contact models leading to variational hemivariational inequalities abstract a frictional contact model under the small deformations hypothesis for static processes is considered we model the behavior of the material by a constitutive law using the subdifferential of a proper convex and lower semicontinuous function the contact is described with a boundary condition involving clarke s generalized gradient our study focuses on the weak solvability of the model based on a fixed point theorem for set valued mappings we prove the existence of at least one weak solution the uniqueness the boundedness and the stability of the weak solution are also discussed the investigation is based on arguments in the theory of variational hemivariational inequalities finally we present several examples of constitutive laws and friction laws for which our theoretical results are valid

subdiffusive quantum transport for 3d hamiltonians with absolutely continuous spectra we exhibit a class of hamiltonians in dimension d 3 describing a quantum particle in an aperiodic medium with absolutely continuous spectrum and subdiffusive behavior the diffusion exponent which characterizes the time growth of the mean square displacement can be chosen slightly bigger than guarneri s lower bound these models are built out of 1d hamiltonians with well understood spectral and transport properties

singular continuous spectrum for palindromic schrodinger operators we give new examples of discrete schrodinger operators with potentials taking finitely many values that have purely singular continuous spectrum if the hullx of the potential is strictly ergodic then the existence of just one potentialx inx for which the operator has no eigenvalues implies that there is a generic set inx for which the operator has purely singular continuous spectrum a sufficient condition for the existence of such anx is that there is az x that contains arbitrarily long palindromes thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset inx the class includes well known substitutions like fibonacci thue morse period doubling binary non pisot and ternary non pisot we also show that the operator has no absolutely continuous spectrum for allx x ifx derives from a primitive substitution for potentials defined by circle maps x n 1 j 0 n we show that the operator has purely singular continuous spectrum for a generic subset inx for all irrational and every half open intervalj

upper bounds on wavepacket spreading for random jacobi matrices a method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random possibly correlated jacobi matrix as an application one obtains sharp upper bounds on the diffusion exponents for random polymer models coinciding with the lower bounds obtained in a prior work the second application is an elementary argument not using multiscale analysis or the aizenman molchanov method showing that under the condition of uniformly positive lyapunov exponents the moments of the position operator grow at most logarithmically in time

the absolutely continuous spectrum of jacobi matrices i explore some consequences of a groundbreaking result of brei messer and pearson on the absolutely continuous spectrum of one dimensional schrodinger operators these include an oracle theorem that predicts the potential and rather general results on the approach to certain limit potentials in particular we prove a denisov rakhmanov type theorem for the general nite gap case the main theme is the following it is extremely dicult to produce abso lutely continuous spectrum in one space dimension and thus its existence has strong implications

on inverse spectral theory for self adjoint extensions mixed types of spectra abstract lethbe a symmetric operator in a separable hilbert space h suppose thathhas some gapj we shall investigate the question about what spectral properties the self adjoint extensions ofhcan have inside the gapjand provide methods on how to construct self adjoint extensions ofhwith prescribed spectral properties insidej under some weak assumptions about the operatorhwhich are satisfied e g provided the deficiency indices ofhare infinite and the operator h 1is compact for one regular point ofh we shall show that for every auxiliary self adjoint operatorm in the hilbert space h and every open subsetj0of the gapjofhthere exists a self adjoint extensionhofhsuch that insidejthe self adjoint extensionhofhhas the same absolutely continuous and the same point spectrum as the given operatorm and the singular continuous spectrum ofhinjequals the closure ofj0inj moreover we shall present a method of how to construct such a self adjoint extensionh via our methods it is possible to construct new kinds of self adjoint realizations of the laplacian on a bounded domain in r d d 1 with spectral properties very different from the spectral properties of the self adjoint realizations known before mathematics subject classification 1991 47a10 47a60 47b25 47e05 47f05

analyses of lattice hydrodynamic model using delayed feedback control with passing abstract delayed feedback control method is used for one dimensional lattice model by incorporating the effect of passing in order to check the stability of system under control theory hurwitz criteria is used and h norm of transfer functions are obtained the efficiency of control signal in minimizing the jamming transitions due to passing is shown through bode plot the results show that the control parameter helps in reducing congestion and makes the flow stable even at higher rate of passing simulations are carried out and are found in good agreement with theoretical results

two velocity difference model for a car following theory abstract in the light of the optimal velocity model a two velocity difference model for a car following theory is put forward considering navigation in modern traffic to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in the car following process than others then we investigate the property of the model using linear and nonlinear analyses the korteweg de vries equation for short the kdv equation near the neutral stability line and the modified korteweg de vries equation for short the mkdv equation around the critical point are derived by applying the reductive perturbation method the traffic jam could be thus described by the kdv soliton and the kink anti kink soliton for the kdv equation and mkdv equation respectively numerical simulations are made to verify the model and good results are obtained with the new model

dynamical analysis of schrodinger operators with growing sparse potentials we consider discrete half line schrodinger operators h with potentials of the form v n s n q n here q is any compactly supported real function open image in new window if n l n and s n 0 otherwise where 0 1 and l n is a very fast growing sequence we study in a rather detailed manner the time averaged dynamics exp ith for various initial states in particular for some we calculate explicitly the intermittency function p which turns out to be nonconstant the dynamical results obtained imply that the spectral measure of h has exact hausdorff dimension for all boundary conditions improving the result of jitomirskaya and last

schrodinger operators with sparse potentials asymptotics of the fourier transform of the spectral measure we study the pointwise behavior of the fourier transform of the spectral measure for discrete one dimensional schrodinger operators with sparse potentials we find a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model we also present an improved version of known results on the spectrum of such operators

a probabilistic approach to one dimensional schrodinger operators with sparse potentials we consider the one dimensional schrodinger equation with sparse potential v i e mainly v 0 it is shown that the asymptotics of the solutions corresponding to positive energies e can be approximately described by an infinite sum of independent random variables using results from probability theory we can then determine the spectral properties of the operators under consideration we prove absolute continuity for a general class of potentials and we also have examples with singular continuous spectrum

solvability of dynamic antiplane frictional contact problems for viscoelastic cylinders abstract we study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation the process is dynamic the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition we derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field then we prove the existence of a weak solution to the model the proof is based on an abstract result for second order evolutionary inclusions in banach spaces also we prove that under additional assumptions the weak solution to the model is unique we complete our results with concrete examples of friction laws for which our results are valid

the stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow abstract a modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice the stability condition of the modified model is obtained through the linear stability analysis the results show that considering the density difference leads to the stabilization of the system the burgers equation and mkdv equation are derived to describe the density waves in the stable and unstable regions respectively numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic

power law subordinacy and singular spectra i half line operators we study hausdorff dimensional spectral properties of certain whole line quasiperiodic discrete schrodinger operators by using the extension of the gilbert pearson subordinacy theory that we previously developed in 19

continuum traffic model with the consideration of two delay time scales this paper presents a continuum traffic model the derivation of this model is based upon the assumption that the stream velocity u reaches the equilibrium velocity u e within the relaxation time t while the equilibrium velocity u e is adjusted to be attained through the driver s reaction time t r it is also assumed that the former delay time scale is greater than the latter a motion equation with nonconstant propagation velocity of a disturbance in traffic flow is derived that can reflect the anisotropy of disturbance propagation in real traffic unlike some other higher order continuum models it indicates that in our model the undesirable wrong way travel phenomenon and gas like behavior have been eliminated the formation and diffusion of traffic shock can be better simulated

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

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

singular continuous spectrum is generic in a variety of contexts we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators those with singular spectrum are a dense g delta

localization for a class of one dimensional quasi periodic schrodinger operators we prove for small and satisfying a certain diophantine condition the operator h varepsilon 2 delta frac 1 2 pi cos 2 pi j alpha theta j in mathbb z has pure point spectrum for almost all a similar result is established at low energy for h frac d 2 dx 2 k 2 cos 2 pi x cos 2 pi alpha x theta providedk is sufficiently large

de localization in the prime schrodinger operator we report a combined numerical approach to study the localization properties of the one dimensional tight binding model with potential modulated along the prime numbers a localization delocalization transition was found as a function of the potential intensity it is also argued that there are delocalized states for any value of the potential intensity

new control strategy for the lattice hydrodynamic model of traffic flow abstract the new delayed feedback control strategy is applied for lattice hydrodynamic model of traffic flow by considering the control signal of the variation rate of the optimal velocity the linear stability condition is derived in the frequency domain with control theory then different feedback gains under the periodic boundary scenery and on ramp scenery are simulated the periodic boundary scenery provides an initial small disturbance situation on the circle road while the on ramp scenery reproduces the disturbance triggered by the on ramp on the open road both the theoretical analysis and simulations show that this new control signal has a positive effect to suppress traffic jams

anderson localization for the almost mathieu equation a nonperturbative proof we prove that for any diophantine rotation angle and a e phase the almost mathieu operator h n n 1 n 1 cos 2 n n has pure point spectrum with exponentially decaying eigenfunctions for 15 we also prove the existence of some pure point spectrum for any 5 4

dynamical upper bounds on wavepacket spreading we derive a general upper bound on the spreading rate of wavepackets in the framework of schrodinger time evolution our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent schrodinger equation we also derive a new lower bound on the spreading rate which is strongly connected with our upper bound we apply these new bounds to the fibonacci hamiltonian the most studied one dimensional model of quasicrystals as a result we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization the bounds have the same qualitative behavior in the limit of large coupling

influence of noise on dynamics with fractal fourier spectra abstract in deterministic dynamics the processes with fractal power spectra occupy the intermediate position between ordered and chaotic temporal behavior we study numerically the influence of different kinds of noise upon these processes in general under the action of noise the spectral measure becomes absolutely continuous and the correlations decay however during the certain intermediate period the autocorrelation retains the pattern which is typical for dynamics with fractal spectra duration of this period is related to the noise intensity by the power law

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

modified kdv equation for jamming transition in the continuum models of traffic abstract continuum models of traffic are proposed to describe the jamming transition in traffic flow on a highway they are the simplified versions of the hydrodynamic model of traffic two continuum models are presented one is described by the partial differential equations and the other is the discrete lattice version the linear stability theory and the nonlinear analysis are applied to the continuum models the modified korteweg de vries equation kdv near the critical point is derived using the reduction perturbation method it is shown that the jamming transition and the density wave in the congested traffic flow are described by the modified kdv equation the solutions of the kdv equations obtained from the two models are compared with that of the optimal velocity model car following model

pure point spectrum under 1 parameter perturbations and instability of anderson localization we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic fora we study the set of all eigenvalues of the operatora t a tp t that belong to its essential spectrum which does not depend on the parametert we prove that this set is empty for a dense set of values oft then we apply this result or its idea to questions of anderson localization for 1 dimensional schrodinger operators discrete and continuous

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

anderson localization for multi dimensional systems at large disorder or large energy we prove that discrete schrodinger operators on d with a random potential have almost surely only pure point spectrum and exponentially decaying eigenfunctions for large disorder or large energy this is the first proof of localization for multi dimensional anderson models

the crack problem for nonhomogeneous materials under antiplane shear loading a displacement based formulation abstract this paper presents a displacement based integral equation formulation for the mode iii crack problem in a nonhomogeneous medium with a continuously differentiable shear modulus which is assumed to be an exponential function i e g x g0exp x this formulation leads naturally to a hypersingular integral equation the problem is solved for a finite crack and results are given for crack profiles and stress intensity factors the results are affected by the parameter describing the material nonhomogeneity this study is motivated by crack problems in strain gradient elasticity theories where higher order singular integral equations naturally arise even in the slope based formulation

special nonuniform lattice snul orthogonal polynomials on discrete dense sets of points difference calculus compatible with polynomials i e such that the divided difference operator of first order applied to any polynomial must yield a polynomial of lower degree can only be made on special lattices well known in contemporary q calculus orthogonal polynomials satisfying difference relations on such lattices are presented in particular lattices which are dense on intervals q 1 are considered

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

the backward looking effect in the lattice hydrodynamic model abstract the novel lattice hydrodynamic model is presented by incorporating the backward looking effect the stability condition for the the model is obtained using the linear stability theory the result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model the korteweg de vries kdv for short equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kdv soliton solution obtained from the kdv equation the simulation result is consistent with the nonlinear analysis

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

universal lower bounds for quantum diffusion abstract we study the connections between dynamical properties of schrodinger operators h on separable hilbert space h and the properties of corresponding spectral measures our main result establishes a relation for the moment of order p of the form x p t t t 1 t 0 x p 2 e ith 2 h dt l p d t 1 here l p d t is a function connected to the behavior of the fourier transform of measures in the subclass of measures absolutely continuous with respect to the spectral measure beyond the intrinsic interest of the general formulation 1 this result allows us to derive necessary conditions for dynamical localization in the presence of a pure point spectrum on the other hand if we focus on subsequences of time t k we can exhibit lower bounds which are in certain cases strictly larger than the well known power law lower bound for all t expressed in terms of the hausdorff dimension of spectral measures

operators with singular continuous spectrum i general operators the baire category theorem implies that the family f of dense sets g in fixed metric space x is a candidate for generic sets since it is closed under countable intersections and if x is perfect has no isolated point then a f has uncountable intersections with any open ball in x

anti plane shear deformations in linear and nonlinear solid mechanics the intent of this expository paper is to draw the attention of the applied mathematics community to an interesting two dimensional mathematical model arising in solid mechanics involving a single second order linear or quasi linear partial differential equation this model has the virtue of relative mathematical simplicity without loss of essential physical relevance anti plane shear deformations are one of the simplest classes of deformations that solids can undergo in anti plane shear or longitudinal shear generalized shear of a cylindrical body the displacement is parallel to the generators of the cylinder and is independent of the axial coordinate thus anti plane shear with just a single scalar axial displacement field may be viewed as complementary to the more complicated yet perhaps more familiar plane strain deformation with its two in plane displacements in recent years considerable attention has been paid to the analysis of anti plane shear deformations within the context of variou

operators with singular continuous spectrum ii rank one operators for an operator a with cyclic vector we studya p wherep is the rank one projection onto multiples of if spec a anda has no a c spectrum we prove thata p has purely singular continuous spectrum on for a denseg of s

boundary conditions of sturm liouville operators with mixed spectra we study bounds on averages of spectral functions corresponding to sturm liouville operators on the half line for different boundary conditions as a consequence constraints are obtained which imply existence of singular spectrum embedded in a c spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval 0 n these constraints are related to estimates on the measure of sets where the spectral density is positive

modified prufer and efgp transforms and deterministic models with dense point spectrum we provide a new proof of the theorem of simon and zhu that in the region e for a e energies d 2 dx 2 cos x 0 1 has lyapunov behavior with a quasi classical formula for the lyapunov exponent we also prove lyapunov behavior for a e e 2 2 for the discrete model with v j 2 e j v n 0 if n 1 4 9 the arguments depend on a direct analysis of the equations for the norm of a solution

trace class perturbations and the absence of absolutely continuous spectra we show that various hamiltonians and jacobi matrices have no absolutely continuous spectrum by showing that under a trace class perturbation they become a direct sum of finite matrices

bounded solutions and absolute continuity of sturm liouville operators this work is a contribution to the theory of the absolutely continuous spectrum of one dimensional schriidinger operators i e sturm liouville operators generated by differential expressions of the form ru u qu in proofs of absolute continuity for such operators and also for the closely related dirac systems always asymptotic properties of solutions of zu lu for real or complex values of 1 have played an important role see for example 18 19 8 4 9 lo in these works and a number of others particular classes of potentials q were treated using properties of solutions in the course of the proof of absolute continuity somewhat more recently the connection between asymptotic properties of solutions and absolute continuity was given a theory i e results of the following form were proved let the solutions of zu lu satisfy some specific asymptotic property for a varying in some subset of r no or almost no a priori assumptions on q then operators generated by z are absolutely continuous in this set a first result of this type was given by carmona 3 who proved that local uniform boundedness of solutions together with their derivatives in some open a set implies pure absolute continuity in this set here we will mostly rely on the concept of non or racy of solutions which was shown by gilbert and pearson 7 12 61 to be a powerful tool in the investigation of the continuous spectrum of sturm liouville operators in section 2 we give some consequences of their results whi ch are useful in proofs of absolute continuity these consequences range from non existence of imbedded eigenvalues and the existence of absolutely continuous parts to pure absolute continuity and the existence of transient 210 0022 247x 92 5 00

anderson localization for the almost mathieu equation iii semi uniform localization continuity of gaps and measure of the spectrum we show that the almost mathieu operator has semi uniform and thus dynamical localization for 15 and a e we also obtain a new estimate on gap continuity in for this operator with 29 or 4 29 and use it to prove that the measure of its spectrum is equal to for in this range and all irrational s

weak solutions for nonlinear antiplane problems leading to hemivariational inequalities abstract we analyze the antiplane shear deformation of an elastic cylinder in frictional contact with a rigid foundation for static processes under the small deformation hypothesis based on the knaster kuratowski mazurkiewicz technique in the theory of the hemivariational inequalities we prove that the model has at least one weak solution moreover we present several examples of constitutive laws and friction laws for which our theoretical results are valid finally we comment on the conditions which guarantee the uniqueness of the solution

operators with singular continuous spectrum iii almost periodic schrodinger operators we prove that one dimensional schrodinger operators with even almost periodic potential have no point spectrum for a dense g in the hull this implies purely singular continuous spectrum for the almost mathieu equation for coupling larger than 2 and a dense g in even if the frequency is an irrational with good diophantine properties

operators with singular continuous spectrum vii examples with borderline time decay we construct one dimensional potentials v x so that if h d 2 dx 2 v x on l 2 then h has purely singular spectrum but for a dense set d d implies that ith c t 1 2 in t for t 2 this implies the spectral measures have hausdorff dimension one and also following an idea of malozemov molchanov provides counterexamples to the direct extension of the theorem of simon spencer on one dimensional infinity high barriers

localization in general one dimensional random systems we discuss two ways of extending the recent ideas of localization from discrete schrodinger operators jacobi matrices to the continuum case one case allows us to prove localization in the goldshade molchanov pastur model for a larger class of functions than previously the other method studies the model v wherev is a random constant in each hyper cube we extend wegner s result on the lipschitz nature of the ids to this model

one dimensional perturbations of unbounded selfadjoint operators with empty spectrum abstract we study spectral properties of one dimensional singular nonselfadjoint perturbations of an unbounded selfadjoint operator and give criteria for the possibility to remove the whole spectrum by a perturbation of this type a counterpart of our results for the case of bounded operators provides a complete description of compact selfadjoint operators whose rank one perturbation is a volterra operator

spectral analysis of n body schrodinger operators for a large class of two body potentials we solve two of the main problems in the spectral analysis of multiparticle quantum hamiltonians explicitly we prove that the point spectrum lies in a closed countable set and describe that set in terms of the eigenvalues of hamiltonians of subsystems and that there is no singular continuous spectrum we accomplish this by extending mourre s work on three body problems to n body problems

rank one perturbations with infinitesimal coupling we consider a positive self adjoint operator a and formal rank one perturbations b a where h 2 a but h 1 a with h s a the usual scale of spaces we show that b can be defined for such and what are essentially negative infinitesimal values of in a sense we will make precise every rank one perturbation is one of three forms i h 1 a r ii h 1 or iii the new type we consider here

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

spectral and quantum dynamical properties of the weakly coupled fibonacci hamiltonian we consider the spectrum of the fibonacci hamiltonian for small values of the coupling constant it is known that this set is a cantor set of zero lebesgue measure here we study the limit as the value of the coupling constant approaches zero of its thickness and its hausdorff dimension we prove that the thickness tends to infinity and consequently the hausdorff dimension of the spectrum tends to one we also show that at small coupling all gaps allowed by the gap labeling theorem are open and the length of every gap tends to zero linearly moreover for a sufficiently small coupling the sum of the spectrum with itself is an interval this last result provides a rigorous explanation of a phenomenon for the fibonacci square lattice discovered numerically by even dar mandel and lifshitz finally we provide explicit upper and lower bounds for the solutions to the difference equation and use them to study the spectral measures and the transport exponents

spectral analysis on infinite sierpinski gaskets we study the spectral properties of the laplacian on infinite sierpin ski gaskets we prove that the laplacian with the neumann boundary condition has pure point spectrum moreover the set of eigenfunctions with compact support is complete the same is true if the infinite sierpin ski gasket has no boundary but is false for the laplacian with the dirichlet boundary condition in all these cases we describe the spectrum of the laplacian and all the eigenfunctions with compact support to obtain these results first we prove certain new formulas for eigenprojectors of the laplacian on finite sierpin ski pre gaskets then we prove that the spectrum of the discrete laplacian on a sierpin ski lattice is pure point and the eigenfunctions are localized 1998 academic press

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

modified prufer and efgp transforms and the spectral analysis of one dimensional schrodinger operators using control of the growth of the transfer matrices wediscuss the spectral analysis of continuum and discrete half line schrodinger operators with slowly decaying potentials among our results we show if where w has compact support and then h has purely a c resp purely s c spectrum on 0 if for n 1 2 a n potentials where a n are independent identically distributed random variables with e a n 0 e a 2 n 1 and 2 we find singular continuous spectrum with explicitly computable fractional hausdorff dimension

value distribution and spectral theory of schrodinger operators with l 2 sparse potentials we apply the methods of value distribution theory to the spectral asymptotics of schrodinger operators with l2 sparse potentials

absolutely continuous spectrum of one dimensional schrodinger operators and jacobi matrices with slowly decreasing potentials we prove that for any one dimensional schrodinger operator with potentialv x satisfying decay condition v x cx 3 4 e the absolutely continuous spectrum fills the whole positive semi axis the description of the set in on which the singular part of the spectral measure might be supported is also given analogous results hold for jacobi matrices

power law bounds on transfer matrices and quantum dynamics in one dimension ii abstract we establish quantum dynamical lower bounds for a number of discrete one dimensional schrodinger operators these dynamical bounds are derived from power law upper bounds on the norms of transfer matrices we develop further the approach from part i and study many examples particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power law bounds on transfer matrices the models discussed in this paper include substitution models sturmian models a hierarchical model the prime model and a class of moderately sparse potentials

existence and uniqueness results for a class of quasi hemivariational inequalities abstract in this paper we are concerned with the study of a nonstandard quasi hemivariational inequality using a fixed point theorem for set valued mappings the existence of at least one solution in bounded closed and convex subsets is established we also provide sufficient conditions for which our inequality possesses solutions in the case of unbounded sets finally the uniqueness and the stability of the solution are analyzed in a particular case

continuous spectrum and uniform localization for ergodic schrodinger operators abstract in this paper we study localization for ergodic families of discrete schrodinger operators we prove that instability of pure point spectrum implies absence of uniform localization

instability of dense point spectrum under finite rank perturbations we prove that if a is a self adjoint operator and r a non negative finite rank operator whose range is cyclic for a then for a generic in the baire sense t in each eigenvalue of the operator has a neighborhood containing no other eigenvalues

transient and recurrent spectrum abstract we deal primarily with spectral analysis of an abstract self adjoint operator h on a hilbert space h we propose a further refinement of the absolutely continuous subspace h ac into the transient absolutely continuous subspace h tac which is the closure of those with e ith o t n for all n and the recurrent absolutely continuous subspace h rac h ac h tac we discuss general features of this breakup in a subsequent paper we construct analytic almost periodic functions v on so that h d 2 dx 2 v x on l 2 has only recurrent absolutely continuous spectrum in the sense that h rac h

singular continuous spectrum for the period doubling hamiltonian on a set of full measure we consider the discrete one dimensional schrodinger operator with potential generated by the period doubling substitution we show that for almost every element in the hull with respect to the unique ergodic measure on there are no eigenvalues combining this with a result proven by kotani we establish purely singular continuous spectrum on a set of full measure

absolutely continuous convolutions of singular measures and an application to the square fibonacci hamiltonian author s damanik d gorodetski a solomyak b abstract 2015 we prove for the square fibonacci hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants this is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact dimensional measures

characteristics of traffic flow at a non signalized intersection in the framework of game theory abstract at a non signalized intersection some vehicles violate the traffic rules to pass the intersection as soon as possible these behaviors may cause many traffic conflicts even traffic accidents in this paper a simulation model is proposed to research the effects of these behaviors at a non signalized intersection vehicle s movement is simulated by the cellular automaton ca model the game theory is introduced for simulating the intersection dynamics two types of driver participate the game process cooperator c and defector d the cooperator obey the traffic rules but the defector does not a transition process may occur when the cooperator is waiting before the intersection the critical value of waiting time follows the weibull distribution one transition regime is found in the phase diagram the simulation results illustrate the applicability of the proposed model and reveal a number of interesting insights into the intersection management including that the existence of defectors is benefit for the capacity of intersection but also reduce the safety of intersection

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

some schrodinger operators with power decaying potentials and pure point spectrum we construct deterministic potentials such that the schrodinger equation on has dense pure point spectrum in for almost all boundary conditions at as a by product we also obtain power decaying potentials for which the spectrum is purely singular continuous on for all boundary conditions