the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

scaling up cosine interesting pattern discovery a depth first method this paper presents an efficient algorithm called cosminer t for interesting pattern discovery the widely used cosine similarity found to possess the null invariance property and the anti cross support pattern property is adopted as the interestingness measure in cosminer t cosminer t is generally an fp growth like depth first traversal algorithm that rests on an important property of the cosine similarity the conditional anti monotone property camp the combined use of camp and the depth first support ascending traversal strategy enables the pre pruning of uninteresting patterns during the mining process of cosminer t extensive experiments demonstrate the high efficiency of cosminer t in interesting pattern discovery in comparison to the breath first strategy and the post evaluation strategy in particular cosminer t shows its capability in suppressing the generation of cross support patterns and discovering rare but truly interesting patterns finally an interesting case of landmark recognition is presented to illustrate the value of cosine interesting patterns found by cosminer t in real world applications

new exact solutions of the broer kaup equations in 2 1 dimensional spaces abstract with the aid of maple several new kinds of exact solutions for the broer kaup equations in 2 1 dimensional spaces are obtained by using a new ansatz this approach can also be applied to other nonlinear evolution equations

looking for a structural characterization of the sparseness measure of frequent closed itemset contexts it is widely recognized that the performances of frequent pattern mining algorithms are closely dependent on data being handled i e sparse or dense the same situation applies to the efficiency of concise representations of frequently occurring patterns with respect to the extraction task and the obtained compactness rates as well as for other data mining techniques such as clustering and for the mining algorithms of different pattern classes such as hypergraphs in this paper we raise a fundamental question how can we formally define the sparseness of an arbitrary context and assess its value as an answer based on the framework of the succinct system of minimal generators we present an innovative characterization of context sparseness as well as a new sparseness measure which results from the aggregation of two complementary measures namely the succinctness and compactness measures of each equivalence class induced by the galois closure operator experiments carried out mainly attain a finer classification of benchmark contexts and then confirm our viewpoint that the dense and sparse labels are not absolute

nonisospectral scattering problems a key to integrable hierarchies we show that certain partial differential equations associated to nonisospectral scattering problems in 2 1 dimensions provide a key to associated integrable hierarchies of both ordinary and partial differential equations this is illustrated using an extension of a known second order and two new third order nonisospectral scattering problems these scattering problems allow us to derive new hierarchies of integrable partial differential equations in both 1 1 and 2 1 dimensions together with their underlying linear problems isospectral and nonisospectral and also new hierarchies of integrable ordinary differential equations again with their underlying linear problems

fiut a new method for mining frequent itemsets this paper proposes an efficient method the frequent items ultrametric trees fiut for mining frequent itemsets in a database fiut uses a special frequent items ultrametric tree fiu tree structure to enhance its efficiency in obtaining frequent itemsets compared to related work fiut has four major advantages first it minimizes i o overhead by scanning the database only twice second the fiu tree is an improved way to partition a database which results from clustering transactions and significantly reduces the search space third only frequent items in each transaction are inserted as nodes into the fiu tree for compressed storage finally all frequent itemsets are generated by checking the leaves of each fiu tree without traversing the tree recursively which significantly reduces computing time fiut was compared with fp growth a well known and widely used algorithm and the simulation results showed that the fiut outperforms the fp growth in addition further extensions of this approach and their implications are discussed

the painleve property and backlund transformations for the sequence of boussinesq equations we investigate the sequence of boussinesq equations by the method of singular manifolds for the boussinesq equation which is known to possess the painleve property a backlund transformation is defined this backlund transformation which is formulated in terms of the schwarzian derivative obtains the system of modified boussinesq equations and the resulting miura type transformation the modified boussinesq equations are found to be invariant under a discrete group of symmetries acting on the dependent variables by linearizing the miura transformation and modified equations the lax pair is readily obtained furthermore by a result of fokas and anderson the recursion operators defining the sequence of higher order boussinesq equations may be constructed from the miura transformation this allows the recursive definition of backlund transformations for this sequence of equations the recursion operator is found to preserve the discrete symmetries of the modified boussinesq equations this leads to the conclusion that the sequences of boussinesq and modified boussinesq equations identically possess the painleve property are meromorphic we also find that by a simple reduction the sequences of caudrey dodd gibbon and kuperschmidt equations are contained within the boussinesq sequence rational solutions are iteratively constructed for the boussinesq equation and a criterion is proposed for the existence of rational solutions of general integrable systems

efficient mining of weighted interesting patterns with a strong weight and or support affinity most algorithms for frequent pattern mining use a support constraint to prune the combinatorial search space but support based pruning is not enough after mining datasets to obtain frequent patterns the resulting patterns can have weak affinity although the minimum support can be increased it is not effective for finding correlated patterns with increased weight and or support affinity interesting measures have been proposed to detect correlated patterns but any approach does not consider both support and weight in this paper we present a new strategy weighted interesting pattern mining wip in which a new measure weight confidence is suggested to mine correlated patterns with the weight affinity a weight range is used to decide weight boundaries and an h confidence serves to identify support affinity patterns in wip without additional computation cost original h confidence is used instead of the upper bound of h confidence for performance improvement wip not only gives a balance between the two measures of weight and support but also considers weight affinity and or support affinity between items within patterns so more correlated patterns can be detected to our knowledge ours is the first work specifically to consider weight affinity between items of patterns a comprehensive performance study shows that wip is efficient and scalable for finding affinity patterns moreover it generates fewer but more valuable patterns with the correlation to decrease the number of thresholds w confidence h confidence and weighted support can be used selectively according to requirement of applications

rational constants of monomial derivations abstract we present some general properties of the field of constants of monomial derivations of k x 1 x n where k is a field of characteristic zero the main result of this paper is a description of all monomial derivations of k x y z with trivial field of constants in this description a crucial role plays the classification result of moulin ollagnier for lotka volterra derivations with strict darboux polynomials several applications of our description are also given in this paper

some notes on the singular manifold method several manifolds and constraints some questions arising when various modifications are made to the singular manifold method are considered the solutions are shown to lie outside the framework of the singular analysis the approach is illustrated by a number of examples with ordinary differential equations further perspectives and the question of optimization of the calculations are also discussed

an algorithm to mine general association rules from tabular data most methods for mining association rules from tabular data mine simple rules which only use the equality operator in their items for quantitative attributes approaches tend to discretize domain values by partitioning them into intervals limiting the operator only to results in many interesting frequent patterns that may not be identified it is obvious that where there is an order between objects operators such as greater than or less than a given value are as important as the equality operator this motivates us to extend association rules from the simple equality operator to a more general set of operators we address the problem of mining general association rules in tabular data where rules can have all operators in their antecedent part the proposed algorithm mining general rules mgr is applicable to datasets with discrete ordered attributes and on quantitative discretized attributes the proposed algorithm stores candidate general itemsets in a tree structure in such a way that supports of complex itemsets can be recursively computed from supports of simpler itemsets the algorithm is shown to have benefits in terms of time complexity memory management and has good potential for parallelization

symmetrically coupled higher order nonlinear schrodinger equations singularity analysis and integrability the integrability of a system of two symmetrically coupled higher order nonlinear schrodinger equations with parameter coefficients is tested by means of singularity analysis it is proven that the system passes the painleve test for integrability only in ten distinct cases of which two are new for one of the new cases a lax pair and a multi field generalization are obtained for the other one the equations of the system are uncoupled by a nonlinear transformation

new variable separation approach application to nonlinear diffusion equations the concept of the derivative dependent functional separable solution ddfss as a generalization to the functional separable solution is proposed as an application it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach as a consequence a complete list of canonical forms for such equations which admit the ddfss is obtained and some exact solutions to the resulting equations are described

the singular manifold method revisited for many completely integrable partial differential equations pdes the singular manifold method of weiss allows the recovery of the lax pair and darboux transformation dt and so also the backlund transformation from a truncated painleve expansion recently the so called two singular manifold method has been proposed in order to handle pdes such as the modified korteweg de vries mkdv equation here we present a more natural extension of the weiss singular manifold method which makes use of only one singular manifold but is capable of dealing with such pdes in this approach we allow the possibility that the dt might in fact correspond to an infinite painleve expansion for a certain choice of the arbitrary coefficients this then leads us to a new and more consistent definition of singular manifold equation sme this can give smes different from those usually presented the summation of infinite painleve expansions is effected by seeking a truncation in a new riccati variable z the use o

high utility pattern mining using the maximal itemset property and lexicographic tree structures the problem of high utility mining is discovering all of the high utility itemsets in a transactional database most algorithms find high utility itemsets in two steps the first step identifies all of the potential itemsets the second step then determines the high utility itemsets from the set of potential itemsets the large number of potential itemsets in the first step is generally the mining bottleneck if we can reduce the number of potential itemsets the mining performance can be improved significantly in this paper we use a maximal itemset property and propose an algorithm called ummi high utility mining using the maximal itemset property to significantly reduce the number of potential itemsets in the first step in the second step ummi uses an effective lexicographic tree structure to determine all of the high utility itemsets in general ummi outperforms all three of the previously used algorithms including ctu pro an optimized twu mining algorithm and two phase in our experiments using synthetic datasets on average ummi is 5 3 and 7 times faster than ctu pro twu mining and two phase respectively in a real data experiment ummi is 6 times faster than two phase the other two algorithms are not capable of completing the mining step in a reasonable amount of time ummi uses an approximately fixed amount of memory which is generally less than the other algorithms for each mining the experimental results show that the proposed algorithm can mine the high utility itemsets efficiently in addition ummi is linearly scalable with respect to the number of transactions

variable separation solutions to the coupled integrable dispersionless equations abstract in this paper the variable separation solutions of the coupled integrable dispersionless equations are derived these solutions include two arbitrary functions and they are more general than the results presented before furthermore some coherent structures of the physical quantity including decaying bell solitary single dromion soliton type breather peakon type breather and loop type breather are constructed

the sine gordon equations complete and partial integrability the sine gordon equation in one space one time dimension is known to possess the painleve property and to be completely integrable it is shown how the method of singular manifold analysis obtains the backlund transform and the lax pair for this equation a connection with the sequence of higher order kdv equations is found the modified sine gordon equations are defined in terms of the singular manifold these equations are shown to be identically painleve also certain rational solutions are constructed iteratively the double sine gordon equation is shown not to possess the painleve property however if the singular manifold defines an affine minimal surface then the equation has integrable solutions this restriction is termed partial integrability the sine gordon equation in n 1 variables n space 1 time where n is greater than one is shown not to possess the painleve property the condition of partial integrability requires the singular manifold to be an einstein space with null scalar curvature the known integrable solutions satisfy this constraint in a trivial manner finally the coupled kdv or hirota satsuma equations possess the painleve property the associated modified equations are derived and from these the lax pair is found

the tzitzeica equation a backlund transformation interpreted as truncated painleve expansion it is shown that the overdetermined system of equations obtained by truncating the painleve expansion for the classical tzitzeica equation admits a solution which defines a backlund transformation

factorization of operators ii we extend the methods of a previous paper j math phys 21 2508 1980 factorizing the general scalar third order differential operator and obtain a miura transformation for the boussinesq equation we give a general factorized eigenvalue problem we also give a hamiltonian structure associated with the factorized eigenvalue problem we derive several isospectral flows some of klein gordon type

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

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

backlund transformation of partial differential equations from the painleve gambier classification i kaup kupershmidt equation among the 50 nonlinear second order differential equations of painleve and gambier those which are linearizable provide a natural scheme for deriving the lax pair and the darboux transformation of a nonlinear partial differential equation when the order of the scattering problem is three this new method allows one to obtain from singularity analysis only the backlund transformation of the kaup kupershmidt equation a result which was missing until now

solutions of a 2 1 dimensional dispersive long wave equation a special type of multisoliton solution with a particular dispersion relation is obtained for wu zhang equation which describes 2 1 dimensional dispersive long waves by the standard weiss tabor carnvale painleve truncation expansion using a nonstandard truncation of a modified conte s invariant painleve expansion two different types of soliton solutions without any dispersive relation is found two types of periodic wave solutions expressed by jacobi elliptic functions are found by the truncations of a special extended painleve expansion the soliton solutions are special cases of the corresponding periodic solutions

the two singular manifold method i modified korteweg de vries and sine gordon equations we address the problem of finding by painleve analysis only the backlund transformation of partial differential equations pdes having two families of movable singularities with opposite principal parts such as the modified korteweg de vries mkdv sine gordon or nonlinear schrodinger equations this first paper gives an almost algorithmic method which extends the singular manifold method of weiss 1986 that is unable to handle these equations first with only one singular manifold at a time we obtain the darboux transformation second we assume that the ratio of two functions defining the singular manifolds satisfies the most general projective riccati system with undetermined coefficients the darboux transformation then generates a very small number of determining equations admitting a unique solution equivalent to the lax pair of the zakharov shabat ablowitz kaup newell segur scheme by the canonical linearization of the riccati system the method is here applied to the mkdv and sine gordon equations

hyper complex four manifolds from the tzitzeica equation it is shown how solutions to the tzitzeica equation can be used to construct a family of pseudo hyper complex metrics in four dimensions

a class of 1 d gas flows soluble by the inverse scattering transform abstract we first show that the euler equations of 1 dimensional adiabatic gas dynamics with arbitrary equation of state present a symmetry s of order three i e such that s3 1 for a particular class of equations of state which may be viewed as representing the geometrical center of the symmetry a higher symmetry exists the sl 3 symmetry in agreement with the results of ref 2 for these equations of state we derive riemann invariants and are thus able to reduce the system of the euler s equations to a mere second order equation versus characteristic coordinates that equation turns out to be soluble by an inverse scattering method with a third order scattering operator as shown in ref 6 we thus provide a first instance of soliton propagation on a nondissipative gaseous background it must be noted however that these are solitons in a mathematical sense only as the space time in which they propagate uniformly does not coincide with ordinary space time

explicit integrability for hamiltonian systems and the painleve conjecture we analyze a class of hamiltonian systems in two dimensions for which we proved that a second constant of motion exists it is shown that using the two first integrals the equations of motion can be written in a form which allows their integration by quadratures an analysis of the equations of motion in this reduced form establishes the behavior of the solutions in the complex time plane it is shown explicitly that the systems belonging to this class possess the weak painleve property i e their solutions in complex time can present singularities of a specific algebraic type

a new truncation in painleve analysis the author observes that when the expansion variable in painleve analysis satisfies a system of riccati equations truncation at a level higher than constant level is allowed this extends the range of exact solutions to nonlinear partial differential equations that one is able to obtain using truncated painleve expansions

factorization of the classical boussinesq system the scalar equation equivalent to the classical boussinesq or broer kaup system is shown to factorize into a differential operator acting on burgers equation the linearizability of this latter equation provides a very simple explanation for the recently found property of fusion and fission of a class of solitons for this system

generalized solitary and periodic wave solutions to a 2 1 dimensional zakharov kuznetsov equation abstract in this paper the exp function method is employed to the zakharov kuznetsov equation as a 2 1 dimensional model for nonlinear rossby waves the observation of solitary wave solutions and periodic wave solutions constructed from the exponential function solutions reveal that our approach is very effective and convenient the obtained results may be useful for better understanding the properties of two dimensional coherent structures such as atmospheric blocking events

backlund transformation of partial differential equations from the painleve gambier classification ii tzitzeica equation from the existing methods of singularity analysis only we derive the two equations which define the backlund transformation of the tzitzeica equation this is achieved by defining a truncation in the spirit of the approach of weiss et al so as to preserve the lorentz invariance of the tzitzeica equation if one assumes a third order scattering problem this truncation admits a unique solution thus leading to a matrix lax pair and a darboux transformation in order to obtain the backlund transformation bt which is the main new result of this paper one represents the lax pair by an equivalent two component riccati pseudopotential this yields two different bts the first one is a bt for the hirota satsuma equation while the second one is a bt for the tzitzeica equation one of the two equations defining the bt is the fifth ordinary differential equation of gambier

darboux transformation and solutions for an equation in 2 1 dimensions painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2 1 dimensions this procedure has allowed us to obtain the lax pair darboux transformation and functions in such a way that a plethora of different solutions with solitonic behavior can be constructed iteratively

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

painleve property and pseudopotentials for nonlinear evolution equations the link between the singularity manifold equation and the pseudopotential equations is found for nonlinear evolution equations both in 1 1 and 2 1 dimensions many examples are given burgers korteweg de vries modified korteweg de vries harry dym a higher order korteweg de vries sawada kotera kaup kuperschmidt kadomtsev petviashvili boussinesq modified kadomtsev petviashvili and 2 1 dimensional sawada kotera equations

algorithmic method for deriving lax pairs from the invariant painleve analysis of nonlinear partial differential equations given a partial differential equation its painleve analysis will first be performed with a built in invariance under the homographic group acting on the singular manifold function then assuming an order for the underlying lax pair a multicomponent pseudopotential of projective riccati type the components of which are homographically invariant is introduced if the equation admits a classical darboux transformation a very small set of determining equations whose solution yields the lax pair will be generated in the basis of the pseudopotential this new method will be applied to find the yet unpublished lax pair of the scalar hirota satsuma equation

rational solutions for schwarzian integrable hierarchies we give an approach to finding rational solutions of completely intagrable hierarchies which makes use of the relationship between modifications and the schwarzian equations obtained via the singular manifold method this extends the recent work of kudryashov which allowed a simple derivation of the iteration used to construct sequences of such solutions we also give a closed form for the index polynomial of the schwarzian korteweg de vries hierarchy in addition we consider the representation of rational solutions using lower families of the hierarchy we give a simple representation under which the rational solutions remain solutions of every flow of the hierarchy this representation also allows the inclusion of arbitrary data corresponding to negative indices we use our method to derive an alternative form of the backlund transformation for the hierarchy of the second painleve equation as well as new solutions of a hierarchy of breaking soliton equations we also present here for the first time a schwarzian version of this breaking soliton hierarchy

constants of cyclotomic derivations let k x k x0 xn 1 and k y k y0 yn 1 be the polynomial rings in n 3 variables over a field k of characteristic zero containing the n th roots of unity let d be the cyclotomic derivation of k x and let be the factorisable derivation of k y associated with d that is d xj xj 1 and yj yj yj 1 yj for all j zn we describe polynomial constants and rational constants of these derivations we prove among others that the field of constants of d is a field of rational functions over k in n n variables and that the ring of constants of d is a polynomial ring if and only if n is a power of a prime moreover we show that the ring of constants of is always equal to k v where v is the product y0 yn 1 and we describe the field of constants of in two cases when n is power of a prime and when n pq

method for deriving rational solutions of some nonlinear evolution equations maps for nonlinear evolution equations are discussed an algorithmic method for deriving rational solutions is presented this approach is illustrated by examples which have solutions in the form of two truncated expansions

adaptive estimated maximum entropy distribution model the estimation of distribution algorithm eda model is an optimization procedure through learning and sampling a conditional probabilistic function the use of conditional density function permits multivariate dependency modelling which is not captured in a population based representation like the classical genetic algorithms the gaussian model is a simple and widely used model for density estimation however an assumption of normality is not realistic for many real life problems alternatively the maximum entropy model can be used which makes no assumption of a normal distribution one disadvantage of the maximum entropy model is the learning cost of its parameters this paper proposes an adaptive estimated maximum entropy distribution adaptive meed model which aims to reduce learning complexity of building a model adaptive meed exploits the fact that samples have a low average fitness in the early stage but they gradually converge to an optima towards the end of the search hence it is not necessary to inference the model with a full account of observed constraints in the early stage of the search the proposed model attempts to estimate the density function with a dynamic set of samples and active constraints in addition the proposed model includes a global sampling function to address the issue of a missing mutation operator the ergodic convergence properties of the proposed model are discussed with the markov chain analysis the preliminary experimental evaluation shows that the proposed model performs well against genetic algorithms on several clustering problems

a note on a class of solitary like solutions of the tzitzeica equation generated by a similarity reduction abstract in this paper new class of solutions of the tzitzeica equation are derived by using the classical lie symmetry analysis the important aspect of this paper however is the fact that the analysis results in a new class of solitary like solutions the so called cusp solitary solutions this special type of solutions are not found in the current literature and represents a necessary contribution for the whole solution manifold the studied equation was originally found in the field of geometry otherwise the tzitzeica equation takes place in many branches of non linear sciences therefore explicit class of solutions connected by a physical meaning are of great importance the analysis is restricted to the case of traveling waves represented by a similarity variable describing any wave propagation a complete characterization of the group properties is given the classical lie point symmetries are derived and algebraic properties are determined similarity solutions and transformations are given in a most general form and have been derived for the first time in terms of jacobian elliptic functions it is worth to mention that the application of known powerful algebraic methods e g special function transform methods are not appropriate to study the solution manifold hence the present paper is therefore suitable to create a deeper insight into the solution manifold with respect to the traveling wave picture

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

analytic structure of the henon heiles hamiltonian in integrable and nonintegrable regimes the solutions of the henon heiles hamiltonian are investigated in the complex time plane the use of the painleve property i e the property that the only movable singularities exhibited by the solution are poles enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes these boundaries have a remarkable self similar structure whose form changes as a function of the nonlinear coupling

su 3 symmetry of the equations of unidimensional gas flow with arbitrary entropy distribution we have shown in an earlier work that assuming a particular class of equations of state the euler equations of one dimensional gas flow are invariant under an su 3 group of transformations and in fact admit of a lie group of symmetry of infinite order they therefore possess an infinite number of conservation laws we show in the present work that the su 3 symmetrical formalism still brings about tremendous simplification and analytical order in the most general case where the equation of state is arbitrary the six characteristic equations assume a vector form and relate two conjugate three dimensional vectors u and x the su 3 symmetry is only broken to a minor extent through the occurrence of a multiplicative factor in the equations the conservation laws take the form of the cauchy integrability condition for the elements of a traceless second rank tensor eij and taken all together form an su 3 octet in the most general case however there exist four conservation laws only five if the

analytic solutions of a microstructure pde and the kdv and kadomtsev petviashvili equations by invariant painleve analysis and generalized hirota techniques abstract truncated painleve expansions invariant painleve analysis and generalized hirota expansions are employed in combination to solve partially reduce to quadrature the integrable kdv and kp equations and a nonintegrable generalized microstructure gms equation although the multisolitons of the kdv and kp equations are very well known the solutions obtained here for all the three nlpdes are novel and non trivial the solutions obtained via invariant painleve analysis are all complicated rational functions with arguments which themselves are confluent hypergeometric kdv or trigonometric gms functions of various distinct non traveling kdv and traveling wave variables in some cases this is slightly reminiscent of doubly periodic elliptic function solutions when nonlinear ode systems are reduced to quadratures the solutions obtained by the use of recently generalized hirota type expansions in the truncated painleve expansions are closer in functional form to conventional hyperbolic secant solutions although with non trivial traveling wave arguments which are distinct for the three nlpdes considered here

cosine interesting pattern discovery recent years have witnessed an increasing interest in computing cosine similarity between high dimensional documents transactions and gene sequences etc most previous studies limited their scope to the pairs of items which cannot be adapted to the multi itemset cases therefore from a frequent pattern mining perspective there exists still a critical need for discovering interesting patterns whose cosine similarity values are above some given thresholds however the knottiest point of this problem is the cosine similarity has no anti monotone property to meet this challenge we propose the notions of conditional anti monotone property and support ascending set enumeration tree sa set we prove that the cosine similarity has the conditional anti monotone property and therefore can be used for the interesting pattern mining if the itemset traversal sequence is defined by the sa set we also identify the anti monotone property of an upper bound of the cosine similarity which can be used in further pruning the candidate itemsets an apriori like algorithm called cosminer is then put forward to mine the cosine interesting patterns from large scale multi item databases experimental results show that cosminer can efficiently identify interesting patterns using the conditional anti monotone property of the cosine similarity and the anti monotone property of its upper bound even at extremely low levels of support

modified singular manifold expansion application to the boussinesq and mikhailov shabat systems we present a modified treatment of the singular manifold method as an improved variant of the painleve analysis for partial differential equations with two branches in the painleve expansion we illustrate the method by fully applying it to the classical boussinesq system and to the mikhailov shabat system

minimal vanishing sums of roots of unity with large coefficients a vanishing sum where n is a primitive nth root of unity and the a i s are non negative integers is called minimal if the coefficient vector a 0 a n 1 does not properly dominate the coefficient vector of any other such non zero sum we show that for every c there is a minimal vanishing sum of nth roots of unity with its greatest coefficient equal to c where n is of the form 3pq for odd primes p q this solves an open problem posed by lenstra jr

closed polynomials and their applications for computations of kernels of monomial derivations abstract in this paper we give some results on closed polynomials and factorially closed polynomials in n variables which are generalizations of results in 7 12 and 13 in particular we give a characterization of factorially closed polynomials in n variables over an algebraically closed field of any characteristic furthermore as an application of results on closed polynomials we determine kernels of non zero monomial derivations on the polynomial ring in two variables over a ufd finally by using this result and the argument in 16 5 for a field k we determine the non zero monomial derivations d on k x y such that the quotient field of the kernel of d is not equal to the kernel of d in k x y

new contiguity relation of the sixth painleve equation from a truncation for the master painleve equation p6 u we define a consistent method adapted from the weiss truncation for partial differential equations which allows us to obtain the first degree birational transformation of okamoto two new features are implemented to achieve this result the first one is the homography between the derivative of the solution u and a riccati pseudopotential the second one is an improvement of a conjecture by fokas and ablowitz on the structure of this birational transformation we then build the contiguity relation of p6 which yields one new second order non autonomous discrete equation

itemset generalization with cardinality based constraints abstract generalized itemset mining is an established data mining technique that focuses on discovering high level correlations among large databases by exploiting a taxonomy built over the data items items are aggregated into higher level concepts and thus data correlations at different abstraction levels can be discovered however since a large number of patterns can be extracted the result of the mining process is often not easily manageable by domain experts we propose a novel approach to discovering a compact subset of generalized itemsets from structured data to guarantee model conciseness and readability a set of itemsets that has a common generalization is generated only when its cardinality is so small that its manual inspection is practically feasible furthermore generalizations are generated only when their knowledge is covered by a large number of low level descendant itemsets and the generalizations are worth considering in place of their many low level descendants only in these cases experiments performed on synthetic benchmark and real data taken from a mobile application scenario demonstrate the effectiveness and efficiency of the proposed approach

common structure of several completely integrable non linear equations the author consider several non linear equations which are known to be completely integrable by the method of inverse scattering transform ranging from sine gordon and the dodd bullough equation 1976 to the axisymmetric stationary einstein maxwell equations such equations are known to be invariant under a fundamental lie group of symmetry g such as sl 2 or sl 3 in the simpler cases the author s treatment starts with the reformulation of the given equations as a system involving the scalar invariants of the lie group g only this scalar formulation is not only g invariant but also manifestly invariant under the continuous group associated with the emergence of a spectral parameter and is thus expected to be more fundamental and simpler in all the cases that the author has considered including the einstein maxwell system vector pseudopotentials of dimension not higher than three have been derived backlund transformations have been found which generate multisolitons starting from the vacuum and have the general reciprocal form x 1 x where x is a component of one of the vector or tensor pseudopotentials the author also mentions the result that kinnersley s formulation 1977 of the ernst vacuum equation 1968 is formally equivalent to the fluid dynamical problem of unidimensional ideal gas flow the dodd bullough equation is equivalent to another particular case of gas motion

reduction technique for matrix nonlinear evolution equations solvable by the spectral transform the main purpose of this paper is to describe a technique of reduction whereby from the class of evolution equations for matrices of order n solvable via the spectral transform associated to the matrix linear schrodinger eigenvalue problem one derives subclasses of nonlinear evolution equations involving less than n2 fields to illustrate the method from the equations for matrices of order 2 two subclasses of equations for 2 fields rather than 4 are obtained the first class coincides or rather includes that solvable via the spectral transform associated to the generalized zakharov shabat spectral problem further reduction to nonlinear evolution equations for a single field reproduces a number of well known equations but also yields a novel one highly nonlinear the second class also yields highly nonlinear equations some examples are given including another novel evolution equation for a single field

integrals of quadratic ordinary differential equations in r3 the lotka volterra system abstract a method already introduced by the last two authors for finding the integrable cases of three dimensional autonomous ordinary differential equations based on the frobenius integrability theorem is described in detail using this method and computer algebra the so called three dimensional lotka volterra system is studied many cases of integrability are thus found the study of this system is completed by the application of painleve analysis and the jacobi last multiplier method the methods used are of general interest and can be applied to many other systems

backlund transformation and the painleve property when a differential equation possesses the painleve property it is possible for specific equations to define a backlund transformation by truncating an expansion about the singular manifold at the constant level term from the backlund transformation it is then possible to derive the lax pair modified equations and miura transformations associated with the completely integrable system under consideration in this paper completely integrable systems are considered for which backlund transformations as defined above may not be directly defined these systems are of two classes the first class consists of equations of toda lattice type e g sine gordon bullough dodd equations we find that these equations can be realized as the minus one equation of sequences of integrable systems although the backlund transformation may or may not exist for the minus one equation it is shown for specific sequences that the backlund transformation does exist for the positive equations of the sequence this in turn allows the derivation of lax pairs and the recursion operation for the entire sequence the second class of equations consists of sequences of harry dym type these equations have branch point singularities and thus do not directly possess the painleve property yet by a process similar to the uniformization of algebraic curves their solutions may be parametrically represented by meromorphic functions for specific systems this is shown to provide a natural extension of the painleve property

tzitzeica transformation is a dressing action we classify the simplest rational elements in a twisted loop group and prove that dressing actions of them on proper indefinite affine spheres give the classical tzitzeica transformation and its dual we also give the group point of view of the permutability theorem construct complex tzitzeica transformations and discuss the group structure for these transformations

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

derivative dependent functional separable solutions for the kdv type equations abstract a complete list of canonical forms for a special kdv type of equations which admit derivative dependent functional separable solutions is obtained by using the generalized conditional symmetry approach some exact solutions to the resulting equations are explicitly obtained

on vanishing sums of roots of unity an unsolved problem in number theory asked the following for a given natural number m what are the possible integers n for which there exist mth roots of unity 1 n c such that 1 n 0 we show in this paper that the set of all possible n s is exactly the collection of n combinations of the prime divisors of m where n denotes the set of all non negative integers the proof is long and involves a subtle analysis of minimal vanishing sums of mth roots of unity couched in the setting of integral group rings of finite cyclic groups our techniques also recovered with ease some of the classical results on vanishing sums of roots of unity such as those of redei de bruijn and schoenberg

analytic solitary waves of nonintegrable equations abstract a major drawback of most methods to find analytic expressions for solitary waves is the a priori restriction to a given class of expressions to overcome this difficulty we present a new method applicable to a wide class of autonomous equations which builds as an intermediate information the first order autonomous ordinary differential equation ode satisfied by the solitary wave we discuss its application to the cubic complex one dimensional ginzburg landau equation and conclude to the elliptic nature of the yet unknown most general solitary wave

on the nonexistence of rational first integrals for systems of linear differential equations abstract we present a description of all systems of linear differential equations which do not admit any rational first integral

image categorization graph edit distance edge direction histogram this paper presents a novel algorithm for computing graph edit distance ged in image categorization this algorithm is purely structural i e it needs only connectivity structure of the graph and does not draw on node or edge attributes there are two major contributions 1 introducing edge direction histogram edh to characterize shape features of images it is shown that ged can be employed as distance of edhs this algorithm is completely independent on cost function which is difficult to be defined exactly 2 computing distance of edhs with earth mover distance emd which takes neighborhood bins into account so as to compute distance of edhs correctly a set of experiments demonstrate that the newly presented algorithm is available for classifying and clustering images and is immune to the planar rotation of images compared with ged from spectral seriation our algorithm can capture the structure change of graphs better and consume 12 79 time used by the former one the average classification rate is 5 and average clustering rate is 25 higher than the spectral seriation method

an order clique based approach for mining maximal co locations most algorithms for mining spatial co locations adopt an apriori like approach to generate size k prevalence co locations after size k 1 prevalence co locations however generating and storing the co locations and table instances is costly a novel order clique based approach for mining maximal co locations is proposed in this paper the efficiency of the approach is achieved by two techniques 1 the spatial neighbor relationships and the size 2 prevalence co locations are compressed into extended prefix tree structures which allows the order clique based approach to mine candidate maximal co locations and co location instances and 2 the co location instances do not need to be stored after computing some characteristics of the corresponding co location which significantly reduces the execution time and space required for mining maximal co locations the performance study shows that the new method is efficient for mining both long and short co location patterns and is faster than some other methods in particular the join based method and the join less method

integrability characteristics of two dimensional generalizations of nls type equations a recent procedure based on truncated painleve expansions is used to derive lax pairs darboux transformations and various soliton solutions for integrable 2 1 generalizations of nls type equations in particular diverse classes of solutions are found analogous to the dromion instanton lump and ring soliton solutions derived recently for 2 1 korteweg de vries type equations the nizhnik novikov veselov equation and the 2 1 broer kaup system

mining maximal hyperclique pattern a hybrid search strategy a hyperclique pattern is a new type of association pattern that contains items which are highly affiliated with each other specifically the presence of an item in one transaction strongly implies the presence of every other item that belongs to the same hyperclique pattern in this paper we present an algorithm for mining maximal hyperclique patterns which specifies a more compact representation of hyperclique patterns and are desirable for many applications such as pattern based clustering our algorithm exploits key advantages of both the depth first search dfs strategy and the breadth first search bfs strategy indeed we adapt the equivalence pruning method one of the most efficient pruning methods of the dfs strategy into the process of the bfs strategy our experimental results show that the performance of our algorithm can be orders of magnitude faster than standard maximal frequent pattern mining algorithms particularly at low levels of support

the two singular manifold method ii classical boussinesq system for pt i see musette et al ibid vol 24 p 3895 1994 the two singular manifold method a generalization of the singular manifold method of weiss 1983 is applied to the classical boussinesq system also known as the broer kaup system from the point of view of its singularity analysis the important feature of this system is the existence of two principal families with opposite principal parts the usual singular manifold method takes into account only one of these families at a time our generalization takes into account both families and in this way we are able to derive the lax pair and darboux transformation and hence the auto backlund transformation for the classical boussinesq system from its painleve analysis