feature interaction in subspace clustering using the choquet integral subspace clustering has recently emerged as a popular approach to removing irrelevant and redundant features during the clustering process however most subspace clustering methods do not consider the interaction between the features this unawareness limits the analysis performance in many pattern recognition problems in this paper we propose a novel subspace clustering technique by introducing the feature interaction using the concepts of fuzzy measures and the choquet integral this new framework of subspace clustering can provide optimal subsets of interacted features chosen for each cluster and hence can improve clustering based pattern recognition tasks various experimental results illustrate the effective performance of the proposed method

analysis and solution of a nonlinear second order differential equation through rescaling and through a dynamical point of view the solutions of the equation y yy y3 0 where is a free parameter are investigated for 1 9 the equation is linearizable through an eight parameter symmetry group and is completely integrable for 1 9 only two symmetries subsist but through a dynamical description the analytical asymptotic solutions and their behavior are given according to the value of and according to the initial conditions

dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates an inhomogeneous layer element method is presented to analyze the dispersion of waves and characteristic wave surfaces in plates of functionally graded piezoelectric material fgpm in this method the fgpm plate is divided into a number of layered elements the elemental elastic and electric properties are assumed as linear functions of the thickness to adopt the variety of the material property of fgpm the hamilton principle is applied to determine the governing equations the phase velocity surface phase slowness surface phase wave surface group velocity surface group slowness surface and group wave surface for fgpm plate are formulated using rayleigh quotient and the orthogonality condition of the eigenvectors these six surfaces are then used to illustrate the characteristics of waves in fgpm plates numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in fgpm plates

symmetry and singularity properties of second order ordinary differential equations of lie s type iii abstract we extend the work of abraham shrauner b abraham shrauner hidden symmetries and linearization of the modified painleve ince equation j math phys 34 1993 4809 4816 on the linearization of the modified painleve ince equation to a wider class of nonlinear second order ordinary differential equations invariant under the symmetries of time translation and self similarity in the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations

type ii hidden symmetries through weak symmetries for nonlinear partial differential equations abstract the type ii hidden symmetries are extra symmetries in addition to the inherited symmetries of the differential equations when the number of independent and dependent variables is reduced by a lie point symmetry in b abraham shrauner k s govinder provenance of type ii hidden symmetries from nonlinear partial differential equations j nonlinear math phys 13 2006 612 622 abraham shrauner and govinder have analyzed the provenance of this kind of symmetries and they developed two methods for determining the source of these hidden symmetries the lie point symmetries of a model equation and the two dimensional burgers equation and their descendants were used to identify the hidden symmetries in this paper we analyze the connection between one of their methods and the weak symmetries of the partial differential equation in order to determine the source of these hidden symmetries we have considered the same models presented in b abraham shrauner k s govinder provenance of type ii hidden symmetries from nonlinear partial differential equations j nonlinear math phys 13 2006 612 622 as well as the wdvv equations of associativity in two dimensional topological field theory which reduces in the case of three fields to a single third order equation of monge ampere type we have also studied a second order linear partial differential equation in which the number of independent variables cannot be reduced by using lie symmetries however when is reduced by using nonclassical symmetries the reduced partial differential equation gains lie symmetries

on the use of computational intelligence in the optimal shape control of functionally graded smart plates functionally graded material fgm plates are an essential component for most advanced integrated systems in terms of vibration and acoustic controls or condition monitoring in general these fgm plates are designed with embedded piezoelectric sensors and actuators to achieve their shape control this optimal control problem is normally required to find appropriate actuator voltage and displacement control gains that will generate the desired shape such an optimal control problem is known to be highly non linear and often posses slope and functional discontinuity that will limit the efficiency of the gradient based methods stochastic zero order population based optimization methods are ideal for solving this class of problems in this paper we introduce a stochastic zero order optimization algorithm based on the principles of learning this algorithm is embedded with three key learning strategies that control who to learn from i e leader identification and leader selection and what to learn i e information acquisition to reach a common goal the leader identification mechanism partitions the individuals into a set of leaders and a set of followers the followers interact with the leaders and move toward the better performing leaders in searching for better solutions the parameter free algorithm provides the designer with the true flexibility that is necessary to handle various forms of design problem effectively and at a computational cost that is comparable to existing stochastic optimization methods in this study numerical results are presented for the shape control of the fgm plates under a temperature gradient by optimizing i the voltage distribution for the open loop control and ii the displacement control gain values for the closed loop feedback control we also examine the effect of the constituent volume fractions of zirconia through the varying of volume fraction exponent n on the optimal voltages and gain values

symmetries of nonlinear differential equations and linearisation a non linear ordinary differential equation is linearisable if it possesses sl 3 r symmetry the conditions under which the abelian two dimensional subalgebras of sl 3 r are sufficient for linearisation are established

hidden and contact symmetries of ordinary differential equations the lie algebra for the maximal contact symmetries of third order ordinary differential equations odes is examined for type i and ii hidden symmetries where the analysis of hidden symmetries for point symmetries is extended to contact symmetries ones invariant under the group associated with the ten dimensional maximal lie algebra may produce type i hidden symmetries for two parameter subgroups and type ii hidden symmetries for certain solvable non abelian three parameter subgroups in the third order odes when they are reduced in order a new class of type ii hidden symmetries is recognized in which contact symmetries transform to point symmetries in some reduction paths two examples of odes invariant under subgroups of the ten parameter group under which y 0 is invariant demonstrate the new class of type ii hidden symmetries

a group theoretical identification of integrable cases of the lienard type equation x f x x g x 0 i equations having nonmaximal number of lie point symmetries we carry out a detailed lie point symmetry group classification of the lienard type equation x f x x g x 0 where f x and g x are arbitrary smooth functions of x we divide our analysis into two parts in the present first part we isolate equations that admit lesser parameter lie point symmetries namely one two and three parameter symmetries and in the second part we identify equations that admit maximal eight parameter lie point symmetries in the former case the invariant equations form a family of integrable equations and in the latter case they form a class of linearizable equations under point transformations further we prove the integrability of all the equations obtained in the present paper through equivalence transformations either by providing the general solution or by constructing time independent hamiltonians several of these equations are being identified for the first time from the group theoretical analysis

response of a multi layered infinite plate to an oblique plane wave by means of transfer matrices starting with the basic equations connecting the state variables of normal stress shear stress tangential velocity and normal velocity a transfer matrix for a solid plate has been derived it has been shown that for the limiting case of normal excitation tangential wave number equalling zero this matrix yields a juxtaposition of the uncoupled 2 2 matrices corresponding to the normal longitudinal waves and transverse shear waves the general transfer matrix relation has been used with the boundary conditions of zero shear stress and appropriate radiation loading on the two exposed surfaces to evaluate the response of the plate to a given external pressure excitation on one of the faces the resulting expressions tally exactly with those available in the literature a method has been indicated for evaluation of the overall transfer matrix of a compound wall by incorporating the transfer matrix of a damping layer as a possible constituent of the wall expressions for the overall reflection transmission and absorption of the acoustic power of the obliquely incident plane wave have been obtained in terms of the overall transfer matrix parameters of the compound wall

a new nonlinear classifier with a penalized signed fuzzy measure using effective genetic algorithm this paper proposes a new nonlinear classifier based on a generalized choquet integral with signed fuzzy measures to enhance the classification accuracy and power by capturing all possible interactions among two or more attributes this generalized approach was developed to address unsolved choquet integral classification issues such as allowing for flexible location of projection lines in n dimensional space automatic search for the least misclassification rate based on choquet distance and penalty on misclassified points a special genetic algorithm is designed to implement this classification optimization with fast convergence both the numerical experiment and empirical case studies show that this generalized approach improves and extends the functionality of this choquet nonlinear classification in more real world multi class multi dimensional situations

finite elements for functionally graded reissner mindlin plates abstract equations governing the behavior of rectangular plates made of functionally graded materials fgms are determined in this paper using the variational approach derivation of such equations is based on reissner mindlin plate theory that is extended to handle two constituent material distribution through the thickness material properties are assumed to vary with the power law in terms of the volume fractions of the constituent within a static analysis framework the main focus of the paper is the proposal of a locking free hierarchic family of finite elements that is numerically tested on plates of different material grading convergence and stability properties of our approach are assessed and comparisons with available solutions presented

analytical solutions for single and multi span functionally graded plates in cylindrical bending abstract a recently developed plate theory using the concept of shape function of the transverse coordinate parameter is extended to determine the stress distribution in an orthotropic functionally graded plate subjected to cylindrical bending the transfer matrix method is presented to derive the shape function the equations governing the plate deformation are then solved analytically using the transfer matrix method for arbitrary boundary conditions for a simply supported functionally graded plate a comparison of the present solution with the exact elasticity solution the first and third order shear deformation plate theories is presented and discussed it is demonstrated that the present method yields more accurate stresses than the first and third order shear deformation theories the effect of boundary conditions and inhomogeneity of material on the displacements and stresses in functionally graded plates are investigated a multi span functionally graded plate with arbitrary boundary conditions is further considered to demonstrate the efficiency of the present method

autonomous self similar ordinary differential equations and the painleve connection we demonstrate an intimate connection between nonlinear higher order ordinary differential equations possessing the two symmetries of autonomy and self similarity and the leading order behaviour and resonances determined in the application of the painleve test similar behaviour is seen for systems of first order differential equations several examples illustrate the theory in an integrable case of the abc system the singularity analysis reveals a positive and a negative resonance and the method of leading order behaviour leads naturally to a laurent expansion containing both

equivalence classes of second order ordinary differential equations with only a three dimensional lie algebra of point symmetries and linearisation there are seven equivalence classes of second order ordinary differential equations possessing only three lie point symmetries and hence not linearisible by means of a point transformation we examine the representatives of these classes for linearisibility by means of other types of transformation in particular we compare the potential for linearisibility and the possession of the painleve property the complete symmetry group is realised in the standard algebra for each of the equivalence classes

invariance of second order ordinary differential equations under two dimensional affine subalgebras of ermakov pinney lie algebra abstract using the only admissible rank two realisations of the lie algebra of the affine group in one dimension in terms of the lie algebra of lie symmetries of the ermakov pinney ep equation some classes of second order nonlinear ordinary differential equations solvable by reduction method are constructed one class includes the standard ep equation as a special case a new ep equation with a perturbed potential but admitting the same solution formula as ep itself arises the solution of the dissipative ep equation is also discussed

a fifth order differential equation for charged perfect fluids we investigate the master nonlinear partial differential equation that governs the evolution of shear free spherically symmetric charged fluids we use an approach which has not been considered previously for the underlying equation in shear free spherically symmetric spacetimes we derive a fifth order purely differential equation that must be satisfied for the underlying equation to admit a lie point symmetry we then perform a comprehensive analysis of this equation utilising the lie symmetry analysis and direct integration this enables us to reduce the fifth order equation to quadratures earlier results are shown to be contained in our general treatment

nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order in this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations odes of arbitrary order related to linear odes through nonlocal relations the procedure makes use of the lie point symmetries of the linear odes and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear odes using these nonlocal symmetries we obtain reduction transformations and reduced equations to specific examples we find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases we also extend this procedure to coupled higher order nonlinear odes with specific reference to second order nonlinear odes

exponential nonlocal symmetries and nonnormal reduction of order the conventional approach to double reduction of the order of an ordinary differential equation using lie symmetries is via the normal subgroups of point symmetries we show that provided that one is prepared to use nonlocal symmetries initial reduction by the nonnormal subgroup does not prevent the double reduction we further illustrate our results with the general third order equations invariant under the nonsolvable algebras sl 2 r of which the chazy equation is a noted example and so 3

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

orthotropic influence on frequency characteristics of a rotating composite laminated conical shell by the generalized differential quadrature method by using the generalized differential quadrature gdq method this paper presents the influence of orthotropic material on the frequency characteristics for a rotating thin truncated circular symmetrical cross ply laminated composite conical shell with simply supported boundary conditions at both edges the present analysis includes the effects of initial hoop tension and the centrifugal and coriolis accelerations due to rotation frequency characteristics is obtained for various orthotropic parameters the orthotropic influences of material on the frequency characteristics are also discussed for different cone angles to validate the accuracy and efficiency of present analysis by the gdq method comparisons are made with those available in open literature very good agreements are achieved

on the determination of non local symmetries the importance of non local symmetries of differential equations lies in their manifestation as lie point symmetries of the equations resulting from reduction of order the reason for the determination of these symmetries in second order equations with only one lie point symmetry is self evident however the disadvantage of non local symmetries is that no systematic approach to their determination exists we present such an approach applicable to differential equations of any order and apply it to some second order ordinary differential equations and show that they have a rich occurrence we also look at possible generalizations of the concept of non local symmetries

type ii hidden symmetries of the linear 2d and 3d wave equations type ii hidden symmetries of the linear two dimensional and three dimensional wave equations are analysed these hidden symmetries are lie point symmetries that appear in addition to the inherited point symmetries when the number of independent and dependent variables of a partial differential equation is reduced by a lie point symmetry the provenance of these hidden symmetries of partial differential equations is identified to be the same as found recently for some nonlinear partial differential equations the appearance of type ii hidden symmetries depends not only on the lie symmetries used but on the order in which the symmetries are applied the presence of type ii hidden symmetries of partial differential equations complicates the prediction of symmetry reductions based on the lie algebra associated with the original lie point symmetries

on the properties of a variant of the riccati system of equations a variant of the generalized riccati system of equations is considered it is shown that for 2n 3 the system admits a bilagrangian description and the dynamics has a node at the origin whereas for much smaller than a critical value the dynamics is periodic the origin being a centre it is found that the solution changes from being periodic to aperiodic at a critical point which is independent of the initial conditions this behaviour is explained by finding a scaling argument via which the phase trajectories corresponding to different initial conditions collapse onto a single universal orbit numerical evidence for the transition is shown further using a perturbative renormalization group argument it is conjectured that the oscillator exhibits isochronous oscillations the correctness of the conjecture is established numerically

eigenfrequencies of line supported rectangular plates abstract a set of series consisting of a combination of free vibrating beam functions and polynomials is used as the admissible functions in the rayleigh ritz method to study the problem of the flexural vibration of thin uniform thickness orthotropic rectangular plates which may be continuous over several supports in one or two directions in practice which kind of free vibrating beam functions are used is determined by the boundary conditions of the plate the starting order of the beam eigenfunctions and the number of terms in the polynomials in each direction depend on the number of intermediate line supports in that direction the coefficients of the polynomials are decided by the boundary conditions of the plate and the locations of the line supports some numerical results are given for the simply supported and or clamped rectangular plates with two and three spans in one and two directions it is demonstrated that the method may be used to tackle such plate problems and has considerable accuracy and fast convergence compared with the available results the difficulty of application not being greater than any other methods

exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates we use reddy s third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a winkler pasternak elastic foundation and subjected to uniform in plane hydrostatic loads young s modulus and the poisson ratio for the material of the plate are assumed to vary only in the thickness direction effects of rotary inertia are considered the problem of determining the critical buckling load or the vibration frequency of the plate is found to be analogous to that of ascertaining the frequency of a membrane clamped at the edges and whose shape coincides with that of the plate the critical buckling load and the vibration frequency are shown to be positive some available results for plates symmetric about the mid plane can be retrieved from the present analysis

the general problem of elastic wave propagation in multilayered anisotropic media exact analytical treatment of the interaction of harmonic elastic waves with n layered anisotropic plates is presented each layer of the plate can possess up to as low as monoclinic symmetry and thus allowing results for higher symmetry materials such as orthotropic transversely isotropic cubic and isotropic to be obtained as special cases the wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle solutions are obtained by using the transfer matrix method according to this method formal solutions for each layer are derived and expressed in terms of wave amplitudes by eliminating these amplitudes the stresses and displacements on one side of the layer are related to those of the other side by satisfying appropriate continuity conditions at interlayer interfaces a global transfer matrix can be constructed which relates the displacements and stresses on one side of the plate to those on the other invoking appropriate boundary conditions on the plates outer boundaries a large variety of important problems can be solved of these mention is made of the propagation of free waves on the plate and the propagation of waves in a periodic media consisting of a periodic repetition of the plate confidence is the approach and results are confirmed by comparisons with whatever is available from specialized solutions a variety of numerical illustrations are included

symmetry lie algebras of nth order ordinary differential equations abstract we show that an nth n 3 order linear ordinary differential equation has exactly one of n 1 n 2 or n 4 the maximum point symmetries the lie algebras corresponding to the respective numbers of point symmetries are obtained then it is shown that a necessary and sufficient conditon for an nth n 3 order equation to be linearizable via a point transformation is that it must admit the n dimensional abelian algebra na1 a1 a1 a1 we discuss in detail the symmetry realizations of n 1 a1 s a1 finally we prove that an nth n 3 order equation q n h t q qn 1 cannot admit exactly an n 3 dimensional algebra of point symmetries which is a subalgebra of na1 gl 2 r

hidden symmetries and linearization of the modified painleve ince equation the linearization and hidden symmetries of the modified painleve ince equation y yy y3 0 where and are constants are presented the linearization of this equation by a nonlocal transformation yields a damped stable or growing unstable harmonic oscillator equation for 0 hidden symmetries are analyzed by transforming the modified painleve ince equation to a third order ordinary differential equation ode which in general is invariant under a three parameter group by a riccati transformation a type i hidden symmetry is found of a second order ode found from the third order ode where a symmetry is lost in the reduction of order by the non normal subgroup invariants a type ii hidden symmetry occurs in the third order ode because the symmetries of a second order ode reduced from the third order ode by another set of normal subgroup invariants are increased

hidden symmetries associated with the projective group of nonlinear first order ordinary differential equations hidden symmetries those not found by the classical lie group method for point symmetries are reported for nonlinear first order ordinary differential equations odes which arise frequently in physical problems these are for the special class of the eight nonabelian two parameter subgroups of the eight parameter projective group the first order odes can be transformed by non local transformations to new separable first order odes which then can be reduced to quadratures the first order odes include riccati equations and equations which in particular cases are of the form of abel s equation the procedure demonstrates the feasibility of integrating nonlinear odes that do not show any apparent lie group point symmetry applications to the vlasov characteristic equation and the reaction diffusion equation are given

symmetries of first integrals and their associated differential equations the relationship between the reduction of order through point symmetries and integration is explored with particular emphasis on the loss and gain of point contact for third order symmetries to and from nonlocal symmetries it is seen that reduction of order can even lead to the loss of all point symmetries at the third order level and their replacement at the second order level from nonlocal symmetries it is evident that nonlocal symmetries should be given more attention in applications

generating functions and existence of contact symmetries of third order scalar ordinary differential equations analyzing the structure of generating functions associated to the contact symmetry condition of third order scalar ordinary differential equations constraints guaranteeing that the ode does not admit contact symmetries are obtained further inspecting the subalgebras generated by contact symmetries having a specific form an alternative procedure to generate third order equations with irreducible contact symmetry algebra sp 4 is developed

fuzzy posterior probabilistic fusion the paradigm of the permanence of updating ratios which is a well proven concept in experimental engineering approximation has recently been utilized to construct a probabilistic fusion approach for combining knowledge from multiple sources this ratio based probabilistic fusion however assumes the equal contribution of attributes of diverse evidences this paper introduces a new framework of a fuzzy probabilistic data fusion using the principles of the permanence of ratios paradigm and the theories of fuzzy measures and fuzzy integrals the fuzzy sub fusion of the proposed approach allows an effective model for incorporating evidence importance and interaction

an optimization algorithm for clustering using weighted dissimilarity measures one of the main problems in cluster analysis is the weighting of attributes so as to discover structures that may be present by using weighted dissimilarity measures for objects a new approach is developed which allows the use of the k means type paradigm to efficiently cluster large data sets the optimization algorithm is presented and the effectiveness of the algorithm is demonstrated with both synthetic and real data sets

symmetry and singularity properties of a system of ordinary differential equations arising in the analysis of the nonlinear telegraph equations we investigate the symmetry and similarity properties of a system of equations arising in the analysis of the nonlinear telegraph equations the system of two equations can be decoupled and integrated although one of equations is linear in one of the dependent variables we are able to perform successfully a singularity analysis we are able to interpret the results of the singularity analysis in terms of the possibility of the existence of a subsidiary solution

lie symmetries for lie systems a lie system is a nonautonomous system of first order differential equations admitting a superposition rule i e a map expressing its general solution in terms of a generic family of particular solutions and some constants using that a lie system can be considered as a curve in a finite dimensional lie algebra of vector fields a so called vessiot guldberg lie algebra we associate every lie system with a lie algebra of lie point symmetries induced by the vessiot guldberg lie algebra this enables us to derive lie symmetries of relevant physical systems described by first and higher order systems of differential equations by means of lie systems in an easier way than by standard methods a generalization of our results to partial differential equations is introduced among other applications lie symmetries for several new and known generalizations of the real riccati equation are studied

first integrals for the modified emden equation q α t q qn 0 it is shown that the modified emden equation q t q qn 0 possesses first integrals for functions t other than kt 1 the function t is obtained explicitly in the case n 3 and parametrically for other n 2 the case n 2 is seen to be particularly difficult to solve