hilbert coefficients and the gorenstein property of the associated graded ring in this article we investigate the gorenstein property of the associated graded ring ga i of an ideal i in a gorenstein local ring a m of positive dimension we especially concentrate on the case where i is m primary assuming that the rees algebra of i is cohen macaulay we then give necessary and sufficient conditions for the gorensteiness of ga i in terms of the hilbert coefficients of i

mean field flow difference model with consideration of on ramp and off ramp abstract in this paper an extended lattice hydrodynamic model is proposed by incorporating the effects of mean field flow difference on ramp and off ramp the linear stability condition is obtained through linear stability theory and the mkdv equation is derived by using nonlinear analysis method therefore the propagation behavior of traffic jam can be described by the kink antikink soliton solution of the mkdv equation furthermore the theoretical findings are verified with the use of numerical simulation which confirms that the stability of traffic flow can be efficiently improved with the consideration of the effects of mean field flow difference on ramp and off ramp

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

on existence and uniqueness results for a coupled system modeling miscible displacement in porous media initial boundary value problems for a nonlinear differential system of two equations are considered in this paper this system of equations one of elliptic form for the pressure and the other of parabolic form for the concentration of one fluid governs the miscible displacement of one incompressible fluid by another in a porous medium under some reasonable assumptions on the data it is proved that the system possesses a weak solution and uniqueness is also established for the semiclassical solution of the system

a new car following model for autonomous vehicles flow with mean expected velocity field abstract due to the development of the modern scientific technology autonomous vehicles may realize to connect with each other and share the information collected from each vehicle an improved forward considering car following model was proposed with mean expected velocity field to describe the autonomous vehicles flow behavior the new model has three key parameters adjustable sensitivity strength factor and mean expected velocity field size two lemmas and one theorem were proven as criteria for judging the stability of homogeneousautonomous vehicles flow theoretical results show that the greater parameters means larger stability regions a series of numerical simulations were carried out to check the stability and fundamental diagram of autonomous flow from the numerical simulation results the profiles hysteresis loop and density waves of the autonomous vehicles flow were exhibited the results show that with increased sensitivity strength factor or field size the traffic jam was suppressed effectively which are well in accordance with the theoretical results moreover the fundamental diagrams corresponding to three parameters respectively were obtained it demonstrates that these parameters play almost the same role on traffic flux i e before the critical density the bigger parameter is the greater flux is and after the critical density the opposite tendency is in general the three parameters have a great influence on the stability and jam state of the autonomous vehicles flow

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

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

characteristic block centered finite difference method for compressible miscible displacement in porous media in this paper the characteristic block centered finite difference method is introduced and analyzed to solve compressible miscible displacement in porous media error estimates for the pressure velocity concentration and its flux in different discrete norms are established rigorously and carefully on non uniform grids finally some numerical experiments are presented to show that the convergence rates are in agreement with the theoretical analysis

a briancon skoda theorem for isolated singularities abstract letabe a normal cohen macaulay local ring which is a homomorphic image of a gorenstein local ring supposing thatais pseudo rational in the punctured spectrum and that there exists a proper birational morphismx spec asuch thatxis pseudo rational we show how one can find an integerk 0 such that i n k infor all idealsi aand integersn 0

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

numerical methods for a model for compressible miscible displacement in porous media a nonlinear parabolic system is derived to describe compressible miscible displace ment in a porous medium the system is consistent with the usual model for incompressible miscible displacement two finite element procedures are introduced to approximate the concentration of one of the fluids and the pressure of the mixture the concentration is treated by a galerkin method in both procedures while the pressure is treated by either a lalerkin method or by a parabolic mixed finite element method optimal order estimates in l2 and essentially optimal order estimates in lx are derived for the errors in the approximate solutions for both methods introduction we shall consider the single phase miscible displacement of one compressible fluid by another in a porous medium under the assumptions that no volume change results from the mixing of the components and that a pressure den sity relation exists for each component in a form that is independent of the mixing these equations of state will imply that the fluids are in the liquid state our model will represent a direct generalization of the model 3 4 7 that has been treated extensively for incompressible miscible displacement the reservoir s will be taken to be of unit thickness and will be identified with a bounded domain in r2 we shall omit gravitational terms for simplicity of exposi tion no significant mathematical questions arise when the lower order terms are included

friction coefficient and radius of curvature effects upon traffic flow on a curved road abstract we investigate the friction coefficient and radius of curvature effects upon traffic flow analytically and numerically a new model is proposed to describe the motion of vehicles running on a curved road the stability condition is obtained by the use of control theories the nonlinear analysis method is taken to derive the modified kdv korteweg de vries equation and the kink antikink solution is obtained near the critical point simulations are carried out to verify the double effects upon traffic flow the flux increases but the stability decreases with an increase of the two parameters numerical results are in good agreement with the analytical results

global weak solutions for a parabolic system modeling a one dimensional miscible flow in porous media abstract we consider an initial boundary value problem for a nonlinear differential system of two equations such a system is formed by the equations of compressible miscible flow in a one dimensional porous medium no assumption about the mobility ratio is involved under some reasonable assumptions on the data we prove the existence of a global weak solution our basic approach is the semi galerkin method we use the technique of renormalized solutions for parabolic equations in the derivation of a priori estimates

stabilization analysis and modified korteweg de vries equation in a cooperative driving system two lattice traffic models are proposed by incorporating a cooperative driving system the lattice versions of the hydrodynamic model of traffic flow are described by the differential difference equation and difference difference equation respectively the stability conditions for the two models are obtained using the linear stability theory the results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink anti kink soliton solutions obtained from the mkdv equations

a novel car following model considering average speed of preceding vehicles group abstract in this paper a new car following model is presented by considering the average speed effect of preceding vehicles group in cyber physical systems cps environment the effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis a modified korteweg de vries mkdv equation was derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point good agreement between the simulation and the analytical results shows that average speed of preceding vehicles group leads to the stabilization of traffic systems and thus can efficiently suppress the emergence of traffic jamming

on a fully coupled nonlinear parabolic problem modelling miscible compressible displacement in porous media we study a model describing a compressible and miscible displacement in a porous medium it consists of a coupled system of nonlinear parabolic partial differential equations using nonclassical estimates and renormalization tools we prove the existence of relevant weak solutions for the problem this is the first existence result obtained for a transport model containing both the coupling due to the compressibility assumption and the coupling due to the concentration dependent viscosity

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

an extended continuum model considering optimal velocity change with memory and numerical tests in this paper an extended continuum model of traffic flow is proposed with the consideration of optimal velocity changes with memory the new model s stability condition and kdv burgers equation considering the optimal velocities change with memory are deduced through linear stability theory and nonlinear analysis respectively numerical simulation is carried out to study the extended continuum model which explores how optimal velocity changes with memory affected velocity density and energy consumption numerical results show that when considering the effects of optimal velocity changes with memory the traffic jams can be suppressed efficiently both the memory step and sensitivity parameters of optimal velocity changes with memory will enhance the stability of traffic flow efficiently furthermore numerical results demonstrates that the effect of optimal velocity changes with memory can avoid the disadvantage of historical information which increases the stability of traffic flow on road and so it improve the traffic flow stability and minimize cars energy consumptions

an extended car following model considering driver s desire for smooth driving on the curved road abstract in real traffic many driver s desire to lower the fuel consumption by driving smoothly in this paper an extended car following model considering the driver s desire for smooth driving on a curved road is proposed the desire for smooth driving can be considered as a control signal including the velocity difference between the steady and history velocity the stability conditions are obtained by the control theory and the modified korteweg de vries mkdv equation is derived via the non linear analysis method the numerical simulations are carried out to analyze the control signal the friction coefficient and radius of curved road effects on traffic flow the results show that the control signal has a positive effect on improving traffic flow stability while the stability decreases with the increase of the two other parameters

an existence result for a coupled system modeling a fully equivalent global pressure formulation for immiscible compressible two phase flow in porous media abstract a new model describing immiscible compressible two phase flow such as water gas through heterogeneous porous media is considered the main feature of this model is the introduction of a new global pressure and the full equivalence to the original equations the resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic equation the global pressure equation and a nonlinear diffusion convection one the saturation equation under some realistic assumptions on the data we show an existence result with the help of appropriate regularizations and a time discretization we use suitable test functions to get a priori estimates in order to pass to the limit in nonlinear terms we also obtain compactness results which are nontrivial due to the degeneracy of the system

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