adaptive numerical simulation of traffic flow density in this paper we describe a one dimensional adaptive moving mesh method and apply it to the traffic flow model introduced in 2006 by sopasakis and katsoulakis and its modified model proposed in 2009 by kurganov and polizzi these models can be written as a scalar conservation law with a global flux the proposed scheme is an extension of the moving non oscillatory central scheme which belongs to a class of moving finite volume methods we also modify the model given by kurganov and polizzi to account for the driver s reaction i e delayed response finally the moving finite volume method is extended accordingly

an analytic study of fisher s equation by using adomian decomposition method in this paper we develop a framework to obtain exact solutions to fisher s equation and to a nonlinear diffusion equation of the fisher type by employing adomian decomposition method the proposed scheme is supported by examining nonlinear diffusion equations of the fisher type

moving mesh discontinuous galerkin methods for pdes with traveling waves abstract in this paper a moving mesh discontinuous galerkin dg method is developed for nonlinear partial differential equations pdes with traveling wave solutions the moving mesh strategy for one dimensional pdes is based on the rezoning approach which decouples the solution of the pde from the moving mesh equation we show that the dg moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal arc length and curvature monitor functions numerical results reveal the efficiency of the proposed moving mesh dg method for solving burgers burgers fisher and schlogl nagumo equations

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

analysis of moving mesh partial differential equations with spatial smoothing two moving mesh partial differential equations mmpdes with spatial smoothing are derived based upon the equidistribution principle this smoothing technique is motivated by the robust moving mesh method of dorfi and drury j comput phys 69 1987 pp 175 195 it is shown that under weak conditions the basic property of no node crossing is preserved by the spatial smoothing and a local quasi uniformity property of the coordinate transformations determined by these mmpdes is proven it is also shown that discretizing the mmpdes using centered finite differences these basic properties are preserved

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

a moving mesh finite element algorithm for singular problems in two and three space dimensions a framework for adaptive meshes based on the hamilton schoen yau theory was proposed by dvinsky in a recent work 2001 j comput phys 170 562 588 we extended dvinsky s method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability in this work we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions in obtaining the variational mesh we will solve an optimization problem with some appropriate constraints which is in contrast to the traditional method of solving the euler lagrange equation directly the key idea of this approach is to update the interior and boundary grids simultaneously rather than considering them separately application of the proposed moving mesh scheme is illustrated with some two and three dimensional problems with large solution gradients the numerical experiments show that our methods can accurately resolve detail features of singular problems in 3d

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

solitary wave solutions of the generalised burgers huxley equation exact solitary wave solutions of the generalised burgers huxley equation delta u delta t alpha udelta delta u delta chi delta 2u delta chi 2 beta u 1 udelta udelta gamma are obtained by using the relevant nonlinear transformations the results obtained are the generalisation of former work the method in this paper can also be applied to the burgers fisher equation

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

travelling wave solutions of generalized forms of burgers burgers kdv and burgers huxley equations in this work exact travelling wave solutions of generalized forms of burgers burgers kdv and burgers huxley equations are obtained the analysis rests mainly on the standard tanh method the work emphasizes the need for a transformation formula for the case where the parameter m is non integer the approach can be used in a variety of many types of nonlinearity

quantum spin chains with quantum group symmetry we consider actions of quantum groups on lattice spin systems we show that if an action of a quantum group respects the local structure of a lattice system it has to be an ordinary group even allowing weakly delocalized quasi local tails of the action we find that there are no actions of a properly quantum group commuting with lattice translations the non locality arises from the ordering of factors in the quantum groupc algebra and can be made one sided thus allowing semi local actions on a half chain under such actions localized quantum group invariant elements remain localized hence the notion of interactions invariant under the quantum group and also under translations recently studied by many authors makes sense even though there is no global action of the quantum group we consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state under weak locality assumptions its gns representation carries no unitary representation of the quantum group

active selection of clustering constraints this paper examines active selection of clustering constraints which has become a topic of significant interest in constrained clustering active selection of clustering constraints which is known as minimizing the cost of acquiring constraints also includes quantifying utility of a given constraint set a sequential method is proposed in this paper to select the most beneficial set of constraints actively the proposed method uses information of boundary points and transition regions extracted by data description methods to introduce a utility measure for constraints since previously selected constraints affect the utility of remaining candidate constraints a method is proposed to update the utility of remaining constraints after selection of each constraint experiments carried out on synthetic and real datasets show that the proposed method improves the accuracy of clustering while reducing human interaction highlightsactive constraint selection as an open issue in constrained clustering is examined the method relies on the information of boundaries and transition regions of data a utility measure based on the description of data is proposed for constraints this utility measure considers the constraint utility dependencies constraints are selected in a sequential approach utilizing the utility measure

a robust moving mesh finite volume method applied to 1d hyperbolic conservation laws from magnetohydrodynamics in this paper we describe a one dimensional adaptive moving mesh method and its application to hyperbolic conservation laws from magnetohydrodynamics mhd the method is robust because it employs automatic control of mesh adaptation when a new model is considered without manually set parameters adaptive meshes are a common tool for increasing the accuracy and reducing computational costs when solving time dependent partial differential equations pdes mesh points are moved towards locations where they are needed the most to obtain a time dependent adaptive mesh monitor functions are used to automatically monitor the importance of the various parts of the domain by assigning a weight value to each location based on the equidistribution principle all mesh points are distributed according to their assigned weights we use a sophisticated monitor function that tracks both small local phenomena as well as large shocks in the same solution the combination of the moving mesh method and a high resolution finite volume solver for hyperbolic pdes yields a serious gain in accuracy at relatively no extra costs the results of several numerical experiments including comparisons with h refinement are presented which cover many intriguing aspects typifying nonlinear magneto fluid dynamics with higher accuracy than often seen in similar publications

adaptive moving mesh computations for reaction diffusion systems in this paper we describe an adaptive moving mesh technique and its application to reaction diffusion models from chemistry the method is based on a coordinate transformation between physical and computational coordinates the transformation can be viewed as a solution of adaptive mesh partial differential equations pdes which is derived from the minimization of a mesh energy integral for an efficient implementation we have used an approach in which the numerical solution of the physical pdes and the adaptive pdes are decoupled further to avoid solving large nonlinear systems a second order implicit explicit time integration method in combination with the iterative method bi cgstab is applied in the method of lines procedure numerical examples are given in one and two space dimensions

graph dual regularization non negative matrix factorization for co clustering low rank matrix factorization is one of the most useful tools in scientific computing data mining and computer vision among of its techniques non negative matrix factorization nmf has received considerable attention due to producing a parts based representation of the data recent research has shown that not only the observed data are found to lie on a nonlinear low dimensional manifold namely data manifold but also the features lie on a manifold namely feature manifold in this paper we propose a novel algorithm called graph dual regularization non negative matrix factorization dnmf which simultaneously considers the geometric structures of both the data manifold and the feature manifold we also present a graph dual regularization non negative matrix tri factorization algorithm dnmtf as an extension of dnmf moreover we develop two iterative updating optimization schemes for dnmf and dnmtf respectively and provide the convergence proofs of our two optimization schemes experimental results on uci benchmark data sets several image data sets and a radar hrrp data set demonstrate the effectiveness of both dnmf and dnmtf

positive representations of general commutation relations allowing wick ordering we consider the problem of representing in hilbert space commutation relations of the form graphics where the tklij are essentially arbitrary scalar coefficients examples comprise the q canonical commutation relations introduced by greenberg bozejko and speicher and the twisted canonical anti commutation relations studied by pusz and woronowicz as well as the quantum group s u 2 using these relations any polynomial in the generators ai and their adjoints can uniquely be written in wick ordered form in which all starred generators are to the left of all unstarred ones in this general framework we define the fock representation as well as coherent representations we develop criteria for the natural scalar product in the associated representation spaces to be positive definite and for the relations to have representations by bounded operators in a hilbert space we characterize the relations between the generators ai not involving a i which are compatible with the basic relations the relations may also be interpreted as defining a non commutative differential calculus for generic coefficients tklij however all differential forms of degree 2 and higher vanish we exhibit conditions for this not to be the case and relate them to the ideal structure of the wick algebra and conditions of positivity we show that the differential calculus is compatible with the involution iff the coefficients t define a representation of the braid group this condition is also shown to imply improved bounds for the positivity of the fock representation finally we study the kms states of the group of gauge transformations defined by aj exp it aj

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

on c algebras generated by pairs of q commuting isometries we consider the c algebras and generated respectively by isometries s1 s2 satisfying the relation s 1s2 qs2s 1 with q 1 the deformed cuntz relation and by isometries s1 s2 satisfying the relation s2s1 qs1s2 with q 1 we show that is isomorphic to the cuntz toeplitz c algebra for any q 1 we further prove that if and only if either q1 q2 or in the second part of our paper we discuss the complexity of the representation theory of we show that is wild for any q in the circle q 1 and hence that is not nuclear for any q in the circle

a self adaptive moving mesh method for the camassa holm equation a self adaptive moving mesh method is proposed for the numerical simulations of the camassa holm equation it is an integrable scheme in the sense that it possesses the exact n soliton solution it is named a self adaptive moving mesh method because the non uniform mesh is driven and adapted automatically by the solution once the non uniform mesh is evolved the solution is determined by solving a tridiagonal linear system due to these two superior features of the method several test problems give very satisfactory results even if by using a small number of grid points

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

adaptive mesh methods for one and two dimensional hyperbolic conservation laws we develop efficient moving mesh algorithms for one and two dimensional hyperbolic systems of conservation laws the algorithms are formed by two independent parts pde evolution and mesh redistribution the first part can be any appropriate high resolution scheme and the second part is based on an iterative procedure in each iteration meshes are first redistributed by an equidistribution principle and then on the resulting new grids the underlying numerical solutions are updated by a conservative interpolation formula proposed in this work the iteration for the mesh redistribution at a given time step is complete when the meshes governed by a nonlinear equation reach the equilibrium state the main idea of the proposed method is to keep the mass conservation of the underlying numerical solution at each redistribution step in one dimension we can show that the underlying numerical approximation obtained in the mesh redistribution part satisfies the desired tvd property which guarantees that the numerical solution at any time level is tvd provided that the pde solver in the first part satisfies such a property several test problems in one and two dimensions are computed using the proposed moving mesh algorithm the computations demonstrate that our methods are efficient for solving problems with shock discontinuities obtaining the same resolution with a much smaller number of grid points than the uniform mesh approach

a rescaling algorithm for the numerical calculation of blowing up solutions on presente un algorithme a invariance d echelle pour le calcul numerique des solutions a singularites explosives des equations d evolution non lineaires

q gaussian processes non commutative and classical aspects we examine for 1 q 1 q gaussian processes i e families of operators non commutative random variables where the a t fulfill the q commutation relations for some covariance function equipped with the vacuum expectation state we show that there is a q analogue of the gaussian functor of second quantization behind these processes and that this structure can be used to translate questions on q gaussian processes into corresponding and much simpler questions in the underlying hilbert space in particular we use this idea to show that a large class of q gaussian processes possesses a non commutative kind of markov property which ensures that there exist classical versions of these non commutative processes this answers an old question of frisch and bourret fb

noncommutative levy processes for generalized particularly anyon statistics let t mathbb r d let a function qt 2 to mathbb c satisfy q s t overline q t s and q s t 1 a generalized statistics is described by creation operators partial t dagger and annihilation operators t t in t which satisfy the q commutation relations partial s partial dagger t q s t partial dagger t partial s delta s t partial s partial t q t s partial t partial s partial dagger s partial dagger t q t s partial dagger t partial dagger s from the point of view of physics the most important case of a generalized statistics is the anyon statistics for which q s t is equal to q if s t here q in mathbb c q 1 we start the paper with a detailed discussion of a q fock space and operators partial t dagger partial t t in t in it which satisfy the q commutation relations next we consider a noncommutative stochastic process white noise omega t partial t dagger partial t lambda partial t dagger partial t t in t here lambda in mathbb r is a fixed parameter the case 0 corresponds to a q analog of brownian motion while 0 corresponds to a centered q poisson process we study q hermite q charlier respectively polynomials of infinitely many noncommutatative variables omega t t in t the main aim of the paper is to explain the notion of independence for a generalized statistics and to derive corresponding levy processes to this end we recursively define q cumulants of a field xi t t in t this allows us to define a q levy process as a field xi t t in t whose values at different points of t are q independent and which possesses a stationarity of increments in a certain sense we present an explicit construction of a q levy process and derive a nualart schoutens type chaotic decomposition for such a process

solution of two dimensional riemann problems of gas dynamics by positive schemes the positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in x d liu and p d lax j fluid dynam 5 1996 pp 133 156 some numerical experiments presented there show how well the method works in this paper we use positive schemes to solve riemann problems for two dimensional gas dynamics

generalized re weighting local sampling mean discriminant analysis despite the general success in the pattern recognition community linear discriminant analysis lda has four intrinsic drawbacks in this paper we propose a new feature extraction algorithm namely local sampling mean discriminant analysis lsmda to make up for the first three drawbacks and a generalized re weighting grw framework to make up for the fourth drawback extensive experiments are conducted on both synthetic and real world datasets to evaluate the classification performance of our work the experimental results demonstrate the effectiveness of both lsmda and the grw framework in classifications

on boson algebras as hopf algebras certain types of generalized undeformed and deformed boson algebras which admit a hopf algebra structure are introduced together with their fock type representations and their corresponding r matrices it is also shown that a class of generalized heisenberg algebras including those underlying physical models such as that of calogero sutherland is isomorphic with one of the types of boson algebra proposed and can be formulated as a hopf algebra

fast affinity propagation clustering a multilevel approach in this paper we propose a novel fast affinity propagation clustering approach fap fap simultaneously considers both local and global structure information contained in datasets and is a high quality multilevel graph partitioning method that can implement both vector based and graph based clustering first a new fast sampling algorithm fs is proposed to coarsen the input sparse graph and choose a small number of final representative exemplars then a density weighted spectral clustering method is presented to partition those exemplars on the global underlying structure of data manifold finally the cluster assignments of all data points can be achieved through their corresponding representative exemplars experimental results on two synthetic datasets and many real world datasets show that our algorithm outperforms the state of the art original affinity propagation and spectral clustering algorithms in terms of speed memory usage and quality on both vector based and graph based clustering

moving mesh partial differential equations mmpdes based on the equidistribution principle this paper considers several moving mesh partial differential equations that are related to the equidistribution principle several of these are new and some correspond to discrete moving mesh equations that have been used by others their stability is analyzed and it is seen that a key term for most of these moving mesh pdes is a source like term that measures the level of equidistribution it is shown that under weak assumptions mesh crossing cannot occur for most of them finally numerical experiments for these various moving mesh pdes are performed to study their relative properties

howe duality for the quantum groups uqu m n uqu m a dual pair is defined to be a pair of mutually centralizing subgroups of the real symplectic group let g g be a dual pair of reductive groups in which g is also compact and consider the decomposition of the metaplectic representation of the symplectic group into gg irreducibles each such irreducible is a tensor product of an irreducible of g with one of g and it turns out there is a bijective correspondence between them a particular irreducible of g only occurring with a particular one of g and vice versa this so called howe duality is here generalized to the quantum group case uqu m n uqu m for q not a root of unity a metaplectic representation for this dual pair is given in terms of the q oscillator algebra and a uqu m n uqu m covariant heisenberg weyl algebra is also constructed and realized on fock space the heart of the proof lies in showing that uqu m n and uqu m are essentially mutual commutants on fock space the duality follows using the compactness of uqu m the proof is i

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

adaptive numerical method for burgers type nonlinear equations abstract in this paper a moving mesh partial differential equation mmpde approach will be applied to some types of nonlinear partial differential equations the method is described in detail and a number of computational examples are presented using different monitor functions applied to the burgers type equations

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

ground truth bias in external cluster validity indices external cluster validity indices cvis are used to quantify the quality of a clustering by comparing the similarity between the clustering and a ground truth partition however some external cvis show a biased behavior when selecting the most similar clustering users may consequently be misguided by such results recognizing and understanding the bias behavior of cvis is therefore crucial it has been noticed that some external cvis exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic directly or inversely in the number of clusters in candidate partitions this type of bias is caused by the functional form of the cvi model for example the popular rand index ri exhibits a monotone increasing ncinc bias while the jaccard index ji index suffers from a monotone decreasing ncdec bias this type of bias has been previously recognized in the literature in this work we identify a new type of bias arising from the distribution of the ground truth reference partition against which candidate partitions are compared we call this new type of bias ground truth gt bias this type of bias occurs if a change in the reference partition causes a change in the bias status e g ncinc ncdec of a cvi for example ncinc bias in the ri can be changed to ncdec bias by skewing the distribution of clusters in the ground truth partition it is important for users to be aware of this new type of biased behavior since it may affect the interpretations of cvi results the objective of this article is to study the empirical and theoretical implications of gt bias to the best of our knowledge this is the first extensive study of such a property for external cvis our computational experiments show that 5 of 26 pair counting based cvis studied in this paper which are all functions of the ri exhibit gt bias following the numerical examples we provide a theoretical analysis of gt bias based on the relationship between the ri and quadratic entropy specifically we prove that the quadratic entropy of the ground truth partition provides a computable test which predicts the nc bias status of the ri we identify the gt bias effect for external validation measures and explain its importance we test and discuss nc bias for 26 popular pair counting based validation measures we prove that the ri and related 4 indices suffer from gt bias we provide theoretical explanations for understanding why and when gt bias happens we present experimental results that support our analysis we present an empirical example to show that the ari also suffers from a modified gt bias

an efficient dynamically adaptive mesh for potentially singular solutions abstract we develop an efficient dynamically adaptive mesh generator for time dependent problems in two or more dimensions the mesh generator is motivated by the variational approach and is based on solving a new set of nonlinear elliptic pdes for the mesh map when coupled to a physical problem the mesh map evolves with the underlying solution and maintains high adaptivity as the solution develops complicated structures and even singular behavior the overall mesh strategy is simple to implement avoids interpolation and can be easily incorporated into a broad range of applications the efficacy of the mesh is first demonstrated by two examples of blowing up solutions to the 2 d semilinear heat equation these examples show that the mesh can follow with high adaptivity a finite time singularity process the focus of applications presented here is however the baroclinic generation of vorticity in a strongly layered 2 d boussinesq fluid a challenging problem the moving mesh follows effectively the flow resolving both its global features and the almost singular shear layers developed dynamically the numerical results show the fast collapse to small scales and an exponential vorticity growth

convergence to equilibrium for the relaxation approximations of conservation laws we study the cauchy problem for 2 2 semilinear and quasilinear hyperbolic systems with a singular relaxation term special comparison and compactness properties are established by assuming the subcharacteristic condition therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to 0 this research was strongly motivated by the recent numerical investigations of s jin and z xin on the relaxation schemes for conservation laws 1996 john wiley sons inc

adaptive grid generation from harmonic maps on reimannian manifolds abstract in this paper we describe a new method for generation of solution adaptive grids based on harmonic maps on riemannian manifolds the reliability of the method is assured by an existence and uniqueness theorem for one to one maps between multidimensional multiconnected domains we formulate an adaptive riemannian metric consistent with this theorem several examples demonstrating application of the developed procedure are provided

the approximation for the boundary optimal control problem of burgers fisher equation with constraints this paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the burgers fisher equation which is a nonlinear evolution equation and is the prototype model for the reaction convection and diffusion phenomena arising in many spatial temporal processes by making use of the element free galerkin efg method the original optimal control problem is discretized spatially to a semi discrete optimal control problem governed by a system of nonlinear ordinary differential equations then by using the control parameterization method the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system which can be solved as a nonlinear optimization problems by using the sequential quadratic programming sqp algorithm the numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method

bilinear forms clifford algebras q commutation relations and quantum groups abstract constructions are described which associate algebras to arbitrary bilinear forms generalising the usual clifford and heisenberg algebras quantum groups of symmetries are discussed both as deformed enveloping algebras and as quantised function spaces a classification of the equivalence classes of bilinear forms is also given

moving mesh methods in multiple dimensions based on harmonic maps in practice there are three types of adaptive methods using the finite element approach namely the h method p method and r method in the h method the overall method contains two parts a solution algorithm and a mesh selection algorithm these two parts are independent of each other in the sense that the change of the pdes will affect the first part only however in some of the existing versions of the r method also known as the moving mesh method these two parts are strongly associated with each other and as a result any change of the pdes will result in the rewriting of the whole code in this work we will propose a moving mesh method which also contains two parts a solution algorithm and a mesh redistribution algorithm our efforts are to keep the advantages of the r method e g keep the number of nodes unchanged and of the h method e g the two parts in the code are independent a framework for adaptive meshes based on the hamilton schoen yau theory was proposed by dvinsky in this work we will extend dvinsky s method to provide an efficient solver for the mesh redistribution algorithm the key idea is to construct the harmonic map between the physical space and a parameter space by an iteration procedure each iteration step is to move the mesh closer to the harmonic map this procedure is simple and easy to program and also enables us to keep the map harmonic even after long times of numerical integration the numerical schemes are applied to a number of test problems in two dimensions it is observed that the mesh redistribution strategy based on the harmonic maps adapts the mesh extremely well to the solution without producing skew elements for multi dimensional computations

numerical simulation of the generalized huxley equation by he s variational iteration method abstract by means of variational iteration method the solution of generalized huxley equation are obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

fourier pade approximations and filtering for spectral simulations of an incompressible boussinesq convection problem in this paper we present rational approximations based on fourier series representation for periodic piecewise analytic functions the well known gibbs phenomenon hampers the convergence of the standard fourier method here for a given set of the fourier coefficients from a periodic piecewise analytic function we define fourier pade galerkin and fourier pade collocation methods by expressing the coefficients for the rational approximations using the fourier data we show that those methods converge exponentially in the smooth region and successfully reduce the gibbs oscillations as the degrees of the denominators and the numerators of the pade approximants increase numerical results are demonstrated in several examples the collocation method is applied as a postprocessing step to the standard pseudospectral simulations for the one dimensional inviscid burgers equation and the two dimensional incompressible inviscid boussinesq convection flow

stability of newton tvd runge kutta scheme for one dimensional euler equations with adaptive mesh abstract in this paper we propose a moving mesh method with a newton total variation diminishing tvd runge kutta scheme for the euler equations our scheme improves time discretization in the moving mesh algorithms by analyzing the semi discrete euler equations with the discrete moving mesh equations as constraints the stability of the newton tvd runge kutta scheme is proved thus we can conclude that the proposed algorithm can generate a weak solution to the euler equations finally numerical examples are presented to verify the theoretical results and demonstrate the accuracy of the proposed scheme

adomian decomposition method for burger s huxley and burger s fisher equations the approximate solutions for the burger s huxley and burger s fisher equations are obtained by using the adomian decomposition method solving frontier problems of physics the decomposition method kluwer boston 1994 the algorithm is illustrated by studying an initial value problem the obtained results are presented and only few terms of the expansion are required to obtain the approximate solution which is found to be accurate and efficient

an adaptive grid with directional control abstract a variational formulation of winslow s variable diffusion method is combined with a directional control functional to derive an adaptive grid generator for adaptive node movement the addition of directional control allows one to align mesh lines with a prescribed vector field while adapting the spacing to resolve the data it is shown that harmonic function theory can be applied to define the conditions under which unique solutions of the resulting elliptic equations exist the grid generator is applied to the complex problem of magnetic field reconnection driven by fluid instability the results demonstrate that the cost of a computation with an adaptive grid with directional control is only one tenth of the cost of either a calculation on an eulerian grid or on an adaptive grid without directional control

maximum modulus principle for holomorphic functions on the quantum matrix ball we describe the shilov boundary ideal for a q analog of the algebra of holomorphic functions on the unit ball in the space of n n matrices and show that its c envelope is isomorphic to the c algebra of continuous functions on the quantum unitary group u q n

a high resolution mapped grid algorithm for compressible multiphase flow problems we describe a simple mapped grid approach for the efficient numerical simulation of compressible multiphase flow in general multi dimensional geometries the algorithm uses a curvilinear coordinate formulation of the equations that is derived for the euler equations with the stiffened gas equation of state to ensure the correct fluid mixing when approximating the equations numerically with material interfaces a c based and a a based model have been described that is an easy extension of the cartesian coordinates counterpart devised previously by the author 30 a standard high resolution mapped grid method in wave propagation form is employed to solve the proposed multiphase models giving the natural generalization of the previous one from single phase to multiphase flow problems we validate our algorithm by performing numerical tests in two and three dimensions that show second order accurate results for smooth flow problems and also free of spurious oscillations in the pressure for problems with interfaces this includes also some tests where our quadrilateral grid results in two dimensions are in direct comparisons with those obtained using a wave propagation based cartesian grid embedded boundary method

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

on wick algebras with additional twisted commutation relations we study the construction of the c symmetric creation and annihilation operators which form a wick algebra with some additional relations this wick algebra is an algebra of the operators which act on the associative algebra of polynomials with noncommutative variables divided by an ideal generated by quadratic relations between the variables as a result the consistency conditions for such a representation are obtained the creators and annihilator have to preserve ideal where which leads us to consistency conditions

contractivity properties of ornstein uhlenbeck semigroup for general commutation relations we study a certain class of von neumann algebras generated by selfadjoint elements i a i a i where a i a i satisfy the general commutation relations

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

a duality for endomorphisms of von neumann algebras we consider endomorphisms of von neumann algebras let m be a von neumann algebra represented on a hilbert space h and let m be the corresponding commutant let end m be given and suppose m has a cyclic vector in h such that the corresponding state leaves invariant then there is a dual completely positive mapping on m which we find and describe each of the two and has an associated spectral group and we show that the group for is contained in that for we consider the following three restrictions on i is a shift on m ii is strongly ergodic and iii is ergodic we give spectral theoretic conditions on using the two groups described above to fall into each of the three classes we also show that the two groups are conjugacy invariants and we discuss the case of cocycle conjugacy

exclusion statistics operator algebras and fock space representations we study exclusion statistics within the second quantized approach we consider operator algebras with positive definite fock space and restrict them in a such a way that certain state vectors in fock space are forbidden ab initio we describe three characteristic examples of such exclusion namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space e g the calogero sutherland type of exclusion statistics exclusion in the single oscillator fock space where some states in single oscillator fock space are forbidden e g the gentile realization of exclusion statistics and a combination of these two exclusions e g green s realization of para fermi statistics for these types of exclusions we discuss the extended haldane statistics parameters g recently introduced by two of us in 1996 mod phys lett a 11 3081 and associated counting rules within these three types of exclusions in fock space the original haldane exclusion statistics cannot be realized

an adaptive moving mesh method with static rezoning for partial differential equations abstract adaptive mesh methods are valuable tools in improving the accuracy and efficiency of the numerical solution of evolutionary systems of partial differential equations if the mesh moves to track fronts and large gradients in the solution then larger time steps can be taken than if it were to remain stationary we derive explicit differential equations for moving the mesh so that the time variation of the solution at the mesh points is minimized moving the mesh based on this approach allows for larger time steps but does not guarantee that the solution is well resolved in space we maintain spatial accuracy when there are new emerging layers or wave fronts by adaptively rezoning the mesh points to equidistribute an error estimate when using a multistep integration method the past solution values are also interpolated so that the same multistep method can be used after rezoning the resulting algorithm has very few problem dependent numerical parameters and is appropriate for a large class of one dimensional partial differential equations we illustrate the performance of the algorithm by examples and demonstrate that the proposed algorithm is efficient and accurate when compared with other adaptive mesh strategies

the spectrum of the algebra of skew differential operators and the irreducible representations of the quantum heisenberg algebra the left spectrum of a wide class of the algebras of skew differential operators is described as a sequence we determine and classify all the algebraically irreducible representations of the quantum heisenberg algebra over an arbitrary field

on commutators of wick products on ccr and car algebras in this paper we study the q commutator of wick products on the ccr canonical commutation relation algebra and on the car canonical anticommutation relation algebra we obtain a formula on q commutator of wick products in terms of wick products of monomials of lower order moreover we give a relation of double q commutator

modified equation for adaptive monotone difference schemes and its convergent analysis a modified parabolic equation for adaptive monotone difference schemes based on equal arclength mesh applied to the linear convection equation is derived and its convergence analysis shows that solutions of the modified equation approach a discontinuous piecewise smooth solution of the linear convection equation at order one rate in the l 1 norm it is well known that solutions of the monotone schemes with uniform meshes and their modified equation approach the same discontinuous solution at a half order rate in the l 1 norm therefore the convergence analysis for the modified equation provided in this work demonstrates theoretically that the monotone schemes with adaptive grids can improve the solution accuracy numerical experiments also confirm the theoretical conclusions

the q deformation of quantum mechanics of one degree of freedom the q quantum mechanics of the one degree of freedom is studied among others the holomorphic representation of q deformed heisenberg weyl algebra and its realization by covariant berezin symbols is described

coherent states of the q canonical commutation relations for theq deformed canonical commutation relationsa f a g 1 q f g 1 qa g a f forf g in some hilbert space we consider representations generated from a vector satisfyinga f where we show that such a representation exists if and only if 1 moreover for 1 these representations are unitarily equivalent to the fock representation obtained for 0 on the other hand representations obtained for different unit vectors are disjoint we show that the universal c algebra for the relations has a largest proper closed two sided ideal the quotient by this ideal is a naturalq analogue of the cuntz algebra obtained forq 0 we discuss the conjecture that ford this analogue should in fact be equal to the cuntz algebra itself in the limiting casesq 1 we determine all irreducible representations of the relations and characterize those which can be obtained via coherent states

variational barrier method of adaptive grid generation in hyperbolic problems of gas dynamics application of the harmonic mapping using a variational approach to generate moving adaptive grids in the hyperbolic problems of gas dynamics is considered using the example of a three point model of adaptation the possibility to generate an unfolded mesh with strong grid lines condensing in the vicinity of discontinuities of the control monitor function is demonstrated the algorithm of redistributing the boundary nodes is suggested and consists of using constrained minimization of the discrete harmonic functional when constraints define the boundary of the domain in real computations due to mesh adaptation it is possible to reduce the errors caused by shock waves smearing over the cells by many factors of ten modeling of the two dimensional 2 d supersonic gas flow in the channel has shown that the same accuracy on the adaptive grid with the same structure as the quasi uniform mesh can be acheived while requiring less cpu memory by a factor of 25 and less running time by a factor of 50 to 60 computational tests of the steady transonic and supersonic flow over an airfoil demonstrate the ability of the method to control mesh sizes across shocks

moving mesh methods for problems with blow up in this paper we consider the numerical solution of pdes with blow up for which scaling invariance plays a natural role in describing the underlying solution structures it is a challenging numerical problem to capture the qualitative behaviour in the blow up region and the use of nonuniform meshes is essential we consider moving mesh methods for which the mesh is determined using so called moving mesh partial differential equations mmpdes specifically the underlying pde and the mmpde are solved for the blow up solution and the computational mesh simultaneously motivated by the desire for the mmpde to preserve the scaling invariance of the underlying problem we study the effect of different choices of mmpdes and monitor functions it is shown that for suitable ones the mmpde solution evolves towards a moving mesh which close to the blow up point automatically places the mesh points in such a manner that the ignition kernel which is well known to be a natural coordinate in describing the behaviour of blow up approaches a constant as t to t the blow up time several numerical examples are given to verify the theory for these mmpde methods and to illustrate their efficacy

robust adaptive embedded label propagation with weight learning for inductive classification we propose a robust inductive semi supervised label prediction model over the embedded representation termed adaptive embedded label propagation with weight learning aelp wl for classification aelp wl offers several properties first our method seamlessly integrates the robust adaptive embedded label propagation with adaptive weight learning into a unified framework by minimizing the reconstruction errors over embedded features and embedded soft labels jointly our aelp wl can explicitly ensure the learned weights to be joint optimal for representation and classification which differs from most existing lp models that perform weight learning separately by an independent step before label prediction second existing models usually precalculate the weights over the original samples that may contain unfavorable features and noise decreasing performance to this end our model adds a constraint that decomposes original data into a sparse component encoding embedded noise removed sparse representations of samples and a sparse error part fitting noise and then performs the adaptive weight learning over the embedded sparse representations third our aelp wl computes the projected soft labels by trading off the manifold smoothness and label fitness errors over the adaptive weights and the embedded representations for enhancing the label estimation power by including a regressive label approximation error for simultaneous minimization to correlate sample features with the embedded soft labels the out of sample issue is naturally solved by minimizing the reconstruction errors over features and embedded soft labels classification error and label approximation error jointly state of the art results are delivered

wavelet representations and fock space on positive matrices abstract we show that every biorthogonal wavelet determines a representation by operators on hilbert space satisfying simple identities which captures the established relationship between orthogonal wavelets and cuntz algebra representations in that special case each of these representations is shown to have tractable finite dimensional co invariant doubly cyclic subspaces further motivated by these representations we introduce a general fock space hilbert space construction which yields creation operators containing the cuntz toeplitz isometries as a special case

endomorphisms of b h ii finitely correlated states on on we identify sets of conjugacy classes of ergodic endomorphisms of b h where h is a fixed separable hilbert space they correspond to certain equivalence classes of pure states on the cuntz algebras onwherenis the powers index these states called finitely correlated states and strongly asymptotically shift invariant states are defined and characterized the subsets of these states defining shifts will in general be identified in a later work but here an interesting cross section for the conjugacy classes of shifts called diagonalizable shifts is introduced and studied

on crossed product of algebras the concept of a crossed tensor product of algebras is studied from a few points of view some related constructions are considered crossed enveloping algebras and their representations are discussed applications to the noncommutative geometry and particle systems with generalized statistics are indicated

the energy operator for a model with a multiparametric infinite statistics in this paper we consider an energy operator a free hamiltonian in the second quantized approach for the multiparameter quon algebras aia j qija jai ij i j i with qij i ji any hermitian matrix of deformation parameters we obtain an elegant formula for normally ordered sometimes called wick ordered series expansions of number operators which determine a free hamiltonian as a main result see theorem 1 we prove that the number operators are given with respect to a basis formed by generalized lie elements by certain normally ordered quadratic expressions with coefficients given precisely by the entries of the inverses of gram matrices of multiparticle weight spaces this settles a conjecture by meljanac s and perica a 1994 j phys a math gen 27 4737 44 these gram matrices are hermitian generalizations of the varchenko matrices associated with a quantum symmetric bilinear form of diagonal arrangements of hyperplanes the solution of the inversion problem of such matrices in meljanac s and svrtan d 1996 math commun 1 1 24 theorem 2 2 17 leads to an effective formula for the number operators studied in this paper the one parameter case in the monomial basis was studied by zagier stanciu and moller

approximations for viscosity solutions of hamilton jacobi equations with locally varying time and space grids a new monotone finite difference scheme is introduced that approximates viscosity solutions of first order nonlinear hamilton jacobi equations the main feature of the scheme is that it allows for locally varying time and space grids making it ideal for use with adaptive algorithms explicit a priori error estimates are given to establish convergence numerical examples including adaptive mesh refinement examples demonstrate the effectiveness of the proposed scheme

wick product for commutation relations connected with yang baxter operators and new constructions of factors we analyze a certain class of von neumann algebras generated by selfadjoint elements for satisfying the general commutation relations such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors where is an orthonormal basis of a hilbert space the operator which represents the vector is denoted by and called the wick product of the operators we describe explicitly the form of this product also we estimate the operator norm of for finally we apply these two results and prove that under the assumption all the von neumann algebras considered are ii 1 factors

analytic study on burgers fisher huxley equations and combined forms of these equations abstract in this work we formally derive travelling wave solutions for the burgers fisher huxley equations and combined forms of these equations the tanh coth method is used to determine these sets of travelling wave solutions kinks and periodic wave solutions are constructed the proposed scheme can be used to a wide class of nonlinear evolution equations

remapping free ale type kinetic method for flow computations based on the integral form of the fluid dynamic equations a finite volume kinetic scheme with arbitrary control volume and mesh velocity is developed different from the earlier unified moving mesh gas kinetic method c q jin k xu an unified moving grid gas kinetic method in eulerian space for viscous flow computation j comput phys 222 2007 155 175 the coupling of the fluid equations and geometrical conservation laws has been removed in order to make the scheme applicable for any quadrilateral or unstructured mesh rather than parallelogram in 2d case since a purely lagrangian method is always associated with mesh entangling in order to avoid computational collapsing in multidimensional flow simulation the mesh velocity is constructed by considering both fluid velocity lagrangian methodology and diffusive velocity regenerating eulerian mesh function therefore we obtain a generalized arbitrary lagrangian eulerian ale method by properly designing a mesh velocity instead of re generating a new mesh after distortion as a result the remapping step to interpolate flow variables from old mesh to new mesh is avoided the current method provides a general framework which can be considered as a remapping free ale type method since there is great freedom in choosing mesh velocity in order to improve the accuracy and robustness of the method the adaptive moving mesh method h z tang t tang adaptive mesh methods for one and two dimensional hyperbolic conservation laws siam j numer anal 41 2003 487 515 can be also used to construct a mesh velocity to concentrate mesh to regions with high flow gradients

fast semi supervised clustering with enhanced spectral embedding in recent years semi supervised clustering ssc has aroused considerable interests from the machine learning and data mining communities in this paper we propose a novel ssc approach with enhanced spectral embedding ese which not only considers the geometric structure information contained in data sets but also can make use of the given side information such as pairwise constraints specially we first construct a symmetry favored k nn graph which is highly robust to noise and outliers and can reflect the underlying manifold structures of data sets then we learn the enhanced spectral embedding towards an ideal data representation as consistent with the given pairwise constraints as possible finally by using the regularization of spectral embedding we formulate learning the new data representation as a semidefinite quadratic linear programming sqlp problem which can be efficiently solved experimental results on a variety of synthetic and real world data sets show that our ese approach outperforms the state of the art ssc algorithms in terms of speed and quality on both vector based and graph based clustering

an adaptive mesh redistribution method for the incompressible mixture flows using phase field model a phase field model which describes the motion of mixtures of two incompressible fluids is presented by liu and shen c liu j shen a phase field model for the mixture of two incompressible fluids and its approximation by a fourier spectral method phys d 179 2003 211 228 the model is based on an energetic variational formulation in this work we develop an efficient adaptive mesh method for solving a phase field model for the mixture flow of two incompressible fluids it is a coupled nonlinear system of navier stokes equations and allen cahn phase equation phase field equation through an extra stress term and the transport term the numerical strategy is based on the approach proposed by li et al r li t tang p w zhang moving mesh methods in multiple dimensions based on harmonic maps j comput phys 170 2001 562 588 to separate the mesh moving and pde evolution in the pde evolution part the phase field equation is numerically solved by a conservative scheme with a lagrange multiplier and the coupled incompressible navier stokes equations are solved by the incremental pressure correction projection scheme based on the semi staggered grid method in the mesh moving part the mesh points are iteratively redistributed by solving the euler lagrange equations with a parameter free monitor function in each iteration the pressure and the phase are updated on the resulting new grid by a conservative interpolation formula while the velocity is re mapped in a non conservative approach a simple method for preserving divergence free is obtained by projecting the velocity onto the divergence free space after generating the new mesh at the last iterative step numerical experiments are presented to demonstrate the effectiveness of the proposed method for solving the incompressible mixture flows

an adaptive grid method and its application to steady euler flow calculations an adaptive remeshing procedure based on a cell volume deformation method is presented starting with an initial grid this method offers direct cell volume control through the specification of the transformation jacobian grid points are moved with appropriate grid velocities so that the specified cell volume distribution can be achieved at the end of the grid movement without adding or removing grid points the grid velocities are determined by solving a scalar poisson equation this method is applied to solving the compressible euler equations computational test cases of transonic flow over an airfoil are presented and demonstrate the desired control of grid sizes across shock waves

on the orthogonal distance to class subspaces for high dimensional data classification the orthogonal distance from an instance to the subspace of a class is a key metric for pattern classification by the class subspace based methods there is a close relationship between the orthogonal distance and the residual standard deviation of a test instance from the class subspace in this paper we shall show that an established and widely used relationship between the residual standard deviation and the sum of squares of the residual pc scores is not precise and thus can lead to incorrect results for the inference of high dimensional data which nowadays are common in practice

moving mesh methods for one dimensional hyperbolic problems using clawpack we develop a one dimensional moving mesh method for hyperbolic systems of conser vation laws this method is based on the high resolution finite volume wave propagation method implemented in the clawpack software package a modified system of conservation laws is solved on a fixed uniform computational grid with a grid mapping function computed simultaneously in such a way that in physical space certain features are tracked by cell interfaces the method is tested on a shock tube problem with multiple reflections where the contact discontinuity is tracked and also on two multifluid problems where the interface between two distinct gases is tracked one is a standard test problem and the other also involves a moving piston whose motion is also tracked by the moving mesh 2003 elsevier science ltd all rights reserved

minimality of the data in wavelet filters abstract orthogonal wavelets or wavelet frames for l2 r are associated with quadrature mirror filters qmf a set of complex numbers which relate the dyadic scaling of functions on r to the z translates in this paper we show that generically the data in the qmf systems of wavelets are minimal in the sense that the data cannot be nontrivially reduced the minimality property is given a geometric formulation in the hilbert space l2 z and it is then shown that minimality corresponds to irreducibility of a wavelet representation of the algebra o 2 and so our result is that this family of representations of o 2 on the hilbert space l2 z is irreducible for a generic set of values of the parameters which label the wavelet representations

adaptive moving mesh upwind scheme for the two species chemotaxis model chemotaxis systems are used to model the propagation aggregation and pattern formation of bacteria cells in response to an external stimulus usually a chemical one a common property of all chemotaxis systems is their ability to model a concentration phenomenon rapid growth of the cell density in small neighborhoods of concentration points curves more precisely the solution may develop singular spiky structures or even blow up in finite time therefore the development of accurate and computationally efficient numerical methods for the chemotaxis models is a challenging task we study the two species patlak keller segel type chemotaxis system in which the two species do not compete but have different chemotactic sensitivities which may lead to a significantly difference in cell density growth rates this phenomenon was numerically investigated in kurganov and lukacova medvid ova discrete contin dyn syst ser b 19 2014 pp 131 152 and chertock et al adv comput math 44 2018 pp 327 350 where second and higher order methods on uniform cartesian grids were developed however in order to achieve high resolution of the density spikes developed by the species with a lower chemotactic sensitivity a very fine mesh had to be utilized and thus the efficiency of the numerical method was affected in this work we consider an alternative approach relying on mesh adaptation which helps to improve the approximation of the singular structures evolved by chemotaxis models we develop in particular an adaptive moving mesh amm finite volume semi discrete upwind method for the two species chemotaxis system the proposed amm technique allows one to increase the density of mesh nodes at the blowup regions this helps to substantially improve the resolution while using a relatively small number of finite volume cells