equivalence of n dimensional roesser and fornasini marchesini models an equivalent roesser model is obtained for an arbitrary fornasini marchesini model in n dimensions and vice versa both the regular and singular cases are covered

partitions of a simplex leading to accurate spectral finite volume reconstruction in this paper we present several systematic techniques based on the voronoi diagram and its variants to partition a one and two dimensional simplex the fekete points are used as input to generate the voronoi diagram as they concentrate near the edges and are almost optimal for polynomial interpolation in a simplex spectral finite volume reconstructions on the resultant partitions have small lebesgue constants when using the dubiner basis the reconstruction matrix is well conditioned moreover the total number of edges of the partitions the total work when being used in spectral volume methods is shown to be at most twice the minimum number of edges of all partitions for reconstructions of the same order accuracy these suggest that the obtained partitions are well suited for spectral volume methods and other numerical methods which rely on reconstructions from cell averages

walsh function analysis of 2 d generalized continuous systems the importance of the generalized or singular 2d continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables a technique is presented for solving these systems in terms of walsh functions the method replaces the solution of a two variable partial differential equation with the solution of a linear algebraic generalized 2d sylvester equation an efficient technique for the recursive solution of the latter equation is offered all the results apply also in the usual roesser 2d state space case

general model of n d system with variable coefficients and its reduction to 1 d system with variable structure a general model of an n d linear discrete system with variable coefficients and its solution are presented a method for reduction of this model to an equivalent 1 d system with a variable structure is given

space time tradeoffs for emptiness queries we develop the first nontrivial lower bounds on the complexity of online hyperplane and halfspace emptiness queries our lower bounds apply to a general class of geometric range query data structures called partition graphs informally a partition graph is a directed acyclic graph that describes a recursive decomposition of space we show that any partition graph that supports hyperplane emptiness queries implicitly defines a halfspace range query data structure in the fredman yao semigroup arithmetic model with the same asymptotic space and time bounds thus results of bronnimann chazelle and pach imply that any partition graph of size s that supports hyperplane emptiness queries in time t satisfies the inequality st d omega n log n d d 1 d 1 using different techniques we improve previous lower bounds for hopcroft s problem given a set of points and hyperplanes does any hyperplane contain a point in dimensions four and higher using this offline result we show that for online hyperplane emptiness queries omega n d mbox polylog n space is required to achieve polylogarithmic query time and omega n d 1 d mbox polylog n query time is required if only o n polylog n space is available these two lower bounds are optimal up to polylogarithmic factors for two dimensional queries we obtain an optimal continuous tradeoff st 2 omega n 2 between these two extremes finally using a lifting argument we show that the same lower bounds hold for both offline and online halfspace emptiness queries in mathbb r d d 3 2

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

matrix rank based conditions for reachability controllability of discrete linear repetitive processes abstract this paper uses both 2d and standard or 1d representations of the dynamics of discrete linear repetitive processes to characterise their reachability controllability properties the major new results are a 1d representation of constant dimensions and characterisations of reachability controllability in terms of matrix rank based conditions

unsteady euler solutions for arbitrarily moving bodies and boundaries a methodology for the computation of unsteady euler flows in configurations with moving boundaries is presented the procedure is composed of a moving and adaptive grid management algorithm and a lagrangian eulerian flow solver the domain discretization is handled via unstructured triangular grids the flow scheme uses a generalized version of roe s approximate riemann solver which takes into account the mesh movement while satisfying in an intrinsic way the geometric conservation laws grid flow coupling is obtained through error estimation the methodology is applied to various flow problems showing moving shock waves and moving geometries

an algorithm for the optimization of directionally stretched triangulations a procedure for the optimization of stretched triangular grids is described the method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non linear spring system the function is minimized using a gradient method based on the steepest descent examples are provided to show the applicability of the method to computational fluid dynamics problems

matrix description of multivariable polynomials abstract a new multiway description of multivariable polynomials is presented applications to linear transformations of polynomial variables the cayley hamilton theorem and polynomial factorizability are given

two dimensional dissipative control and filtering for roesser model this paper investigates the problems of two dimensional 2 d dissipative control and filtering for a linear discrete time roesser model first a novel sufficient condition is proposed such that the discrete time roesser system is asymptotically stable and 2 d q s r hbox alpha dissipative special cases such as 2 d passivity performance and 2 d h infty performance and feedback interconnected systems are also discussed based on this condition new 2 d q s r hbox alpha dissipative state feedback and output feedback control problems are defined and solved for a discrete time roesser model the design problems of 2 d q s r hbox alpha dissipative filters of observer form and general form are also considered using a linear matrix inequality lmi approach two examples are given to illustrate the effectiveness and potential of the proposed design techniques

computing the state difference equations for discrete overdetermined linear m d systems we derive an algorithm that computes the state difference equations for a given set of poles of linear discrete overdetermined autonomous m d systems these difference equations allow the realization of the dynamical system by means of delay multiplication and addition elements in simulation diagrams in doing so we generalize the classical cayley hamilton theorem to multivariate polynomial ideals and provide a system theoretic interpretation to the notion of polynomial ideals leading monomials and grobner bases furthermore we extend the problem to include poles at infinity and so arrive at a description of overdetermined descriptor systems this results in a new state space description of autonomous m d descriptor systems in addition we discuss the separation of the state variables of singular m d systems into a regular and singular part a sufficient condition under which these two state vector parts can be interpreted as a forward evolving regular part and a backward evolving singular part is given the robustness and efficiency of the developed algorithms are demonstrated via numerical experiments

on the analysis of discrete linear time invariant singular systems the discrete singular equation over an interval can represent a two point boundary value problem or it can be considered as a dynamical relation developing forward in time a theory is provided by giving analytic solutions and discussing system properties in both cases that encompasses both interpretations the singular system fundamental matrix is used to provide analytic solutions to a time invariant discrete singular equation defined over an interval the two distinct cases in which the singular relation is interpreted as a two point boundary value problem or as a forward dynamical system on the interval are both considered also considered is the case in which the singular relation is considered as a backward dynamical system and the relationship between the index of nilpotence and the laurent series coefficients resulting from the solutions of certain state space equations is shown reachability and observability are discussed and the point is made that these properties are different depending on how the singular relation is interpreted

hybrid prismatic tetrahedral grid generation for viscous flow applications a method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed the prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions whereas the tetrahedral grid covers the rest of the computational domain the delaunay approach for tetrahedral grid generation is used the proposed prismatic grid is structured in directions normal to the boundary faces but the number of prisms generated from one boundary face is variable from face to face unlike conventional prismatic grid generators this technique works well even in regions of cavities and gaps the delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms particular attention is given to the boundary constraining problem a robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

algebraic turbulence modeling for unstructured and adaptive meshes an algebraic turbulence model based on the baldwin lomax model has been implemented for use on unstructured grids the implementation is based on the use of local background turbulence meshes at each time step flow variables are interpolated from the unstructured mesh onto the background structured meshes the turbulence model is executed on these meshes and the resulting eddy viscosity values are interpolated back to the unstructured mesh modifications to the algebraic model were required to enable the treatment of more compli cated flows such as confluent boundary layers and wakes the model is used in conjunction with an efficient unstructured multigrid finite element navier stokes solver in order to compute compressible turbulent flows on fully unstructured meshes solutions about single and multiple element airfoils are obtained and compared with experimental data he use of unstructured mesh techniques for computa tional fluid dynamics cfd problems has become more widespread in recent years due to the flexibility they afford in discretizing arbitrarily complex geometries and due to the possibility they offer in resolving highly localized flow phenomena through the use of adaptive meshing however research on unstructured mesh techniques for cfd has con centrated almost exclusively on the solution of the euler equa tions in two or three dimensions for viscous flow calculations about nonsimple geometries hybrid meshes have generally been employed 1 3 where a thin structured mesh is placed in the boundary layer and wake regions and an unstructured mesh is constructed in the outer inviscid region of the flowfield besides leading to an increase in coding complexity this type of compromise limits the generality of the unstruc tured mesh approach in dealing with arbitrarily complex geometries such as multiple body geometries with close toler ances where confluent boundary layers or wakes may occur and complicates the task of performing adaptive meshing in the inviscid as well as viscous regions of flow it appears that the difficulties associated with generating highly stretched unstructured meshes which are required for efficiently resolv ing viscous shear layers as well as the efficient implementa tion of a turbulence model on such meshes has generally im peded the use of fully unstructured meshes for viscous flows the use of unstructured meshes throughout the entire flowfield is advocated in the present work previous work by the author has shown how a highly stretched unstructured mesh suitable for high reynolds number viscous flow calcula tions may be constructed4 and has also discussed the develop ment of an efficient unstructured navier stokes solver for laminar flows 5 this paper is thus concerned with the effi cient implementation of a turbulence model for computing high reynolds number turbulent flows using fully unstruc tured meshes

the linear quadratic optimal regulator for singular 2 d systems with variable coefficients the linear quadratic optimal regulator problem for singular 2 d linear systems with variable coefficients has been formulated sufficient conditions for the existence of a solution to the problem have been established an optimal sequence of input vectors can be found with slight modification the considerations can be extended for singular n d linear systems with variable coefficients

delay dependent exponential stabilization of positive 2d switched state delayed systems in the roesser model this paper deals with the controller synthesis for a class of positive two dimensional 2d switched delay systems described by the roesser model this kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative some delay dependent sufficient conditions for the exponential stability of positive 2d switched systems with state delays are given furthermore the design of positive state feedback controller under which the resulting closed loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities lmis an example is included to illustrate the effectiveness of the proposed approach

two dimensional unsteady navier stokes solution method with moving overset grids a simple numerical algorithm to localize intergrid boundary points and to interpolate unsteady solution variables across two dimensional structured overset grids is presented overset grids are allowed to move in time relative to each other intergrid boundary points are localized in a triangular stencil on the donor grid by a directional search algorithm the final parameters of the search algorithm give the interpolation weights at the intergrid boundary point numerical results are presented for steady and unsteady viscous flow solutions over an airfoil undergoing a sinusoidal flapping motion computed flowfields demonstrate the accuracy of the method and excellent agreement is obtained against the single grid solutions the method is independent of numerical solution algorithms and it may easily be implemented on any two dimensional single block flow solver to make it a multiblock zonal solver with arbitrarily overset overlapping computational grids

solutions to the output regulation problem of linear singular systems in this paper we revisit the output regulation problem for linear singular systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated we derive a necessary and sufficient condition for the regulation problem to be solvable via either full information feedback or error feedback then we show how full information feedback and error feedback controllers can be constructed explicitly

perfect observers for singular 2 d fornasini marchesini models a concept of the perfect observer for singular two dimensional 2 d fornasini marchesini models is proposed sufficient conditions are established for the existence of the perfect observer a procedure for design of the perfect observer is also derived and illustrated by a numerical example

spectra of uniform hypergraphs abstract we present a spectral theory of uniform hypergraphs that closely parallels spectral graph theory a number of recent developments building upon classical work has led to a rich understanding of symmetric hyperdeterminants of hypermatrices a k a multidimensional arrays symmetric hyperdeterminants share many properties with determinants but the context of multilinear algebra is substantially more complicated than the linear algebra required to address spectral graph theory i e ordinary matrices nonetheless it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally we apply this notion to the adjacency hypermatrix of a uniform hypergraph and prove a number of natural analogs of basic results in spectral graph theory open problems abound and we present a number of directions for further study

subspace algorithms for identifying separable in denominator 2d systems with deterministic stochastic inputs abstractin this paper we present an algorithm for identifying two dimensional 2d causal recursive and separable in denominator crsd state space models in the roesser form with deterministic stochastic inputs the algorithm implements the n4sid po moesp and cca methods which are well known in the literature on 1d system identification but here we do so for the 2d crsd roesser model the algorithm solves the 2d system identification problem by maintaining the constraint structure imposed by the problem i e toeplitz and hankel and computes the horizontal and vertical system orders system parameter matrices and covariance matrices of a 2d crsd roesser model from a computational point of view the algorithm has been presented in a unified framework where the user can select which of the three methods to use furthermore the identification task is divided into three main parts 1 computing the deterministic horizontal model parameters 2 computing the deterministic vertical model parameters

a review of 2 d implicit systems abstract the one dimensional notion of causality has no counterpart in the two dimensional plane where at best partial orderings of i j may be defined two dimensional implicit systems unlike the familiar state space 2 d models do not require any notion of causality or recursibility instead they require the milder notion of regularity thus the implicit models are more suited to the description of naturally occurring two dimensional systems such as are described by the hyperbolic equation and the heat equation as well as for applications in image processing this paper provides a brief summary of the current state of the theory of 2 d implicit systems

general response formula and minimum energy control for the general singular model of 2 d systems the general response formula for the general singular model of 2 d linear systems is derived the concepts of local reachability and local controllability are extended to the singular model necessary and sufficient conditions for local reachability and local controllability are established the minimum energy control problem for the singular model is formulated and solved

input output finite region stability and stabilization for discrete 2 d fornasini marchesini models abstract this paper establishes input output finite region stability i o frs and stabilization analysis methods to investigate the transient behavior of output signals for discrete two dimensional 2 d fornasini marchesini fm models for 2 d systems with two classes of input signals by building special recursive formulas sufficient i o frs conditions are formulated in terms of solvability of linear matrix inequalities lmis furthermore aiming at designing static state feedback controllers i o finite region stabilization issues are analyzed for the corresponding 2 d systems and sufficient conditions are reported to guarantee i o frs of the closed loop systems to conclude the paper we provide some numerical examples to confirm the validity of the proposed methods

a geometric approach to the theory of 2 d systems the authors develop a geometric approach to the theory of 2 d two dimensional systems defining in a suitable way the notion of a sub 1 2 b sub 1 2 invariant subspaces and of controlled invariant subspaces such subspaces are shown to have good computational and feedback properties which make them useful in application in particular sufficient conditions and constructive procedures are obtained for the solutions of disturbance decoupling and model matching problems moreover it is shown that certain structural properties of a 2 d system can be described by means of a set of indexes defined in geometric terms and that such structural indexes can be used to reformulate the sufficient condition for model matching

boundary recursion for descriptor variable systems it is shown that if an n dimensional descriptor variable system satisfies the properties of solvability and controllability the family of solutions is n dimensional and the set of two point boundary values that are consistent with the system can be expressed as the solutions to a linear system of equations involving only the boundary values this equation is termed a boundary mapping equation and it provides a compact representation of the system the boundary mapping generalizes the state transition matrix associated with state variable systems the author presents the boundary mapping theory describes the recursive processes required and applies both to some special cases including general linear time invariant systems and adjoint systems

efficient unstructured mesh generation by means of delaunay triangulation and bowyer watson algorithm this work is devoted to the description of an efficient unstructured mesh generation method entirely based on the delaunay triangulation the distinctive characteristic of the proposed method is that point positions and connections are computed simultaneously this result is achieved by taking advantage of the sequential way in which the bowyer watson algorithm computes the delaunay triangulation two methods are proposed which have great geometrical flexibility in that they allow us to treat domains of arbitrary shape and topology and to generate arbitrarily nonuniform meshes the methods are computationally efficient and are applicable both in two and three dimensions

two dimensional peak to peak filtering for stochastic fornasini marchesini systems this paper is concerned with the problem of two dimensional 2 d stochastic peak to peak filter design for fornasini marchesini local state space fm lss systems with state multiplicative noise first a novel sufficient condition is established which guarantees that the underlying fm lss system is stochastically mean square stable with 2 d stochastic peak to peak performance a deterministic fm lss system case is also discussed subsequently based on the result a new 2 d stochastic peak to peak filter of general form is designed for fm lss systems with state multiplicative noise finally a numerical example is presented to show the effectiveness of the proposed 2 d stochastic peak to peak filter

block tensors and symmetric embeddings abstract well known connections exist between the singular value decomposition of a matrix a and the schur decomposition of its symmetric embedding sym a 0 a a t 0 in particular if is a singular value of a then and are eigenvalues of the symmetric embedding the top and bottom halves of sym a s eigenvectors are singular vectors for a power methods applied to a can be related to power methods applied to sym a the rank of sym a is twice the rank of a in this paper we develop similar connections for tensors by building on l h lim s variational approach to tensor singular values and vectors we show how to embed a general order d tensor a into an order d symmetric tensor sym a through the embedding we relate power methods for a s singular values to power methods for sym a s eigenvalues finally we connect the multilinear and outer product rank of a to the multilinear and outer product rank of sym a

generalization of cayley hamilton theorem for multivariate rational matrices the two equivalent generalizations of the famous cayley hamilton theorem for multivariate rational matrices over any number field are proposed which are also generalizations of the nine known generalized cayley hamilton theorems restricting our results to a smaller range leads to the two equivalent generalized cayley hamilton theorems for multivariate polynomial matrices over any number field one of which is more efficient in some cases than a known result

when does the local controllability of the general model of 2 d linear systems imply its local reachability abstract a relationship between the local controllability of the general model of two dimensional linear systems and its local reachability is considered sufficient conditions are established under which the local controllability of the general model implies its local reachability

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

computation of the transfer function matrix and its laurent expansion of generalized two dimensional systems an algorithm is developed for the computation of the transfer function matrix of a two dimensional system which is given in its generalized form the algorithm is a recursion in terms of the original system matrix and does not require the inversion of a two variable polynomial matrix an algorithm for the evaluation of the laurent expansion of the inverse of a two variable polynomial matrix is also presented

the general state space model for a two dimensional linear digital system the general state space model for a 2 d linear digital system is presented a new definition of state transition matrix is given based on the definition it is easy to calculate the state transition matrix for any linear digital system the general response formula for a system follows simply from the definition a new definition of the characteristic function of a system and a theorem parallel to the cayley hamilton theorem are also given the presented results apply to any linear causal system

quality estimates and stretched meshes based on delaunay triangulations any other vertex is exploited for the automation of the grid generation process moreover delaunay grids have many interesting properties an extensive documentation of which can be found in ref 10 in the following we will first describe the different elements of frod the derivation of the background mesh as well as the vertex generation for the viscous and inviscid regions the latter half of this paper presents the quality measures that can be derived for the isotropic vertex generation part

descriptor systems expanded descriptor equation and markov parameters generalized concepts of solvability and conditionability are presented for descriptor systems and tests are given for these generalized properties an expression is derived for descriptor system markov parameters the notion of expanded descriptor equation is presented

minimum energy control for general model of 2 d linear systems a new definition of the straight line controllability for the general model of 2 d linear systems is presented necessary and sufficient conditions for the straight line controllability of the general model are established the minimum energy control problem for the general model of 2 d systems with constant coefficients is formulated and solved

the hamiltonian properties of supergrid graphs in this paper we first introduce a novel class of graphs namely supergrid supergrid graphs include grid graphs and triangular grid graphs as their subgraphs the hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be np complete however they are unknown for supergrid graphs the hamiltonian cycle path problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines in this paper we will prove that the hamiltonian cycle problem for supergrid graphs is np complete it is easily derived from the hamiltonian cycle result that the hamiltonian path problem on supergrid graphs is also np complete we then show that two subclasses of supergrid graphs including rectangular parallelism and alphabet always contain hamiltonian cycles

icp registration using invariant features investigates the use of euclidean invariant features in a generalization of iterative closest point icp registration of range images pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances it is shown that under ideal noise free conditions correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone in addition monotonic convergence to at least a local minimum is shown to hold for this method when noise is present a method that automatically sets the optimal relative contribution of features and positions is described this method trades off the error in feature values due to noise against the error in positions due to misalignment experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model

the singular general model of 2d systems and its solution a general singular model for 2d linear discrete systems with constant coefficients is defined necessary and sufficient conditions for the existence of a solution to the model are established the considerations of the author s previous work 1986 can be extended to singular models of 2d linear systems with variable coefficients

fuzzy modeling and h control for general 2d nonlinear systems this paper investigates h control for general 2d nonlinear systems based on a 2d takagi sugeno t s fuzzy model the system under consideration is an extension of the general 2d linear system to a nonlinear case taking the spatial and structural features into consideration a 2d t s fuzzy model is first established in designing the h controller the inputs are regarded as variables independent from the states and then basis dependent free matrices are introduced it has been shown that separation of the input and state variables does not lead to any conservativeness compared with the commonly used method thus a fuzzy h controller is designed using a common free matrix resulting in only r linear matrix inequalities the computational advantage is obvious for fuzzy systems with a large number of fuzzy rules we also demonstrate that the proposed method is less computationally expensive than the approach in which the input variable state variable and its forward stepping state are all separately considered although these two methods can achieve the same optimal h performance simulation examples are used to demonstrate the technique and its advantages

a fundamental notion of equivalence for linear multivariable systems a fundamental form of equivalence of polynomial matrix descriptions of linear multivariable systems is defined based on the existence of a bijective map between the finite and infinite solution sets of the differential equations describing the two systems the connection with the system matrix relationship of full system equivalence is established

structure of a simple scheduling polyhedron in a one machine nonpreemptive scheduling problem the feasible schedules may be defined by the vector of the corresponding job completion times for given positive processing times the associated simple scheduling polyhedronp is the convex hull of these feasible completion time vectors the main result of this paper is a complete description of the minimal linear system definingp we also give a complete combinatorial description of the face lattice ofp and a simple o n logn separation algorithm this algorithm has potential usefulness in cutting plane type algorithms for more difficult scheduling problems

voronoi diagram and medial axis algorithm for planar domains with curved boundaries i theoretical foundations in this first installment of a two part paper the underlying theory for an algorithm that computes the voronoi diagram and medial axis of a planar domain bounded by free form polynomial or rational curve segments is presented an incremental approach to computing the voronoi diagram is used wherein a single boundary segment is added to an existing boundary segment set at each step the introduction of each new segment entails modifying the voronoi regions of the existing boundary segments and constructing the voronoi region of the new segment we accomplish this by i computing the bisector of the new segment with each of the current boundary segments ii updating the voronoi regions of the current boundary segments by partitioning them with these bisectors and iii constructing the voronoi region of the new segment as a union of regions obtained from the partitioning in ii when all boundary segments are included and their voronoi regions have been constructed the voronoi diagram of the boundary is obtained as the union of the voronoi polygons for each boundary segment to construct the medial axis of a planar domain we first compute the voronoi diagram of its boundary the medial axis is then obtained from the voronoi diagram by i removing certain edges of the voronoi diagram that do not belong to the medial axis and ii adding certain edges that do belong to the medial axis but are absent from the voronoi diagram unambiguous characterizations for edges in both these categories are given details of algorithms based on this theory are deferred to the second installment of this two part paper

straight line reachability of roesser model a new definition of straight line reachability for the roesser model is presented necessary and sufficient conditions for straight line teachability of the roesser model are established a relationship between local reachability and straight line reachability of the roesser model is discussed

elementary operations and equivalence of two dimensional systems this paper employs two dimensional elementary operations to construct a number of singular and standard roesser type state space realizations of two dimensional linear systems the main result consists of the development of the basic algorithm together with some algebraic properties

stability of nonlinear parameter varying digital 2 d systems a general state space model for nonlinear parameter varying digital two dimensional 2 d systems is proposed sufficient conditions for system stability are given presented theorem can be considered as a generalization of the lyapunov stability theorem for one dimensional nonlinear systems given results can be useful in stability analysis for systems described by 2 d models

an approach to multidimensional fornasini marchesini state space model realization w r t columns of transfer matrices abstract this paper proposes a new approach that can generate a low order fornasini marchesini f m model realization for a given n d system by taking into account the column structural properties of its transfer matrix specifically a new necessary and sufficient realization condition is developed for the f m model realization based on a resolvent invariant space associated with the gleason s problem specified by the given n d transfer matrix then a new constructive procedure with respect to the columns of a given transfer matrix is proposed for constructing a low order f m model realization in order to apply this procedure to the multiple input multiple output case more effectively an improved realization procedure based on a polynomial description is also proposed it will be shown by both algorithmic analysis and illustrative examples that for a transfer matrix having more rows than columns the proposed realization approach may generate a much lower realization order than the existing one with respect to the rows of a given n d transfer matrix recently developed by cheng et al particularly for a given scalar transfer function our new approach always generates an f m model realization with lower order than the existing methods

anisotropic adaptive simulation of transient flows using discontinuous galerkin methods an anisotropic adaptive analysis procedure based on a discontinuous galerkin finite element discretization and local mesh modification of simplex elements is presented the procedure is applied to transient two and three dimensional problems governed by euler s equation a smoothness indicator is used to isolate jump features where an aligned mesh metric field in specified the mesh metric field in smooth portions of the domain is controlled by a hessian matrix constructed using a variational procedure to calculate the second derivatives the transient examples included demonstrate the ability of the mesh modification procedures to effectively track evolving interacting features of general shape as they move through a domain copyright c 2004 john wiley sons ltd

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

an algorithm for the computation of 2 d eigenvalues in this paper a definition for the eigenvalues of two dimensional 2 d general discrete state space models is proposed this definition is consistent with that known for 2 d roesser models also a programmable algorithm is developed to compute the 2 d eigenvalues

geometric classification of triangulations and their enumeration in a convex polygon abstract triangulation of polygons is a classical problem in computational geometry for an arbitrary polygon the triangulation may depend on its shape in this paper we describe a new geometric classification of triangulations of a convex polygon and then derive expressions for counting the number of nonisomorphic triangulations in each class

positive real control for 2 d discrete delayed systems via output feedback controllers this paper considers the problem of positive real control for two dimensional 2 d discrete delayed systems in the fornasini marchesini second local state space model attention is focused on the design of dynamic output feedback controllers which guarantee that the closed loop system is asymptotically stable and the closed loop transfer function is extended strictly positive real we first present a sufficient condition for extended strictly positive realness of 2 d discrete delayed systems based on this a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality lmi when the lmi is feasible an explicit parametrization of a desired output feedback controller is presented finally we provide a numerical example to demonstrate the application of the proposed method

algorithms for the computation of the transfer function matrix for two dimensional regular and singular general state space models the problem of computing the transfer function matrices for regular and singular discrete two dimensional general state space models 2d gm is discussed and some programmable algorithms are developed that generalize the well known leverrier algorithm to 2d systems of general form the results also show that the transfer function matrices for regular and singular 2d gm can also be formulated via the state transition matrices of the systems

reduction of bivariate polynomials from convex dense to dense with application to factorizations in this article we present a new algorithm for reducing the usual sparse bivariate factorization problems to the dense case this reduction simply consists in computing an invertible monomial transformation that produces a polynomial with a dense size of the same order of magnitude as the size of the integral convex hull of the support of the input polynomial this approach turns out to be very efficient in practice as demonstrated with our implementation

the fornasini marchesini and the roesser models algebraic methods for recasting this paper is devoted to giving a new method for recasting the fornasini marchesini model of the two dimensional system to the roesser form endowed with an important feature that the dimensions of both models are the same the two dimensional similarity transformation and spectral transformations of the transfer function variables are used for this purpose both the standard and singular cases are considered

combinatorial methods for the spectral p norm of hypermatrices abstract the spectral p norm of r matrices generalizes the spectral 2 norm of 2 matrices in 1911 schur gave an upper bound on the spectral 2 norm of 2 matrices which was extended in 1934 by hardy littlewood and polya to r matrices recently kolotilina and independently the author strengthened schur s bound for 2 matrices the main result of this paper extends the latter result to r matrices thereby improving the result of hardy littlewood and polya the proof is based on combinatorial concepts like r partite r matrix and symmetrant of a matrix which appear to be instrumental in the study of the spectral p norm in general thus another application shows that the spectral p norm and the p spectral radius of a symmetric nonnegative r matrix are equal whenever p r this result contributes to a classical area of analysis initiated by mazur and orlicz back in 1930 additionally a number of bounds are given on the p spectral radius and the spectral p norm of r matrices and r graphs

analytic methods for uniform hypergraphs abstract this paper presents some analytic methods for studying uniform hypergraphs its starting point is the spectral theory of 2 graphs in particular the largest and the smallest eigenvalues and min of 2 graphs first these two parameters are extended to weighted uniform hypergraphs second the eigenvalues numbers and min are extended to eigenvalues functions p and min p which also encompass other graph parameters like the lagrangian and the number of edges in this way the functions p and min p seamlessly join spectral and traditional results in hypergraphs in particular this new viewpoint helps to show that spectral extremal and edge extremal problems are asymptotically equivalent naturally all results about p and min p also extend spectral hypergraph theory but delve into deeper problems than before in fact the resulting theory is new even for 2 graphs where some well settled topics become research challenges again the paper covers a multitude of topics with more than a hundred concrete statements to underpin an analytic theory for hypergraphs essential among these topics are a perron frobenius type theory and methods for extremal hypergraph problems many open problems are raised and directions for possible further research are outlined

recursive moving window dft algorithm a recursive algorithm is presented for computing the discrete fourier transform dft the algorithm is developed for a moving window type processing the computational structure is fully concurrent and allows a vectorized updating of the dft the total time required for the updating could be as low as that of only one multiplication and two additions regardless of the number of points a possible structure for executing the computations is developed and possible enhancements are analyzed

a fuzzy approach to visibility maps creation over digital terrains the construction of inter visibility models for a terrain is an important tool for environmental and animal studies efficient crisp algorithms are known to address this problem directly on a raster digital elevation map dem of the study area randomness plays an important role several factors like vegetation height of the observer presence of unmapped human artifacts etc cannot be modeled in advance into a traditional dem model we propose the use of fuzzy terrain models to incorporate uncertainty and unpredictable variability of the landscape accordingly we propose a suitable definition of visibility to obtain intervisibility models an algorithm that uses approximation of fuzzy numbers with a discrete family of intervals is proposed the proposed model produces sound results and can be extended to model complex situations like triangulating a radio source using two directional receivers all of these situations are difficult to manage with a precise stochastic model and are a frequent occurrence in animal behavior studies under field conditions the proposed techniques have been implemented inside a user friendly software package that may easily exchange data with the most common giss we report also some experimental results obtained using over artificial terrain under controlled noise and under sampling conditions

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

adaptive mesh generation for viscous flows using delaunay triangulation abstract a method for generating an unstructured triangular mesh in two dimensions suitable for computing high reynolds number flows over arbitrary configurations is presented the method is based on a delaunay triangulation which is perfored in a locally stretched space in order to obtain very high aspect ratio tiangles in the boundary layer and wake regions it is shown how the method can be coupled with an unstructured navier stokes solver to produce a solution adaptive mesh generation procedure for viscous flows

unstructured grid optimization for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients multipoint flux approximation mpfa techniques are commonly applied for discretizing the porous media flow equations within the context of finite volume numerical procedures although these methods can be applied to heterogeneous anisotropic systems on generally unstructured grids the inverse of the resulting linear operator can suffer from a loss of monotonicity at high permeability anisotropy ratios resulting in spurious oscillations of the pressure solution the purpose of this paper is to develop a method for optimizing unstructured grids in two and three dimensions such that the monotonicity behavior of the mpfa technique is significantly improved the method employs anisotropic triangulation and can be readily combined with permeability upscaling procedures results are presented for a variety of examples and the technique is shown to perform well on problems involving complex grid point distributions and heterogeneous permeability fields with strong anisotropy ratios of o 100 oscillation free pressure solutions are achieved in all cases considered even for examples in which the original grid shows large oscillations

comments on 2 d descriptor systems abstract this paper discusses general 2 d descriptor systems of the form ex i 1 j 1 ax i j bx i 1 j cx i j 1 d 0 u i j d 1 u i 1 j d 2 u i j 1 solution formula and structural forms are developed for several large classes of 2 d descriptor systems the idea of a recursive chain is introduced it is shown that these systems include several types of behavior not discussed elsewhere in the literature

m dimensional cayley hamilton theorem the theorem states that every block square matrix satisfies its own m d m dimensional m or 1 matrix characteristic polynomial the exact statement and a simple proof of this theorem are given the theorem refers to a matrix a subdivided into m blocks and hence having dimension at least m the conclusion is that every square matrix a with dimension m satisfies several m d characteristic matrix polynomials with degrees n sub 1 n sub m such that n sub 1 n sub m

realization of noncausal 2 d systems based on a descriptor model it is shown that a class of linear discrete noncausal two dimensional systems can be represented by discrete descriptor systems whose coefficients are functions that admit laurent series expansions on the unit circle in the complex plane the basic idea is to obtain a conventional state space realization with coefficient functions for causal and anticausal subsystems in one direction and then view them as a descriptor system a single entity the resulting model is a 1 d descriptor system with coefficient functions defined on the unit circle in the complex plane some properties of this model concerning minimality are also investigated

adaptive triangular quadrilateral mesh generation in this paper we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps by means of the generation of a unit mesh with respect to a riemannian structure we propose then an automatic triangular to quadrilateral mesh conversion scheme which generalizes the standard case to the anisotropic context in addition we introduce an optimal vertex smoothing procedure application test examples in particular a cfd test are given to demonstrate the eciency of the proposed method 1998 john wiley sons ltd int j numer meth engng 41 915 934 1998

an analysis of simplex shape measures for anisotropic meshes this paper analyses and generalises several simplex shape measures documented in the literature and currently used for mesh adaptation and mesh optimisation it first summarises important properties of simplices and their degeneration in euclidean space different simplex shape measures are then defined and validated according to a validity criterion the shape measures are generalised to riemannian spaces in order to extend their use to anisotropic meshes they are then analysed and compared using complementary approaches a visualisation method helping to show their regularity some theoretical relations establishing their equivalence and a discussion on the evaluation of the global quality of a mesh conclusions are drawn on the choice of a simplex shape measure to guide mesh optimisation

the generalized cayley hamilton theorem for standard pencils abstract the cayley hamilton theorem is extended from the case of one matrix to that of two matrices the developed theorem is suitable for the standard form pencil se a let s det se a r 0 n a r s r then we show that r 0 n a r a r e n r 0 such a neat result which is very similar to the original theorem also is due to some nice properties of the standard pair e a for example e and a commute and share the same eigenspaces

symmetric nonnegative tensors and copositive tensors abstract we first prove two new spectral properties for symmetric nonnegative tensors we prove a maximum property for the largest h eigenvalue of a symmetric nonnegative tensor and establish some bounds for this eigenvalue via row sums of that tensor we show that if an eigenvalue of a symmetric nonnegative tensor has a positive h eigenvector then this eigenvalue is the largest h eigenvalue of that tensor we also give a necessary and sufficient condition for this we then introduce copositive tensors this concept extends the concept of copositive matrices symmetric nonnegative tensors and positive semi definite tensors are examples of copositive tensors the diagonal elements of a copositive tensor must be nonnegative we show that if each sum of a diagonal element and all the negative off diagonal elements in the same row of a real symmetric tensor is nonnegative then that tensor is a copositive tensor some further properties of copositive tensors are discussed

unbiased minimum variance fault and state estimation for linear discrete time varying two dimensional systems the fault and state estimation problem is addressed for a class of linear discrete time varying two dimensional systems subject to state and measurement noises two estimators are proposed to compute the estimation of the system state and or fault recursively both of which are unbiased with minimum variance through formulating the estimation problem as the solvability problem of the corresponding matrix equations of estimator gains and system constraint the necessary and sufficient condition of the existence and the solution for the proposed estimators are given an example is used to demonstrate the effectiveness of the proposed estimators

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner