fix points of meromorphic functions and iterated entire functions let f be a rational function of degree k and let g be a transcendental meromorphic function gross and osgood 13 proved that the composite function fog has infinitely many fix points if k 3 if k 2 then fog may have only a finite number of fix points and all such f and g have been characterized by gross and osgood there is a corresponding result for the case that f is a transcendental meromorphic function and that g is a polynomial in fact the two cases are closely connected since as pointed out by gross and yang 14 p 214 proof of theorem 23 fog has infinitely many fix points if and only if gof does this paper deals with the fix points offog wherefand g are both transcendental it has been proved in 6 that f 0 g has infinitely many fix points if f and g are entire this confirmed a conjecture of gross 111 there are a number of papers s 12 14 22 27 283 besides 6 dealing with fix points of fog for entire f and g but their methods do not seem to extend to the case of meromorphic f and in fact very little seems to be known about this case gross 1 l has asked whether fog has infinitely many fix points if f is transcendental and meromorphic and if g is transcendental and entire using some ideas from 6 we shall prove that this is indeed the case iffsatisfies a certain condition to be discussed afterward

two energy conserving numerical schemes for the sine gordon equation two explicit conservative numerical schemes for the sine gordon equation are proposed their stability and convergence are proved numerical simulation of a sine gordon soliton shows that the new schemes are very accurate and fast

a simple and accurate scheme based on complex space c to calculate boundary integrals of 2d boundary elements method abstract in this work a semi analytical algorithm is presented to calculate the boundary integrals of higher order which appear in boundary elements method bem in fact treating singularity and near singularity of the boundary integrals using complex space c is the main aim of this paper the integrals are computed for linear quadratic cubic and other higher order elements when the geometry of the boundary elements is curved the main advantages of the new algorithm are its applicability simplicity and high accuracy which enable the conventional higher order bem to solve poisson s problems accurately the potentials at the interior points very close to boundary can be evaluated by the scheme developed in this report some test problems are given and numerical simulations are presented numerical results demonstrate that the new algorithm proposed in the current paper can effectively handle singular and near singular boundary integrals of bem specially for solving partial differential equations which arise in thin body problems

normal families new perspectives this paper surveys some surprising applications of a lemma characterizing normal families of meromorphic functions on plane domains these include short and efficient proofs of generalizations of i the picard theorems ii gol dberg s theorem a meromorphic function on c which is the solution of a first order algebraic differential equation has finite order and iii the fatou julia theorem the julia set of a rational function of degree d 2 is the closure of the repelling periodic points we also discuss bloch s principle and provide simple solutions to some problems of hayman connected with this principle over twenty years ago on the way to a partial explication of the phenomenon known as bloch s principle i proved a little lemma characterizing normal families of holomorphic and meromorphic functions on plane domains 68 over the years the lemma has grown and in dextrous hands proved amazingly versatile with applications to a wide variety of topics in function theory and related areas with the renewed interest in normal families arising largely from the important role they play in complex dynamics it seems sensible to survey some of the most striking of these applications to the one variable theory with the aim of making this technique available to as broad an audience as possible that is the purpose of this report one pleasant aspect of the theory is that judicious application of the lemma often leads to proofs which seem almost magical in their brevity in such cases we have made no effort to resist the temptation to write out complete proofs hardly anything beyond a basic knowledge of function theory is required to understand what follows so the reader is urged to take courage and plough on through and now we turn to our tale 1 let d be a domain in the complex plane c we shall be concerned with analytic maps i e meromorphic functions f d r2 received by the editors october 15 1997 and in revised form may 26 1998 1991 mathematics subject classification primary 30d45 secondary 30d35 34a20 58f23

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

on factorization of certain entire functions abstract let p and q be polynomials and let be an entire function suppose that q and are nonconstant we show that the function h z p z e z q z has a factorization h z g z with nonlinear meromorphic left and right factors and g if and only if p q and have such a factorization with a common right factor this confirms conjectures of f gross g d song and c c yang

the solution of the two dimensional sine gordon equation using the method of lines the method of lines is used to transform the initial boundary value problem associated with the two dimensional sine gordon equation in two space variables into a second order initial value problem the finite difference methods are developed by replacing the matrix exponential term in a recurrence relation with rational approximants the resulting finite difference methods are analyzed for local truncation error stability and convergence to avoid solving the nonlinear system a predictor corrector scheme using the explicit method as predictor and the implicit as corrector is applied numerical solutions for cases involving the most known from the bibliography line and ring solitons are given

a semiparametric approach to canonical analysis summary classical canonical correlation analysis is one of the fundamental tools in statistics to investigate the linear association between two sets of variables we propose a method called semiparametric canonical analysis to generalize canonical correlation analysis to incorporate the important non linear association semiparametric canonical analysis is easy to implement and interpret statistical properties are proved a consistent estimation method is developed selection of significant semiparametric canonical analysis components is discussed simulations suggest that the methods proposed have satisfactory performance in finite samples one environmental data set and one data set in social science are investigated in which non linear canonical associations are observed and interpreted

spectral methods using legendre wavelets for nonlinear klein sine gordon equations klein sine gordon equations are very important in that they can accurately model many essential physical phenomena in this paper we propose a new spectral method using legendre wavelets as basis for numerical solution of klein sine gordon equations due to the good properties of wavelets basis the proposed method can obtain good spatial and spectral resolution moreover the presented method can save more memory and computation time benefit from save more computation time benefit from the hierarchical scale structure of legendre wavelets 1d and 2d examples are included to demonstrate the validity and applicability of the new technique numerical results show the exponential convergence property and error characteristics of presented method

remarks on functional canonical variates alternating least squares methods and ace we discuss properties of some data analytic methods which are intimately related to each other alternating least squares als correspondence analysis and more recently breiman and friedman s ace algorithm the application of these methods to regression produces nonparametric estimators of nonlinear transformations both of the response and the predictors we point out some anomalies as well as some curiosities in the mathematics of these methods and we relate them to some areas in computer aided tomography projection pursuit regression and nonlinear devices in the theory of noise

the use of continuous boundary elements in the boundary elements method for domains with non smooth boundaries via finite difference approach a numerical method is presented in this article to deal with the drawback of boundary elements method bem at corner points the use of continuous elements instead of the discontinuous ones has been recommended in the bem literature widely because of the simplicity and accuracy however the continuous elements lead to certain difficulties for problems where their domains contain corners in this paper the finite difference method fdm has been applied to obtain some constraints for boundary points near the corners to deal with this drawback because of its simplicity and capability the new scheme is applicable on bem problems for all geometries all governing equations and general boundary conditions easily since the dirichlet boundary condition is more critical than the other ones we will focus on it in the numerical implementation the numerical results show that the new treatment improves the accuracy of bem significantly

a boundary integral method for the three dimensional heat equation subject to specification of energy a boundary integral method is proposed for the numerical solution of the three dimensional heat equation subject to specification of energy a specific test problem is solved using the method

testing conditional independence using maximal nonlinear conditional correlation in this paper the maximal nonlinear conditional correlation of two random vectors x and y given another random vector z denoted by 1 x y z is defined as a measure of conditional association which satisfies certain desirable properties when z is continuous a test for testing the conditional independence of x and y given z is constructed based on the estimator of a weighted average of the form nz k 1 f z z k 2 1 x y z z k where f z is the probability density function of z and the z k s are some points in the range of z under some conditions it is shown that the test statistic is asymptotically normal under conditional independence and the test is consistent

solution of poisson s equation by analytical boundary element integration the solution of poisson s equation is essential for many branches of science and engineering such as fluid mechanics geosciences and electrostatics solution of two dimensional poisson s equations is carried out by bem based on galerkin vector method in which the integrals that appear in the boundary element method are expressed by analytical integration in this paper the galerkin vector method is developed for more general case than presented in the previous works the integrals are computed for constant and linear elements in bem by employing analytical integration in bem computation the numerical schemes and coordinate transformations can be avoided the presented method can also be used for the multiple domain case the results of the analytical integration are employed in bem code and the obtained analytical expression will be applied to several examples where the exact solution exists the produced results are in good agreement with the exact solution

kernel methods for measuring independence we introduce two new functionals the constrained covariance and the kernel mutual information to measure the degree of independence of random variables these quantities are both based on the covariance between functions of the random variables in reproducing kernel hilbert spaces rkhss we prove that when the rkhss are universal both functionals are zero if and only if the random variables are pairwise independent we also show that the kernel mutual information is an upper bound near independence on the parzen window estimate of the mutual information analogous results apply for two correlation based dependence functionals introduced earlier we show the kernel canonical correlation and the kernel generalised variance to be independence measures for universal kernels and prove the latter to be an upper bound on the mutual information near independence the performance of the kernel dependence functionals in measuring independence is verified in the context of independent component analysis

implementation of meshless lbie method to the 2d non linear sg problem in this paper the meshless local boundary integral equation lbie method for numerically solving the non linear two dimensional sine gordon sg equation is developed the method is based on the lbie with moving least squares mls approximation for the mls nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables the approximation functions are constructed entirely using a set of scattered nodes and no element or connectivity of the nodes is needed for either the interpolation or the integration purposes a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of method to deal with the unsteady non linear problems in large domains copyright 2009 john wiley sons ltd

canonical analysis relative to a closed subspace first a maximum coefficient notion between two real closed hilbertian subspaces relative to a third one is given many examples illustrate the study when the third subspace is trivial or not then a relative canonical analysis between two closed subspaces relative to a third one is introduced it leads to relative or partial association measures and allows a notion of relative information between subspaces

improvement of the accuracy in boundary element method based on high order discretization the boundary element method bem is a popular method to solve various problems in engineering and physics and has been used widely in the last two decades in high order discretization the boundary elements are interpolated with some polynomial functions these polynomials are employed to provide higher degrees of continuity for the geometry of boundary elements and also they are used as interpolation functions for the variables located on the boundary elements the main aim of this paper is to improve the accuracy of the high order discretization in the two dimensional bem in the high order discretization both the geometry and the variables of the boundary elements are interpolated with the polynomial function p m where m denotes the degree of the polynomial in the current paper we will prove that if the geometry of the boundary elements is interpolated with the polynomial function p m 1 instead of p m the accuracy of the results increases significantly the analytical results presented in this work show that employing the new approach the order of convergence increases from o l 0 m to o l 0 m 1 without using more cpu time where l 0 is the length of the longest boundary element the theoretical results are also confirmed by some numerical experiments

corner treatment by assigning dual tractions to every node for elastodynamics in td bem in this study a corner treatment on the boundary for time domain boundary element method td bem by assigning dual tractions to every node is proposed the proposed corner treatment on boundary mimics the real mechanical situation on the physical boundary for elastodynamic problem and the computation accuracy is good taking the rectangular boundary as an example the numerical implementation of the proposed corner treatment on boundary by assigning dual tractions to every node is demonstrated two verification examples one dimensional rod in finite medium and two dimensional circular cavity in infinite medium under dynamic loads are conducted in which the results from the td bem based on the proposed corner treatment on boundary are compared with the results from the analytical solutions good agreement between the analytical results and the td bem results based on the proposed corner treatment on boundary for td bem is achieved for the two verification examples

on uniqueness of numerical solution of boundary integral equations with 3 times monotone radial kernels the uniqueness of solution of boundary integral equations bies is studied here when geometry of boundary and unknown functions are assumed piecewise constant in fact we will show bies with 3 times monotone radial kernels have unique piecewise constant solution in this paper nonnegative radial function f 3 is introduced which has important contribution in proving the uniqueness it can be found from the paper if 3 is sufficiently small then eigenvalues of the boundary integral operator are bigger than f 3 2 note that there is a smart relation between 3 and boundary discretization which is reported in the paper clearly in this article an appropriate constant c 0 is found which ensures uniqueness of solution of bie with logarithmic kernel ln c 0 r as fundamental solution of laplace equation as a result an upper bound for condition number of constant galerkin bems system matrix is obtained when the size of boundary cells decreases the upper bound found depends on three important issues geometry of boundary size of boundary cells and the kernel function also non singular bies are proposed which can be used in boundary elements method bem instead of singular ones to solve partial differential equations pdes then singular boundary integrals are vanished from bem when the non singular bies are used finally some numerical examples are presented which confirm the analytical results

invariant conserving finite difference algorithms for the nonlinear klein gordon equation a formalism for systematicaiiy deriving second order accurate finite difference algorithms which conserve certain invariant quantities in the original nonlinear pdes is presented three algorithms are derived for the nonlinear klein gordon equation nlkge based on the proposed formalism the local conservation laws of the nlkge form the basic starting point in our derivation which hinges essentially on the commutativity of certain finite difference operators such commutativity in the discrete approximations allows a preservation of the derivation properties of the continuous counterparts at the pde level with appropriate boundary conditions the proposed algorithms preserve in the discrete sense either the total system energy or the system s linear momentum several variants of the present algorithms and their relation to previously proposed algorithms are discussed an analysis of the accuracy and stability is conducted to compare the different variants of the proposed algorithms the preservation of energy of the present algorithms for the nlkge can also be viewed as providing a method of stabilization for conditionally stable algo thms for the linear wave equation the computer impiementation of the proposed algorithms with the treatment of the boundary conditions is presented in detail numerical examples are given concerning soliton collisions in the sine gordon equation the double sine gordon equation and the cb phi four equation the numerical results demonstrate that the present algorithms can preserve accurately up to 10 decimal digits the total system energy for a very coarse grid reliable algorithms for josephson junction models which contain dissipation damping mechanisms and driving bias current are obtained as direct by products of the proposed invariant conserving algorithms for the nlkge even though presented mainly for the 1 d case the proposed algorithms are generalizable to the 2 d and 3 d cases and to the case of complex valued nlkge

kernel based nonlinear canonical analysis and time reversibility we consider a kernel based approach to nonlinear canonical correlation analysis and its implementation for time series we deduce a test procedure of the reversibility hypothesis the method is applied to the analysis of stochastic differential equation from high frequency data on stock returns

tensor products and statistics abstract a dictionary between operator based and matrix based languages in multivariate statistical analysis is proposed then this formulary is applied to asymptotic factorial analyses especially for giving asymptotic covariance matrices and operators in an explicit form finally we present the mathematical foundations on which are based the functional tools i e tensor products of linear spaces of vectors and of operators

high order implicit galerkin legendre spectral method for the two dimensional schrodinger equation abstract in this paper we propose galerkin legendre spectral method with implicit runge kutta method for solving the unsteady two dimensional schrodinger equation with nonhomogeneous dirichlet boundary conditions and initial condition we apply a galerkin legendre spectral method for discretizing spatial derivatives and then employ the implicit runge kutta method for the time integration of the resulting linear first order system of ordinary differential equations in complex domain we derive the spectral rate of convergence for the proposed method in the l 2 norm for the semidiscrete formulation numerical experiments show our formulation have high order accuracy

on the fixpoints of composite entire functions of finite order suppose that f and g are transcendental entire functions such that the composition f f g has finite order and suppose that q is a nonconstant rational function we show that n r 1 f q o t r f the theorem is related to results of bergweiler goldstein and others

on the fix points of composite transcendental entire functions a transcendental entire function f z is called composite iff f z f g z for some nonlinear entire functionsf and g a point z0 in the complex plane is called a fix point of f iff f z zo gross 3 conjectured that every composite transcendental entire function must have infinitely many fix points it has been shown thus far that the conjecture is valid for finite order entire functions by several authors e g z 4 71 via different approaches in a previous paper 111 we investigated the fixpoints of a certain type of infinite order composite entire function there it is required that g be an entire function of positive finite order with a finite nevanlinna exceptional value and f be an arbitrary entire function such that the hyperorder off g is less than the order of g in this note we shall treat some other class of composite entire functions the tools are as usual based on nevanlinna s theory of meromorphic functions and an elegant result due to steinmetz s corollary i our result is the following theorem

composite meromorphic functions and growth of the spherical derivative abstract let f and h be transcendental meromorphic and g a transcendental entire function it is shown that if h grows slower than g in a suitable sense then there exists an unbounded sequence zn such that f g zn h zn

expected conditional characteristic function based measures for testing independence we propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions the

composite bank laine functions and a question of rubel a bank laine function is an entire function e satisfying e z 1 at every zero of e we determine all bank laine functions of form e fog with f g entire further we prove that if h is a transcendental entire function of finite order then there exists a path tending to infinity on which h and all its derivatives tend to infinity thus establishing for finite order a conjecture of rubel

representations of solutions of periodic second order linear differential equations on considere l equation y g z y h z y 0 a coefficients entiers periodiques arbitraires g z et h z de periode 0 et des solutions y z ayant la propriete que l exposant de convergence de la suite nulle est finie

fixed points of composite meromorphic functions and normal families we show that there exists a function f meromorphic in the plane c such that the family of all functions g holomorphic in the unit disc d for which f g has no fixed point in d is not normal this answers a question of hinchliffe who had shown that this family is normal if f c does not consist of exactly one point in d we also investigate the normality of the family of all holomorphic functions g such that f g z h z for some non constant meromorphic function h

nonlinear principal components and long run implications of multivariate diffusions we investigate a method for extracting nonlinear principal components npcs these npcs maximize variation subject to smoothness and orthogonality constraints but we allow for a general class of constraints and multivariate probability densities including densities without compact support and even densities with algebraic tails we provide primitive sufficient conditions for the existence of these npcs by exploiting the theory of continuous time reversible markov diffusion processes we give a different interpretation of these npcs and the smoothness constraints when the diffusion matrix is used to enforce smoothness the npcs maximize long run variation relative to the overall variation subject to orthogonality constraints moreover the npcs behave as scalar autoregressions with heteroskedastic innovations this supports semiparametric identification and estimation of a multivariate reversible diffusion process and tests of the overidentifying restrictions implied by such a process from low frequency data we also explore implications for stationary possibly nonreversible diffusion processes finally we suggest a sieve method to estimate the npcs from discretely sampled data

meshless local petrov galerkin mlpg approximation to the two dimensional sine gordon equation during the past few years the idea of using meshless methods for numerical solution of partial differential equations pdes has received much attention throughout the scientific community and remarkable progress has been achieved on meshless methods the meshless local petrov galerkin mlpg method is one of the truly meshless methods since it does not require any background integration cells the integrations are carried out locally over small sub domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions in this paper the mlpg method for numerically solving the non linear two dimensional sine gordon sg equation is developed a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of proposed method to deal with the unsteady non linear problems in large domains

space time spectral method for the two dimensional generalized sine gordon equation abstract in this paper we propose a space time spectral method for solving the generalized two dimensional sine gordon equation with nonhomogeneous dirichlet boundary conditions and initial conditions the proposed method is based on the legendre galerkin spectral method in space and the spectral collocation method or block spectral collocation method in time we derive a priori error estimates in both l 2 and h 1 norms for the semidiscrete formulation our formulation has spectral accuracy in both space and time our numerical results confirm the exponential convergence of the proposed method in both space and time

the dual reciprocity boundary element method drbem for two dimensional sine gordon equation this paper presents the dual reciprocity boundary element method drbem for solving two dimensional sine gordon sg equation the integral equation formulation employs the fundamental solution of the laplace equation and hence a domain integral arises in the boundary integral equation furthermore the time derivatives are approximated by the time stepping method and the domain integral also appears from these approximations the domain integral is transformed into boundary integral by using the dual reciprocity method drm the linear radial basis function rbf is employed for drm the dynamics of line solitons and ring solitons of circular and elliptic shapes are studied numerical results are presented for some problems involving line and ring solitons to demonstrate the usefulness and accuracy of this approach

nonlinear canonical analysis and independence tests measures of association between two random variables r v that are symmetric nondecreasing functions of the canonical coefficients provided by the nonlinear canonical analysis of the r v s are studied these measures can be used to characterize independence their estimators are obtained by estimating a suitable approximation to nonlinear canonical analysis when some conditions ae satisfied asymptotic distributions of the estimators both under the independence hypothesis and under dependence are given a class of tests of independence with asymptotic level of significance can be investigated 1 introduction several measures of association between two random variables r v based on the canonical analysis of these r v s have been introduced in the literature and a review of such measures can be found in cramer and nicewander 1979 and lazraq and cleroux 1988 a general enough study of these measures is proposed in lin 1987 and more recently in dauxois and nkiet 1997 where a global study of the induced tests is developed in these works the measures considered are constructed using linear canonical analysis lca of the r v s and thus characterize only lack of a linear relationship it can be interesting to look for another class of measures of association which characterize independence the properties of nonlinear canonical analysis nlca suggest that such a class can be derived from this analysis but there is little work in this direction the canonical coefficients from nlca have already been used for testing independence but uniquely when the related random variables are categorical see for instance tsai and sen 1990 that is restrictive because one knows that in this particular case nlca is a lca of suitable random vectors and thus it suffices to use classical measures of association consequently it appears that the use of nlca is more interesting when the related random variables are not categorical in this paper we propose a class of measures of association between random variables with values in any measurable spaces constructed using symmetric nondecreasing functions and the canonical coefficients derived from nlca the properties of these measures show that they are appropriate to characterize independence without any assumption on the distribution of

a time stepping dual reciprocity boundary element method for anisotropic heat diffusion subject to specification of energy a two dimensional problem which requires determining the non steady temperature distribution in a thermally anisotropic body and a temperature control function on a certain part of the boundary of the body given that the total amount of heat energy in the body is known at all time is considered it is solved numerically using a time stepping dual reciprocity boundary element method numerical results are obtained for specific test problems

numerical solution of the sine gordon equation two new difference schemes are proposed for the sine gordon equation they have the advantage that there is a discrete energy which is conserved their stability and convergence is proved also we show some numerical computations using one of these schemes

consistent nonparametric tests of independence three simple and explicit procedures for testing the independence of two multi dimensional random variables are described two of the associated test statistics l1 log likelihood are defined when the empirical distribution of the variables is restricted to finite partitions a third test statistic is defined as a kernel based independence measure two kinds of tests are provided distribution free strong consistent tests are derived on the basis of large deviation bounds on the test statistics these tests make almost surely no type i or type ii error after a random sample size asymptotically level tests are obtained from the limiting distribution of the test statistics for the latter tests the type i error converges to a fixed non zero value and the type ii error drops to zero for increasing sample size all tests reject the null hypothesis of independence if the test statistics become large the performance of the tests is evaluated experimentally on benchmark data

dual reciprocity boundary element analysis of inverse heat conduction problems abstract this paper presents an application of the dual reciprocity boundary element method drbem to inverse heat conduction problems to deal with the ill posed nature of the problem iterative regularization methods of conjugate gradient type have been used preconditioned biconjugate pbcg method has been used for the solution if the discretized boundary element system has as many equations as the total number of unknowns preconditioned conjugate gradient pcg method has been utilized for the general case in which more equations are available than unknowns numerical results show that pbcg algorithm is useful only for inverse problems having unspecified boundary conditions on a small fraction of the boundary whereas the pcg algorithm works well for any problem flux estimates with both the methods are seen to be sensitive to the location of measurement points and measurement errors in contrast temperature estimates are very accurate nearly insensitive to measurement errors and only weakly sensitive to location of measurement points further constant elements work much better than the linear elements in terms of accuracy as well as stability of the numerical solution and should be preferred in drbe analysis of inverse heat conduction problems

dimensionality reduction by mixed kernel canonical correlation analysis in this paper we propose a novel method named mixed kernel cca mkcca to achieve easy yet accurate implementation of dimensionality reduction mkcca consists of two major steps first the high dimensional data space is mapped into the reproducing kernel hilbert space rkhs rather than the hilbert space with a mixture of kernels i e a linear combination between a local kernel and a global kernel meanwhile a uniform design for experiments with mixtures is also introduced for model selection second in the new rkhs kernel cca is further improved by performing principal component analysis pca followed by cca for effective dimensionality reduction we prove that mkcca can actually be decomposed into two separate components i e pca and cca which can be used to better remove noises and tackle the issue of trivial learning existing in cca or traditional kernel cca after this the proposed mkcca can be implemented in multiple types of learning such as multi view learning supervised learning semi supervised learning and transfer learning with the reduced data we show its superiority over existing methods in different types of learning by extensive experimental results