modeling self consistent multi class dynamic traffic flow abstract in this study we present a systematic self consistent multiclass multilane traffic model derived from the vehicular boltzmann equation and the traffic dispersion model the multilane domain is considered as a two dimensional space and the interaction among vehicles in the domain is described by a dispersion model the reason we consider a multilane domain as a two dimensional space is that the driving behavior of road users may not be restricted by lanes especially motorcyclists the dispersion model which is a nonlinear poisson equation is derived from the car following theory and the equilibrium assumption under the concept that all kinds of users share the finite section the density is distributed on a road by the dispersion model in addition the dynamic evolution of the traffic flow is determined by the systematic gas kinetic model derived from the boltzmann equation multiplying boltzmann equation by the zeroth first and second order moment functions integrating both side of the equation and using chain rules we can derive continuity motion and variance equation respectively however the second order moment function which is the square of the individual velocity is employed by previous researches does not have physical meaning in traffic flow although the second order expansion results in the velocity variance equation additional terms may be generated the velocity variance equation we propose is derived from multiplying boltzmann equation by the individual velocity variance it modifies the previous model and presents a new gas kinetic traffic flow model by coupling the gas kinetic model and the dispersion model a self consistent system is presented

observables on quantum structures an observable on a quantum structure is any s homomorphism of quantum structures from the borel s algebra into the quantum structure we show that our partial information on an observable known only for all intervals of the form t is sufficient to derive the whole information about the observable defined on quantum structures like s mv algebras s lattice effect algebras boolean s algebras monotone s complete effect algebras with the riesz decomposition property the effect algebra of effect operators of a hilbert space and systems of functions effect tribes

an ode traffic network model we are interested in models for vehicular traffic flow based on partial differential equations and their extensions to networks of roads in this paper we simplify a fluidodynamic traffic model and derive a new traffic flow model based on ordinary differential equations odes this is obtained by spatial discretization of an averaged density evolution and a suitable approximation of the coupling conditions at junctions of the network we show that the new model inherits similar features of the full model e g traffic jam propagation we consider optimal control problems controlled by the ode model and derive the optimality system we present numerical results on the simulation and optimization of traffic flow in sample networks

projective injective modules serre functors and symmetric algebras we describe serre functors for generalisations of the category o associated with a semisimple complex lie algebra in our approach projective injective modules that is modules which are both

twisted filtrations of soergel bimodules and linear rouquier complexes abstract we consider twisted standard filtrations of soergel bimodules associated to arbitrary coxeter groups and show that the graded multiplicities in these filtrations can be interpreted as structure constants in the hecke algebra this corresponds to the positivity of the polynomials occurring when expressing an element of the canonical basis in a generalized standard basis twisted by a biclosed set of roots in the sense of dyer and comes as a corollary of soergel s conjecture we then show the positivity of the corresponding inverse polynomials in the case where the biclosed set is an inversion set of an element or its complement by generalizing a result of elias and williamson on the linearity of the rouquier complexes associated to lifts of these basis elements in the artin tits group these lifts turn out to be generalizations of mikado braids as introduced in a joint work with digne this second positivity property generalizes a result of dyer and lehrer from finite to arbitrary coxeter groups

pseudo bck algebras as partial algebras it is well known that the representation of several classes of residuated lattices involves lattice ordered groups an often applicable method to determine the representing group or groups from a residuated lattice is based on partial algebras the monoidal operation is restricted to those pairs that fulfil a certain extremality condition and else left undefined the subsequent construction applied to the partial algebra is easy transparent and leads directly to the structure needed for representation in this paper we consider subreducts of residuated lattices the monoidal and the meet operation being dropped the resulting algebras are pseudo bck semilattices assuming divisibility we can pass on to partial algebras also in this case to reconstruct the underlying group structure from this partial algebra if applicable is again straightforward we demonstrate the elegance of this method for two classes of pseudo bck semilattices semilinear divisible pseudo bck algebras and cone algebras

generalized continuous and left continuous t norms arising from algebraic semantics for fuzzy logics this paper focuses on the issue of how generalizations of continuous and left continuous t norms over linearly ordered sets should be from a logical point of view taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation we advocate linearly ordered bl algebras and mtl algebras as adequate generalizations of continuous and left continuous t norms respectively in both cases the underlying basic structure is that of linearly ordered residuated lattices although the residuation property is equivalent to left continuity in t norms continuous t norms have received much more attention due to their simpler structure we review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to bl chains in particular we show the good behavior of bl algebras over a finite or complete chain and discuss the partial knowledge of rational bl chains then we move to the general non continuous case corresponding to left continuous t norms and mtl chains the unsolved problem of describing the structure of left continuous t norms is presented together with a fistful of construction decomposition techniques that apply to some distinguished families of t norms and finally we discuss the situation in the general study of mtl chains as a natural generalization of left continuous t norms

analysis of non isentropic compressible euler equations with relaxation abstract this paper is contributed to the study of the one dimensional non isentropic compressible euler equations with relaxation it is shown that classical solutions do not exist globally in time under general conditions on initial data indeed finite time blowup occurs in a quantity related to the first moment on the other hand when the initial datum is sufficiently close to a constant equilibrium state it is shown that the equations possess a unique global in time classical solution and the solution converges to the equilibrium state in the long time run when the domain is finite the convergence rate is shown to be exponential due to boundary effects

on filter theory of residuated lattices the aim of this paper is to develop the filter theory of general residuated lattices first we extend some particular types of filters and fuzzy filters in bl algebras and mtl algebras naturally to general residuated lattices and further enumerate some relative results obtained in bl algebras or mtl algebras which still hold in general residuated lattices next we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices which are two new types of filters and fuzzy filters and derive some of their characterizations finally we discuss the relations between fuzzy regular filters and several other special fuzzy filters and also characterize some special classes of residuated lattices by filters or fuzzy filters

the pasting constructions of lattice ordered effect algebras the aim of this paper is to present some ways of constructing a lattice ordered effect algebra from the given family of mv algebras the loop lemma of lattice ordered effect algebras is proved then the definitions of greechie diagrams of effect algebras are given all these results have generalized those of orthomodular lattices as applications of loop lemma and greechie diagrams some lattice ordered effect algebras without states are presented

states on finite monoidal t norm based algebras the aim of this paper is to study the existences of bosbach states and riecan states on finite monoidal t norm based algebras mtl algebras for short we give some examples to show that there exist mtl algebras having no bosbach states and riecan states the conditions under which mtl algebras have bosbach states and riecan states are investigated respectively we prove that riecan states on mtl algebras are reduced to states on imtl algebras furthermore the necessary and sufficient conditions for finite linearly ordered locally finite mtl algebras and peculiar mtl algebras having bosbach states and riecan states are obtained respectively in addition the notions of pseudo quasi equivalent and a subalgebra under pseudo quasi equivalent are proposed and some of their properties are investigated

quivers floer cohomology and braid group actions we consider the derived categories of modules over a certain family a m of graded rings and floer cohomology of lagrangian intersections in the symplectic manifolds which are the milnor fibres of simple singularities of type a m we show that each of these two rather different objects encodes the topology of curves on an m 1 punctured disc we prove that the braid group b m 1 acts faithfully on the derived category of a m modules and that it injects into the symplectic mapping class group of milnor fibers the philosophy behind our results is as follows using floer cohomology one should be able to associate to the milnor fibre a triangulated category its construction has not been carried out in detail this triangulated category should contain a full subcategory which is equivalent up to a slight difference in the grading to the derived category of a m modules the full embedding would connect the two occurrences of the braid group thus explaining the similarity between them

improved fluid dynamic model for vehicular traffic the fluid dynamic traffic model of kerner and konh auser phys rev e 48 2335 1993 50 54 1994 is extended by an equation for the vehicles velocity variance it is able to describe the observed increase of velocity variance immediately before a traffic jam develops another modification takes into account the finite amount of space that each vehicle needs as a consequence the improved traffic model does not produce densities that exceed the maximum vehicle density or negative velocities like former models did

modeling simulation and optimization of traffic flow networks a new model for highway traffic networks based on a detailed description of the junctions is presented to obtain suitable conditions at the junctions multilane equations are introduced and investigated the new model is compared with currently known models for traffic flow networks for several situations finally the model is used for network simulation and optimization

a non associative generalization of hajek s bl algebras hajek introduced basic logic bl as the logic of continuous t norms and their residua basic logic is a fuzzy logic i e it is complete with respect to linearly ordered models algebraic semantics of bl is the variety of bl algebras it was proved by cignoli esteva godo and torrens that the variety of bl algebras is generated just by the continuous t norms on the interval 0 1 of reals the main goal of the paper is to present a non associative generalization of hajek s bl logic which has a class nabl of non associative bl algebras as its algebraic semantics moreover it is shown that nabl forms a variety generated just by non associative t norms consequently the non associative bl logic is the logic of non associative t norms and their residua

essence of conservation forms in the traveling wave solutions of higher order traffic flow models this paper shows the essence of conservation forms when applying the weak solution theory to solve the traveling wave solution of a wide cluster in the payne whitham pw model the consideration of the conservation form for the acceleration equation is an important ingredient in the development of higher order traffic flow models but it is largely ignored in the research community to fix the idea we define two conservation forms for the same pw model and consequently derive two solutions with different sets of characteristic parameters of the wide cluster the analytical results are in good agreement with those that are obtained from numerical simulations moreover these two solutions are also shown to be asymptotic to those of the well known kuhne and kerner konhauser models with a viscosity term more importantly the careful treatment of the conservation form for the acceleration equation closes the important gap in the literature without the conservation form the solution obtained depends very much on the design of numerical schemes and can be quite arbitrary and may not adequately conform to the physically relevant properties

navier stokes like equations for traffic flow the macroscopic traffic flow equations derived from the reduced paveri fontana equation are closed starting with the maximization of the informational entropy the homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of chapman enskog method is developed to calculate the traffic pressure at the navier stokes level numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed

the hodge theory of soergel bimodules we prove soergel s conjecture on the characters of indecomposable soergel bimodules we deduce that kazhdan lusztig polynomials have positive coecients for arbitrary coxeter systems using results of soergel one may deduce an algebraic proof of the kazhdan lusztig conjecture

on sequential data assimilation for scalar macroscopic traffic flow models a b s t r a c t we consider the problem of sequential data assimilation for transportation networks using optimal filtering with a scalar macroscopic traffic flow model properties of the distribution of the uncertainty on the true state related to the specific nonlinearity and non differentiability inherent to macroscopic traffic flow models are investigated derived analytically and analyzed we show that nonlinear dynamics by creating discontinuities in the traffic state affect the performances of classical filters and in particular that the distribution of the uncertainty on the traffic state at shock waves is a mixture distribution the non differentiability of traffic dynamics around stationary shock waves is also proved and the resulting optimality loss of the estimates is quantified numerically the properties of the estimates are explicitly studied for the godunov scheme and thus the cell transmission model leading to specific conclusions about their use in the context of filtering which is a significant contribution of this article analytical proofs and numerical tests are introduced to support the results presented a java implementation of the classical filters used in this work is available on line at http traffic berkeley edu for facilitating further efforts on this topic and fostering reproducible research

loomis sikorski representation of monotone σ complete effect algebras we show that monotone s complete effect algebras with the riesz decomposition property are s homomorphic images of effect tribes with the riesz decomposition property which are effect algebras of fuzzy sets closed under pointwise limits of nondecreasing fuzzy sets

thermodynamical path choice model in steady state urban commuter traffic abstract the paper is concerned with the problem of distributing a current of vehicular traffic on a conducting net between a source domain a and a destination domain b it is investigated how local decision making influences globally averaged quantities the effects of a local boltzmann like probability distribution structural and statistical variations are discussed in the limiting cases of zero and infinite temperature and put in perspective

equivariant sheaves on flag varieties we show that the borel equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of differential graded modules over the extension algebra of the direct sum of the simple equivariant perverse sheaves this proves a conjecture of soergel and lunts in the case of flag varieties

path functional theory for optimal transport in steady state urban traffic networks abstract path choice problems in vehicular traffic in urban environments are dominated by an interplay of local decision making and global optimization with local routing uncertainties being taken account of by the introduction of an repulsive interaction of paths a variational principle for the formation of the paths can be formulated theoretically the shape of the resulting description bears strong resemblance to the density functional theory dft introduced in 1964 for coulomb systems some examples together with thermodynamical implications are discussed within the framework of this paper

markov kernels and tribes abstract we define an ordering on the set of bounded markov kernels associated with a tribe of fuzzy sets we show that under this order the set of bounded markov kernels is a dedekind complete lattice in addition we define a sum of bounded markov kernels such that the set of bounded markov kernels is a lattice ordered semigroup if we concentrate only to sharp bounded markov kernels then this set is even a dedekind complete l group with strong unit we show that our methods work also for bounded markov kernels associated with t s tribes of fuzzy sets where t s is any frank t norm and s 0

high resolution numerical approximation of traffic flow problems with variable lanes and free flow velocities this paper develops macroscopic traffic flow models for a highway section with variable lanes and free flow velocities that involve spatially varying flux functions to address this complex physical property we develop a riemann solver that derives the exact flux values at the interface of the riemann problem based on this solver we formulate godunov type numerical schemes to solve the traffic flow models numerical examples that simulate the traffic flow around a bottleneck that arises from a drop in traffic capacity on the highway section are given to illustrate the efficiency of these schemes

a statistical approach to vehicular traffic abstract a two dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of the four directions the flow of cars obeys realistic traffic rules we investigate the dependence of the average velocity of cars on the global traffic density at a critical threshold for the density the average velocity reduces drastically caused by jamming for the low density regime we provide analytical results which agree with the numerical results

observables on perfect mv algebras abstract an observable on an mv algebra is any homomorphism from the borel algebra b r into the mv algebra which maps a sequence of disjoint borel sets onto summable elements of the mv algebra we establish that there is a one to one correspondence between observables on rad dedekind complete perfect mv algebras with principal radicals and their spectral resolutions it means that we show that our partial information on an observable known only on all intervals of the form t is sufficient to determine the whole information about the observable in addition this correspondence allows us to define the olson order which is a partial order on the set o m of all observables on an mv algebra m as well as we can define a sum of observables so that o m becomes a lattice ordered semigroup

derivation and empirical validation of a refined traffic flow model abstract the gas kinetic foundation of fluid dynamic traffic equations suggested in previous papers d helbing physica a 219 1995 375 and 391 is further refined by applying the theory of dense gases and granular materials to the boltzmann like traffic model by paveri fontana it is shown that despite the phenomenologically similar behaviour or ordinary and granular fluids the relations for these cannot directly be transferred to vehicular traffic the dissipative and anisotropic interactions of vehicles as well as their velocity dependent space requirements lead to a considerably different structure of the macroscopic traffic equations also in comparison with the previously suggested traffic flow models as a consequence the instability mechanisms of emergent density waves are different crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures

theoretical foundation of macroscopic traffic models abstract on the basis of the elementary laws of individual driver behavior concerning the acceleration and interaction of vehicles a gas kinetic traffic model is constructed this yields theoretical relations for the fundamental diagram and the equilibrium variance density relation but above all it allows the derivation of macroscopic traffic equations these build a hierarchy of non closed equations which can be closed by different zeroth order approximations in this way one obtains the traffic equations of lighthill and whitham or those of phillips alternatively one can derive euler like traffic equations which are proposed here since they include additional dynamical equations for the velocity variance the new variance equation is able to describe the empirically observed increase of variance directly before a traffic jam develops

nonlinear analysis of a differential difference equation with next nearest neighbour interaction for traffic flow we analyse the newell whitham type car following model described by a differential difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the headway of the immediately preceding one linear stability analysis shows that the model is stabilized for larger delay time by taking into account the headway of the immediately preceding car from the nonlinear analysis the propagating kink solution for traffic jams is obtained the fundamental diagram and the relation between the headway and the delay time are examined by numerical simulation we find that the result from the nonlinear analysis is in good agreement with that obtained from the numerical simulation

the variety of modular basic algebras generated by mv chains and horizontal sums of three element chain basic algebras basic algebras or lattices with section antitone involutions turned out to be appropriate structures when axiomatizing both many valued and quantum logics see e g 11 the aim of the present paper is to describe the variety of basic algebras generated by mv chains and horizontal sums of three element chain basic algebras