unconditional security from noisy quantum storage we consider the implementation of two party cryptographic primitives based on the sole assumption that no large scale reliable quantum storage is available to the cheating party we construct novel protocols for oblivious transfer and bit commitment and prove that realistic noise levels provide security even against the most general attack such unconditional results were previously only known in the so called bounded storage model which is a special case of our setting our protocols can be implemented with present day hardware used for quantum key distribution in particular no quantum storage is required for the honest parties

master symmetries for differential difference equations of the volterra type abstract it is demonstrated that in the case of integrable differential difference equations similar to the well known volterra equation unlike the korteweg de vries and nonlinear schrodinger equations there are many instances in which local master symmetries can be found those master symmetries are new interesting examples of local evolution chains explicitly depending on the time and discrete variable and integrable in a special sense the examples are constructed by a direct and elementary approach which enables one to get new integrable equations using miura type transformations

the operational meaning of min and max entropy in this paper we show that the conditional min entropy h min a b of a bipartite state rhoab is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the b part of rhoab are allowed in the special case where a is classical this overlap corresponds to the probability of guessing a given b in a similar vein we connect the conditional max entropy h max a b to the maximum fidelity of rhoab with a product state that is completely mixed on a in the case where a is classical this corresponds to the security of a when used as a secret key in the presence of an adversary holding b because min and max entropies are known to characterize information processing tasks such as randomness extraction and state merging our results establish a direct connection between these tasks and basic operational problems for example they imply that the logarithm of the probability of guessing a given b is a lower bound on the number of uniform secret bits that can be extracted from a relative to an adversary holding b

the riemann hilbert approach to strong asymptotics for orthogonal polynomials on 1 1 abstract we consider polynomials that are orthogonal on 1 1 with respect to a modified jacobi weight 1 x 1 x h x with 1 and h real analytic and strictly positive on 1 1 we obtain full asymptotic expansions for the monic and orthonormal polynomials outside the interval 1 1 for the recurrence coefficients and for the leading coefficients of the orthonormal polynomials we also deduce asymptotic behavior for the hankel determinants and for the monic orthogonal polynomials on the interval 1 1 for the asymptotic analysis we use the steepest descent technique for riemann hilbert problems developed by deift and zhou and applied to orthogonal polynomials on the real line by deift kriecherbauer mclaughlin venakides and zhou in the steepest descent method we will use the szeg function associated with the weight and for the local analysis around the endpoints 1 we use bessel functions of appropriate order whereas deift et al use airy functions

secure bit commitment from relativistic constraints we investigate two party cryptographic protocols that are secure under assumptions motivated by physics namely special relativity and quantum mechanics in particular we discuss the security of bit commitment in the so called split models i e models in which at least one of the parties is not allowed to communicate during certain phases of the protocol we find the minimal splits that are necessary to evade the mayers lo chau no go argument and present protocols that achieve security in these split models furthermore we introduce the notion of local versus global command a subtle issue that arises when the split committer is required to delegate noncommunicating agents to open the commitment we argue that classical protocols are insecure under global command in the split model we consider on the other hand we provide a rigorous security proof in the global command model for kent s quantum protocol the proof employs two fundamental principles of modern physics the no signaling property of relativity and the uncertainty principle of quantum mechanics

a symbolic computational method for constructing exact solutions to difference differential equations in this paper we extended tanh method to solve difference differential equations and pure difference equations with the projective riccati equation as an example we applied this method to a 2 1 dimensional toda lattice equation as a result many exact solutions are obtained with the help of symbolic system maple including soliton solutions presented by hyperbolic functions sinh and cosh periodic solutions presented by sin and cos and rational solutions this method can also be used to other nonlinear difference differential equations

generalizing homotopy analysis method to solve lotka volterra equation in the paper we generalized the homotopy analysis method to solve lotka volterra equation as a simple but typical example it illustrates the validity and the great potential of the homotopy analysis method to solve differential difference equations comparisons are made between the results of the proposed method and exact solutions the results reveal that the proposed method is valid for the lotka volterra equation

on the homotopy analysis method for nonlinear problems a powerful easy to use analytic tool for nonlinear problems in general namely the homotopy analysis method is further improved and systematically described through a typical nonlinear problem i e the algebraically decaying viscous boundary layer flow due to a moving sheet two rules the rule of solution expression and the rule of coefficient ergodicity are proposed which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering an explicit analytic solution is given for the first time with recursive formulas for coefficients this analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem

uncertainty relation for smooth entropies uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted while established uncertainty relations apply to cases where the predictions are based on purely classical data e g a description of the system s state before measurement an extended relation which remains valid in the presence of quantum information has been proposed recently berta et al nature phys 6 659 2010 here we generalize this uncertainty relation to one formulated in terms of smooth entropies since these entropies measure operational quantities such as extractable secret key length our uncertainty relation is of immediate practical use to illustrate this we show that it directly implies security of quantum key distribution protocols our security claim remains valid even if the implemented measurement devices deviate arbitrarily from the theoretical model

uniform asymptotics of the pollaczek polynomials via the riemann hilbert approach the pollaczek weight is an example of the non szeg class in this paper we investigate the asymptotics of the pollaczek polynomials via the riemannhilbert approach in the analysis the original e

conditions for the existence of higher symmetries of evolutionary equations on the lattice in this paper we construct a set of five conditions necessary for the existence of generalized symmetries for a class of differential difference equations depending only on nearest neighboring interaction these conditions are applied to prove the existence of new integrable equations belonging to this class

adomian decomposition and pade approximate for solving differential difference equation abstract in this paper we apply the adomian decomposition method and pade approximate to solving the differential difference equations ddes for the first time a simple but typical example is used to illustrate the validity and the great potential of the adomian decomposition method adm in solving ddes comparisons are made between the results of the proposed method and exact solutions the results show that adm is an attractive method in solving the differential difference equations

construction scheme for discrete miura transformations a direct and elementary scheme for the construction of miura type transformations and discrete differential equations related to them scalar and vector is presented the scheme is illustrated using as examples the volterra and toda models a discrete differential analogue of the calogero degasperis equation is discussed in detail this example is used to show how to construct conservation laws higher symmetries and solutions for an equation obtained with the help of the scheme

stability and bifurcation analysis for a discrete time model of lotka volterra type with delay a discrete model of lotka volterra type with delay is considered and a bifurcation analysis is undertaken for the model we derive the precise conditions ensuring the asymptotic stability of the positive equilibrium with respect to two characteristic parameters of the system it is shown that for certain values of these parameters fold or neimark sacker bifurcations occur but codimension 2 fold neimark sacker double neimark sacker and resonance 1 1 bifurcations may also be present the direction and the stability of the neimark sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory

approximate solutions to a parameterized sixth order boundary value problem in this paper the homotopy analysis method ham is applied to solve a parameterized sixth order boundary value problem which for large parameter values cannot be solved by other analytical methods for finding approximate series solutions convergent series solutions are obtained no matter how large the value of the parameter is

strong asymptotics of orthogonal polynomials with respect to exponential weights we consider asymptotics of orthogonal polynomials with respect to weights w x dx e q x dx on the real line where q x 2m k 0 qkx k q2m 0 denotes a polynomial of even order with positive leading coefficient the orthogonal polynomial problem is formulated as a riemann hilbert problem following 22 23 we employ the steepest descent type method introduced in 18 and further developed in 17 19 in order to obtain uniform plancherel rotach type asymptotics in the entire complex plane as well as asymptotic formulae for the zeros the leading coefficients and the recurrence coefficients of the orthogonal polynomials c 1999 john wiley sons inc

discrete painleve equations and their appearance in quantum gravity we discuss an algorithmic approach for both deriving discrete analogues of painleve equations as well as using such equations to characterize similarity reductions of spatially discrete integrable evolution equations as a concrete example we show that a discrete analogue of painleve i can be used to characterize similarity solutions of the kac moerbeke equation it turns out that these similarity solutions also satisfy a special case of painleve iv equation in addition we discuss a methodology for obtaining the relevant continuous limits not only at the level of equations but also at the level of solutions as an example we use the wkb method in the presence of two turning points of the third order to parametrize at the continuous limit the solution of painleve i in terms of the solution of discrete painleve i finally we show that these results are useful for investigating the partition function of the matrix model in 2d quantum gravity associated with the measure exp t1z2 t2z4 t3z6

bessel type asymptotic expansions via the riemann hilbert approach a bessel type asymptotic expansion is established for the monic polynomials n x that are orthogonal with respect to the modified jacobi weight x 1 1 where 1 and h x is real analytic and st