation and nuclear physics since up to an overall scale these systems display a free liquid surface behavior

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

on the structure of p local abelian groups a uniqueness theorem in terms of numerical invariants is established for certain mixed p local groups called b modules which include both the balanced projective groups and the torsion a groups in general a b module does not contain a decomposition basis and when it does it reduces to a direct sum of an a group and a balanced projective group a special class of b modules the members of which are called s modules constitutes a natural generalization of s groups and the following fact is proved if h is an isotype subgroup of the p local balanced projective group g with gh countable then h is an s module

the hirota s direct method and the tanh coth method for multiple soliton solutions of the sawada kotera ito seventh order equation abstract in this work the sawada kotera ito seventh order equation is studied the tanh coth method is applied to obtain soliton solution of this equation the hirota s direct method combined with the simplified hereman s method are applied to determine the n soliton solutions for this equation the study highlights the significant features of the employed methods and its capability of handling completely integrable equations

g g expansion method for the fifth order forms of kdv sawada kotera equation in this work we establish the traveling wave solution with parameters of the kdv sawada kotera equation by using the g g expansion method this method is effectively employed when the parameters are taken as special values solitary periodic and rational solutions are obtained

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

representation similarity measures and aggregation methods using fuzzy sets for content based recommender systems representation of features of items and user feedback and reasoning about their relationships are major problems in recommender systems this is because item features and user feedback are subjective imprecise and vague the paper presents a fuzzy set theoretic method ftm for recommender systems that handles the non stochastic uncertainty induced from subjectivity vagueness and imprecision in the data and the domain knowledge and the task under consideration the research further advances the application of fuzzy modeling for content based recommender systems initially presented by ronald yager the paper defines a representation method similarity measures and aggregation methods as well as empirically evaluates the methods performance through simulation using a benchmark movie data ftm consist of a representation method for items features and user feedback using fuzzy sets and a content based algorithm based on various fuzzy set theoretic similarity measures the fuzzy set extensions of the jaccard index cosine proximity or correlation similarity measures and aggregation methods for computing recommendation confidence scores the maximum minimum or weighted sum fuzzy set theoretic aggregation methods compared to the baseline crisp set based method csm presented the empirical evaluation of the ftm using the movie data and simulation shows an improvement in precision without loss of recall moreover the paper provides a guideline for recommender systems designers that will help in choosing from a combination of one of the fuzzy set theoretic aggregation methods and similarity measures

local exponential stabilization of fisher s equation using the backstepping technique abstract this paper deals with the boundary stabilization problem for the 1d fisher s partial differential equation pde defined on a bounded interval which is a nonlinear unstable distributed parameter system the stabilizing controller derived using the backstepping technique for linear parabolic pdes associated with fisher s pde can be extended to the nonlinear case in the work we can prove that the boundary controller based on the linear backstepping synthesis approach can make the closed loop nonlinear fisher s system exponentially stable with any desired decay rate locally in both l 2 0 1 and h 1 0 1 respectively the effectiveness of the control synthesis approach is illustrated by a numerical simulation

the sine cosine and the tanh methods reliable tools for analytic treatment of nonlinear dispersive equations the sine cosine method and the tanh method are used for analytic treatment of nonlinear dispersive equations nonlinear variants of boussinesq equation are used as vehicles to show the strength of these methods solutions of distinct physical structures solitons compactons solitary patterns solutions and periodic solutions are formally derived the results show that the change in physical structures of the obtained solutions depends mainly on exponents and on the coefficients of the derivatives involved

exact solutions for the nonlinear schrodinger equation with variable coefficients using the generalized extended tanh function the sine cosine and the exp function methods abstract in this article we find the exact traveling wave solutions of the generalized nonlinear schrodinger gnls equation with variable coefficients using three methods via the generalized extended tanh function method the sine cosine method and the exp function method the main objective of this article is to compare the efficiency of these methods by delivering the exact traveling wave solutions of the proposed nonlinear equation

the tanh coth method for solitons and kink solutions for nonlinear parabolic equations abstract the tanh coth method is used to derive solitons and kink solutions for some of the well known nonlinear parabolic partial differential equations the equations include the fisher equation newell whithead equation allen cahn equation fitzhugh nagumo equation fisher s equation and the burgers fisher equation the new tanh coth approach provides abundant solitons and kink solutions in addition to the existing ones the power of this manageable method is confirmed

on weierstrass elliptic function solutions for a n 1 dimensional potential kdv equation this paper is concerned with several aspects of travelling wave solutions for a n 1 dimensional potential kdv equation the weierstrass elliptic function solutions the jaccobi elliptic function solutions solitary wave solutions periodic wave solutions to the equation are acquired under certain circumstances it is shown that the coefficients of derivative terms in the equation cause the qualitative changes of physical structures of the solutions

the extended g g expansion method and its applications to the whitham broer kaup like equations and coupled hirota satsuma kdv equations in this paper based on a new general ansatze the extended g g expansion method is proposed to seek exact solutions of nonlinear evolution equations being concise and straightforward this method is applied to construct travelling wave solutions of whitham broer kaup like equations and coupled hirota satsuma kdv equations by using this method new exact solutions involving parameters expressed by three types of functions which are the hyperbolic functions the trigonometric functions and the rational functions are obtained when the parameters are taken as special values some solitary wave solutions are derived from the hyperbolic function solutions

new exact jacobi elliptic functions solutions for the generalized coupled hirota satsuma kdv system abstract in this paper an generalized jacobi elliptic functions expansion method with computerized symbolic computation is used for constructing more new exact jacobi elliptic functions solutions of the generalized coupled hirota satsuma kdv system as a result eight families of new doubly periodic solutions are obtained by using this method some of these solutions are degenerated to solitary wave solutions and triangular functions solutions in the limit cases when the modulus of the jacobi elliptic functions m 1 or 0 which shows that the applied method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

nonlinear preconditioning for diffuse interfaces a method of transforming problems with diffuse interfaces is presented which leads to equations that are easier to compute accurately information obtained by internal layer asymptotic analysis is utilized to motivate transformations of the dependent variables the new evolution equations which result from this change of variables can be solved numerically in a straightforward manner numerical experiments indicate that truncation errors can be significantly reduced in such problems allowing a coarser grid to be used applications to several well known models are presented

exact solutions of the combined kdv burgers equation with variable coefficients in this letter the exp function method is used to obtain generalized solitary solutions and periodic solutions of the general types of combined kdv burgers equation with variable coefficients it is shown that the exp function method via symbolic computation provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations with variable coefficients in mathematical physics

similarity of personal preferences theoretical foundations and empirical analysis we study the problem of defining similarity measures on preferences from a decision theoretic point of view we propose a similarity measure called probabilistic distance that originates from the kendall s tau function a well known concept in the statistical literature we compare this measure to other existing similarity measures on preferences the key advantage of this measure is its extensibility to accommodate partial preferences and uncertainty we develop efficient methods to compute this measure exactly or approximately under all circumstances these methods make use of recent advances in the area of markov chain monte carlo simulation we discuss two applications of the probabilistic distance in the construction of the decision theoretic video advisor diva and in robustness analysis of a theory refinement technique for preference elicitation

applications of extended tanh method to special types of nonlinear equations in this paper we explore more applications of extended tanh method to some special nonlinear equations such equations are not of differential polynomial form so that cannot be directly dealt with by tanh method or extended tanh method as examples we apply a recently proposed extended tanh method to build some new explicit solutions for 2 1 dimensional sine gordon equation dodd bullough mikhailov equation and coupled schrodinger kdv equation

multiple periodic soliton solutions to kadomtsev petviashvili equation abstract based on the extended homoclinic test technique we introduce two new ansatz functions to construct multiple periodic soliton solutions of kadomtsev petviashvili kp equation by the hirota s bilinear method some entirely new periodic soliton solutions are obtained the obtained results show that there exist multiple periodic solitary waves in the different directions for the kp equation which differ from complexiton the employed approach is powerful and can be also applied to solve other nonlinear differential equations

on nonlinear population waves we discuss a model system of partial differential equations for description of the spatio temporal dynamics of interacting populations we are interested in the waves caused by migration of the populations we assume that the migration is a diffusion process influenced by the changing values of the birth rates and coefficients of interaction among the populations for the particular case of one population and one spatial dimension the general model is reduced to analytically tractable pde with polynomial nonlinearity up to 4th order we investigate this particular case and obtain two kinds of solutions i approximate solution for small value of the ratio between the coefficient of diffusion and the wave velocity and ii exact solutions which describe nonlinear kink and solitary waves in an appropriate phase space the kinks correspond to a connection between two states represented by a saddle point and a stable node finally we derive conditions for the asymptotic stability of the obtained solutions

new solitons and kinks solutions to the sharma tasso olver equation abstract in this work the sharma tasso olver sto equation is investigated the tanh method the extended tanh method and other ansatze involving hyperbolic and exponential functions are efficiently used for analytic study of this equation new solitons and kinks solutions are formally derived the proposed schemes are reliable and manageable

new travelling wave solutions to some nonlinear equations via a combined method abstract based on the sine gordon and the sinh gordon equations transformations are introduced in a variable separated ode method to construct entirely new doubly periodic jacobian elliptic function solutions of some nonlinear differential equations which are powerful and simple distinct sets of exact doubly periodic solutions that possess distinct physical structures are obtained for the mkdv sine gordon the mkdv sinh gordon equations and born infeld equation when the module m 1 or 0 the corresponding solitary wave solutions are also found this approach can be also applied to solve other nonlinear differential equations

user preferences discovery using fuzzy models user preferences discovery aims to learn the patterns of user preferences for various services or items such as movies preferences discovery is essential to the development of intelligent personalization applications based on decision and utility theories traditional approaches to preferences discovery explicitly query users about the behavior of value function or utility of every outcome with respect to each decision criterion consequently these approaches are generally error prone and labor intensive although implicit elicitation approaches have been proposed to address the above limitations extent approaches largely ignore multi valued nature of item features and uncertainty associated with item features and user preferences to address uncertainty due to vagueness and imprecision this research proposed a general framework for preferences discovery based on fuzzy set theories in addition new fuzzy models were created for preferences discovery and representation further an algorithm was developed to predict user preferences with uncertainty and visualization of item features user feedback and the discovered preferences helped improve the interpretation of the discovered knowledge the results of the simulation evaluation using a benchmark movie dataset revealed that the proposed preference discovery method 1 doubled the accuracy of preference discovery as compared to random prediction and 2 outperformed conventional techniques in making movie recommendation these findings suggest that fuzzy models are effective for preferences patterns discovery and personalized recommendation application

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

the tanh method for traveling wave solutions of nonlinear equations in this work we employ the tanh method for traveling wave solutions of nonlinear equations the study is extended to equations that do not have tanh polynomial solutions the efficiency of the method is demonstrated by applying it for a variety of selected equations