new candidates for arbitrage free stock price models via generalized conditional symmetry method abstract in this paper a new perspective upon generating arbitrage free stock price models is proposed the generalized conditional symmetry gcs method is applied to the governing second order 1 1 partial differential equation which does contain a rational parameter p drawn from the interval 1 2 1 we investigate the conditions that yield the concerned equation admitting a special class of second order gcss the determining system is solved in several special cases and from invariance surface condition associated to each of the gcs operator for all values of p some invariant solutions are pointed out new candidate models for arbitrage free stock price are derived

feature selection via dependence maximization we introduce a framework for feature selection based on dependence maximization between the selected features and the labels of an estimation problem using the hilbert schmidt independence criterion the key idea is that good features should be highly dependent on the labels our approach leads to a greedy procedure for feature selection we show that a number of existing feature selectors are special cases of this framework experiments on both artificial and real world data show that our feature selector works well in practice

generalized conditional symmetries of evolution equations we analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector fields in involution earlier results on the connection between generalized conditional invariance and generalized reduction of evolution equations are revisited this leads to a no go theorem on determining equations for operators of generalized conditional symmetry it is also shown that up to certain equivalences there exists a one to one correspondence between generalized conditional symmetries of an evolution equation and parametric families of its solutions

conditional lie backlund symmetry second order differential constraint and direct reduction of diffusion systems abstract the equivalence relation between conditional lie backlund symmetry higher order differential constraint and direct reduction is presented in the case of evolution systems the second order nonlinear conditional lie backlund symmetries and corresponding induced differential constraints admitted by nonlinear diffusion systems are identified as an application of the conditional lie backlund symmetry of evolution systems consequently the corresponding symmetry reductions are obtained due to the compatibility of the resulting differential constraints and the governing systems

conditional lie backlund symmetries and solutions to n 1 dimensional nonlinear diffusion equations this paper discusses a class of n 1 dimensional nonlinear diffusion equations with source term which arises in nonlinear shear flows of non newtonian fluids it is shown that some radially symmetric equations admit certain types of conditional lie backlund symmetries as a result exact solutions to the resulting equations are obtained those solutions extend the known ones such as instantaneous source solutions of the porous medium equation with absorption term the phenomena of extinction and blow up and behavior to many of the solutions are described

double regularization methods for robust feature selection and svm classification via dc programming abstract in this work two novel formulations for embedded feature selection are presented a second order cone programming approach for support vector machines is extended by adding a second regularizer to encourage feature elimination the one and the zero norm penalties are used in combination with the tikhonov regularization under a robust setting designed to correctly classify instances up to a predefined error rate even for the worst data distribution the use of the zero norm leads to a nonconvex formulation which is solved by using difference of convex dc functions extending dc programming to second order cones experiments on high dimensional microarray datasets were performed and the best performance was obtained with our approaches compared with well known feature selection methods for support vector machines

maximal sign invariants of quasilinear parabolic equations with gradient diffusivity we consider quasilinear parabolic equations with gradient diffusivity ut div u u f u x rn t 0 where 1 is a fixed constant and f u is a given smooth function we also study quasilinear parabolic equations with a gradient dependent coefficient ut h u u f u with a smooth function h p for both classes of equations we derive first order sign invariants i e first order operators preserving their signs on the evolution orbits u t t 0 we give a complete description of maximal sign invariants of prescribed structures as a consequence we construct new exact solutions of some quasilinear equations

conditional lie backlund symmetries and differential constraints for inhomogeneous nonlinear diffusion equations due to linear determining equations abstract the method of linear determining equations is developed to study conditional lie backlund symmetries for evolution equations which is more general than the classical determining equations for lie s generators as an application of this approach the complete classification is presented for the inhomogeneous nonlinear diffusion equations which admit the second order and third order conditional lie backlund symmetries several examples are given to illustrate the corresponding symmetry reductions due to the compatibility of the invariant conditions and the governing equations

non classical symmetry reduction example of the boussinesq equation a symmetry of an equation will leave the set of all solutions invariant a conditional symmetry will leave only a subset of solutions defined by some differential condition invariant the authors show how a specific class of conditional symmetries can be used to reduce a partial differential equation to an ordinary one in particular for the boussinesq equation these conditional symmetries together with the ordinary ones provide all possible reductions to ordinary differential equations a group theoretical explanation of the recently obtained new reductions is provided

conditional symmetry of a porous medium equation abstract we obtain an exhaustive description of conditional symmetries admitted by a nonlinear porous medium equation in one spatial dimension it is proved that solving the determining equations for the conditional symmetries either yields classical lie symmetries or is equivalent to solving the porous medium equation itself the second possibility is shown to be typical for an arbitrary evolution type partial differential equation in one spatial variable we show that this very property is responsible for the well known phenomenon when using non classical symmetries yield exact solutions which prove to be invariant ones

reduction operators of burgers equation abstract the solution of the problem on reduction operators and nonclassical reductions of the burgers equation is systematically treated and completed a new proof of the theorem on the special no go case of regular reduction operators is presented and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case all possible nonclassical reductions of the burgers equation to single ordinary differential equations are exhaustively described any lie reduction of the burgers equation proves to be equivalent via the hopf cole transformation to a parameterized family of lie reductions of the linear heat equation

symmetries of the fisher kolmogorov petrovskii piskunov equation with a nonlocal nonlinearity in a semiclassical approximation abstract the classical group analysis approach used to study the symmetries of integro differential equations in a semiclassical approximation is considered for a class of nearly linear integro differential equations in a semiclassical approximation an original integro differential equation leads to a finite consistent system of differential equations whose symmetries can be calculated by performing standard group analysis the approach is illustrated by the calculation of the lie symmetries in explicit form for a special case of the one dimensional nonlocal fisher kolmogorov petrovskii piskunov population equation

symmetry reductions and exact solutions of a class of nonlinear heat equations abstract classical and nonclassical symmetries of the nonlinear heat equation ut uxx f u are considered the method of differential grobner bases is used both to find the conditions on f u under which symmetries other than the trivial spatial and temporal translational symmetries exist and to solve the determining equations for the infinitesimals a catalogue of symmetry reductions is given including some new reductions for the linear heat equation and a catalogue of exact solutions of the nonlinear heat equation for cubic f u in terms of the roots of f u 0

direct reduction and differential constraints direct reductions of partial differential equations to systems of ordinary differential equations are in one to one correspondence with compatible differential constraints the differential constraint method is applied to prove that a parabolic evolution equation admits infinitely many characteristic second order reductions but admits a non characteristic second order reduction if and only if it is linearizable

statistical estimation of polynomial generalized covariance functions and hydrologic applications minimum variance unbiased linear estimation theory has found many applications in the analysis of spatial rainfall and hydrogeologic data estimation of point values or areal averages calculation of variances of estimation error and network design however the important problem of inferring the spatial structure or interdependence of the function of interest has received relatively less attention three methods for the estimation of the parameters of matheron s polynomial generalized covariance function a useful model for nonstationary functions are presented and evaluated maximum likelihood ml minimum variance unbiased quadratic mvuq and minimum norm least squares the estimation error covariance matrix of the parameters is calculated with each of these methods ml and mvuq estimation have very good properties and for reasonably large samples give very similar results minimum norm estimation is appropriate for preliminary data analysis the application of these methodologies is illustrated with a set of rainfall data and problems of implementation are discussed it is shown that the estimation of the parameters of the covariance function involves sizeable errors it is suggested that in practice it may be rather difficult to identify the parameters of all but simple models it is important that future research evaluate the effects of parameter uncertainty in the circulation of estimation error variances of point or areal averages and in the design of hydrologic data collection networks

on the weak symmetry groups of partial differential equations abstract we define an algorithm to characterize all weak symmetry groups of a partial differential equation new invariant solutions to the fokker planck equation are found

conditional lie backlund symmetries and solutions of inhomogeneous nonlinear diffusion equations abstract the second order conditional lie backlund symmetries of nonlinear diffusion equations with variable coefficients are studied a number of examples are considered and some exact solutions are constructed via the compatibility of conditional lie backlund symmetries and the governing equations these solutions possess the extended forms of the separation of variables including the extensions of the instantaneous source solutions of the porous medium equations

conditional lie backlund symmetry and reduction of evolution equations we suggest a generalization of the notion of invariance of a given partial differential equation with respect to a lie backlund vector field such a generalization proves to be effective and enables us to construct principally new ansatz reducing evolution type equations to several ordinary differential equations in the framework of the said generalization we obtain principally new reductions of a number of nonlinear heat conductivity equations ut uxx f u ux with poor lie symmetry and obtain their exact solutions it is shown that these solutions cannot be constructed by means of the symmetry reduction procedure

invariant modules and the reduction of nonlinear partial differential equations to dynamical systems abstract we completely characterize all nonlinear partial differential equations leaving a given finite dimensional vector space of analytic functions invariant existence of an invariant subspace leads to a reduction of the associated dynamical partial differential equations to a system of ordinary differential equations and provides a nonlinear counterpart to quasi exactly solvable quantum hamiltonians these results rely on a useful extension of the classical wronskian determinant condition for linear independence of functions in addition new approaches to the characterization of the annihilating differential operators for spaces of analytic functions are presented

a multi class svm approach based on the l1 norm minimization of the distances between the reduced convex hulls multi class classification is an important pattern recognition task that can be addressed accurately and efficiently by support vector machine svm in this work we present a novel svm based multi class classification approach based on the center of the configuration a point which is equidistant to all classes the center of the configuration is obtained from the dual formulation by minimizing the distances between the reduced convex hulls using the l1 norm while the decision functions are subsequently constructed from this point this work also extends the ideas of zhou et al 2002 37 to multi class classification the use of l1 norm provides a single linear programming formulation which reduces the complexity and confers scalability compared with other multi class svm methods based on quadratic programming formulations experiments on benchmark datasets demonstrate the virtues of our approach in terms of classification performance and running times compared with various other multi class svm methods highlightsnovel linear programming approach for multi class svm a geometrically grounded method based on the concept of reduced convex hulls good classification performance is achieved with short running times

on the distance between two ellipsoids we study the fundamental geometric problem of finding the distance between two ellipsoids an algorithm is proposed for computing the distance and locating the two closest points the algorithm is based on a local approximation of the two ellipsoids by balls it is simple geometric in nature and has excellent convergence properties

a graphical procedure for determining nonstationarity in time series abstract integrated processes as models for time series data have proved to be an important component of the highly flexible class of arima p d q models determining the amount of differencing d has been a difficult task too little and the process is not yet second order stationary too much and the process is more variable than it need be it is shown that by introducing the notion of generalized covariances developed by matheron 1973 for spatial processes the amount of differencing needed can be read easily from a sequence of graphs showing averages of squares of primary data increments formal inference to determine if the last difference really is necessary can then be carried out time series data are analyzed in this way and compared with the hypothesis testing approach illustrated by dickey bell and miller 1986 once the order of differencing has been diagnosed either the differenced time series can be analyzed or the generalized covariance of the undifferenced series can be estimated

conditional lie backlund symmetries and functionally generalized separable solutions to the generalized porous medium equations with source abstract the functionally generalized separable solutions of the generalized porous medium equations with power law and exponential diffusivity are studied by using the conditional lie backlund symmetry method the variant forms of the considered equations which admit the linear conditional lie backlund symmetries are identified a number of examples are considered and some exact solutions defined on the polynomial trigonometric and exponential invariant subspaces determined by the linear conditional lie backlund symmetries are constructed

building sparse twin support vector machine classifiers in primal space abstract twin support vector machines tsvm obtain faster training speeds than classical support vector machines svm however tsvm augmented vectors lose sparsity in this paper a rapid sparse twin support vector machine stsvm classifier in primal space is proposed to improve the sparsity and robustness of tsvm based on a simple back fitting strategy the stsvm iteratively builds each nonparallel hyperplanes by adding one support vector sv from the corresponding class at one time this process is terminated using an adaptive and stable stopping criterion stsvm learning is implemented by linear equation computing systems through introducing a quadratic function to approximate the empirical risk the computational results on several synthetic and benchmark datasets indicate that the stsvm obtains a sparse separating hyperplane at a low cost without sacrificing its generalization performance

multi class second order cone programming support vector machines novel multiclass approach that simultaneously constructs all required hyperplanes extensions of ovo and ova multiclass svm to second order cone programming svm best classification performance is achieved in experiments on benchmark datasets this paper presents novel second order cone programming socp formulations that determine a linear multi class predictor using support vector machines svms we first extend the ideas of ovo one versus one and ova one versus all svm formulations to socp svm providing two interesting alternatives to the standard svm formulations additionally we propose a novel approach mc socp that simultaneously constructs all required hyperplanes for multi class classification based on the multi class svm formulation mc svm the use of conic constraints for each pair of training patterns in a single optimization problem provides an adequate framework for a balanced and effective prediction

on a reduction and solutions of nonlinear wave equations with broken symmetry a generalised definition for invariance of partial differential equations is proposed exact solutions of the equations with broken symmetry are obtained

separation of variables in the nonlinear wave equation we develop a technique making it possible to handle the problem of separation of variables in nonlinear differential equations using it we obtain a number of new two dimensional nonlinear wave equations admitting separation of variables and construct their exact solutions

evolution equations invariant surface conditions and functional separation of variables abstract this paper is devoted to a discussion of the reduction methods for evolution equations based on invariant surface conditions related to functional separation of variables the relationship of these methods with nonclassical and weak point symmetries is stressed applications to diffusion equations with an inhomogeneous reaction term or with saturating dissipation are provided

combining uncertainty and imprecision in models of medical diagnosis the paper presents a unified fuzzy probabilistic framework for modeling processes of medical diagnosis the two basic concepts of the dempster shafer theory i e focal elements and a basic probability assignment correspond to disease symptoms and the significance of an individual symptom in the diagnosis respectively the belief computation is related to diagnostic inference the final conclusion of the inference is the diagnosis with the greatest belief value fuzzy sets are used to describe focal elements it is shown how their membership functions and basic probability assignments are estimated on the basis of experimental data the interpretation of focal elements as fuzzy sets along with individual consideration of evidence imprecision and uncertainty of diagnosis are the essential new aspects of the presented method experimental studies have demonstrated the superiority of the proposed approach over some other modeling alternatives

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

second order cone programming formulations for feature selection this paper addresses the issue of feature selection for linear classifiers given the moments of the class conditional densities the problem is posed as finding a minimal set of features such that the resulting classifier has a low misclassification error using a bound on the misclassification error involving the mean and covariance of class conditional densities and minimizing an l1 norm as an approximate criterion for feature selection a second order programming formulation is derived to handle errors in estimation of mean and covariances a tractable robust formulation is also discussed in a slightly different setting the fisher discriminant is derived feature selection for fisher discriminant is also discussed experimental results on synthetic data sets and on real life microarray data show that the proposed formulations are competitive with the state of the art linear programming formulation

a robust minimax approach to classification when constructing a classifier the probability of correct classification of future data points should be maximized we consider a binary classification problem where the mean and covariance matrix of each class are assumed to be known no further assumptions are made with respect to the class conditional distributions misclassification probabilities are then controlled in a worst case setting that is under all possible choices of class conditional densities with given mean and covariance matrix we minimize the worst case maximum probability of misclassification of future data points for a linear decision boundary this desideratum is translated in a very direct way into a convex second order cone optimization problem with complexity similar to a support vector machine problem the minimax problem can be interpreted geometrically as minimizing the maximum of the mahalanobis distances to the two classes we address the issue of robustness with respect to estimation errors in the means and covariances of the classes via a simple modification of the input data we also show how to exploit mercer kernels in this setting to obtain nonlinear decision boundaries yielding a classifier which proves to be competitive with current methods including support vector machines an important feature of this method is that a worst case bound on the probability of misclassification of future data is always obtained explicitly

discriminating between nonstationary and nearly nonstationary time series models a simulation study abstract this paper describes empirical evidence that it may often be possible to very simply discriminate between homogeneous once integrated nonstationary time series models and nearly nonstationary approximations to them we show that in such a situation there can be a feature of the serial correlation structure which enables the pair of models to be distinguished with considerable confidence this observation appears to be useful in the context of the box jenkins identification of time series models and we believe it opens up a promising field for new research complementary to the currently well established tests for unit roots

initial value problems for evolutionary partial differential equations and higher order conditional symmetries we suggest a new approach to the problem of dimensional reduction of initial boundary value problems for evolution equations in one spatial variable the approach is based on higher order generalized conditional symmetries of the equations involved it is shown that reducibility of an initial value problem for an evolution equation to a cauchy problem for a system of ordinary differential equations can be fully characterized in terms of conditional symmetries which leave invariant the equation in question we also give some examples of the solution of initial value problems for second and third order nonlinear differential equations by reduction by their conditional symmetries we give a systematic classification of general second order partial differential equations admitting second order conditional symmetries based on lie s classification of invariant second order ordinary differential equations this yields five classes of principally new initial value problems for nonlinear evolution equations which admit no lie symmetries and are reducible via second order conditional symmetries

extended rotation and scaling groups for nonlinear evolution equations a 1 1 dimensional nonlinear evolution equation is invariant under the rotation group if it is invariant under the infinitesimal generator v x u u x then the solution satisfies the condition ux x u for equations that do not admit the rotation group we provide an extension of the rotation group the corresponding exact solution can be constructed via the invariant set r0 u ux xf u of a contact first order differential structure where f is a smooth function to be determined the time evolution on r0 is shown to be governed by a first order dynamical system we introduce an extension of the scaling groups characterized by an invariant set tilde s 0 that depends on two constants and n 1 when 0 it reduces to the invariant set s0 introduced by galaktionov we also introduce a generalization of both the scaling and rotation groups which is described by an invariant set e0 with parameters a and b when a 0 or b 0 it respectively reduces to r0 or s0 these approaches are used to obtain exact solutions and reductions of dynamical systems of nonlinear evolution equations

singular reduction operators in two dimensions the notion of singular reduction operators i e of singular operators of nonclassical conditional symmetry of partial differential equations in two independent variables is introduced all possible reductions of these equations to first order odes are exhaustively described as examples properties of singular reduction operators of 1 1 dimensional evolution and wave equations are studied it is shown how to favourably enhance the derivation of nonclassical symmetries for this class by an in depth prior study of the corresponding singular vector fields

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

a precise definition of reduction of partial differential equations we give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry classical and non classical reductions of partial differential equations using the introduced definition of reduction of differential equations we establish equivalence of the non classical conditional symmetry and direct ansatz approaches to reduction of partial differential equations as an illustration we give an example of non classical reduction of the nonlinear wave equation in 1 3 dimensions the conditional symmetry approach when applied to the equation in question yields a number of non lie reductions which are far reaching generalizations of the well known symmetry reductions of the nonlinear wave equations

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

second order cone programming approaches for handling missing and uncertain data we propose a novel second order cone programming formulation for designing robust classifiers which can handle uncertainty in observations similar formulations are also derived for designing regression functions which are robust to uncertainties in the regression setting the proposed formulations are independent of the underlying distribution requiring only the existence of second order moments these formulations are then specialized to the case of missing values in observations for both classification and regression problems experiments show that the proposed formulations outperform imputation

alternative second order cone programming formulations for support vector classification this paper presents two novel second order cone programming socp formulations that determine a linear predictor using support vector machines svms inspired by the soft margin svm formulation our first approach x socp svm proposes a relaxation of the conic constraints via a slack variable penalizing it in the objective function the second formulation r socp svm is based on the lp svm formulation principle the bound of the vc dimension is loosened properly using the l norm and the margin is directly maximized the proposed methods have several advantages the first approach constructs a flexible classifier extending the benefits of the soft margin svm formulation to second order cones the second method obtains comparable results to the socp svm formulation with less computational effort since one conic restriction is eliminated experiments on well known benchmark datasets from the uci repository demonstrate that our approach accomplishes the best classification performance compared to the traditional socp svm formulation lp svm and to standard linear svm

constructing conditionally integrable evolution systems in 1 1 dimensions a generalization of invariant modules approach given a generalized lie backlund vector field satisfying certain nondegeneracy assumptions we explicitly describe all 1 1 dimensional evolution systems that admit this vector field as a generalized conditional symmetry the connection with the theory of symmetries of systems of odes and with the theory of invariant modules is discussed

graphical perception theory experimentation and application to the development of graphical methods abstract the subject of graphical methods for data analysis and for data presentation needs a scientific foundation in this article we take a few steps in the direction of establishing such a foundation our approach is based on graphical perception the visual decoding of information encoded on graphs and it includes both theory and experimentation to test the theory the theory deals with a small but important piece of the whole process of graphical perception the first part is an identification of a set of elementary perceptual tasks that are carried out when people extract quantitative information from graphs the second part is an ordering of the tasks on the basis of how accurately people perform them elements of the theory are tested by experimentation in which subjects record their judgments of the quantitative information on graphs the experiments validate these elements but also suggest that the set of elementary tasks should be expanded the theory provides a guideline for graph construction

on form preserving point transformations of partial differential equations new identities are presented relating arbitrary order partial derivatives of and for the general point transformation these identities are used to study the nature of those point transformations which preserve the general form of a wide class of 1 1 partial differential equations these results facilitate the search for point symmetries both discrete and continuous lie and assist the search for point transformations which reduce equations to canonical but similar form a simple test for the existence of hodograph type transformations between equations of similar form is given

group analysis of general burgers korteweg de vries equations the complete group classification problem for the class of 1 1 dimensional rth order general variable coefficient burgers korteweg de vries equations is solved for arbitrary values of r greater than or equal to two we find the equivalence groupoids of this class and its various subclasses obtained by gauging equation coefficients with equivalence transformations showing that this class and certain gauged subclasses are normalized in the usual sense we reduce the complete group classification problem for the entire class to that for the selected maximally gauged subclass and it is the latter problem that is solved efficiently using the algebraic method of group classification similar studies are carried out for the two subclasses of equations with coefficients depending at most on the time or space variable respectively applying an original technique we classify lie reductions of equations from the class under consideration with respect to its equivalence group studying alternative gauges for eq

linear programming support vector machines abstract based on the analysis of the conclusions in the statistical learning theory especially the vc dimension of linear functions linear programming support vector machines or svms are presented including linear programming linear and nonlinear svms in linear programming svms in order to improve the speed of the training time the bound of the vc dimension is loosened properly simulation results for both artificial and real data show that the generalization performance of our method is a good approximation of svms and the computation complex is largely reduced by our method

group invariant solutions of differential equations we introduce the concept of a weak symmetry group of a system of partial differential equations that generalizes the nonclassical method introduced by bluman and cole for finding group invariant

new explicit solutions of quasilinear heat equations with general first order sign invariants abstract for the one dimensional quasilinear heat equations ut u uxx f u with smooth functions u 0 and f u we derive conditions under which a general quadratic hamilton jacobi operator h u ut h2 u ux 2 h1 u ux h0 u with the functions h2 h1 h0 to be determined preserves both the signs 0 and 0 on the solutions u x t h u is then called a sign invariant of the given parabolic equation several types of different sign invariants are established which are governed by a linear second order ordinary differential equations new explicit solutions via finite dimensional dynamical systems corresponding to zero preserving of the first order operator are constructed