some uniform estimates and large time behavior of solutions to one dimensional compressible navier stokes system in unbounded domains with large data we study the large time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible navier stokes system describing the one dimensional motion of a viscous heat conducting perfect polytropic gas in unbounded domains the temperature is proved to be bounded from below and above independent of both time and space moreover it is shown that the global solution is asymptotically stable as time tends to infinity note that the initial data can be arbitrarily large this result is proved by using elementary energy methods

nonlocality asymmetry and distinguishing bipartite states entanglement is a useful resource because some global operations cannot be locally implemented using classical communication we prove a number of results about what is and what is not locally possible we focus on orthogonal states which can always be globally distinguished we establish the necessary and sufficient conditions for a general set of 2 ifmmode times else texttimes fi 2 quantum states to be locally distinguishable and for a general set of 2 ifmmode times else texttimes fi n quantum states to be distinguished given an initial measurement of the qubit these results reveal a fundamental asymmetry to nonlocality which is the origin of nonlocality without entanglement and we present a very simple proof of this phenomenon

a class of euclidean routing problems with general rout cost functions in most vehicle routing problems a given set of customers is to be partitioned into a collection of regions each of which is assigned to a single vehicle starting at a depot and returning there after visiting all of the region s customers exactly once in a route in this paper we consider problem settings where the cost of a route may depend on its length as well as m the number of points on the route according to some general function f m assumed to be nondecreasing and concave in we describe a class of o n logn or o n2 heuristics and show under mild probabilistic assumptions that the solutions generated are asymptotically optimal we also show that lower and upper bounds on the system wide costs may be computed with even simpler procedures and that these bounds are asymptotically tight under the same assumptions

local distinguishability of quantum states in infinite dimensional systems we investigate local distinguishability of quantum states by use of convex analysis of joint numerical range of operators on a hilbert space we show that any two orthogonal pure states are distinguishable by local operations and classical communications even for infinite dimensional systems an estimate of the local discrimination probability is also given for some families of more than two pure states

global existence and exponential stability for the pth power viscous reactive gas in this chapter we prove the global existence and exponential stability of solutions in h i i 2 4 for the compressible navier stokes equations which arise in the study of a thermal explosion and describe the dynamic combustion for a reactive newtonian fluid confined between two infinite parallel plates

global existence and large time behavior of solutions to the cauchy problem of one dimensional viscous radiative and reactive gas abstract in this paper we consider the global existence and large time behavior of solutions of one dimensional viscous radiative and reactive gas with large initial data in precedent studies the case for the initial boundary value problem in bounded domain has been investigated and our main purpose focuses on the corresponding problem in unbounded domain if the initial data is a large perturbation of a non vacuum constant equilibrium state and is assumed to be without vacuum mass concentrations or vanishing temperatures then we can show that its cauchy problem admits a unique global smooth non vacuum solution which tends time asymptotically to such an equilibrium state the key point in the analysis is to deduce the uniform positive lower and upper bounds on the specific volume and the absolute temperature

discontinuous solutions of the navier stokes equations for multidimensional flows of heat conducting fluids we prove the global existence of weak solutions of the navier stokes equations for compressible heat conducting fluids in two and three space dimensions when the initial density is close to a constant in l 2 l the initial temperature is close to a constant in l 2 and the initial velocity is small in h s l 4 where s 0 when n 2 and when n 3 the l p norms must be weighted slightly when n 2 in particular the initial data may be discontinuous across a hypersurface of n a great deal of qualitative information about the solution is obtained for example we show that the velocity vorticity and temperature are relatively smooth in positive time as is the effective viscous flux f which is the divergence of the velocity minus a certain multiple of the pressure we find that f plays a central role in the entire analysis particularly in closing the required energy estimates and in understanding rates of regularization near the initial layer moreover f is precisely the quantity through which the hyperbolicity of the corresponding equations for inviscid fluids shows itself an effect which is crucial for obtaining time independent pointwise bounds for the density

when do local operations and classical communication suffice for two qubit state discrimination in this paper we consider the conditions under which a given ensemble of two qubit states can be optimally distinguished by local operations and classical communication locc we begin by completing the perfect distinguishability problem of two qubit ensembles both for separable operations and locc by providing necessary and sufficient conditions for the perfect discrimination of one pure and one mixed state then for the well known task of minimum error discrimination it is shown that almost all two qubit ensembles consisting of three pure states cannot be optimally discriminated using locc this is surprising considering that any two pure states can be distinguished optimally by locc special attention is given to ensembles that lack entanglement and we prove an easy sufficient condition for when a set of three product states cannot be optimally distinguished by locc thus providing new examples of the phenomenon known as non locality without entanglement we next consider an example of n parties who each share the same state but who are ignorant of its identity the state is drawn from the rotationally invariant trine ensemble and we establish a tight connection between the n copy ensemble and shor s lifted single copy ensemble for any finite n we prove that optimal identification of the states cannot be achieved by locc however as n locc can indeed discriminate the states optimally this is the first result of its kind finally we turn to the task of unambiguous discrimination and derive new lower bounds on the locc inconclusive probability for symmetric states when applied to the double trine ensemble this leads to a rather different distinguishability character than when the minimum error probability is considered

large time behavior of solutions to the equations of a viscous heat conducting flow with shear viscosity in unbounded domains abstract we consider the initial and initial boundary value problems for a viscous heat conducting flow with shear viscosity in unbounded domains with general large initial data we prove that the temperature is bounded from below and above uniformly in time and space and that the global solution is asymptotically stable as the time tends to infinity our approach relies upon the energy estimate method

classical randomness in quantum measurements similarly to quantum states also quantum measurements can be mixed corresponding to a random choice within an ensemble of measuring apparatuses such mixing is equivalent to a sort of hidden variable which produces a noise of purely classical nature it is then natural to ask which apparatuses are indecomposable i e do not correspond to any random choice of apparatuses this problem is interesting not only for foundations but also for applications since most optimization strategies give optimal apparatuses that are indecomposable mathematically the problem is posed describing each measuring apparatus by a positive operator valued measure povm which gives the statistics of the outcomes for any input state the povms form a convex set and in this language the indecomposable apparatuses are represented by extremal points the analogous of pure states in the convex set of states differently from the case of states however indecomposable povms are not necessarily rank one e g von neumann measurements in this paper we give a complete classification of indecomposable apparatuses for discrete spectrum by providing different necessary and sufficient conditions for extremality of povms along with a simple general algorithm for the decomposition of a povm into extremals as an interesting application informationally complete measurements are analysed in this respect the convex set of povms is fully characterized by determining its border in terms of simple algebraic properties of the corresponding povms

symmetric nonbarotropic flows with large data and forces we prove the global existence of weak solutions of the navier stokes equations of compressible nonbarotropic flow in three space dimensions with initial data and external forces which are large discontinuous and spherically or cylindrically symmetric the analysis allows for the possibility that a vacuum state emerges at the origin or axis of symmetry and the equations hold in the sense of distributions in the set where the density is positive in addition the mass and momentum equations hold weakly in the entire space time domain but with a nonstandard interpretation of the viscosity terms as distributions solutions are obtained as limits of solutions in annular regions between two balls or cylinders and the analysis allows for the possibility that energy is absorbed into the origin or axis and is lost in the limit as the inner radius goes to zero

realizing a 2 d positive operator valued measure by local operations and classical communication we study the realization of a 2 d positive operator valued measure povm by local operations and classical communication locc we derive that any povm on a 2 d hilbert space in which each party s space is finite dimensional can be realized by one way locc this implies that any optimal discrimination of quantum states spanning such a 2 d hilbert space is possible by one way locc regardless of the optimality criterion used and how entangled the states are

global well posedness of classical solutions with large oscillations and vacuum to the three dimensional isentropic compressible navier stokes equations we establish the global existence and uniqueness of classical solutions to the cauchy problem for the isentropic compressible navier stokes equations in three spatial dimensions with smooth initial data that are of small energy but possibly large oscillations with constant state as far field which could be either vacuum or nonvacuum the initial density is allowed to vanish and the spatial measure of the set of vacuum can be arbitrarily large in particular the initial density can even have compact support these results generalize previous results on classical solutions for initial densities being strictly away from vacuum and are the first for global classical solutions that may have large oscillations and can contain vacuum states 2012 wiley periodicals inc

global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain we consider the equations of a viscous polytropic ideal gas in the domain exterior to a ball in n n 2 or 3 and prove the global existence of spherically symmetric smooth solutions for large initial data with spherical symmetry the large time behavior of the solutions is also discussed to prove the existence we first study an approximate problem in a bounded annular domain and then obtain a priori estimates independent of the boundedness of the annular domain letting the diameter of the annular domain tend to infinity we get a global spherically symmetric solution as the limit

large time behavior of solutions to the equations of a one dimensional viscous polytropic ideal gas in unbounded domains the large time behavior of solutions to the initial and initial boundary value problems for a one dimensional viscous polytropic ideal gas in unbounded domains is investigated using a special cut off function to localize the problem we derive a local representation for the specific volume with the help of the local representation and certain new estimates for the temperature and the stress and the weighted energy estimates we prove that in any bounded interval the specific volume is pointwise bounded from below and above for all t 0 and a generalized solution is convergent as time goes to infinity

bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication we show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally the number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement a similar general condition is also shown for pure and mixed states these results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement

how continuous quantum measurements in finite dimensions are actually discrete we show that in finite dimensions a quantum measurement with a continuous set of outcomes can be always realized as a continuous random choice of measurements with a finite number of outcomes

local indistinguishability more nonlocality with less entanglement we provide a first operational method for checking local indistinguishability of orthogonal states it originates from that in ghosh et al phys rev lett 87 5807 2001 though we deal with pure states our method shows that probabilistic local distinguishing is possible for a complete multipartite orthogonal basis if and only if all vectors are product also it leads to local indistinguishability of a set of orthogonal pure states of 3 multiply sign in circle 3 which shows that one can have more nonlocality with less entanglement where more nonlocality is in the sense of increased local indistinguishability of orthogonal states this is to our knowledge the only known example where d orthogonal states in d multiply sign in circle d are locally indistinguishable

asymptotic behavior of compressible p th power newtonian fluid with large initial data abstract in this paper we study a large time behavior of the global spherically or cylindrically symmetric solutions in h 1 for the p th power compressible newtonian fluid in multi dimension with large initial data precisely if the initial data is spherically symmetric the space dimension can be taken not less than two on the other hand if the initial data is cylindrically symmetric the smallness of initial data is not needed the main concern of the present paper is to investigate the exponential decay rate of a solution toward the stationary solution as time goes to infinity we get the uniform positive lower and upper bounds of the density by using different methods

global existence and exponential stability of solutions in h 4 for the compressible navier stokes equations with the cylinder symmetry abstract this paper is concerned with the global existence and exponential stability of solutions in h 4 for the compressible navier stokes equations with the cylinder symmetry in r 3 when the initial total energy is sufficiently small moreover the global existence and exponential stability of the classical solution can be also derived

on temporal asymptotics for the pth power viscous reactive gas abstract in this paper we investigate the long time behaviour of solutions to the system governing a heat conductive viscous reactive pth power gas confined between two parallel plates for initial boundary value problems with the end points held at a prescribed temperature or insulated we prove the global existence of physically relevant solutions and establish their rate of convergence to equilibria for generic initial data the estimates for different boundary conditions are presented in a unified manner

distinguishability and indistinguishability by local operations and classical communication it is well known that orthogonal quantum states can be distinguished perfectly however if we assume that these orthogonal quantum states are shared by spatially separated parties the distinguishability of these shared quantum states may be completely different we show that a set of linearly independent quantum states formula see text where u m n are generalized pauli matrices cannot be discriminated deterministically or probabilistically by local operations and classical communication on the other hand any l maximally entangled states from this set are locally distinguishable if l l 1 or 2d the explicit projecting measurements are obtained to locally discriminate these states as an example we show that four werner states are locally indistinguishable

symmetric flows for compressible heat conducting fluids with temperature dependent viscosity coefficients abstract we consider the navier stokes equations for compressible heat conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature a global in time spherically or cylindrically symmetric classical solution to the initial boundary value problem is shown to exist uniquely and converge exponentially to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent the initial data can be large if is sufficiently close to 1 these results are of nishida smoller type and extend the work liu et al 2014 16 restricted to the one dimensional flows

distinguishability of quantum states by separable operations in this paper we study the distinguishability of multipartite quantum states by separable operations we first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations an analytical version of this condition is derived for the case of d 1 pure states where d is the total dimension of the state space under consideration a number of interesting consequences of this result are then carefully investigated remarkably we show there exists a large class of 2 otimes 2 separable operations not being realizable by local operations and classical communication before our work only a class of 3 otimes 3 nonlocal separable operations was known bennett phys rev a 59 1070 1999 we also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of one or two orthogonal product states i e has an orthogonal schmidt number not less than three thus generalize the recent work about indistinguishable bipartite subspaces watrous phys rev lett 95 080505 2005 notably we obtain an explicit construction of indistinguishable subspaces of dimension 7 or 6 by considering a composite quantum system consisting of two qutrits resp three qubits which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8

distinguishability of bell states more than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication locc are allowed we show that four bell states cannot be discriminated by locc even probabilistically using the separability properties of a four party unlockable bound entangled state using an existing inequality among the measures of entanglement we show that any three bell states cannot be discriminated with certainty by locc exploiting the inequality we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states

asymptotic behavior of compressible navier stokes equations with density dependent viscosity and vacuum in this paper we study the one dimensional navier stokes equations connecting to vacuum state with a jump in density when the viscosity depends on the density precisely when the viscosity coefficient is proportional to with 0 where is the density we give the asymptotic behavior and the decay rate of the density function x t furthermore the behavior of the density function x t near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied the analysis is based on some new mathematical techniques and some new useful estimates this fills a final gap on studying navier stokes equations with the viscosity coefficient dependent on the density

establishing consistent and realistic reorder intervals in production distribution systems the objective of this paper is to present a model and algorithm that can be used to find consistent and realistic reorder intervals for each item in large scale production distribution systems we assume such systems can be represented by directed acyclic graphs demand for each end item is assumed to occur at a constant and continuous rate production is instantaneous and no backorders are allowed both fixed setup costs and echelon holding costs are charged at each stage we limit our attention to nested and stationary policies furthermore we restrict the reorder interval for each stage to be a power of 2 times a base planning period the model that results from these assumptions is an integer nonlinear programming problem the optimal solution can be found using the proposed algorithm which is a polynomial time algorithm a real world example is given to illustrate the procedure

universal attractor in h4 for the nonlinear one dimensional compressible navier stokes equations abstract this paper is concerned with the regularity exponential stability of solutions and existence of universal attractor in h 4 for a nonlinear one dimensional compressible navier stokes equations describing a motion of heat conductive viscous real gas in a bounded domain 0 1 some new ideas and more delicated estimates are introduced to prove these results

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

effective heuristics for multiproduct partial shipment models motivated by real applications we consider the problem of shipping products to multiple customers from limited inventory after formulating the optimization problems under different restrictions on partial shipments we find that commercially available packages applied directly are unsatisfactory as are simple greedy approaches we develop a scheme of heuristics that enables the user to select a good balance between computation time and effectiveness a detailed computational study of one and two period industrial sized problems indicates that these heuristics are computationally practical and generate solutions that are on average within 34 of the optimum

global spherically symmetric flows for a viscous radiative and reactive gas in an exterior domain abstract we consider the equations for a viscous compressible radiative and reactive gas pressure p r a 4 3 internal energy e c v a 4 over an unbounded exterior domain in r n where n 2 is the space dimension the existence uniqueness and large time behavior of global spherically symmetric solutions are established for large initial data the key point in the analysis is to deduce certain uniform a priori estimates on the solutions especially on lower and upper bounds of the specific volume and temperature

global well posedness of the cauchy problem for the navier stokes equations of nonisentropic flow with discontinuous initial data abstract we prove the global existence uniqueness and continuous dependence on initial data for discontinuous solutions of the navier stokes equations for nonisentropic compressible flow in one space dimension a great deal of information is obtained concerning the qualitative behavior of the solution including an analysis of the convection and evolution of jump discontinuities the derivation of sharp rates of smoothing and the l asymptotic behavior

exact and heuristic solutions for a shipment problem with given frequencies we consider the problem of shipping several products from an origin to a destination when a discrete set of shipping frequencies is available in such a way that the sum of the transportation and inventory costs is minimized this problem which is known to be np hard has applications in transportation planning and in location analysis in this paper we derive dominance rules for the problem solutions that allow a tightening of the bounds on the problem variables and improve the efficiency of a known branch and bound algorithm moreover we present some heuristics and compare them with two different modifications of an eoq type algorithm for the solution of the problem with continuous frequencies

determining optimal reorder intervals in capacitated production distribution systems the problem of determining consistent and realistic reorder intervals in complex production distribution environments was formulated as a large scale nonlinear integer programming problem by maxwell and muckstadt maxwell w l j a muckstadt 1985 establishing consistent and realistic reorder intervals in production distribution systems oper res 33 6 november december 1316 1341 they show how the special structure of the problem permits its solution by a standard network flow algorithm in this paper we review the maxwell muckstadt model provide necessary and sufficient conditions that characterize the solution and show that the optimal partition of nodes in the production distribution network is invariant to an arbitrary scaling of the set up and holding cost parameters we consider two capacitated versions of the model one with a single constrained work center and the other with multiple constrained work centers for single constraint problems the invariance corollary provides a simp

global existence and asymptotic behavior in nonlinear thermoviscoelasticity abstract we study global existence uniqueness and asymptotic behavior as time tends to infinity of weak solutions to the system of nonlinear thermoviscoelasticity various boundary conditions are considered it is shown that for any initial data u 0 v 0 0 l w 1 h 1 there is a unique global solution u v deformation gradient velocity temperature such that u c 0 l v c 0 w 1 l 0 w 1 c 0 h 1 the constitutive assumptions for the helmholtz free energy include the models for the study of phase transition problems in shape memory alloys