uniqueness and asymptotic stability of riemann solutions for the compressible euler equations we prove the uniqueness of riemann solutions in the class of entropy solutions in l bvloc for the 3 3 system of compressible euler equations under usual assumptions on the equation of state for the pressure which imply strict hyperbolicity of the system and genuine nonlinearity of the first and third characteristic families in particular if the riemann solutions consist of at most rarefaction waves and contact discontinuities we show the global l2 stability of the riemann solutions even in the class of entropy solutions in l with arbitrarily large oscillation for the 3 3 system we apply our framework established earlier to show that the uniqueness of riemann solutions implies their inviscid asymptotic stability under l1 perturbation of the riemann initial data as long as the corresponding solutions are in l and have local bounded total variation satisfying a natural condition on its growth with time no specific reference to any particular method for constructing the entropy solutions is made our uniqueness result for riemann solutions can easily be extended to entropy solutions u x t piecewise lipschitz in x for any t 0

dynamical localization for the random dimer schrodinger operator we study the one dimensional random dimer model with hamiltonian h v where for all x mathbb z v 2x v 2x 1 and where the v 2x are i i d bernoulli random variables taking the values v v 0 we show that for all values of vand with probability one in the spectrum of his pure point if v 1 and v 1 sqrt 2 the lyapunov exponent vanishes only at the two critical energies given by e v for the particular value v 1 sqrt 2 respectively v sqrt 2 we show the existence of new additional critical energies at e 3 sqrt 2 respectively e 0 on any compact interval inot containing the critical energies the eigenfunctions are then shown to be semi uniformly exponentially localized and this implies dynamical localization for all q 0 and for all ell 2 mathbb z with sufficiently rapid decrease mathop sup limits t r psi i left q right kern 1pt left t right mathop sup limits t left langle p i left h omega right psi t left x right q p i left h omega right psi t right rangle infty here psi t e ih omega t psi and pi h is the spectral projector of h onto the interval i in particular if v 1 and v sqrt 2 these results hold on the entire spectrum so that one can take i h

spectra and transport in almost periodic dimers we study spectral properties of discrete schrodinger operators with potentials obtained via dimerization of a class of aperiodic sequences it is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic full probability singular continuous spectrum in the hull of primitive and palindromic four block substitution potentials are robust under dimerization generic results also hold for circle potentials we illustrate these results with numerical studies of the quantum mean square displacement as a function of time the numerical techniques provide a very fast algorithm for the time evolution of wave packets

almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small bv initial data abstract in the present paper the author investigates the initial problem for genuinely nonlinear quasilinear hyperbolic systems of conservation laws under small bv perturbations of the riemann initial data where the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms combining the techniques employed by li and kong with the modified glimm s functional the author obtains the almost global existence and lifespan of classical discontinuous solutions to the above problem this result is also applied to the system of one dimensional isentropic flow

a simple method to compute economic order quantities abstract in this note a simple method by using the arithmetic geometric mean inequality theorem is proposed to computer the global minimum economic order quantities without taking complex differential calculus or using tedious algebraic manipulations in contrast to minner s 2007 a note on how to compute economic order quantity without derivatives by cost comparisons international journal of production economics 105 293 296 wee h m wang w t chung c j 2009 a modified method to computer economic order quantities without derivatives by cost difference comparisons european journal of operational research based on a local cost minimum initially to derive the solution and then proven it s the global minimum the proposed method yields the global minimum cost immediately and explicitly without using the cost comparisons and letting the time horizon to infinity

divergence measure fields and hyperbolic conservation laws we analyze a class of l infty vector fields called divergence measure fields we establish the gauss green formula the normal traces over subsets of lipschitz boundaries and the product rule for this class of l infty fields then we apply this theory to analyze l infty entropy solutions of initial boundary value problems for hyperbolic conservation laws and to study the ways in which the solutions assume their initial and boundary data the examples of conservation laws include multidimensional scalar equations the system of nonlinear elasticity and a class of m x m systems with affine characteristic hypersurfaces the analysis in l infty also extends to l p

well posedness theory for hyperbolic conservation laws the paper presents a well posedness theory for the initial value problem for a general system of hyperbolic conservation laws we will start with the refinement of glimm s existence theory and discuss the principle of nonlinear through wave tracing our main goal is to introduce a nonlinear functional for two solutions with the property that it is equivalent to the l1 x distance between the two solutions and is time decreasing moreover the functional is constructed explicitly in terms of the wave patterns of the solutions through the nonlinear superposition it consists of a linear term measuring the l1 x distance a quadratic term measuring the coupling of waves and distance and a generalized entropy functional 1999 john wiley sons inc

riemann problem for the relativistic chaplygin euler equations abstract the relativistic euler equations for a chaplygin gas are studied the riemann problem is solved constructively there are five kinds of riemann solutions in which four only contain different contact discontinuities and the other involves delta shock waves under suitable generalized rankine hugoniot relation and entropy condition the existence and uniqueness of delta shock solutions are established

relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non bv perturbations we develop a theory based on relative entropy to show the uniqueness and l 2 stability up to a translation of extremal entropic rankine hugoniot discontinuities for systems of conservation laws typically 1 shocks n shocks 1 contact discontinuities and n contact discontinuities of large amplitude among bounded entropic weak solutions having an additional trace property the existence of a convex entropy is needed no bv estimate is needed on the weak solutions considered the theory holds without smallness conditions the assumptions are quite general for instance strict hyperbolicity is not needed globally for fluid mechanics the theory handles solutions with vacuums

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

extended divergence measure fields and the euler equations for gas dynamics a class of extended vector fields called extended divergence measure fields is analyzed these fields include vector fields in l p and vector valued radon measures whose divergences are radon measures such extended vector fields naturally arise in the study of the behavior of entropy solutions of the euler equations for gas dynamics and other nonlinear systems of conservation laws a new notion of normal traces over lipschitz deformable surfaces is developed under which a generalized gauss green theorem is established even for these extended fields an explicit formula is obtained to calculate the normal traces over any lipschitz deformable surface suitable for applications by using the neighborhood information of the fields near the surface and the level set function of the lipschitz deformation surfaces as an application we prove the uniqueness and stability of riemann solutions that may contain vacuum in the class of entropy solutions of the euler equations for gas dynamics

lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small bv initial data shocks and contact discontinuities abstract this work is a continuation of our previous work z q shao global structure stability of riemann solutions for linearly degenerate hyperbolic conservation laws under small bv perturbations of the initial data nonlinear anal real world appl 11 2010 3791 3808 in the present paper we investigate the global structure stability of riemann solutions for general quasilinear hyperbolic systems of conservation laws under small bv perturbations of the initial data where the riemann solution only contains the shocks and contact discontinuities and at least a shock wave the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms we get a lower bound of the lifespan of the piecewise c 1 solution to a class of the generalized riemann problem which can be regarded as a small bv perturbation of the corresponding riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in physics particularly to one dimensional euler equations of gas dynamics for a compressible inviscid non heat conducting gas in eulerian coordinates are also given

perturbation theory for the random dimer model the authors study a one dimensional tight binding model with a random potential taking two values or nu with the restriction that on pairs of two neighbouring sites the potentials take the same value this random dimer model proposed by dunlap phillips and wu 1990 has a vanishing lyapunov exponent for the energy e or nu they compute the lyapunov exponent and the density of states perturbatively in the vicinity of this energy using the invariant measure formalism

long time stability in systems of conservation laws using relative entropy energy we study the long time stability of shock free solutions of hyperbolic systems of conservation laws under an arbitrarily large initial disturbance in l2 l we use the relative entropy method a robust tool which allows us to consider rough and large disturbances we display practical examples in several space dimensions for scalar equations as well as isentropic gas dynamics for full gas dynamics we use a trick from chen 1 in which the estimate is made in terms of the relative mechanical energy instead of the relative mathematical entropy

critical energies in random palindrome models we investigate the occurrence of critical energies where the lyapunov exponent vanishes in random schrodinger operators when the potentials have some local order which we call random palindrome models we give necessary and sufficient conditions for the presence of such critical energies the commutativity of finite word elliptic transfer matrices finally we perform some numerical calculations of the lyapunov exponents showing their behavior near the critical energies and the respective time evolution of an initially localized wave packet obtaining the exponent ruling the algebraic growth of the second momentum we also consider special random palindrome models with one letter bounded gap property the transport effects of such long range order are showed numerically

dynamical localization for discrete and continuous random schrodinger operators we show for a large class of random schrodinger operators h on and on that dynamical localization holds i e that with probability one for a suitable energy interval i and for q a positive real here is a function of sufficiently rapid decrease and p i h is the spectral projector of h corresponding to the interval i the result is obtained through the control of the decay of the eigenfunctions of h and covers in the discrete case the anderson tight binding model with bernoulli potential dimension 1 or singular potential 1 and in the continuous case anderson as well as random landau hamiltonians

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

uniqueness and stability of riemann solutions with large oscillation in gas dynamics we prove the uniqueness of riemann solutions in the class of entropy solutions in with arbitrarily large oscillation for the 3 3 system of euler equations in gas dynamics the proof for solutions with large oscillation is based on a detailed analysis of the global behavior of shock curves in the phase space and the singularity of centered rarefaction waves near the center in the physical plane the uniqueness of riemann solutions yields their inviscid large time stability under arbitrarily large perturbation of the riemann initial data as long as the corresponding solutions are in l and have local bounded total variation satisfying a natural condition on its growth with time no specific reference to any particular method for constructing the entropy solutions is needed the uniqueness result for riemann solutions can easily be extended to entropy solutions u x t piecewise lipschitz in x for any t 0 with arbitrarily large oscillation

boundary value problems for the 2d steady relativistic euler equations with general equation of state abstract we consider several types of boundary value problems including goursat problem mixed initial boundary value problem and centered wave problem for the two dimensional steady relativistic euler system with a general equation of state p p which is assumed to satisfy 0 p 1 and p p 2 p 1 p 0 global classical solutions to these boundary value problems are constructed by the method of characteristic decomposition using these results we also construct a global supersonic relativistic jet flow out of a semi infinite convex duct intovacuum

dynamical delocalization for the 1d bernoulli discrete dirac operator a 1d tight binding version of the dirac equation is considered after checking that it recovers the usual discrete schrodinger equation in the nonrelativistic limit it is found that for two valued bernoulli potentials the zero mass case presents the absence of dynamical localization for some specific values of the energy albeit it has no continuous spectrum for the other energy values again excluding some very specific ones the bernoulli dirac system is localized independently of the mass

dynamical localization ii with an application to the almost mathieu operator several recent works have established dynamical localization for schrodinger operators starting from control on the localization length of their eigenfunctions in terms of their centers of localization we provide an alternative way to obtain dynamical localization without resorting to such a strong condition on the exponential decay of the eigenfunctions furthermore we illustrate our purpose with the almost mathieu operator h cos 2 x 15 and with good diophantine properties more precisely for almost all for all q 0 and for all functions l2 mathbb z of compact support we show that mathop sup limits t left langle e ith theta lambda omega psi left x right q e ith theta lambda omega psi right rangle c psi the proof applies equally well to discrete and continuous random hamiltonians in all cases it uses as input a repulsion principle of singular boxes supplied in the random case by the multi scale 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

quantum hamiltonians with quasi ballistic dynamics and point spectrum abstract consider the family of schrodinger operators and also its dirac version on l 2 z or l 2 n h s w f s n w where s is a transformation on compact metric f is a real lipschitz function and w is a sufficiently fast power decaying perturbation under certain conditions it is shown that h s w presents quasi ballistic dynamics for in a dense g set applications include potentials generated by rotations of the torus with analytic condition on f doubling map axiom a dynamical systems and the anderson model if w is a rank one perturbation examples of h s w with quasi ballistic dynamics and point spectrum are also presented

a constrained multi products epq inventory model with discrete delivery order and lot size abstract this paper proposes an alternative heuristic algorithm for a multi product economic production quantity epq vendor buyer integrated model with just in time jit philosophy and a budget constraint this type of problem is usually solved by a mixed integer non linear problem minlp which is complex and computationally expensive the proposed heuristic algorithm involves less computation and therefore it is less expensive than the previously published algorithms furthermore the heuristic algorithm is simpler as it derives the integer values for all discrete variables in a straightforward manner through empirical experimentation it is demonstrated that the heuristic algorithm provides solutions closer to the lower bound in a very short time

revisiting lot sizing for an inventory system with product recovery this note investigates the study by teunter 2004 1 on lot sizing for inventory systems with product recovery where lot sizing formulae for two recovery policies 1 r and p 1 are derived instead of applying the classical optimization technique we develop an integrated solution procedure for each of the two policies using algebraic approaches numerical analysis show that our examples result in a lower total cost for both policies

dynamical lower bounds for 1d dirac operators quantum dynamical lower bounds for continuous and discrete one dimensional dirac operators are established in terms of transfer matrices then such results are applied to various models including the bernoulli dirac one and in contrast to the discrete case critical energies are also found for the continuous dirac case with positive mass

initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws we consider initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws through the scalar case the entropy solutions we address assume their initial data only in the sense of weak star in l as t 0 and satisfy the entropy inequality in the sense of distributions for t 0 we prove that if the flux function has weakly genuine nonlinearity then the entropy solutions are always unique and the initial layers do not appear we also discuss applications to the zero relaxation limit for hyperbolic systems of conservation laws with relaxation

a modified method to compute economic order quantities without derivatives by cost difference comparisons this note presents a modified method to compute economic order quantities without derivatives by cost difference comparisons extensions to allow backorders are done for the eoq epq models in contrast to previous literatures limiting values on a finite planning horizon are used rather than algebraic manipulations for the cost function comparisons

large time behavior of entropy solutions of conservation laws abstract we are concerned with the large time behavior of discontinuous entropy solutions for hyperbolic systems of conservation laws we present two analytical approaches and explore their applications to the asymptotic problems for discontinuous entropy solutions these approaches allow the solutions of arbitrarily large oscillation without a priori assumption on the ways from which the solutions come the relation between the large time behavior of entropy solutions and the uniqueness of riemann solutions leads to an extensive study of the uniqueness problem we use a direct method to show the large time behavior of large l solutions for a class of m m systems including a model in multicomponent chromatography we employ the uniqueness of riemann solutions and the convergence of self similar scaling sequence of solutions to show the asymptotic behavior of large bv solutions for the 3 3 system of euler equations in thermoelasticity these results indicate that the riemann solution is the unique attractor of large discontinuous entropy solutions whose initial data are l l 1 or bv l 1 perturbation of the riemann data for these systems these approaches also work for proving the large time behavior of approximate solutions to hyperbolic conservation laws

two dimensional relativistic euler equations in a convex duct abstract in this paper we investigate the motion of supersonic flow governed by 2 d steady isentropic irrotational relativistic euler system entered into a convex duct we will give the propagation and interactions of rarefaction waves between the upward and downward wall and obtain the global existence of piecewise continuous solutions furthermore in some cases the vacuum state may appear and we also give a sufficient condition to the appearance of the vacuum in finite domain

global radial solutions to 3d relativistic euler equations for non isentropic chaplygin gases in this paper we investigate the smooth spherically symmetric solutions to 3d relativistic chaplygin gases with variable entropy whose initial data is assumed to be a small smooth perturbation to a constant state due to the structure of the equation we can still take advantage of the null condition which is satisfied by the potential equation for isentropic and spacetime irrotational relativistic chaplygin gases and obtain the global existence of smooth solution by continuity method this generalizes the result for classical chaplygin gases of godin j math pures appl 87 9 91 117 2007 to the relativistic case

an easy method to derive eoq and epq inventory models with backorders recently a cost minimization method to determine the lot size for the eoq epq models with backorders was published this method is based on the well known arithmetic geometric mean inequality although the cost minimization method is correct and interesting it does not focus on deriving the backorders level this paper proposes another simple approach the proposed method finds both the lot size and the backorders level

a note on optimal replenishment policy for imperfect quality emq model with rework and backlogging a recent article on optimal replenishment policy of imperfect emq model by chiu s w chiu optimal replenishment policy for imperfect quality emq model with rework and backlogging applied stochastic models in business and industry 23 2007 165 178 used mathematical modeling and differential calculus to derive the optimal ordering policy that minimizes overall costs this paper presents a straightforward algebraic approach to replace the use of calculus on the cost function for determining the optimal replenishment solutions as well as the long run average production inventory costs for such an imperfect emq model the algebraic method presented in this paper may enable students or practitioners with little or no knowledge of calculus to learn or to manage with ease the real life manufacturing systems

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

the economic lot size of the integrated vendor buyer inventory system derived without derivatives a simple derivation abstract in this paper we first complement an inappropriate mathematical error on the total cost in two previous published research papers in inventory field then an arithmetic geometric inequality method is proposed not only to simplify the algebraic method of completing prefect squares but also to complement their shortcomings in addition we also provide a closed form optimal solution to the integrated vendor buyer inventory system without using complex derivatives finally the proposed method seems to be easy to understand and simple to apply by individuals who are not familiar with differential calculus

sparse 1d discrete dirac operators i quantum transport abstract some dynamical lower bounds for one dimensional discrete dirac operators with different classes of sparse potentials are presented and the particular role of the particle mass is emphasized

reflectionless modes in chains with large size homogeneous impurities the authors study the spectra and localization properties of tight binding chains with randomly distributed binary blocks of arbitrary size m one having site energies epsilon a and the other epsilon b respectively they demonstrate that for block size m greater than one and delta mod epsilon a epsilon b less than a critical value delta c m perfect transmission resonance modes exist in the band their number is proportional to m and they occur via dominant 1 e2 divergencies of the localization length no transmission is found for delta delta c m the results are understood by solving exactly the scattering problem from a single homogeneous impurity block of arbitrary size m in the limit of hard impurities m to infinity transmission stops only when delta delta c infinity 4v v being the intersite matrix element that is when the pure a and b bands become detached

a study of one dimensional correlated disordered systems using the invariant measure method the behaviour of electronic states of one dimensional correlated disordered systems which are modelled by a tight binding hamiltonian is studied analytically using the invariant measure method the approach of bovier is generalized to include the possibility of different site energies and nearest neighbour hopping integrals inside the correlated sites or the cluster the process is further elaborated by applying to the symmetric random trimer model which contains in it many hitherto known models of this category an alternative mathematical definition of the exceptional energy from the invariant measure density along with physical arguments substantiating it is presented furthermore the procedure for obtaining exceptional energies is outlined and applied to the symmetric random trimer model to derive conditions for obtaining doubly degenerate exceptional energies the lyapunov exponent or the inverse localization length of states around the exceptional energy is found to vary as in the leading order n denotes the degeneracy of the exceptional energy the density of states at the exceptional energies are calculated we further propose that one dimensional correlated disordered systems can be mapped to a lloyd model in which the width of the distribution of site energies is determined by the reflection coefficient of the cluster embedded in the lattice of the other constituent the importance of our results is discussed

some comments on a simple method to compute economic order quantities abstract in this note we emphasize that the arithmetic geometric mean inequality approach proposed by teng teng j t 2008 a simple method to compute economic order quantities european journal of operational research doi 10 1016 j ejor 2008 05 019 is not a general solution method teng s approach happens to work and give the correct results when the two terms in an objective function are any functions such that their product is a constant the classical eoq model works fine since the product of the two terms is indeed a constant when the product is not a constant teng s approach is of little use this is exemplified in comment 1 via solving the eoq model with complete backorders where the model is regarded as having two decision variables comment 2 is generally valid for an algebraic method when it is used to solve an objective function with two decision variables

absence of localization in disordered systems with local correlation in an early work by dunlap et al 1990 it was conjectured using a matrix transfer approach that diagonal disordered systems with local correlation dimer models exhibit an absence of anderson localization in this letter we find explicitly these delocalized states and energies using a suitable unitary transformation and the symmetries related to the model moreover we expand these states around the critical energy and find a new 1 square root e ec divergence

stability of riemann solutions with large oscillation for the relativistic euler equations abstract we are concerned with entropy solutions of the 2 2 relativistic euler equations for perfect fluids in special relativity we establish the uniqueness of riemann solutions in the class of entropy solutions in l bv loc with arbitrarily large oscillation our proof for solutions with large oscillation is based on a detailed analysis of global behavior of shock curves in the phase space and on special features of centered rarefaction waves in the physical plane for this system the uniqueness result does not require specific reference to any particular method for constructing the entropy solutions then the uniqueness of riemann solutions yields their inviscid large time stability under arbitrarily large l 1 l bv loc perturbation of the riemann initial data as long as the corresponding solutions are in l and have local bounded total variation that allows the linear growth in time we also extend our approach to deal with the uniqueness and stability of riemann solutions containing vacuum in the class of entropy solutions in l with arbitrarily large oscillation