new block quadrature rules for the approximation of matrix functions abstract golub and meurant have shown how to use the symmetric block lanczos algorithm to compute block gauss quadrature rules for the approximation of certain matrix functions we describe new block quadrature rules that can be computed by the symmetric or nonsymmetric block lanczos algorithms and yield higher accuracy than standard block gauss rules after the same number of steps of the symmetric or nonsymmetric block lanczos algorithms the new rules are block generalizations of the generalized averaged gauss rules introduced by spalevic applications to network analysis are presented

on the defining equations of the tangent cone of a numerical semigroup ring abstract let a a 1 a r be a sequence of positive integers and let h a denote the semigroup generated by a 1 a r for an integer k 0 we denote by a k the shifted sequence a 1 k a r k fix a field k we show that for all k 0 the tangent cone of the semigroup ring k h a k is cohen macaulay and that it has the same betti numbers as k h a k itself as a consequence we show that the number of defining equations of the tangent cone of a numerical semigroup ring is bounded by a value depending only on the width of the semigroup where the width of a numerical semigroup is defined to be the difference of the largest and the smallest element in the minimal generating set of the semigroup we also provide a conjectured upper bound of the above number of equations and we verify it in some cases

representations of the schrodinger group and matrix orthogonal polynomials the representations of the schrodinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states these representations are seen to involve matrix orthogonal polynomials in a discrete variable that have charlier and meixner polynomials as building blocks the underlying lie theoretic framework allows for a systematic derivation of the structural formulas recurrence relations difference equations rodrigues formula etc that these matrix orthogonal polynomials satisfy

a note on the maximization of matrix valued hankel determinants with applications in this note we consider the problem of maximizing the determinant of moment matrices of matrix measures the maximizing matrix measure can be characterized explicitly by having equal matrix valued weights at the zeros of classical one dimensional orthogonal polynomials the results generalize classical work of schoenberg indag math 62 1959 282 to the case of matrix measures as a statistical application we consider several optimal design problems in linear models which generalize the classical weighing design problems

matrix orthogonal polynomials on the unit circle the properties of matrix orthogonal polynomials on the unit circle are investigated beginning with their recurrence formulas the techniques of scattering theory and banach algebras are used in the investigation a matrix generalization of a theorem of baxter is proved

spectral decomposition and matrix valued orthogonal polynomials the relation between the spectral decomposition of a self adjoint operator which is realizable as a higher order recurrence operator and matrix valued orthogonal polynomials is investigated a general construction of such operators from scalar valued orthogonal polynomials is presented two examples of matrix valued orthogonal poly nomials with explicit orthogonality relations and three term recurrence relation are pre sented which both can be considered as 2 2 matrix valued analogues of subfamilies of askey wilson polynomials

matrix polynomial solutions of tangential lagrange sylvester interpolation conditions of low mcmillan degree abstract a matrix polynomial of mcmillan degree n 1 which satisfies n tangential lagrange interpolation conditions is constructed explicitly in realization form analogous results are given for more general bitangential lagrange sylvester interpolation conditions a corollary is a type of euclidean algorithm for matrix polynomials and mcmillan degree the main tool is the recent parametrization of all matrix polynomial solutions of a set of lagrange sylvester interpolation conditions due to ball gohberg and rodman

on polynomials orthogonal with respect to an inner product involving differences abstract in this paper we consider the inner product r x g x d x c g c where c r and is a distribution function with infinite spectrum such that has no points of increase in the interval c c 1 furthermore 0 and g are functions on r and c c 1 c let qn x be the sequence of monic orthogonal polynomials with respect to this inner product and pn x pnc x the sequences of monic standard orthogonal polynomials 0 with respect to d x and x c x c 1 d x respectively we derive an explicit representation for qn x in terms of pn x and pnc x and we present some results on the distribution of the zeros of qn x in relation to the zeros of pn x finally we treat the special case where pn x are charlier polynomials and c 0

a new car following model considering the related factors of a gyroidal road abstract a novel car following model was proposed to describe the motion of the vehicles on a single lane gyroidal road we explore the related effects of gyroidal road upon uniform traffic flow analytically and numerically the analytical result shows that the related factors of gyroidal road including the friction coefficient radius of curvature and slope have great influences on the stability of the uniform flow respectively the modified kdv korteweg de vries equation is derived in the unstable area and the kink solution is obtained near the critical point a series of simulations are conducted to verify the effects upon uniform traffic flow under different road conditions it is shown that the amplitudes of the headway oscillation wave were affected by the friction coefficient radius of curvature and slope respectively the numerical results are in good agreement with the analytical results

shohat favard type theorem for orthogonal series a function f is considered in the form of its formal series expansion k 0 f kp k where p k k 0 denotes a given system of orthogonal polynomials with respect to a measure on the real line we prove that the denominators numerators and residuals of their frobenius pade approximation satisfy a five term recurrence relation the converse result is obtained starting from the sequence of denominators the function f is reconstructed i e the analogous of the classical shohat favard theorem is done

cmv block matrices for symmetric matrix measures on the unit circle abstract in this contribution we study the relationship between the cmv block matrices associated with two symmetric positive definite matrix measures supported on the unit circle we also consider certain transformations of an orthogonality matrix measure supported on the unit circle and deduce connection formulas for the corresponding orthogonal families and their verblunsky matrix coefficients

on the hypergeometric matrix function abstract this paper deals with the study of the hypergeometric function with matrix arguments f a b c z conditions for matrices a b c so that the series representation of the hypergeometric function be convergent for z 1 and satisfies a matrix differential equation are given after the study of beta and gamma matrix functions an integral representation of f a b c z is obtained for the case where b c and c b are positive stable matrices with bc cb

on a class of matrix orthogonal polynomials on the real line abstract it is shown how to construct matrix orthogonal polynomials on the real line provided we have a sequence of scalar orthogonal polynomials over an algebraic harmonic curve we consider the moment matrix associated with a distribution on and related to a basis of the linear space of polynomials obtained through the polynomial which defines the curve this particular moment matrix can be regarded as a hankel block matrix and thus matrix orthogonal polynomials appear in a natural way

equivalence of linear response among extended optimal velocity models we investigate the property of extended optimal velocity ov models of traffic flow in which a driver looks at arbitrary number of vehicles that precede we prove an equivalence of linear response among extended models this equivalence provides a natural understanding of the improvement of the stability of traffic flow

the hilbert function of a maximal cohen macaulay module we study hilbert functions of maximal cm modules over cm local rings when a is a hypersurface ring with dimension d 0 we show that the hilbert function of m with respect to open image in new window is non decreasing if a q f for some regular local ring q we determine a lower bound for e0 m and e1 m and analyze the case when equality holds when a is gorenstein a relation between the second hilbert coefficient of m a and sa m syza1 m is found when g m is cm and depthg a d 1 we give bounds for the first hilbert coefficients of the canonical module of a cm local ring and analyze when equality holds we also give good bounds on hilbert coefficients of m when m is maximal cm and g m is cm

gaussian quadrature formulae for matrix weights we study gaussian quadrature formulae for a matrix weight we firstly show how to generate gaussian quadrature formulae such that the sum of the rank of the quadrature matrix coefficients is a given nonnegative integer l the nodes are the eigenvalues of certain perturbation of the truncated n jacobi matrix of size l or equivalently the zeros of certain matrix combination of two consecutive orthonormal polynomials and the quadrature coefficients are the coefficients in the partial fraction decomposition of the ratio between the inverse of this orthonormal matrix polynomial and the associated polynomial of the second kind we secondly prove that any gaussian quadrature formula for a matrix weight must be of this form

a survey on orthogonal matrix polynomials satisfying second order differential equations the subject of orthogonal polynomials cuts across a large piece of mathematics and its applications two notable examples are mathematical physics in the 19th and 20th centuries as well as the theory of spherical functions for symmetric spaces it is also clear that many areas of mathematics grew out of the consideration of problems like the moment problem that are intimately associated to the study of scalar valued orthogonal polynomials matrix orthogonality on the real line has been sporadically studied during the last half century since krein devoted some papers to the subject in 1949 see ams translations series 2 vol 97 providence rhode island 1971 pp 75 143 dokl akad nauk sssr 69 2 1949 125 in the last decade this study has been made more systematic with the consequence that many basic results of scalar orthogonality have been extended to the matrix case the most recent of these results is the discovery of important examples of orthogonal matrix polynomials many families of orthogonal matrix polynomials have been found that as the classical families of hermite laguerre and jacobi in the scalar case satisfy second order differential equations with coefficients independent of n the aim of this paper is to give an overview of the techniques that have led to these examples a small sample of the examples themselves and a small step in the challenging direction of finding applications of these new examples

analysis of optimal velocity model with explicit delay we analyze the optimal velocity model ovm with explicit delay the properties of congestion and the delay time of car motion are investigated by analytical and numerical methods it is shown that the small explicit delay time has almost no effects in the case of the large explicit delay time a new phase of congestion pattern of ovm seems to appear

a speed feedback control strategy for car following model abstract a speed feedback control mechanism was introduced into the system to improve the dynamical performance of the traffic flow the modern control theory was used to analyze the stability of the system it is found that the stability region varies with the feedback coefficient proportionally in addition the unit step responses in time domain and phase frequency curves in frequency domain were given with different feedback coefficients in step response diagram and bode diagram respectively the overshoot and phase margins are inversely proportional to the speed feedback coefficients in an underdamped condition the simulations were conducted to verify the validity of the improvement the conclusion can be drawn that the analytical result and the simulation result are in good agreement with each other

cohen macaulayness of almost complete intersection tangent cones abstract we prove that associated graded rings of complete intersection monomial curves of codimension three are cohen macaulay if their defining ideals are generated by at most four elements

kink soliton characterizing traffic congestion we study traffic congestion by analyzing a one dimensional traffic flow model developing an asymptotic method to investigate the long time behavior near a critical point we derive the modified korteweg de vries mkdv equation as the lowest order model there is an infinite number of kink solitons to the mkdv equation while it has been found by numerical simulations that the kink pattern arising in traffic congestion is uniquely determined irrespective of initial conditions in order to resolve this selection problem we consider higher order corrections to the mkdv equation and find that there is a kink soliton that can deform continuously with the perturbation represented by the addition of these corrections with numerical confirmation we show that this continuously deformable kink soliton characterizes traffic congestion we also discuss the relationship between traffic congestion and the slugging phenomenon in granular flow

lattice hydrodynamic modeling of two lane traffic flow with timid and aggressive driving behavior abstract in this paper a new two lane lattice hydrodynamic traffic flow model is proposed by considering the aggressive or timid characteristics of driver s behavior the effect of driver s characteristic on the stability of traffic flow is examined through linear stability analysis it is shown that for both the cases of lane changing or without lane changing the stability region significantly enlarges reduces as the proportion of aggressive timid drivers increases to describe the propagation behavior of a density wave near the critical point nonlinear analysis is conducted and mkdv equation representing kink antikink soliton is derived the effect of anticipation parameter with more aggressive timid drivers is also investigated and found that it has a positive negative effect on the stability of two lane traffic flow dynamics simulation results are found consistent with the theoretical findings which confirm that the driver s characteristics play a significant role in a two lane traffic system

stieltjes continued fraction and qd algorithm scalar vector and matrix cases the definition in previous studies of vector stieltjes continued fractions in connection with spectral properties of band operators with intermediate zero diagonals left unsolved the question of a direct definition of their coefficients in terms of the original data a vector of stieltjes series the subject was more undefined in the matrix case a new version of the qd algorithm for matrix problem allows to extend to the vector and matrix cases the result of stieltjes expansion of a scalar function in terms of a stieltjes continued fraction beside this connection it solves the inverse miura transform and gives interesting identities between general band matrix and sparse band matrix finally as a consequence we extend to some dynamical systems a method known for toda lattices

derivation properties and simulation of a gas kinetic based nonlocal traffic model we derive macroscopic traffic equations from specific gas kinetic equations dropping some of the assumptions and approximations made in previous papers the resulting partial differential equations for the vehicle density and average velocity contain a non local interaction term which is very favorable for a fast and robust numerical integration so that several thousand freeway kilometers can be simulated in real time the model parameters can be easily calibrated by means of empirical data they are directly related to the quantities characterizing individual driver vehicle behavior and their optimal values have the expected order of magnitude therefore they allow to investigate the influences of varying street and weather conditions or freeway control measures simulation results for realistic model parameters are in good agreement with the diverse non linear dynamical phenomena observed in freeway traffic

proportional differential effects in traffic car following model system abstract traffic flow system s stability analysis can be seen as a typical control system problem which has three kinds of damping ratio properties from the viewpoint of control theory to discover the damping ratio characteristics of traffic flow system under sudden outer impulse firstly we proposed a new method to build the traffic flow model based on state space theory secondly we deduced one form of state transfer matrix from system closed loop transfer function reversely lastly we fully investigated the proportional differential effects in the traffic car following model system analytically and numerically for unsteady traffic flow system with the proportional differential pd term in order to suppress the traffic jam we derived a kind of decoupled delay feedback control algorithm which used h norm and the numerical simulation method to find the feedback gain k and delay time the traffic flow system s transient performance formula was presented with and without pd term and we found out the important impact of pd term on traffic flow system stability the numerical simulation results substantiate our theoretical and analytical results

differential coefficients of orthogonal matrix polynomials we find explicit formulas for raising and lowering first order differential operators for orthogonal matrix polynomials we derive recurrence relations for the coefficients in the raising and lowering operators some examples are given

matrix valued orthogonal polynomials on the real line some extensions of the classical theory in the work presented below the classical subject of orthogonal polynomials on the real line is discussed in the matrix setting an analogue of the determinant definition of orthogonal polynomials is presented the classical properties such as the recurrence relation the kernel polynomials and the christoffel darboux formula are discussed a function for the system of matrix valued orthogonal polynomials on the real line is presented some properties of the functions are investigated

exceptional laguerre and jacobi polynomials and the corresponding potentials through darboux crum transformations a simple derivation is presented of the four families of infinitely many shapeinvariant hamiltonians corresponding to the exceptional laguerre and jacobi polynomials the darboux crum transformations are applied to connect the well known shape invariant hamiltonians of the radial oscillator and the darboux p oschl teller potential to the shape invariant potentials of odake sasaki dutta and roy derived the two lowest members of the exceptional laguerre polynomials by this method the method is expanded to its full generality and many other ramifications including the aspects of the generalized bochner problem and the bispectral property of the exceptional orthogonal polynomials are discussed

matrix measures moment spaces and favard s theorem for the interval 0 1 and 0 abstract in this paper we study the moment spaces corresponding to matrix measures on compact intervals and on the nonnegative line 0 a representation for nonnegative definite matrix polynomials is obtained which is used to characterize moment points by properties of generalized hankel matrices we also derive an explicit representation of the orthogonal polynomials with respect to a given matrix measure which generalizes the classical determinant representation of the one dimensional case moreover the coefficients in the recurrence relations can be expressed explicitly in terms of the moments of the matrix measure these results are finally used to prove a refinement of the well known favard theorem for matrix measures which characterizes the domain of the underlying measure of orthogonality by properties of the coefficients in the recurrence relationships

a class of matrix orthogonal polynomials on the unit circle abstract the study of matrix orthogonal polynomials on the unit circle is connected with problems of applied mathematics such as filtering theory prediction theory and scattering theory in this paper some families of matrix orthogonal polynomials on the unit circle are given explicitly the decomposition a z z a z z h 1 a z where is the linear space of complex algebraic polynomials is the main idea for this approach

jacobi matrix differential equation polynomial solutions and their properties in this paper jacobi matrix polynomials are introduced starting from the hypergeometric matrix function the differential equation satisfied by them is presented a rodrigues formula orthogonality and a three terms matrix recurrence relationship are then developed for jacobi matrix polynomials

the korteweg de vries soliton in the lattice hydrodynamic model abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but is also closely connected with the microscopic car following model the modified korteweg de vries mkdv equation about the density wave in congested traffic has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail in the car following model so we devote ourselves to obtaining the kdv equation from the lattice hydrodynamic model and obtaining the kdv soliton solution describing the traffic jam numerical simulation is conducted to demonstrate the nonlinear analysis result

hilbert function of local artinian level rings in codimension two abstract in this paper we characterize the possible hilbert functions of a local artinian level ring of given type and socle degree in the codimension two case in particular given an admissible numerical function h an effective method is given to produce a zero dimensional ideal i of r k x y such that r i is a local artinian level ring having h as hilbert function as a consequence we recover the well known result proved by briancon and iarrobino concerning the hilbert functions of a complete intersection of height two we extend notions of standard or grobner bases from the graded to the local algebra context the principal tools concern the concepts of enhanced standard basis and generic initial ideals which are defined for an ideal in the formal power series ring r k x 1 x n

matrix valued spherical functions associated to the complex projective plane abstract the main purpose of this paper is to compute all irreducible spherical functions on g su 3 of arbitrary type k where k s u 2 u 1 u 2 this is accomplished by associating to a spherical function on g a matrix valued function h on the complex projective plane p2 c g k it is well known that there is a fruitful connection between the hypergeometric function of euler and gauss and the spherical functions of trivial type associated to a rank one symmetric pair g k but the relation of spherical functions of types of dimension bigger than one with classical analysis has not been worked out even in the case of an example of a rank one pair the entries of h can be described by solutions of two systems of ordinary differential equations there is no ready made approach to such a pair of systems or even to a single system of this kind in our case the situation is very favorable and the solution to this pair of systems can be exhibited explicitly in terms of a special class of generalized hypergeometric functions p 1fp

stabilization effect of traffic flow in an extended car following model based on an intelligent transportation system application an extended car following model is proposed by incorporating an intelligent transportation system in traffic the stability condition of this model is obtained by using the linear stability theory the results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by applying the reductive perturbation method the traffic jam could be thus described by the kink antikink soliton solution for the mkdv equation from the simulation of space time evolution of the vehicle headway it is shown that the traffic jam is suppressed efficiently with taking into account the information about the motion of more vehicles in front and the analytical result is consonant with the simulation one

orthogonal polynomials and analytic functions associated to positive definite matrices abstract for a positive definite infinite matrix a we study the relationship between its associated sequence of orthonormal polynomials and the asymptotic behaviour of the smallest eigenvalue of its truncation a n of size n n for the particular case of a being a hankel or a hankel block matrix our results lead to a characterization of positive measures with finite index of determinacy and of completely indeterminate matrix moment problems respectively

the leading ideal of a complete intersection of height two part ii abstract let s n be a regular local ring and let i f g be an ideal in s generated by a regular sequence f g of length two let r s i and m n i as in s goto w heinzer m k kim the leading ideal of a complete intersection of height two j algebra 298 2006 238 247 we examine the leading form ideal i of i in the associated graded ring g gr n s if gr m r is cohen macaulay we describe precisely the hilbert series h gr m r in terms of the degrees of homogeneous generators of i and of their successive gcd s if d gcd f g is a prime element of gr n s that is regular on gr n s f d g d we prove that i is 3 generated and a perfect ideal if ht gr n s f g h 2 where h i is such that h is of minimal degree in i f g gr n s we prove i is 3 generated and a perfect ideal of gr n s so gr m r gr n s i is a cohen macaulay ring we give several examples to illustrate our theorems

trace formulas and borg type theorems for matrix valued jacobi and dirac finite difference operators abstract borg type uniqueness theorems for matrix valued jacobi operators h and supersymmetric dirac difference operators d are proved more precisely assuming reflectionless matrix coefficients a b in the self adjoint jacobi operator h as a s b with s the right left shift operators on the lattice z and the spectrum of h to be a compact interval e e e e we prove that a and b are certain multiples of the identity matrix an analogous result which however displays a certain novel nonuniqueness feature is proved for supersymmetric self adjoint dirac difference operators d with spectrum given by e 1 2 e 1 2 e 1 2 e 1 2 0 e e our approach is based on trace formulas and matrix valued exponential herglotz representation theorems as a by product of our techniques we obtain the extension of flaschka s borg type result for periodic scalar jacobi operators to the class of reflectionless matrix valued jacobi operators

stabilization and enhancement of traffic flow by the next nearest neighbor interaction the car following model of traffic is extended to take into account the car interaction before the next car ahead the next nearest neighbor interaction the traffic behavior of the extended car following model is investigated numerically and analytically it is shown that the next nearest neighbor interaction stabilizes the traffic flow the jamming transition between the freely moving and jammed phases occurs at a higher density than the threshold of the original car following model by increasing the maximal velocity the traffic current is enhanced without jam by the stabilization effect the jamming transition is analyzed with the use of the linear stability and nonlinear perturbation methods the traffic jam is described by the kink solution of the modified korteweg char21 de vries equation the theoretical coexisting curve is in good agreement with the simulation result

cyclic tridiagonal pairs higher order onsager algebras and orthogonal polynomials abstract the concept of cyclic tridiagonal pairs is introduced and explicit examples are given for a fairly general class of cyclic tridiagonal pairs with cyclicity n we associate a pair of divided polynomials the properties of this pair generalize the ones of tridiagonal pairs of racah type the algebra generated by the pair of divided polynomials is identified as a higher order generalization of the onsager algebra it can be viewed as a subalgebra of the q onsager algebra for a proper specialization at q the primitive 2 n th root of unity orthogonal polynomials beyond the leonard duality are revisited in light of this framework in particular certain second order dunkl shift operators provide a realization of the divided polynomials at n 2 or q i

orthogonal matrix polynomials and applications orthogonal matrix polynomials on the real line or on the unit circle have properties which are natural generalizations of properties of scalar orthogonal polynomials appropriately modified for the matrix calculus we show that orthogonal matrix polynomials both on the real line and on the unit circle appear at various places and we describe some of them the spectral theory of doubly infinite jacobi matrices can be described using orthogonal 2 x 2 matrix polynomials on the real line scalar orthogonal polynomials with a sobolev inner product containing a finite number of derivatives can be studied using matrix orthogonal polynomials on the real line orthogonal matrix polynomials on the unit circle are related to unitary block hessenberg matrices and are very useful in multivariate time series analysis and multichannel signal processing finally we show how orthogonal matrix polynomials can be used for gaussian quadrature of matrix valued functions parallel algorithms for this purpose have been implemented using pvm and some examples are worked out

gaussian quadrature for matrix valued functions on the real line abstract parallel versions of the block chebyshev algorithm to generate the recursion coefficients of orthonormal matrix polynomials and the gaussian quadrature algorithm to approximate matrix integrals on the real line are implemented on an sp1

perturbations in the nevai matrix class of orthogonal matrix polynomials in this paper we study a jacobi block matrix and the behavior of the limit of its entries when a perturbation of its spectral matrix measure by the addition of a dirac delta matrix measure is introduced 2001 elsevier science inc all rights reserved

computation of matrix valued formally orthogonal polynomials and applications we present a computational procedure for generating formally orthogonal polynomials associated with a given bilinear hankel form with rectangular matrix valued moments our approach covers the most general case of moments of any size and is not restricted to square moments moreover our algorithm has a built in deflation procedure to handle linearly dependent or almost linearly dependent columns and rows of the block hankel matrix associated with the bilinear form possible singular or close to singular leading principal submatrices of the deflated block hankel matrix are avoided by means of look ahead techniques applications of the computational procedure to eigenvalue computations reduced order modeling the solution of multiple linear systems and the fast solution of block hankel systems are also briefly described

on weyl titchmarsh theory for singular finite difference hamiltonian systems we develop the basic theory of matrix valued weyl titchmarsh m functions and the associated green s matrices for whole line and half line self adjoint hamiltonian finite difference systems with separated boundary conditions

on the hilbert function of one dimensional local complete intersections abstract the sequences that occur as hilbert functions of standard graded algebras a are well understood by macaulay s theorem those that occur for graded complete intersections are elementary and were known classically however much less is known in the local case once the dimension of a is greater than zero or the embedding dimension is three or more using an extension to the power series ring r of grobner bases with respect to local degree orderings we characterize the hilbert functions h of one dimensional quadratic complete intersections a r i i f g of type 2 2 that is that are quotients of the power series ring r in three variables by a regular sequence f g whose initial forms are linearly independent and of degree 2 we also give a structure theorem up to analytic isomorphism of a for the minimal system of generators of i given the hilbert function more generally when the type of i is 2 b we are able to give some restrictions on the hilbert function in this case we can also prove that the associated graded algebra of a is cohen macaulay if and only if the hilbert function of a is strictly increasing

n extremal matrices of measures for an indeterminate matrix moment problem in this paper we study the n extremal matrices of measures associated to a completely indeterminate matrix moment problem i e those matrices of measure w solutions of a completely indeterminate matrix moment problem for which the linear space of matrix polynomials is dense in the corresponding l2 w

polynomial interpolation and gaussian quadrature for matrix valued functions abstract the techniques for polynomial interpolation and gaussian quadrature are generalized to matrix valued functions it is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the highest degree of precision

global bifurcation investigation of an optimal velocity traffic model with driver reaction time we investigate an optimal velocity model which includes the reflex time of drivers after an analytical study of the stability and local bifurcations of the steady state solution we apply numerical continuation techniques to investigate the global behavior of the system specifically we find branches of oscillating solutions connecting hopf bifurcation points which may be super or subcritical depending on parameters this analysis reveals several regions of multistability

rational driver approximation in car following theory the problem of a car following a lead car driven with constant velocity is considered to derive the governing equations for the following car dynamics a cost functional is constructed this functional ranks the outcomes of different driving strategies which applies to fairly general properties of the driver behavior assuming rational driver behavior the existence of the nash equilibrium is proved rational driving is defined by supposing that a driver corrects continuously the car motion to follow the optimal path minimizing the cost functional the corresponding car following dynamics is described quite generally by a boundary value problem based on the obtained extremal equations linearization of these equations around the stationary state results in a generalization of the widely used optimal velocity model under certain conditions the dense traffic limit the rational car dynamics comprises two stages fast and slow during the fast stage a driver eliminates the velocity difference between the cars the subsequent slow stage optimizes the headway in the dense traffic limit an effective hamiltonian description is constructed this allows a more detailed nonlinear analysis finally the differences between rational and bounded rational driver behavior are discussed the latter in particular justifies some basic assumptions used recently by the authors to construct a car following model lying beyond the frameworks of rationality

on some n 1 symmetric linear functionals abstract many authors have dealt with problems related to the symmetrization of sequences of orthogonal polynomials on a real line or on a unit circle particular aspects are treated for quadratic or cubic decompositions in this paper we present a technique that unifies the treatment of these topics for an arbitrary positive order of decomposition n by considering a more general definition of orthogonality this technique is based on the decomposition with respect to the cyclic group of order n the main theorem is applied to the orthogonality on n 1 symmetric curves some particular cases are singled out these results may be useful in studying hermite pade approximations vector continued fractions and dynamical systems

a new car following model with the consideration of anticipation optimal velocity abstract in this paper a new anticipation optimal velocity model aovm is proposed by considering anticipation effect on the basis of the full velocity difference model fvdm for car following theory on single lane the linear stability condition is derived from linear stability analysis starting and braking process is investigated for the car motion under a traffic signal which shows that the results accord with empirical traffic values especially aovm can avoid the disadvantage of the unrealistically high deceleration appearing in fvdm furthermore numerical simulation shows that aovm might avoid the disadvantage of negative velocity and headway that occur at small sensitivity coefficients in the fvdm since the anticipation effect is taken into account in aovm which means that collision disappears with the consideration of an appropriate anticipation parameter

interactions of waves in the speed gradient traffic flow model abstract in this paper we use the speed gradient sg model proposed by jiang et al transportation research part b 36 2002 405 419 to study the initial value problem of traffic flow the evolution of multi traffic waves is examined through setting piecewise continuous initial density numerical results show that distinct shocks and smooth transition layers appear instantaneously for some initial densities and the shock front is smoothed by the smooth transition layer ahead of or behind it if in the initial density the length of shock section or the length of lower density section before the shock is very short we thus verify that the sg model can satisfyingly reproduce the evolution of multi traffic waves with various initial densities

generalized chebyshev polynomials and discrete schrodinger operators we investigate a solution of the difference equation with the boundary conditions u0a b i u 1a b 0 where a b are hermitian elements of a c algebra una b are usually called generalized chebyshev polynomials of the second kind the equation cannot be easily simplified as in the scalar case because a and b do not need to commute however we are able to compute the spectrum of the corresponding orthogonality measure which is very important for the investigation of the discrete schrodinger operator related to una b

a note on the matrix valued q d algorithm and matrix orthogonal polynomials on 0 1 and 0 in this note a matrix version of the q d algorithm is introduced it is shown that the algorithm may be used to obtain the coefficients of the recurrence relations for matrix orthogonal polynomials on the interval 0 and 0 1 from its moment generating functional the algorithm is illustrated by several examples which generalize classical orthogonal polynomials on the real line

on matrix integration of matrix polynomials this paper is the result of having read a series of recent papers on the quadrature formula for matrix integrals which caused a strong want of clarifying the circumstances for this purpose we have had to revise orthogonality for matrix polynomials being supported by a desire of using means adequate to needs and at the same time of trying to simplify the set up

matrix differential equations and scalar polynomials satisfying higher order recursions abstract we show that any scalar differential operator with a family of polynomials as its common eigenfunctions leads canonically to a matrix differential operator with the same property the construction of the corresponding family of matrix valued polynomials has been studied in a duran a generalization of favard s theorem for polynomials satisfying a recurrence relation j approx theory 74 1993 83 109 a duran on orthogonal polynomials with respect to a positive definite matrix of measures canad j math 47 1995 88 112 a duran w van assche orthogonal matrix polynomials and higher order recurrence relations linear algebra appl 219 1995 261 280 but the existence of a differential operator having them as common eigenfunctions had not been considered this correspondence goes only one way and most matrix valued situations do not arise in this fashion we illustrate this general construction with a few examples in the case of some families of scalar valued polynomials introduced in f a grunbaum l haine bispectral darboux transformations an extension of the krall polynomials int math res not 8 1997 359 392 we take a first look at the algebra of all matrix differential operators that share these common eigenfunctions and uncover a number of phenomena that are new to the matrix valued case

orthogonal matrix polynomials and quadrature formulas we prove that the nodes of a quadrature formula for a matrix weight with the highest degree of precision must necessarily be the zeros of a certain orthonormal matrix polynomial with respect to the matrix weight and the quadrature coefficients are then the coefficients in the partial fraction decomposition of the ratio between the inverse of this orthonormal matrix polynomial and the associated polynomial of the second kind we also extend this result for quadrature formulas with degree of precision one unit smaller than the highest possible

relative asymptotics for orthogonal matrix polynomials in this paper we study sequences of matrix polynomials that satisfy a non symmetric recurrence relation to study this kind of sequences we use a vector interpretation of the matrix orthogonality in the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class we study the generalized matrix chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples the concept of a dirac delta functional is introduced we show how the vector model that includes a dirac delta functional is a representation of a discrete sobolev inner product it also allows to reinterpret such perturbations in the usual matrix nevai class finally the relative asymptotics between a polynomial in the generalized matrix nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a dirac delta functional is deduced

the leading ideal of a complete intersection of height two abstract let s n be a noetherian local ring and let i f g be an ideal in s generated by a regular sequence f g of length two assume that the associated graded ring gr n s of s with respect to n is a ufd we examine generators of the leading form ideal i of i in gr n s and prove that i is a perfect ideal of gr n s if i is 3 generated thus in this case letting r s i and m n i if gr n s is cohen macaulay then gr m r gr n s i is cohen macaulay as an application we prove that if r m is a one dimensional gorenstein local ring of embedding dimension 3 then gr m r is cohen macaulay if the reduction number of m is at most 4

on a weyl titchmarsh theory for discrete symplectic systems on a half line recently bohner and sun introduced basic elements of a weyl titchmarsh theory into the study of discrete symplectic systems we extend this development through the introduction of weyl titchmarsh functions together with a preliminary study of their properties a limit point criterion is described and characterized green s function for the half line is introduced as a limit of such functions in the regular case and half line solutions obtained are seen to satisfy lambda dependent boundary conditions at infinity

on a multivariable extension of jacobi matrix polynomials the classical jacobi matrix polynomials only for commutative matrices were first studied by defez et al e defez l jodar a law jacobi matrix differential equation polynomial solutions and their properties comput math appl 48 2004 789 803 the main aim of this paper is to construct a multivariable extension with the help of the classical jacobi matrix polynomials jmps generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived furthermore general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented

stability of the car following model on two lanes in the case of two lane traffic vehicle drivers always worry about the lane changing actions from neighbor lane this paper studies the stability of a car following model on two lanes which incorporates the lateral effects in traffic the stability condition of the model is obtained by using the linear stability theory the modified korteweg de vries equation is constructed and solved and three types of traffic flows in the headway sensitivity space stable metastable and unstable are classified both analytical and simulation results show that the anxiousness about lane changing from neighbor lane indeed has influence upon people s driving behavior and the consideration of lateral effects could stabilize the traffic flows on both lanes

a class of orthogonal polynomials on the radial rays in the complex plane abstract we introduce a class of polynomials orthogonal on some radial rays in the complex plane and investigate their existence and uniqueness a recurrence relation for these polynomials a representation and the connection with standard polynomials orthogonal on 0 1 are derived it is shown that their zeros are simple and distributed symmetrically on the radial rays with the possible exception of a multiple zero at the origin an analogue of the jacobi polynomials and the corresponding problem with the generalized laguerre polynomials are also treated

a connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line szego s procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on 1 1 is generalized to nonsymmetric measures it generates the so called semi orthogonal functions on the linear space of laurent polynomials and leads to a new orthogonality structure in the module this structure can be interpreted in terms of a 2 2 matrix measure on 1 1 and semi orthogonal functions provide the corresponding sequence of orthogonal matrix polynomials this gives a connection between orthogonal polynomials on the unit circle and certain classes of matrix orthogonal polynomials on 1 1 as an application the strong asymptotics of these matrix orthogonal polynomials is derived obtaining an explicit expression for the corresponding szego s matrix function

delay effect on phase transitions in traffic dynamics a dynamical model of traffic is proposed to take into account the effect of acceleration delay in the limit of no delay the model reproduces the optimal velocity model of traffic when the delay is small it is shown that the phase transition among the freely moving phase the coexisting phase and the uniform congested phase occurs below the critical point above the critical point no phase transition occurs the value a c of the critical point increases with increasing delay time 1 b where a is the friction coefficient or sensitivity parameter when the delay time is longer than frac 1 2 the critical point disappears and the phase transition always occurs the linear stability theory and nonlinear analysis are applied the critical point predicted by the linear stability theory agrees with the simulation result the modified korteweg de vries kdv equation is obtained from the nonlinear analysis near the critical point the phase separation line obtained from the modified kdv equation is consistent with the simulation result

orthogonal matrix polynomials and higher order recurrence relations abstract it is well known that orthogonal polynomials on the real line satisfy a three term recurrence relation and conversely every system of polynomials satisfying a three term recurrence relation is orthogonal with respect to some positive borel measure on the real line we extend this result and show that every system of polynomials satisfying some 2 n 1 term recurrence relation can be expressed in terms of orthonormal matrix polynomials for which the coefficients are n n matrices we apply this result to polynomials orthogonal with respect to a discrete sobolev inner product and other inner products in the linear space of polynomials as an application we give a short proof of krein s characterization of orthogonal polynomials with a spectrum having a finite number of accumulation points

full velocity difference model for a car following theory in this paper we present a full velocity difference model for a car following theory based on the previous models in the literature to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in car following process than others this point is verified by numerical simulation then we investigate the property of the model using both analytic and numerical methods and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion

comment on analysis of optimal velocity model with explicit delay the effect of including an explicit delay time due to driver reaction on the optimal velocity model is studied for a platoon of vehicles to avoid collisions many vehicle simulations demonstrate that delay times must be well below the critical delay time determined by a linear analysis for the response of a single vehicle safe platoons require rather small delay times substantially smaller than typical reaction times of drivers the present results do not support the conclusion of bando et al m bando k hasebe k nakanishi and a nakayama phys rev e 58 5429 1998 that explicit delay plays no essential role

the theoretical analysis of the lattice hydrodynamic models for traffic flow theory abstract the lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model but also connected with the microscopic car following model closely the modified korteweg de vries mkdv equation related to the density wave in a congested traffic region has been derived near the critical point since nagatani first proposed it but the korteweg de vries kdv equation near the neutral stability line has not been studied which has been investigated in detail for the car following model we devote ourselves to obtaining the kdv equation from the original lattice hydrodynamic models and the kdv soliton solution to describe the traffic jam especially we obtain the general soliton solution of the kdv equation and the mkdv equation we review several lattice hydrodynamic models which were proposed recently we compare the modified models and carry out some analysis numerical simulations are conducted to demonstrate the nonlinear analysis results

phase diagram of a non signalized t shaped intersection abstract in this paper we investigated a non signalized t shaped intersection using the cellular automata model under the open boundary condition two different priority rules at intersection are introduced rule 1 rule 2 to eliminate the jam packed state phase diagram and its variation with the ratios of right and or left turning vehicles are investigated the space time and the density profiles are also studied the simulation results indicate that the system does not show the same performance under different priority rules where rule 1 resp rule 2 can be better than rule 2 resp rule 1 according to the ratios of turning vehicles

quadrature formulas for matrix measures a geometric approach a geometric approach to quadrature formulas for matrix measures is presented using the relations between the representations of the boundary points of the moment space generated by all matrix measures and quadrature formulas simple proofs of existence and uniqueness of quadrature formulas of maximal degree of precision are given several new quadrature formulas for matrix measures supported on a compact interval are presented and several examples are discussed additionally a special construction of degenerated quadrature formulas is discussed and some results regarding the location of the zeros of polynomials orthogonal with respect to a matrix measure on a compact interval are obtained as a by product