analysis of a darcy flow model with a dynamic pressure saturation relation we consider a new model for groundwater flow the model differs from previous models in that the saturation pressure relation is extended with a dynamic term namely the time derivative of the saturation the resulting model equation is of nonlinear degenerate pseudoparabolic type we give a rigorous analysis of travelling wave solutions and the local behavior near fronts part of this analysis is then used in a formal asymptotic analysis of solutions with initial support in a half line as an illustrative special case we also consider heaviside initial data

a linear time algorithm for obtaining the convex hull of a simple polygon in this paper a linear time algorithm is described for finding the convex hull of a simple i e non self intersecting polygon

boundary control for a class of pseudo parabolic differential equations abstract the boundary stabilization problem for a class of linear and nonlinear pseudo parabolic differential equations is considered the proposed control laws are used to achieve global exponential stability for the linear system and semi global exponential stability for the nonlinear system in the h 1 sense an h 2 bound of the solution for the nonlinear system is also derived a numerical example is included to illustrate the application of the proposed control laws

sorted random projections for robust rotation invariant texture classification this paper presents a simple novel yet very powerful approach for robust rotation invariant texture classification based on random projection the proposed sorted random projection maintains the strengths of random projection in being computationally efficient and low dimensional with the addition of a straightforward sorting step to introduce rotation invariance at the feature extraction stage a small set of random measurements is extracted from sorted pixels or sorted pixel differences in local image patches the rotation invariant random features are embedded into a bag of words model to perform texture classification allowing us to achieve global rotation invariance the proposed unconventional and novel random features are very robust yet by leveraging the sparse nature of texture images our approach outperforms traditional feature extraction methods which involve careful design and complex steps we report extensive experiments comparing the proposed method to six state of the art methods rp patch lbp wmfs and the methods of lazebnik et al and zhang et al in texture classification on five databases curet brodatz uiuc umd and kth tips our approach leads to significant improvements in classification accuracy producing consistently good results on each database including what we believe to be the best reported results for brodatz umd and kth tips

the richards equation with hysteresis and degenerate capillary pressure abstract we study the richards equation with a dynamic capillary pressure including hysteresis we provide existence and approximation results for degenerate capillary pressure curves p c treating two cases in the first case the permeability function k can be degenerate but the initial saturation does not take the critical values in the second case the permeability function k is strictly positive but the capillary pressure function can be multi valued in both cases the degenerate behavior of p c leads to the physically desired uniform bounds for the saturation variable our approach exploits maximum principles and relies on the corresponding uniform bounds for pressure and saturation a new compactness result for the saturation variable allows to take limits in nonlinear terms the solution concept uses tools of convex analysis

soft clustering using weighted one class support vector machines this paper describes a new soft clustering algorithm in which each cluster is modelled by a one class support vector machine oc svm the proposed algorithm extends a previously proposed hard clustering algorithm also based on oc svm representation of clusters the key building block of our method is the weighted oc svm woc svm a novel tool introduced in this paper based on which an expectation maximization type soft clustering algorithm is defined a deterministic annealing version of the algorithm is also introduced and shown to improve the robustness with respect to initialization experimental results show that the proposed soft clustering algorithm outperforms its hard clustering counterpart namely in terms of robustness with respect to initialization as well as several other state of the art methods

remarks on the stability of shock profiles for conservation laws with dissipation two remarks are made the first is to establish the stability of monotone shock profiles of the kdv burgers equation based on an energy method of goodman the second remark illustrates specifically in burgers equation that uniform rates of decay are not to be expected for perturbations of shock profiles in typical norms introduction we will prove two results the first is to establish the orbital stability of monotone shock profile solutions 4 x st of the kdv burgers equation 1 1 ut uux uxx uxxx 0 0 the second is to show that for shock profile solutions of viscous conservation laws and specifically for burgers equation 1 2 ut uux uxx one cannot expect perturbations to decay at any uniform rate algebraic or otherwise in ordinary norms such as lp the first result is related to goodman s conditional stability result in 5 for small amplitude shock profiles x st in systems of genuinely nonlinear conservation laws with viscosity u f u x buxx u e rm the second is intended to be relevant to the question of full stability for shock profiles of such systems the nonlinear stability to small perturbations of constant state solutions u0 x c of the system u f u x b u ux x where b c is a strictly stable viscosity matrix see 9 can be demonstrated based on a uniform rate of decay of solutions to the linearized equation the method used is similar to that developed in 8 and 10 for systems in n 1 space dimensions faster decay rates in higher space dimensions make the method easier to apply when n is large but it does just work for conservation laws with stable viscosities in one space dimension see 13 thus for example assuming c 0 if iiuo iih6 ll is sufficiently small then iiu t llh4 ct 1 4iiuoii h4 n la in this note we want to point out that such uniform decay rates cannot be valid for perturbations of shock profiles in particular for the shock profile solution of burgers equations we construct a family of perturbations which decay to zero but do so at no uniform rate in most ordinary norms including all lp norms thus for received by the editors october 15 1984 and in revised form december 19 1984 1980 mathematics subject classification primary 35q20 35l65 1985 american mathematical society 0002 9947 85 1 00 25 per page

selective ensemble of svdds with renyi entropy based diversity measure abstract in this paper a novel selective ensemble strategy for support vector data description svdd using the renyi entropy based diversity measure is proposed to deal with the problem of one class classification in order to obtain compact classification boundary the radius of ensemble is defined as the inner product of the vector of combination weights and the vector of the radii of svdds to make the center of ensemble achieve the optimal position the renyi entropy of the kernelized distances between the images of samples and the center of ensemble in the high dimensional feature space is defined as the diversity measure moreover to fulfill the selective ensemble an l 1 norm based regularization term is introduced into the objective function of the proposed ensemble the optimal combination weights can be iteratively obtained by the half quadratic optimization technique experimental results on two synthetic data sets and twenty benchmark data sets demonstrate that the proposed selective ensemble method is superior to the single svdd and the other four related ensemble approaches

general support vector representation machine for one class classification of non stationary classes novelty detection also referred to as one class classification is the process of detecting abnormal behavior in a system by learning the normal behavior novelty detection has been of particular interest to researchers in domains where it is difficult or expensive to find examples of abnormal behavior such as in medical equipment diagnosis and it network surveillance effective representation of normal data is of primary interest in pursuing one class classification while the literature offers several methods for one class classification very few methods can support representation of non stationary classes without making stringent assumptions about the class distribution this paper proposes a one class classification method for non stationary classes using a modified support vector machine and an efficient online version for reducing computational time the presented method is applied to several simulated datasets and actual data from a drilling machine in addition we present comparison results with other methods that demonstrate its superior performance

a new maximum margin algorithm for one class problems and its boosting implementation in this paper each one class problem is regarded as trying to estimate a function that is positive on a desired slab and negative on the complement the main advantage of this viewpoint is that the loss function and the expected risk can be defined to ensure that the slab can contain as many samples as possible inspired by the nature of svms the intuitive margin is also defined as a result a new linear optimization problem to maximize the margin and some theoretically motivated learning algorithms are obtained moreover the proposed algorithms can be implemented by boosting techniques to solve nonlinear one class classifications

the buckley leverett equation with dynamic capillary pressure the buckley leverett equation for two phase flow in a porous medium is modified by including dependence of the capillary pressure on the rate of change of saturation this model due to hassanizadeh and gray results in a nonlinear pseudoparabolic partial differential equation phase plane analysis including a separation function to measure the distance between invariant manifolds is used to determine when the equation supports traveling waves corresponding to undercompressive shocks the riemann problem for the underlying conservation law is solved and the structures of the various solutions are confirmed with numerical simulations of the partial differential equation

a model problem for groundwater flow with dynamic capillary pressure stability of travelling waves modelling vertical nonsteady groundwater flow with dynamic capillary pressure leads to a nonlinear diffusion convection equation extended with a nonlinear third order term with two space derivatives and one time derivative we consider the special case in which the original equation is the burgers equation and the third order term is linear we investigate stability of travelling wave solutions of the resulting pseudo parabolic burgers equation for which we first obtain well posedness results

remarks on the gauss quadrature rule for a particular class of finite part integrals the method of finite part hadamard type or hypersingular integrals is already a standard approach in applied numerical methods in engineering and mainly in acoustics fluid dynamics elasticity and fracture mechanics here we study the convergence of the non classical possessing a negative node outside the integration interval as well as a negative weight corresponding to this node gauss legendre quadrature rule for finite part integrals on the interval 0 1 with the weight function 1 y and we prove its validity for integrands possessing a continuous first derivative the case of integrands possessing a higher order derivative is also considered and the rate of convergence is established these results are based on the derivation of a bound for the negative node in the above quadrature rule and further on the theory of convergence of the classical gauss quadrature rule numerical results verifying the results of this paper are also displayed the present results can be generalized to the gauss laguerre similarly non classical quadrature rule for finite part integrals on the interval 0 as well as to the two special but important in engineering applications non classical gaussian quadrature rules for cauchy type principal value integrals and mangler type finite part integrals have been proposed by tsamasphyros and dimou

indirect finite element evaluation of two dimensional finite part integral using fourier transformation a broad class of engineering problems in fracture mechanics thermal fluid transport and electromagnetic theory involve the evaluation of two dimensional finite part integrals of the form a method for evaluation of such integrals is developed by deriving an equivalent integral using fourier transformation this equivalent integral does not involve a kernel with singular behaviour consequently standard numerical integration methodologies with conventional analytical evaluation techniques can be used in the finite element computations the accuracy and convergence of the developed numerical procedure are successfully demonstrated by numerical examples for planar fracture geometries

the gradient of the finite element variational indicator with respect to nodal and applications in fracture mechanics and mesh optimization we derive a closed form expression for the change in the variational indicator of a finite element mesh with respect to perturbations in nodal point co ordinates the expression is evaluated very effectively from standard finite element data obtained in one solution and may be easily programmed as part of a general finite element code we present the derivation for two and three dimensional isoparametric elements used in linear and nonlincar elasticity the expression has practical applications in the computation of stress intensity factors in fracture mechanics and in the determination of the optimal mesh with a given element node connectivity we demonstrate both applications by accurately determining the stress intensity factor of a mode i crack using a finite element mesh which was improved using mesh optimization

a global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure in this paper we investigate the pseudoparabolic equation tc div k c pc c c tc g en where is a positive constant c is the moisture content k is the hydraulic conductivity and pc is the static capillary pressure this equation describes unsaturated flows in porous media with dynamic capillary pressure saturation relationship in general such models arise in a number of cases when non equilibrium thermodynamics or extended non equilibrium thermodynamics are used to compute the flux for this equation existence of the traveling wave type solutions was extensively studied nevertheless the existence seems to be known only for the non degenerate case when k is strictly positive we use the approach from statistical hydrodynamics and construct the corresponding entropy functional for the regularized problem such approach permits to get existence for any time interval of an appropriate weak solution with square integrable first derivatives in x and in t and square integrable time derivative of the gradient negative part of such weak solution is small in l2 norm with respect to x uniformly in time as the square root of the relative permeability at the value of the regularization parameter next we control the regularized entropy a fine balance between the regularized entropy and the degeneracy of the capillary pressure permits to get an lq uniform bound for the time derivative of the gradient these estimates permit passing to the limit when the regularization parameter tends to zero and obtaining the existence of global nonnegative weak solution

derivation of a new analytical solution for a general two dimensional finite part integral applicable in fracture mechanics an exact expression is derived for the general finite part integral over an inclined ellipticaldomain r denotes the distance of a point in to the singular point is a general function of the cartesian co ordinates x0 y0 the boundary of the region represents the equation z x0 y0 o these integrals appear during the numerical solution of plane crack problems in three dimensional elasticity where they are the dominant part of a hypersingular integral equation the availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and simultaneously lead to quicker numerical results the considered finite part integral can be expressed in closed form as function of complete elliptical integrals or gauss hypergeometric functions respectively formuias for special cases and some i j values and their numerical verification are given in appendices ii and iii

numerical solution of three dimensional crack problem by using hypersingular integral equation in this paper a flat crack with the normal boundary loading on the crack face is embedded in an infinite medium the relevant problem is called the three dimensional crack problem hereafter the hypersingular integral equation is used to solve the mentioned problem two innovative points are suggested in this paper a the involved hypersingular integrals are evaluated in a polar coordinate system and are converted to the repeated integrals b one of the repeated integral is hypersingular and the involved integrated function is approximated by a product of the weight function and chebyshev polynomials the hypersingular integrals can be evaluated numerically by using a known result therefore the hypersingular integral equation for the three dimensional crack problem can be solved immediately finally numerical examples are given to demonstrate the efficiency of the suggested approach

oscillatory instability of traveling waves for a kdv burgers equation the stability of traveling wave solutions of a generalization of the kdv burgers equation o u u p o u 03u a o u is studied as the parameters p and a are varied the eigenvalue problem for the linearized evolution of perturbations is analyzed by numerically computing evans function d a an analytic function whose zeros correspond to discrete eigenvalues in particular the number of unstable eigenvalues in the complex plane is evaluated by computing the winding number of d a analytical and numerical evidence suggests that a hopf bifurcation occurs for oscillatory traveling wave profiles in certain parameter ranges dynamic simulations suggest that the bifurcation is subcritical no stable time periodic solution is found

generalized nonequilibrium capillary relations for two phase flow through heterogeneous media for two phase flow in porous media the natural medium heterogeneity necessarily gives rise to capillary nonequilibrium effects the relaxation to the equilibrium is a slow process which should be introduced in macroscopic flow models many nonequilibrium models are based on a phenomenological approach at the same time there exists a rigorous mathematical way to develop the nonequilibrium equations its formalism developed by bourgeat and panfilov computational geosciences 2 191 1998 is based on the homogenization of the microscale flow equations over medium heterogeneities in contrast with the mentioned paper in which the case of a sufficiently fast relaxation was analyzed we consider the case of long relaxation which leads to the appearance of long term memory on the macroscale due to coupling between the nonlinearity and nonlocality in time the macroscopic model remains however incompletely homogenized in the general case at the same time frequently only the relationship for the nonequilibrium capillary pressure is of interest for applications in the present paper we obtain such an exact relationship in two different independent forms for the case of long term memory this relationship is more general than that obtained by bourgeat and panfilov in addition we prove the comparison theorem which determines the upper and lower bounds for the macroscopic model these bounds represent linear flow models which are completely homogenized the results obtained are illustrated by numerical simulations

3 d boundary element method for cracks in a plate new fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a 3 d boundary element method bem for crack problems the bem features a new integration scheme for highly singular kernels the capability is achieved through a part analytic and part numerical integration procedure such that the analytic part of the integration is similar for all slip opening variations part through elliptic cracks in an elastic plate with traction free surfaces are analysed and the stress intensity factor sif values along the crack front are found to compare favourably with widely accepted numerically obtained sif results by raju and newman 1

three dimensional crack analysis using singular boundary elements a multi domain method of solving three dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed the displacement and traction behaviours near a crack front are incorporated in special crack elements the elimination of singularities arising from the term combined with kelvin s kernel for displacement in the integrals is discussed in detail stress intensity factors of modes i ii and iii are obtained directly from crack front nodal values without any extrapolation as in some other methods no differentiation of conventional boundary integral equations with kelvin s tensor kernels is necessary in the current approach this method is applicable to cracks of arbitrary shape infinite bodies are modelled precisely as such not approximated as large finite bodies numerical solutions of stress intensity factors are given for several problems involving a penny shaped crack

gauss quadrature rules for finite part integrals we construct a set of polynomials n x which are orthogonal with respect to w x x 2 where wx is a weight function these polynomials can be used for the definition of a gauss quadrature formula for the finite part integral the process is exactly the same as the one used for the extraction of the classical gauss formula for the riemann integrals three different methods are derived the first and most accurate quadrature formula is successfully tested in some numerical examples the proposed quadrature formulas have many applications in problems of mathematical physics mechanics etc

a linear discriminant analysis framework based on random subspace for face recognition linear discriminant analysis lda often suffers from the small sample size problem when dealing with high dimensional face data random subspace can effectively solve this problem by random sampling on face features however it remains a problem how to construct an optimal random subspace for discriminant analysis and perform the most efficient discriminant analysis on the constructed random subspace in this paper we propose a novel framework random discriminant analysis rda to handle this problem under the most suitable situation of the principal subspace the optimal reduced dimension of the face sample is discovered to construct a random subspace where all the discriminative information in the face space is distributed in the two principal subspaces of the within class and between class matrices then we apply fisherface and direct lda respectively to the two principal subspaces for simultaneous discriminant analysis the two sets of discriminant analysis features from dual principal subspaces are first combined at the feature level and then all the random subspaces are further integrated at the decision level with the discriminating information fusion at the two levels our method can take full advantage of useful discriminant information in the face space extensive experiments on different face databases demonstrate its performance

computational geometry an introduction from the reviews this book offers a coherent treatment at the graduate textbook level of the field that has come to be known in the last decade or so as computational geometry the book is well organized and lucidly written a timely contribution by two founders of the field it clearly demonstrates that computational geometry in the plane is now a fairly well understood branch of computer science and mathematics it also points the way to the solution of the more challenging problems in dimensions higher than two

semi supervised classification based on random subspace dimensionality reduction graph structure is vital to graph based semi supervised learning however the problem of constructing a graph that reflects the underlying data distribution has been seldom investigated in semi supervised learning especially for high dimensional data in this paper we focus on graph construction for semi supervised learning and propose a novel method called semi supervised classification based on random subspace dimensionality reduction ssc rsdr in short different from traditional methods that perform graph based dimensionality reduction and classification in the original space ssc rsdr performs these tasks in subspaces more specifically ssc rsdr generates several random subspaces of the original space and applies graph based semi supervised dimensionality reduction in these random subspaces it then constructs graphs in these processed random subspaces and trains semi supervised classifiers on the graphs finally it combines the resulting base classifiers into an ensemble classifier experimental results on face recognition tasks demonstrate that ssc rsdr not only has superior recognition performance with respect to competitive methods but also is robust against a wide range of values of input parameters

new green s function for stress field and a note of its application in quantum wire structures abstract the elastic field caused by the lattice mismatch between the quantum wires and the host matrix can be modeled by a corresponding two dimensional hydrostatic inclusion subjected to plane strain conditions the stresses in such a hydrostatic inclusion can be effectively calculated by employing the green s functions developed by downes and faux which tend to be more efficient than the conventional method based on the green s function for the displacement field in this study downes and faux s paper is extended to plane inclusions subjected to arbitrarily distributed eigenstrains an explicit green s function solution which evaluates the stress field due to the excitation of a point eigenstrain source in an infinite plane directly is obtained in a closed form here it is demonstrated that both the interior and exterior stress fields to an inclusion of any shape and with arbitrarily distributed eigenstrains are represented in a unified area integral form by employing the derived green s functions in the case of uniform eigenstrain the formulae may be simplified to contour integrals by green s theorem however special care is required when green s theorem is applied for the interior field the proposed green s function is particularly advantageous in dealing numerically or analytically with the exterior stress field and the non uniform eigenstrain two examples concerning circular inclusions are investigated a linearly distributed eigenstrain is attempted in the first example resulting in a linear interior stress field the second example solves a circular thermal inclusion where both the interior and exterior stress fields are obtained simultaneously

uniform object generation for optimizing one class classifiers in one class classification one class of data called the target class has to be distinguished from the rest of the feature space it is assumed that only examples of the target class are available this classifier has to be constructed such that objects not originating from the target set by definition outlier objects are not classified as target objects in previous research the support vector data description svdd is proposed to solve the problem of one class classification it models a hypersphere around the target set and by the introduction of kernel functions more flexible descriptions are obtained in the original optimization of the svdd two parameters have to be given beforehand by the user to automatically optimize the values for these parameters the error on both the target and outlier data has to be estimated because no outlier examples are available we propose a method for generating artificial outliers uniformly distributed in a hypersphere an relative efficient estimate for the volume covered by the one class classifiers is obtained and so an estimate for the outlier error results are shown for artificial data and for real world data

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

numerical schemes for a pseudo parabolic burgers equation discontinuous data and long time behaviour we consider a simplified model for vertical non stationary groundwater flow which includes dynamic capillary pressure effects specifically we consider a viscous burgers type equation that is extended with a third order term containing mixed derivatives in space and time we analyse the one dimensional boundary value problem and investigate numerically its long time behaviour the numerical schemes discussed here take into account possible discontinuities of the solution

computing the convex hull of a simple polygon abstract an algorithm for computing the convex hull of a simple polygon is presented its correctness and complexity are also shown

calculation of fracture mechanics parameters for an arbitrary three dimensional crack by the equivalent domain integral method summary in this paper an equivalent domain integral edi method and the attendant numerical algorithms arc presented for the computation of a near crack tip field parameter the vector je integral and its variation along the front of an arbitrary three dimensional crack in a structural component account is taken of possible non elastic strains present in the structure in this case the near tip je values may be significantly different from the far field values jf especially under non proportional loading

hypersingular integral equation for multiple curved cracks problem in plane elasticity the complex variable function method is used to formulate the multiple curved crack problems into hypersingular integral equations these hypersingular integral equations are solved numerically for the unknown function which are later used to find the stress intensity factor sif for the problem considered numerical examples for double circular arc cracks are presented

approximate polytope ensemble for one class classification in this work a new one class classification ensemble strategy called approximate polytope ensemble is presented the main contribution of the paper is threefold first the geometrical concept of convex hull is used to define the boundary of the target class defining the problem expansions and contractions of this geometrical structure are introduced in order to avoid over fitting second the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process finally a tiling strategy is proposed in order to model non convex structures experimental results show that the proposed strategy is significantly better than state of the art one class classification methods on over 200 datasets highlightsthe methodology uses a convex hull for modeling one class classification problems random projections are used to approximate the convex hull in high dimensional spaces expansions of the approximate hulls are considered to set the optimal operating point exhaustive validation is performed on three different typologies of problems