convergence of the generalized volume averaging method on a convection diffusion problem a spectral perspective this paper proposes a thorough investigation of the convergence of the volume averaging method described by whitaker the method of volume averaging kluwer academic norwell ma 1999 as applied to convection diffusion problems inside a cylinder a spectral description of volume averaging brings to the fore new perspectives about the mathematical analysis of those approximations this spectral point of view is complementary with the lyapunov schmidt reduction technique and provides a precise framework for investigating convergence it is shown for convection diffusion inside a cylinder that the spectral convergence of the volume averageddescription depends on the chosen averaging operator as well as on the boundary conditions a remarkable result states that only part of the eigenmodes among the infinite discrete spectrum of the full solution can be captured by averaging methods this leads to a general convergence theorem which was already examined with the use of the center manifold theorem g n

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

quantum bit commitment with cheat sensitive binding and approximate sealing this paper proposes a cheat sensitive quantum bit commitment scheme based on single photons in which alice commits a bit to bob here bob s probability of success at cheating as obtains the committed bit before the opening phase becomes close to just like performing a guess as the number of single photons used is increased and if alice alters her committed bit after the commitment phase her cheating will be detected with a probability that becomes close to 1 as the number of single photons used is increased the scheme is easy to realize with present day technology

unconditional security in quantum cryptography basic techniques to prove the unconditional security of quantum crypto graphy are described they are applied to a quantum key distribution protocol proposed by bennett and brassard 1984 the proof considers a practical variation on the protocol in which the channel is noisy and photos may be lost during the transmission each individual signal sent into the channel must contain a single photon or any two dimensional system in the exact state described in the protocol no restriction is imposed on the detector used at the receiving side of the channel except that whether or not the received system is detected must be independent of the basis used to measure this system

dunford pettis properties hilbert spaces and projective tensor products we study complete continuity properties of operators onto 2 and prove several results in the dunford pettis theory of jb triples and their projective tensor products culminating in characterisations of the alternative dunford pettis property for e f where e and f are jb triples

quantum data hiding we expand on our work on quantum data hiding hiding classical data among parties who are restricted to performing only local quantum operations and classical communication locc we review our scheme that hides one bit between two parties using bell 1964 states and we derive upper and lower bounds on the secrecy of the hiding scheme we provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme we give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement a candidate data hiding scheme that does not use entanglement is presented we show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme

why quantum bit commitment and ideal quantum coin tossing are impossible abstract there had been well known claims of unconditionally secure quantum protocols for bit commitment however we and independently mayers showed that all proposed quantum bit commitment schemes are in principle insecure because the sender alice can almost always cheat successfully by using an einstein podolsky rosen epr type of attack and delaying her measurements one might wonder if secure quantum bit commitment protocols exist at all we answer this question by showing that the same type of attack by alice will in principle break any bit commitment scheme the cheating strategy generally requires a quantum computer we emphasize the generality of this no go theorem unconditionally secure bit commitment schemes based on quantum mechanics fully quantum classical or quantum but with measurements are all ruled out by this result since bit commitment is a useful primitive for building up more sophisticated protocols such as zero knowledge proofs our results cast very serious doubt on the security of quantum cryptography in the so called post cold war applications we also show that ideal quantum coin tossing is impossible because of the epr attack this no go theorem for ideal quantum coin tossing may help to shed some lights on the possibility of non ideal protocols

implications of superstrong non locality for cryptography non local boxes are hypothetical machines that give rise to superstrong non local correlations leading to a stronger violation of bell clauser horne shimony holt inequalities than is possible within the framework of quantum mechanics we show how non local boxes can be used to perform any two party secure computation we first construct a protocol for bit commitment and then show how to achieve oblivious transfer using non local boxes both have been shown to be impossible using quantum mechanics alone

hyperbolic homogenized models for thermal and solutal dispersion we formulate a general theory based on a lyapunov schmidt expansion for averaging thermal and solutal dispersion phenomena in multiphase reactors with specific attention to the important taylor mechanism due to transverse intraphase and interphase capacitance weighted velocity gradients we show that the classical taylor dispersion phenomena are better described in terms of low dimensional models that are hyperbolic and contain an effective local time or length scale in place of the traditional taylor dispersion coefficient this description eliminates the use of an artificial exit boundary condition associated with parabolic homogenized equations as well as the classical upstream feedback and infinite propagation speed anomalies our approach is also applicable for describing steady dispersion in the presence of reaction and thermal generation or consumption for two phase systems maximum dispersion is found to exist at an optimum fraction epsilon f of the lower capacitance phase for the disp

nonlinear interactions of tearing modes in the vicinity of a bifurcation point of codimension two abstract the interaction of two different tearing modes in slab geometry is examined for certain physical parameter values the linearized problem has a four dimensional nullspace corresponding to two different marginal tearing modes with the center manifold theory the original partial differential equations could be reduced to a four dimensional system of ordinary ones these amplitude equations are equivalent under o 2 actions due to the symmetries of the physical problem because of these symmetries there exist many interesting spatial and spatio temporal solutions in the neighbourhood of the critical parameters such as standing travelling and modulated waves and a structural stable heteroclinic orbit see ambruster guckenheimer and holmes physica d 29 1988 257 282

a new derivation of the taylor aris theory of solute dispersion in a capillary the transport of a dilute solute under viscous motion in a straight capillary is described at three distinct space time scales these are the kinetic fluid mechanical and taylorian scales the transition from one scale to the next higher scale is shown to be a consequence of the central limit theorem clt of probability theory the taylor aris dispersion equation is derived by an application of a recently proved clt for markov processes an alternative computation of the dispersion coefficient is given using a differential equation averaging approach a third method which also applies to solute transport in porous media is illustrated for an approximate computation of the dispersion coefficient

a centre manifold description of containment dispersion in channels with varying flow properties high order asymptotic approximations to the equation governing the longitudinal dispersion of a passive contaminant in poiseuille channel flow are derived and their validity discussed the derivation uses centre manifold theory which provides a systematic and near rigorous approach to calculating each successive approximation it also enables the derivation of the correct initial conditions for the taylor model of shear dispersion approximations that are valid when the channel is of a varying cross section are systematically derived via this approach and the effects of time dependent flow and variable diffusivity are also investigated the resultant modifications to the effective advection velocity and the effective dispersion coefficient are calculated and some general trends indicated

general tooth boundary conditions for equation free modeling we are developing a framework for multiscale computation which enables models at a microscopic level of description for example lattice boltzmann monte carlo or molecular dynamics simulators to perform modeling tasks at macroscopic length scales of interest the plan is to use the microscopic rules restricted to small patches of the domain the teeth using interpolation to bridge the gaps here we explore general boundary conditions coupling the widely separated teeth of the microscopic simulation that achieve high order accuracy over the macroscale we present the simplest case when the microscopic simulator is the quintessential example of a pde we argue that classic high order interpolation of the macroscopic field provides the correct forcing in whatever boundary condition is required by the microsimulator such interpolation leads to tooth boundary conditions which achieve arbitrarily high order consistency the high order consistency is demonstrated on a class of linear pdes in two ways first through the eigenvalues of the scheme for selected numerical problems and second using the dynamical systems approach of holistic discretization on a general class of linear pdes analytic modeling shows that for a wide class of microscopic systems the subgrid fields and the effective macroscopic model are largely independent of the tooth size and the particular tooth boundary conditions when applied to patches of microscopic simulations these tooth boundary conditions promise efficient macroscale simulation we expect the same approach will also accurately couple patch simulations in higher spatial dimensions

kuramoto sivashinsky dynamics on the center unstable manifold this paper studies the dynamical behavior of solutions of the kuramoto sivashinsky partial differential equation with periodic boundary conditions on a spatial interval 0 h the length h is the bifurcation parameter and reduction is made to a two complex dimensional system on a local center unstable manifold near the second bifurcation point h 2 from the trivial solution the resulting o 2 equivariant system displays all the behavior found in high precision simulations of the partial differential equation near this bifurcation point in particular bifurcation sequences to stable traveling waves unstable modulated traveling waves and attracting heteroclinic cycles are reproduced qualitatively and quantitatively within 1 in the parameter range h 2 pm 20 a clear understanding of the global dynamical behavior in this region is thus obtained

on subspaces of non commutative lp spaces abstract we study some structural aspects of the subspaces of the non commutative haagerup l p spaces associated with a general non necessarily semi finite von neumann algebra if a subspace x of l p contains uniformly the spaces l p n n 1 it contains an almost isometric almost 1 complemented copy of l p if x contains uniformly the finite dimensional schatten classes s p n it contains their l p direct sum too we obtain a version of the classical kadec pelczynski dichotomy theorem for l p spaces p 2 we also give operator space versions of these results the proofs are based on previous structural results on the ultrapowers of l p together with a careful analysis of the elements of an ultrapower l p u which are disjoint from the subspace l p these techniques permit to recover a recent result of n randrianantoanina concerning a subsequence splitting lemma for the general non commutative l p spaces various notions of p equiintegrability are studied one of which is equivalent to randrianantoanina s one and some results obtained by haagerup rosenthal and sukochev for l p spaces based on finite von neumann algebras concerning subspaces of l p containing l p are extended to the general case

an efficient two party quantum private comparison protocol with decoy photons and two photon entanglement following some ideas of the quantum secret sharing qss protocol 2008 phys lett a 372 1957 we propose an efficient quantum private comparison qpc protocol for comparing information of equality with the help of a third party tp the protocol can ensure fairness efficiency and security the protocol is fair which means that one party knows the sound result of the comparison if and only if the other one knows the result the protocol is efficient with the help of the tp for calculating however the tp cannot learn any information about the players respective private inputs and even about the comparison result and cannot collude with any player the protocol is secure for the two players that is any information about their respective secret inputs will not leak except the final computation result a precise proof of security of the protocol is presented applications of this protocol may include private bidding and auctions secret ballot elections commercial business identification in a number of scenarios and so on

grothendieck s inequalities for real and complex jbw triples we prove that if m 4 1 2 3 and e 0 if v and w are complex jbw triples with preduals v andw respectively and if u is a separately weak continuous bilinear form on v w then there exist norm one functionals 1 2 v and 1 2 w satisfying u x y m u x 2 2 e 2 x 2 1 1 2 y 2 2 e 2 y 2 1 1 2 for all x y v w here for a norm one functional on a complex jb triple v stands for the prehilertian seminorm on v associated to in bf1 we arrive in this grothendieck s inequality through results of c h chu b iochum and g loupias cil and a corrected version of the little grothendieck s inequality for complex jb triples due to t barton and y friedman bf1 we also obtain extensions of these results to the setting of real jb triples 2000 mathematics subject classification 17c65 46k70 46l05 46l10 and 46l70

quantum key distribution based on orthogonal states allows secure quantum bit commitment for more than a decade it was believed that unconditionally secure quantum bit commitment qbc is impossible but based on a previously proposed quantum key distribution scheme using orthogonal states here we build a qbc protocol in which the density matrices of the quantum states encoding the commitment do not satisfy a crucial condition on which the no go proofs of qbc are based thus the no go proofs could be evaded our protocol is fault tolerant and very feasible with currently available technology it reopens the venue for other post cold war multi party cryptographic protocols e g quantum bit string commitment and quantum strong coin tossing with an arbitrarily small bias this result also has a strong influence on the clifton bub halvorson theorem which suggests that quantum theory could be characterized in terms of information theoretic constraints

multiple time scale analysis of macrotransport processes abstract convective and diffusive transport of a brownian tracer corpuscle is analyzed within a multidimensional space decomposed into local internal and global external subspaces multiple time scale methods are employed to successively eliminate from the kinetic equation governing the multidimensional microtransport process its dependence upon each of the internal coordinates the resulting long time equation describing the residual global space macrotransport process derived by this systematic perturbation procedure is shown to accord with the well established results of generalized taylor dispersion theory heretofore obtained by ad hoc arguments by way of example this macrotransport description is used to analyze the taylor dispersion of a solute in a poiseuille type solvent flow occuring within a rectangular duct of small but non zero aspect ratio elementary dispersion results obtained by ignoring the side walls apply only for relatively short times for longer times the perturbing presence of the side walls acts to substantially increase the axial dispersivity even in the limit of zero aspect ratio where intuition would strongly suggest otherwise

on the decompositions of a quantum state abstract we classify all the decompositions of a quantum state as a weighted sum of one dimensional projectors in particular we describe explicitly the set of irreducible decompositions the physical interest in this problem rests on the possibility of interpreting the decomposition in terms of a classical mixture

quantum cryptography without bell s theorem ekert has described a cryptographic scheme in which einstein podolsky rosen epr pairs of particles are used to generate identical random numbers in remote places while bell s theorem certifies that the particles have not been measured in transit by an eavesdropper we describe a related but simpler epr scheme and without invoking bell s theorem prove it secure against more general attacks including substitution of a fake epr source finally we show our scheme is equivalent to the original 1984 key distribution scheme of bennett and brassard which uses single particles instead of epr pairs

ck centre unstable manifolds we consider the existence and smoothness of global centre unstable manifolds for finite and infinite dimensional flows or maps we show that every global centre unstable manifold can be expressed as a graph of a c k map provided that the nonlinearities are c k smooth the proofs are based on a lemma by d henry on a necessary and sufficient condition for a lipschitz map to be continuously differentiable

facial structure in operator algebra theory we give a complete description of the closed faces in twelve kinds of convex sets that appear in operator algebra theory these consist of positive parts of unit balls for c algebras and their dual spaces and for von neumann algebras and their pre duals of self adjoint parts of unit balls in the same four classes and finally of general unit balls in the four classes all these faces are shown to be semi exposed and naturally paired with a polar face in the dual or pre dual space

measurement theory in local quantum physics in this paper we aim to establish foundations of measurement theory in local quantum physics for this purpose we discuss a representation theory of completely positive cp instruments on arbitrary von neumann algebras we introduce a condition called the normal extension property nep and establish a one to one correspondence between cp instruments with the nep and statistical equivalence classes of measuring processes we show that every cp instrument on an atomic von neumann algebra has the nep extending the well known result for type i factors moreover we show that every cp instrument on an injective von neumann algebra is approximated by cp instruments with the nep the concept of posterior states is also discussed to show that the nep is equivalent to the existence of a strongly measurable family of posterior states for every normal state two examples of cp instruments without the nep are obtained from this result it is thus concluded that in local quantum physics not every cp instrument represents a measuring process but in most of physically relevant cases every cp instrument can be realized by a measuring process within arbitrary error limits as every approximately finite dimensional von neumann algebra on a separable hilbert space is injective to conclude the paper the concept of local measurement in algebraic quantum field theory is examined in our framework in the setting of the doplicher haag roberts and doplicher roberts theory describing local excitations we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a cp instrument with the nep provided that the split property holds for the net of local algebras

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

remote preparation of arbitrary ensembles and quantum bit commitment the hughston jozsa wootters theorem shows that any finite ensemble of quantum states can be prepared at a distance and it has been used to demonstrate the insecurity of all bit commitment protocols based on finite quantum systems without superselection rules in this paper we prove a generalized hjw theorem for arbitrary ensembles of states on a c algebra we then use this result to demonstrate the insecurity of bit commitment protocols based on infinite quantum systems and quantum systems with abelian superselection rules

quantum bit string commitment a bit string commitment protocol securely commits n classical bits so that the recipient can extract only m n bits of information about the string classical reasoning suggests that bit string commitment implies bit commitment and hence given the mayers lo chau theorem that nonrelativistic quantum bit string commitment is impossible not so there exist nonrelativistic quantum bit string commitment protocols with security parameters epsilon and m that allow a to commit n n m epsilon bits to b so that a s probability of successfully cheating when revealing any bit and b s probability of extracting more than n n m bits of information about the n bit string before revelation are both less than epsilon with a restrictive definition of security against a n can be taken to be o exp cn for a positive constant c i briefly discuss possible applications

perturbation of ell_1 copies in preduals of jbw triples abstract it is known that two normal functionals on a jbw triple are orthogonal i e they have orthogonal support tripotents if and only if they are l orthogonal meaning that they span an isometric copy of l 1 2 this is shown to be stable under small norm perturbations in the following sense if the linear span of the two functionals is isometric up to 0 to l 1 2 then the functionals are less far in norm than e 0 from two orthogonal functionals where e 0 as 0 analogous statements for finitely and even infinitely many functionals hold as well and so does a corresponding statement for non normal functionals

analytical and variational numerical methods for unstable miscible displacement flows in porous media the miscible displacement of one fluid by another in a porous medium has received considerable attention in sub surface environmental and petroleum engineering applications when a fluid of higher mobility displaces another of lower mobility unstable patterns referred to as viscous fingering may arise their physical and mathematical study has been the object of numerous investigations over the past century the objective of this paper is to present a review of these contributions with particular emphasis on variational methods these algorithms are tailored to real field applications thanks to their advanced features handling of general complex geometries robustness in the presence of rough tensor coefficients low sensitivity to mesh orientation in advection dominated scenarios and provable convergence with fully unstructured grids this paper is dedicated to the memory of dr jim douglas jr for his seminal contributions to miscible displacement and variational numerical methods

amplitude equations for systems with competing instabilities we describe how to derive ordinary differential equations to predict the time dependence of a system governed by partial differential equations when that system is near to the polycritical condition for the onset of several instabilities the method is illustrated for the general case of two competing instabilities and then a specific physical example of this case is worked out in detail the basic idea is to extend the krylov bogolyubov mitropolsky method of nonlinear mechanics to bifurcation problems

non commutative generalisations of urysohn s lemma and hereditary inner ideals abstract we establish several generalisations of urysohn s lemma in the setting of jb triples which provide full answers to problems 1 12 and 1 13 in fernandez polo and peralta 2007 22 these results extend the previous generalisations obtained by c a akemann g k pedersen and l g brown in the setting of c algebras a generalised kadison s transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in jbw triples we introduce the notion of positively open tripotent in the bidual of a jb triple as an extension of a concept which was already considered in the setting of ternary rings of operators we investigate the connections appearing between positively open tripotents and hereditary inner ideals