phase transition and critical phenomenon in traffic flow model with velocity dependent sensitivity the traffic flow model with optimal velocity is extended to take into account the velocity dependent sensitivity the dependence of the jamming transition upon the sensitivity is investigated in the extended optimal velocity model the phase transition among the freely moving phase the coexisting phase and the homogeneous congested phase is studied by computer simulation order parameter s which is different from zero below the critical point is shown the phase diagrams are obtained for the sensitivity parameters depending upon the car velocity it is shown that the phase boundaries and the critical point depend largely upon the sensitivity parameters the scaling properties of the headway the car velocity and the jam s propagation velocity are found near the critical point it is shown that the scaling exponents are independent upon the velocity dependent sensitivity

classification of finite dimensional modules of singly atypical type over the lie superalgebras sl m n we classify the finite dimensional indecomposable sl m n modules with at least a typical or singly atypical primitive weight we do this classification not only for weight modules but also for generalized weight modules we obtain that such a generalized weight module is simply a module obtained by linking subquotient modules of generalized kac modules by applying our results to sl m 1 we have in fact completely classified all finite dimensional sl m 1 modules

highest weight representations for gl m n and gl m n it is shown how vector coherent state vcs theory enlightens the simultaneous discussion of representation theory for classical lie algebras and superalgebras and provides an optimal framework for the explanation of the noted similarities and dissimilarities of their representations reducibility atypicality and the positive definitiveness of inner products in vcs representation spaces are discussed the discussion is exemplified through the parallel and explicit construction of highest weight ladder representations of the lie algebra gl m n and superalgebra gl m n in gl m gl n bases

composite young diagrams supercharacters of u m n and modification rules the supercharacter of u m n associated with an arbitrary composite young diagram is defined the distinction is made between standard and non standard supercharacters a modification rule is presented which may be used to express any non standard supercharacter in terms of standard supercharacters in the case n 0 the rule reduces to the rule already known to be appropriate to u m

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

finite dimensional representations of the special linear lie superalgebra sl 1 n i typical representations in a series of two papers all finite dimensional irreducible representations of the special linear lie superalgebra sl 1 n are written down in a matrix form this paper develops a background for constructing the representations expressions for the transformation of the basis under the action of the generators are given for all induced and hence for all typical sl 1 n modules

finite dimensional irreducible representations of the lie superalgebra sl 1 3 in a gel fand zetlin basis a concept of a gel fand zetlin pattern for the lie superalgebra sl 1 3 is introduced within every finite dimensional irreducible sl 1 3 module the set of the gel fand zetlin patterns constitute an orthonormed basis called a gel fand zetlin basis expressions for the transformation of this basis under the action of the generators are written down for every finite dimensional irreducible representation

fock representations of the lie superalgebra q n 1 for the lie superalgebra q n 1 a description is given in terms of creation and annihilation operators in such a way that the defining relations of q n 1 are determined by quadratic and triple supercommutation relations of these operators fock space representations vp of q n 1 are defined by means of these creation and annihilation operators these new representations are introduced as quotient modules of some induced module of q n 1 the representations vp are not graded but they possess a number of properties that are of importance for physical applications for p a positive integer these representations vp are finite dimensional with a unique highest weight of multiplicity one the hermitian form that is consistent with the natural adjoint operation on q n 1 is shown to be positive definite on vp for q 2 these representations are dispin for the general case of q n 1 many structural properties of vp are derived

finite dimensional representations of the quantum superalgebra uq gl 2 2 ii nontypical representations at generic q the construction approach proposed in the previous paper n a ky j math phys 35 2583 1994 allows us there and in the present paper to construct at generic deformation parameter q all finite dimensional representations of the quantum lie superalgebra uq gl 2 2 the finite dimensional uq gl 2 2 modules wq constructed in the previous paper are either irreducible or indecomposable if a module wq is indecomposable i e when the condition 4 41 in the previous paper does not hold there exists an invariant maximal submodule of wq say iqk such that the factor representation in the factor module wq iqk is irreducible and called nontypical here in this paper indecomposable representations and nontypical finite dimensional representations of the quantum lie superalgebra uq gl 2 2 are considered and classified as their module structures are analyzed and the matrix elements of all nontypical representations are written down explicitly

branching rules for typical and atypical representations of gl n 1 the gl n 1 down arrow gl n gl 1 branching rules are determined for all finite dimensional irreducible typical and atypical representations of gl n mod 1 using a recently introduced induced module construction for atypical modules and confirm those found recently by palev 1988 by another method the lowest weights and characters of the irreducible representations are found and the validity for gl n mod 1 of the character formula conjectured by hughes and king 1987 is confirmed some generalisations and extensions of the method are discussed

wigner quantum oscillators we present three groups of non canonical quantum oscillators the position and momentum operators of each group generate basic lie superalgebras namely sl 1 3 osp 1 6 and osp 3 2 the sl 1 3 oscillators have finite energy spectrum and finite dimensions the osp 1 6 oscillators are related to the para bose statistics the internal angular momentum s of the osp 3 2 oscillators takes no more than three half integer values in a particular representation s 1 2

mixed supertableaux of the superunitary groups ii su n m the young supertableaux of the superunitary groups are studied we give the conditions on the size of legal supertableaux the type of atypicity for tensor representations which are irreducible making the link between the kac dynkin parameters and those of the supertableau a discussion is given on nonfully reducible representations and generalized atypical supertableaux

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

primitive vectors of kac modules of the lie superalgebras sl m n it was conjectured by hughes et al j math phys 33 470 491 1992 that there exists a bijection between the composition factors of a kac module and the so called permissible codes in a previous paper it was proved that to any unlinked code there corresponds a composition factor of the kac module here it is proved that to any linked code there corresponds a composition factor of the kac module

affine walled brauer algebras and super schur weyl duality abstract a new class of associative algebras referred to as affine walled brauer algebras are introduced these algebras are free with infinite rank over a commutative ring containing 1 then level two walled brauer algebras over c are defined which are some cyclotomic quotients of affine walled brauer algebras we establish a super schur weyl duality between affine walled brauer algebras and general linear lie superalgebras and realize level two walled brauer algebras as endomorphism algebras of tensor modules of kac modules with mixed tensor products of the natural module and its dual over general linear lie superalgebras under some conditions we also prove the weakly cellularity of level two walled brauer algebras and give a classification of their simple modules over c this in turn enables us to classify the indecomposable direct summands of the said tensor modules

scaling behaviour in discrete traffic models we investigate the noisy discrete single lane highway traffic model proposed by nagel and schreckenberg 1992 and demonstrate by computer simulations that as a function of the car density there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity the critical density is close to the position of the maximum in the fundamental diagram we give estimates of the critical exponents related to this jamming transition the critical density of the geometrical 1 1 dimensional percolation transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character

weak and strong fuzzy interval orders abstract the purpose of this paper is to introduce and investigate the fuzzification of the classical interval order one of the most interesting classical preference structures without incomparability in this study we consider fuzzy preference structures as defined by de baets et al fuzzy preference structures without incomparability receive special attention their fuzzy preference and fuzzy large preference relations share certain types of the t n ferrers property two special types of the j n ferrers property are introduced the weak ferrers and strong ferrers properties the classical interval order is briefly reviewed t fuzzy interval orders are introduced and it is shown that their fuzzy preference relation is sup t transitive two special types of t fuzzy interval orders are considered weak and strong fuzzy interval orders corresponding to transforms of w and to m the particular intermediate role of the weak ferrers property of the fuzzy preference relation of a fps without incomparability is demonstrated on the one hand it is a necessary condition for the fps to be a strong fuzzy interval order while on the other hand it is a sufficient condition for this structure to be a weak fuzzy interval order finally the concept of an cut of a fps is introduced leading to an interesting characterization of the strong ferrers property of a fps without incomparability

on the composition factors of kac modules for the lie superalgebras sl m n in the classification of finite dimensional modules of lie superalgebras kac distinguished between typical and atypical modules kac introduced an induced module the so called kac module v with highest weight which was shown to be simple if is a typical highest weight if is an atypical highest weight the kac module is indecomposable and the simple module v can be identified with a quotient module of v in the present paper the problem of determining the composition factors of the kac modules for the lie superalgebra sl m n is considered an algorithm is given to determine all these composition factors and conversely an algorithm is given to determine all the kac modules containing a given simple module as a composition factor the two algorithms are presented in the form of conjectures and illustrated by means of detailed examples strong evidence in support of the conjectures is provided the combinatorial way in which the two algorithms are intertwined is both surprising and interesting and is a convincing argument in favor of the solution to the composition factor problem presented here

traffic jams granular flow and soliton selection the flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow in a certain range of traffic density steady flow becomes unstable against the growth of a cluster or phantom traffic jam which moves at a slower speed than the otherwise homogeneous flow we show that near the onset of this instability traffic flow is described by a perturbed korteweg de vries kdv equation the traffic jam can be identified with a soliton solution of the kdv equation the perturbation terms select a unique member of the continuous family of kdv solitons these results may also apply to the dynamics of granular relaxation

structure of atypical representations of the lie superalgebras sl m n in contrast to lie algebras lie superalgebras contain typical and atypical irreducible representations character formulae for typical representations of classical lie superalgebras have been known for a long time but the structure of atypical representations remained unsolved the author constructs the character formula for atypical representations of the special linear lie superalgebras sl m n

indicators of fuzzy relations in this paper first we give the definitions of various indicators of fuzzy relations and their basic properties then we investigate the relationships between these indicators particularly between those of t transitivity negative s transitivity t s semitransitivity and t s ferrers property the investigation is divided into three parts results in the general case results under a condition proposed by peng et al and results under special t norms and t conorms on account of our research certain results on fuzzy relations in the literature are extended to the degree description

composition factors of kac modules for the general linear lie superalgebras the composition factors of kac modules for the general linear lie superalgebras open image in new window are explicitly determined in particular a conjecture of hughes king and van der jeugt in j math phys 33 1992 470 491 is proved

a unified description of the representations of the graded lie algebra gsl 2 indecomposable representations of the graded lie algebra gsl 2 are analyzed in detail it is further shown that the study of the irreducible representations finite and infinite dimensional is intimately related to the study of these indecomposable representations

irreducible finite dimensional representations of the lie superalgebra gl n 1 in a gel fand zetlin basis all finite dimensional irreducible representations of the general linear lie superalgebra gl n 1 are studied for each representation a concept of a gel fand zetlin basis is defined expressions for the transformation of the basis under the action of the generators are written down

finite dimensional representations of the lie superalgebra gl 2 2 in a gl 2 gl 2 basis ii nontypical representations all finite dimensional irreducible representations of the general linear lie superalgebra gl 2 2 are written down in matrix form the basis within each representation space is chosen in such a way that it makes evident the decomposition of gl 2 2 into irreducible representations of its even subalgebra gl 2 gl 2 special attention is devoted to the analysis of all nontypical representations and some indecomposible representations

atypical representations for type i lie superalgebras a new modified induced module construction is presented for all finite dimensional irreducible typical and atypical modules of a type i basic classical lie superalgebra the method is illustrated with some low dimensional representations of gl m mod n and all representations of gl 2 mod 1

fuzzy preference structures without incomparability abstract in this paper we establish important relationships between the basic properties of the components of a fuzzy preference structure without incomparability this study is carried out for the fuzzy preference structures introduced recently by de baets van de walle and kerre a set of remarkable theorems gives detailed insight in the relationships between the sup t transitivity of the fuzzy preference and indifference relations and the sup t transitivity of the fuzzy large preference relation several paths of thought involving t norms with or without zero divisors are explored and where required illustrative counterexamples confirm the falsity of certain implications finally we introduce the t n ferrers property of a binary fuzzy relation and show that the fuzzy preference and fuzzy large preference relations share certain types of this ferrers property

generalised verma modules for the orthosymplectic lie superalgebra ospk 2 abstract the composition factors with their multiplicities and the submodule lattices are determined for generalised verma modules over the orthosymplectic lie superalgebra osp k 2 the results enable us to obtain explicit formulae for the formal characters and dimensions of the finite dimensional irreducible modules applying these results we also compute the first and second cohomology groups of the lie superalgebra with coefficients in finite dimensional kac modules and irreducible modules

indecomposable representations of special linear lie superalgebras abstract the main result of this paper is a classification of finite dimensional representations of the lie superalgebras sl m 1 of supertraceless endomorphisms of the vector superspace of dimension m 1 the classification extends to the so called singly atypical blocks of the lie superalgebras sl m n but there exist wild representation type blocks as soon as bothmandnare 2

representation theory of sl 2 1 abstract in this note we present a complete analysis of finite dimensional representations of the lie superalgebra click to view the mathml source this includes in particular the decomposition of all tensor products into their indecomposable building blocks our derivation makes use of a close relation with the representation theory of click to view the mathml source for which analogous results are described and derived keywords lie superalgebras representation theory

cohomology of lie superalgebras m n and 2 2n we explicitly compute the first and second cohomology groups of the classical lie superalgebras mathfrak sl m n and mathfrak osp 2 2n with coefficients in the finite dimensional irreducible modules and the kac modules we also show that the second cohomology groups of these lie superalgebras with coefficients in the respective universal enveloping algebras under the adjoint action vanish the latter result in particular implies that the universal enveloping algebras rm u mathfrak sl m n and rm u mathfrak osp 2 2n do not admit any non trivial formal deformations of gerstenhaber type

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

fuzzy semi orders the case of t norms without zero divisors for crisp relations the concept of a semi order can be stated in a number of equivalent ways when trying to extend this concept to the fuzzy setting we observe that the generalized definitions fail to be equivalent in this contribution we discuss which is the most natural definition of a fuzzy semi order and study the hierarchy among the alternative definitions in particular when using a t norm without zero divisors

deterministic models for traffic jams abstract we study several deterministic one dimensional traffic models for integer positions and velocities we find the typical high and low density phases separated by a simple transition if positions and velocities are continuous variables the model shows self organized critically driven by the slowest car

gas kinetic derivation of navier stokes like traffic equations macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies therefore this paper shows how to construct a logically consistent fluid dynamic traffic model from basic laws for the acceleration and interaction of vehicles these considerations lead to the gas kinetic traffic equation of paveri fontana its stationary and spatially homogeneous solution implies equilibrium relations for the fundamental diagram the variance density relation and other quantities which are partly difficult to determine empirically paveri fontana s traffic equation allows the derivation of macroscopic moment equations which build a system of non closed equations this system can be closed by the well proved method of chapman and enskog which leads to euler like traffic equations in zeroth order approximation and to navier stokes like traffic equations in first order approximation the latter are finally corrected for the finite space requirements of vehicles it is shown that the resulting model is able to withstand the above mentioned criticism

finite and infinite dimensional representations of the orthosymplectic superalgebra osp 3 2 the shift operator technique is used to give a complete analysis of all finite and infinite dimensional irreducible representations of the orthosymplectic superalgebra osp 3 2 for all cases the star or grade star conditions for the algebra are investigated only two finite dimensional representations are grade star representations if the representation space is required to be a graded hilbert space when the even part is so 3 sp 2 r su 2 su 1 1 an infinite class of infinite dimensional star representations is found one of them can be realized in terms of two valued functions of a complex variable this representation reduces to the sum of two metaplectic representations of sp 2 we show that it is precisely this metaplectic representation for osp 3 2 which gives the spin energy eigenstates for the one dimensional harmonic oscillator with spin 1 2 states