fast sweeping algorithms for a class of hamilton jacobi equations we derive a godunov type numerical flux for the class of strictly convex homogeneous hamiltonians that includes h p q sqrt ap 2 bq 2 2cpq c 2 ab we combine our godunov numerical fluxes with simple gauss seidel type iterations for solving the corresponding hamilton jacobi hj equations the resulting algorithm is fast since it does not require a sorting strategy as found e g in the fast marching method in addition it providesa way to compute solutions to a class of hj equations for which the conventional fast marching method is not applicable our experiments indicate convergence after a few iterations even in rather difficult cases

boundedness of inhomogeneous journe s type operators on multi parameter local hardy spaces abstract in this paper we establish a boundedness criterion of a class of inhomogeneous journe s type of multi parameter singular integral operators on multi parameter local hardy spaces h p r n 1 r n k recently introduced in ding et al 2019 the consideration of such inhomogeneous journe s type of multi parameter singular integral operators is motivated by the study of the multi parameter pseudo differential operators on multi parameter local hardy spaces the lack of the vanishing moments of both the corresponding functions in the multi parameter local calderon reproducing formula and the multi parameter local littlewood paley stein functions as well as the lack of vanishing moments of atoms in the multi parameter local hardy spaces h p r n 1 r n k with large size all create substantial difficulties in our proofs

some weighted norm inequalities for cordoba s maximal function where r is a rectangle in 6r the family of all rectangles whose sides are parallel to the coordinate axes in r 3 and whose side lengths in the x y and z directions are given by s t and s t respectively here s t 0 are arbitrary in this note our purpose will be to give the necessary and sufficient condition on w for the weighted inequality r f pw cp r if i w for p 1

inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation in this paper we first give the solvability condition for the following inverse eigenproblem iep given a set of vectors xi i 1m in cn and a set of complex numbers i i 1m find a centrosymmetric or centroskew matrix c in rn n such that xi i 1m and i i 1m are the eigenvectors and eigenvalues of c respectively we then consider the best approximation problem for the ieps that are solvable more precisely given an arbitrary matrix b in rn n we find the matrix c which is the solution to the iep and is closest to b in the frobenius norm we show that the best approximation is unique and derive an expression for it

the sharp bound for the hilbert transform on weighted lebesgue spaces in terms of the classical ap characteristic we show that the norm of the hilbert transform as an operator in the weighted space l p r for 2 p oo is bounded by a constant multiple of the first power of the classical ap characteristic of this result is sharp we also prove a bilinear imbedding theorem with simple conditions

experiment and simulation of pedestrian counter flow abstract pedestrian counter flow is investigated by experiment and simulation the experiment is performed for the channel with open boundaries two types of walkers going to the right and to the left are taken into account the video recordings and measurements of individual arrival times are evaluated the pattern formation and jamming transition are discussed the experiment is mimicked by the lattice gas simulation where each person is simulated by a biased random walker taking into account following the front persons with the same direction the experimental result is compared with the simulation result it is shown that the arrival time obtained from experiment is consistent with that of the simulation also the jamming transition does not occur in the experiment because of the finite size effect

on adaptive evd asymptotic distribution of centro symmetric covariance matrices this article investigates the gain in statistical performance complexity of the adaptive estimation of the eigenvalue decomposition evd of covariance matrices when the centro symmetric cs structure of such matrices is utilized after deriving the asymptotic distribution of the evd estimators it is shown in particular that the closed form expressions for the asymptotic covariance of batch and adaptive evd estimators are very similar provided that the number of samples is replaced by the inverse of the step size

an efficient discontinuous galerkin method on triangular meshes for a pedestrian flow model in this paper we develop a discontinuous galerkin method on triangular meshes to solve the reactive dynamic user equilibrium model for pedestrian flows the pedestrian density in this model is governed by the conservation law in which the flow flux is implicitly dependent on the density through the eikonal equation to solve the eikonal equation efficiently at each time level we use the fast sweeping method two numerical examples are then used to demonstrate the effectiveness of the algorithm copyright 2008 john wiley sons ltd

multiparameter maximal functions along dilation invariant hypersurfaces consider the hypersurface sn l ll x7 i in rn l the asso ciated maximal function operator is defined as the supremum of means taken over those parts of the surface lying above the rectangles 0 1 an analogous result is proved for a quadratic surface in r3

weighted norm inequalities for the continuous square function we prove new weighted norm inequalities for real variable analogues of the lusin area function we apply our results to obtain new i weighted norm inequalities for singular integral operators ii weighted sobolev inequalities iii eigenvalue estimates for degenerate schrodinger operators

bcr method for solving generalized coupled sylvester equations over centrosymmetric or anti centrosymmetric matrix abstract this paper introduces another version of biconjugate residual method bcr for solving the generalized coupled sylvester matrix equations over centrosymmetric or anti centrosymmetric matrix we prove this version of bcr algorithm can find the centrosymmetric solution group of the generalized coupled matrix equations for any initial matrix group within finite steps in the absence of round off errors furthermore a method is provided for choosing the initial matrices to obtain the least norm solution of the problem at last some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed

multi parameter singular radon transforms ii the lp theory the purpose of this paper is to study the l2 boundedness of operators of the form f x f t x k t dt where t x is a c function defined on a neighborhood of the origin in t x n n satisfying 0 x x is a c cut off function supported on a small neighborhood of 0 n and k is a multi parameter singular kernel supported on a small neighborhood of 0 n the goal is given an appropriate class of kernels k to give conditions on such that every operator of the above form is bounded on l2 the case when k is a calderon zygmund kernel was studied by christ nagel stein and wainger we generalize their conditions to the case when k has a multi parameter structure for example when k is given by a product kernel even when k is a calderon zygmund kernel our methods yield some new results this is the first paper in a three part series the later two of which are joint with e m stein the second paper deals with the related question of lp boundedness while the third paper deals with the special case when is real analytic

estimates for operator norms on weighted spaces and reverse jensen inequalities we examine the dependence on the a p norm of w of the operator norms of singular integrals maximal functions and other operators in l p w we also examine connections between some fairly general reverse jensen inequalities and the a p and rh p weight conditions

a microscopic pedestrian simulation model and its application to intersecting flows abstract we develop a microscopic pedestrian simulation model in which pedestrian positions are updated at discrete time steps at each time step each pedestrian probabilistically selects a direction of movement from a predetermined set according to a logit type function that considers the dynamics of other pedestrians around and then selects a step size that satisfies a certain distribution we perform a number of field experiments on real intersecting pedestrian flows with four different angles we then validate and calibrate the model using sample data on the deviation angles step velocities and velocity density relations obtained from the experiments

a higher order macroscopic model for pedestrian flows abstract this paper develops a higher order macroscopic model of pedestrian crowd dynamics derived from fluid dynamics that consists of two dimensional euler equations with relaxation the desired directional motion of pedestrians is determined by an eikonal type equation which describes a problem that minimizes the instantaneous total walking cost from origin to destination a linear stability analysis of the model demonstrates its ability to describe traffic instability in crowd flows the algorithm to solve the macroscopic model is composed of a splitting technique introduced to treat the relaxation terms a second order positivity preserving central upwind scheme for hyperbolic conservation laws and a fast sweeping method for the eikonal type equation on unstructured meshes to test the applicability of the model we study a challenging pedestrian crowd flow problem of the presence of an obstruction in a two dimensional continuous walking facility the numerical results indicate the rationality of the model and the effectiveness of the computational algorithm in predicting the flux or density distribution and the macroscopic behavior of the pedestrian crowd flow the simulation results are compared with those obtained by the two dimensional lighthill whitham richards pedestrian flow model with various model parameters which further shows that the macroscopic model is able to correctly describe complex phenomena such as stop and go waves observed in empirical pedestrian flows

efficient subspace based algorithm for adaptive bearing estimation and tracking in some practical applications of array processing the directions of the incident signals should be estimated adaptively and or the time varying directions should be tracked promptly in this paper an adaptive bearing estimation and tracking abest algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow band signals impinging on a uniform linear array ula based on the subspace based method without eigendecomposition sumwe where a linear operator is obtained from the array data to form a basis for the null space by exploiting the array geometry and its shift invariance property specifically the null space is estimated using the least mean square lms or normalized lms nlms algorithm and the directions are updated using the approximate newton method the transient analyses of the lms and nlms algorithms are studied where the weight i e the linear operator is in the form of a matrix and there is a correlation between the additive noise and input data that involve the instantaneous correlations of the received array data in the updating equation and the step size stability conditions are derived explicitly in addition the analytical expressions for the mean square error mse and mean square deviation msd learning curves of the lms algorithm are clarified the effectiveness of the abest algorithm is verified and the theoretical analyses are corroborated through numerical examples simulation results show that the abest algorithm is computationally simple and has good adaptation and tracking abilities

multiparameter operators and sharp weighted inequalities this article is concerned with the operators from harmonic analysis which are naturally associated to a multiple parameter family of dilations we are especially interested here in dealing with questions from the theory of such operators whose answers cannot be obtained by a reduction to the case of product operators we also introduce a new tool in order to carry out this multiparameter analysis which comes from the classical theory this is the concept of sharp weighted inequalities where for operators such as the hilbert transform or classical square function one asks for hilbert space inequalities which imply the correct estimates of the norm on lp of these operators as p becomes large 0 introduction in this article our main goal is to study classes of oper ators associated with multiparameter groups of dilations on rn in some sense the consideration of these operators is a natural next step or simplest case after those of the classical calderon zygmund theory and the product space theory it turns out that in order to obtain estimates for the multiparameter operators we shall be led to the following type of extremely classical question how does one obtain l2 estimates on r1 for the hilbert transform or other singular integrals which yield sharp estimates on the lp rl operator norm of h as p approaches 1 or oc these sharp weighted inequalities are of some independent interest and their study will be seen to be essentially equivalent to the deep work of chang wilson and wolff 3 on the exponential square integrability of functions whose area integral is bounded they also have other applications for example they provide an immediate extension of the chang wilson wolff estimates to product spaces as given by pipher in 12 at this point let us be more specific about the exact nature of the multipa rameter operators which we shall consider consider in r3 the dilations given by ps t x y z sx ty9 stz for s91 0 then there is a maximal operator first considered by zygmund ml and singular integrals tl introduced by ricci and stein 13 naturally associated to these dilations the maximal operator af3 is defined by

the lagrangian coordinate system and what it means for two dimensional crowd flow models abstract a continuum crowd flow model is solved using the lagrangian coordinate system the system has proven to give computational advantages over the traditional eulerian coordinate system for one dimensional road traffic flow our extension of the model and simulation method to two dimensional crowd flow paves the way to explore the advantages for crowd flow simulation detailed analysis of the advantages is left for future research however this paper provides a first exploration and shows that a model and simulation method for two dimensional crowd flow can be developed using lagrangian numerical techniques and that it leads to accurate simulation results

sharp weighted estimates for classical operators abstract we give a general method based on dyadic calderon zygmund theory to prove sharp one and two weight norm inequalities for some of the classical operators of harmonic analysis the hilbert and riesz transforms the beurling ahlfors operator the maximal singular integrals associated to these operators the dyadic square function and the vector valued maximal operator in the one weight case we prove the sharp dependence on the a p constant by finding the best value for the exponent p such that t f l p w c n t w a p p f l p w for the hilbert transform the riesz transforms and the beurling ahlfors operator the sharp value of p was found by petermichl and volberg 2007 2008 2002 47 48 49 their proofs used approximations by the dyadic haar shift operators bellman function techniques and two weight norm inequalities our proofs again depend on dyadic approximation but avoid bellman functions and two weight norm inequalities we instead use a recent result due to a lerner 2010 34 to estimate the oscillation of dyadic operators by applying this we get a straightforward proof of the sharp dependence on the a p constant for any operator that can be approximated by haar shift operators in particular we provide a unified approach for the hilbert and riesz transforms the beurling ahlfors operator and their corresponding maximal singular integrals dyadic paraproducts and haar multipliers furthermore we completely solve the open problem of sharp dependence for the dyadic square functions and vector valued hardy littlewood maximal function in the two weight case we use the very same techniques to prove sharp results in the scale of a p bump conditions for the singular integrals considered above we show they map l p v into l p u 1 p if the pair u v satisfies sup q u 1 p a q v 1 p b q where a b p and b b p are orlicz functions this condition is sharp furthermore this condition characterizes in the scale of these a p bump conditions the corresponding two weight norm inequality for the hardy littlewood maximal operator m and its dual i e m l p v l p u and m l p u 1 p l p v 1 p muckenhoupt and wheeden conjectured that these two inequalities for m are sufficient for the hilbert transform to be bounded from l p v into l p u thus in the scale of a p bump conditions we prove their conjecture we prove similar sharp two weight results for the dyadic square function and the vector valued maximal operator

an extrapolation theorem with applications to weighted estimates for singular integrals abstract we prove an extrapolation theorem saying that the weighted weak type 1 1 inequality for a 1 weights implies the strong l p w bound in terms of the l p w operator norm of the maximal operator m the weak muckenhoupt wheeden conjecture along with this result allows us to conjecture that the following estimate holds for a calderon zygmund operator t for any p 1 t l p w c m l p w p the latter conjecture would yield the sharp estimates for t l p w in terms of the a q characteristic of w for any 1 q p in this paper we get a weaker inequality t l p w c m l p w p log 1 m l p w with the corresponding estimates for w a q when 1 q p

extrapolation of weights revisited new proofs and sharp bounds abstract we use an appropriate factorization of the a p weights to give another proof of the extrapolation theorem of rubio de francia it provides sharp bounds in terms of the a p constant of the weights then we extend the result to more general settings including off diagonal and partial range extrapolation among the applications we prove by iteration a multivariable extrapolation theorem and give a sharp bound for calderon zygmund operators on l p w for weights in a q q p

inverse eigenproblem for r symmetric matrices and their approximation let email protected c n x n be a nontrivial involution i e r r 1 i n we say that email protected c n x n is r symmetric if rgr g the set of all nxnr symmetric matrices is denoted by gsc n x n in this paper we first give the solvability condition for the following inverse eigenproblem iep given a set of vectors x i i 1 m in c n and a set of complex numbers l i i 1 m find a matrix email protected gsc n x n such that x i i 1 m and l i i 1 m are respectively the eigenvalues and eigenvectors of a we then consider the following approximation problem given an nxn matrix email protected find email protected email protected s e such that email protected email protected email protected min a s email protected email protected email protected where s e is the solution set of iep and email protected email protected is the frobenius norm we provide an explicit formula for the best approximation solution email protected by means of the canonical correlation decomposition

asymptotic performance analysis of subspace adaptive algorithms introduced in the neural network literature in the neural network literature many algorithms have been proposed for estimating the eigenstructure of covariance matrices we first show that many of these algorithms when presented in a common framework show great similitudes with the gradient like stochastic algorithms usually encountered in the signal processing literature we derive the asymptotic distribution of these different recursive subspace estimators a closed form expression of the covariances in distribution of eigenvectors and associated projection matrix estimators are given and analyzed in particular closed form expressions of the mean square error of these estimators are given it is found that these covariance matrices have a structure very similar to those describing batch estimation techniques the accuracy of our asymptotic analysis is checked by numerical simulations and it is found to be valid not only for a small step size but in a very large domain finally convergence speed and deviation from orthonormality of the different algorithms are compared and several tradeoffs are analyzed

weighted lp estimates for the area integral associated with self adjoint operators on homogeneous space abstract let x be a metric space with doubling measure and l be a non negative self adjoint operator such that the corresponding heat kernels satisfy gaussian bounds this article is concerned with some weighted norm inequalities for area integrals associated with l as an application we obtain sharp estimates for the operator norm of the area integrals on l p x as p becomes large

numerical simulation of a continuum model for bi directional pedestrian flow an algorithm for an extended reactive dynamic user equilibrium model of pedestrian counterflow as a continuum is developed it is based on a cell centered high resolution finite volume scheme with a fast sweeping method for an eikonal type equation on an orthogonal grid a high order total variation diminishing runge kutta method is adopted for the time integration of semi discrete equations the numerical results demonstrate the rationality of the model and efficiency of the algorithm some crowd pedestrian flow phenomena such as dynamic lane formation in bi directional flow are observed which are helpful for a global comprehension of pedestrian dynamics also the model can be utilized with different potential applications

iterative method to solve the generalized coupled sylvester transpose linear matrix equations over reflexive or anti reflexive matrix abstract the iterative method of generalized coupled sylvester transpose linear matrix equations a x b c y t d s 1 e x t f g y h s 2 over reflexive or anti reflexive matrix pair x y is presented on the condition that the coupled matrix equations are consistent we show that the solution pair x y proposed by the iterative method can be obtained within finite iterative steps in the absence of roundoff error for any initial value given a reflexive or anti reflexive matrix moreover the optimal approximation reflexive or anti reflexive matrix solution pair to an arbitrary given reflexive or anti reflexive matrix pair can be derived by searching the least frobenius norm solution pair of the new generalized coupled sylvester transpose linear matrix equations finally some numerical examples are given which illustrate that the introduced iterative algorithm is quite efficient

sharp a2 inequality for haar shift operators as a corollary to the main result of the paper we give a new proof of the inequality rm t f l 2 w lesssim w a 2 f l 2 w where t is either the hilbert transform amer j math 129 5 1355 1375 2007 a riesz transform proc amer math soc 136 4 1237 1249 2008 or the beurling operator duke math j 112 2 281 305 2002 the weight w is non negative and the linear growth in the a2 characteristic on the right is sharp prior proofs relied strongly on haar shift operators cr acad sci paris ser i math 330 6 455 460 2000 and bellman function techniques the new proof uses haar shifts and then uses an elegant two weight t 1 theorem of nazarov treil volberg math res lett 15 3 583 597 2008 to immediately identify relevant carleson measure estimates which are in turn verified using an appropriate corona decomposition of the weight w

the modified conjugate gradient methods for solving a class of generalized coupled sylvester transpose matrix equations in this paper we consider the iteration solutions of generalized coupled sylvester transpose matrix equations a1xb1 c1ytd1 f1 a2yb2 c2xtd2 f2 when the coupled matrix equations are consistent we propose a modified conjugate gradient method to solve the equations and prove that a solution x y can be obtained within finite iterative steps in the absence of roundoff error for any initial value furthermore we show that the minimum norm solution can be got by choosing a special kind of initial matrices when the coupled matrix equations are inconsistent we present another modified conjugate gradient method to find the least squares solution with the minimum norm finally some numerical examples are given to show the behavior of the considered algorithms

on stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix abstract in applications of signal processing and pattern recognition eigenvectors and eigenvalues of the statistical mean of a random matrix sequence are needed iterative methods are suggested and analyzed in which no sample moments are used convergence is shown by stochastic approximation theory

tauberian conditions muckenhoupt weights and differentiation properties of weighted bases let b be a homothecy invariant collection of convex sets in r given a measure the associated weighted geometric maximal operator mb is defined by mb f x sup x b b 1

the exact dependence on a2 w for the lp r w maximal inequalities abstract buckley 1993 3 proved the linear dependence m l 2 r n w c n a of the l 2 r n w norm for the hardy littlewood maximal operator m on the classical a 2 constant a a 2 w sup q q w q w 1 where the supremum is taken over all cubes with sides parallel to the axes we prove in the case n 1 that for p 0 1 a 1 a p 2 the dependence on the constant a is precisely preserved m l p r w c p a 1 p 2 p a 1 p 1 and it is impossible to decrease the value of p 0 similar exact continuation theorems hold for the l 2 norm inequalities of weighted maximal operators

a higher order macroscopic model for bi direction pedestrian flow abstract in this paper a higher order macroscopic model for bi direction pedestrian flow is presented to investigate macroscopic crowd patterns of bi direction pedestrian movement for each group the macroscopic model consists of two dimensional euler equations with relaxation and an eikonal type equation the magnitude of the desired velocity is described by an empirical relation between density and speed while its direction is chosen to minimize the total instantaneous walking cost which satisfies a reactive user equilibrium assignment pattern the dynamic model is numerically solved by a splitting technique and a cell centered finite volume method on an orthogonal grid typical numerical examples of bi direction pedestrian flow walking in a channel are designed to validate the rationality of the dynamic model and the effectiveness of the numerical algorithm

generalized reflexive solutions of the matrix equation axb d and an associated optimal approximation problem let r c m x m and s c n x n be nontrivial unitary involutions i e r h r r 1 i m and s h s s 1 i n we say that g c m x n is a generalized reflexive matrix if rgs g the set of all mxn generalized reflexive matrices is denoted by grc m x n in this paper a sufficient and necessary condition for the matrix equation axb d where a c p x m b c n x q and d c p x q to have a solution x grc m x n is established and if it exists a representation of the solution set s x is given an optimal approximation between a given matrix x c m x n and the affine subspace s x is discussed an explicit formula for the unique optimal approximation solution is presented and a numerical example is provided

multi parameter local hardy spaces abstract though multi parameter hardy space theory has been well developed in the past half century not much has been studied for a local hardy space theory in the multi parameter settings such multi parameter local hardy spaces can play an important role in studying the boundedness of multi parameter pseudo differential operators multi parameter singular integrals of non convolution type and applications to partial differential equations etc by establishing a bi parameter local reproducing formula bi parameter local hardy space h p r n 1 r n 2 is introduced in this paper this space coincides with l p r n 1 n 2 when p 1 while p 1 this space is substantially different from the classical bi parameter hardy spaces h p r n 1 r n 2 we will establish its atomic decomposition of the bi parameter local hardy spaces and as an application we prove the boundedness from h p r n 1 r n 2 to l p r n 1 n 2 of the bi parameter singular integral operators in inhomogeneous journe class for p near 1 for the simplicity we have chosen to present all the results in the bi parameter setting nevertheless all of them hold for arbitrary number of parameters the multi parameter local theory developed in this paper can serve as a model case for similar theory in other multi parameter settings

jamming transition in pedestrian counter flow a lattice gas model with biased random walkers is presented to mimic the pedestrian counter flow in a channel under the open boundary condition of constant density there are two types of walkers without the back step the one is the random walker going to the right and the other is the random walker going to the left it is found that a dynamical jamming transition from the freely moving state at low density to the stopped state at high density occurs at the critical density the transition point is given by pc 0 45 0 01 not depending on the system size the transition point depends on the strength of drift and decreases with increasing drift also we present the extended model to take into account the traffic rule in which a pedestrian walks preferably on the right hand side of the channel