Limit relations for records with confirmation

The asymptotic behavior of records with confirmation is considered and the corresponding limiting distributions are obtained.     

An Efficient Protocol for Authenticated Key Agreement

This paper proposes an efficient two-pass protocol for authenticated key agreement in the asymmetric (public-key) setting. The protocol is based on Diffie-Hellman key agreement and can be modified to work in an arbitrary finite group and, in particular, elliptic curve groups. Two modifications of this protocol are also presented: a one-pass authenticated key agreement protocol suitable for environments where only one entity is on-line, and a three-pass protocol in which key confirmation is additionally provided. Variants of these protocols have been standardized in IEEE P1363 [17], ANSI X9.42 [2], ANSI X9.63 [4] and ISO 15496-3 [18], and are currently under consideration for standardization and by the U.S. government's National Institute for Standards and Technology [30].     

Asymptotic behavior of permutation records

We study the asymptotic behavior of two statistics defined on the symmetric group Sn when n tends to infinity: the number of elements of Sn having k records, and the number of elements of Sn for which the sum of the positions of their records is k. We use a probabilistic argument to show that the scaled asymptotic behavior of these statistics can be described by remarkably simple functions.     

Coherent random permutations with biased record statistics

We consider random permutations that are defined coherently for all values of n, and for each n have a probability distribution which is conditionally uniform given the set of upper and lower record values. Our central example is a two-parameter family of random permutations that are conditionally uniform given the counts of upper and lower records. This family may be seen as an interpolation between two versions of Ewens’ distribution. We discuss characterisations of the conditionally uniform permutations, their asymptotic properties, constructions and relations to random compositions.     

A Characteristic Martingale Related to the Counting Process of Records

Let (X _n ) be a sequence of nonnegative, integrable, independent and identically distributed random variables, with common distribution function F. We consider the problem of finding all distribution functions F such that N _n −cM _n is a discrete time martingale, where N _n is the counting process of upper records, M _n =max {X ₁,…,X _n } is the process of partial maxima and c is a positive constant. We solve the problem by explicitly giving the solution with finite support and using this for constructing the solution for the general case by a limiting process. We show that the set of solutions can be parameterized by their support and the mass at the leftmost point of the support.     

On the concept of solution for fractional differential equations with uncertainty

We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented.     

k-STABILITY OF NONLINEAR NEUTRAL DELAY SYSTEMS

In this paper,we first introduce the concept of k-globally asymptotic stabi- lity and present a differential-difference inequality with infinite delay.By com- bining nonlinear inequality and nonlinear variation-of-parameters formula,we derive the k-globally asymptotic stability criteria for nonlinear neutral system with infinite delay.In the end of this paper,an example is given to illustrate our theory.     

Partial Sum Process for Records

Suppose the upper records from a sequence of i.i.d. random variables is in the domain of attraction of a normal distribution. Consider the D(0,1]-valued process {Z_n(·)} constructed by usual interpolation of the partial sums of the records. We prove that under some mild conditions, {Z_n} converges to a limiting Gaussian process in D(0,1]. As a consequence, the partial sums of records is asymptotically normal. AMS 2000 Subject Classification Primary—60F17 Secondary—60G70     

Application of principal component analysis to multi-disk concurrent accessing

This paper is concerned with the allocation of multi-attribute records on several disks so as to achieve high degree of concurrency of disk access when responding to partial match queries.An algorithm to distribute a set of multi-attribute records onto different disks is presented. Since our allocation method will use the principal component analysis, this concept is first introduced. We then use it to generate a set of real numbers which are the projections on the first principal component direction and can be viewed as hashing addresses.Then we propose an algorithm based upon these hashing addresses to allocate multi-attribute records onto different disks. Some experimental results show that our method can indeed be used to solve the multi-disk data allocation problem for concurrent accessing.     

Local search for the undirected capacitated arc routing problem with profits

This paper deals with a recently introduced routing problem variant called the undirected capacitated arc routing problem with profits (UCARPP). The UCARPP model considered in the present study is primarily aimed at generating the route set which maximizes the profit collected from a set of potential customers, represented by edges of the examined transportation network. The secondary objective is to minimize the total route travel time. The generated routes are subject both to capacity and travel time constraints. To tackle the examined problem, we propose a local search metaheuristic development which explores two solution neighborhood structures. The conducted search is effectively diversified by means of the promises concept which is based on the aspiration criteria used in tabu search approaches. The proposed algorithm was tested on UCARPP benchmark instances taken from the literature. It efficiently produced high-quality results, improving several previously best known solutions.     

On the fractional differential equations with uncertainty

This paper is based on the concept of fuzzy differential equations of fractional order introduced by Agarwal et al. [R.P. Agarwal, V. Lakshmikantham, J.J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal. 72 (2010) 2859-2862]. Using this concept, we prove some results on the existence and uniqueness of solutions of fuzzy fractional differential equations.     

含参量无穷限反常积分的一致收敛性

借助两个具体的含参量无穷限反常积分的一致收敛性问题,分析一致收敛性的一些几何直观特征,希望有助于读者加深理解与认识.     

Convergence of tail sum for records

Suppose is the sequence of lower records from a distribution F, where F is continuous with . We derive conditions under which logarithm of the tail sum of records, ∑ _j=n ^∞ R _n ^(L) (F), properly centered and scaled, converge weakly. We also prove two results on Π-varying and regularly varying functions, which are of independent interest.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.     

Rational solutions of the graphsack problem

A graphsack problem is a certain binary linear optimization problem with applications in optimal network design. From there a rational graphsack problem is derived by allowing the variables to vary continuously between 0 and 1. In this paper we deal with rational graphsack problems. First we develop the concept of compressed solutions and the concept of augmenting cuts. Making use of these concepts a very simple optimality criterion is derived. Finally an efficient algorithm solving rational graphsack problems is given which is polynomially bounded in time and which is closely related to the simplex algorithm.     

A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.     

Open-Loop Viable Control Under Uncertain Initial State Information

We consider the problem of open-loop viable control of a nonlinear system in Rⁿ in the case of a nonexactly known initial state. We characterize the family of those initial sets for which the problem is solvable. The characterization employs the notion of a contingent field to a given collection of sets introduced in the paper. It also involves an appropriate set-dynamic equation that describes the evolution of the state estimation within a prescribed collection of sets. An extension of the classical concept of viability kernel with respect to this set-dynamic equation is the key tool. We present an approximation scheme for the viability kernel which is numerically realizable in the case of low dimension and simple collections of sets chosen for state estimation (balls, ellipsoids, polyhedrons, etc.). As an application, we consider a viability differential game, where the uncertainty may enter also in the dynamics of the system as an input which is not known in advance. The control is then sought as a nonanticipative strategy depending on the uncertain input.     

Existence of $\mu$-pseudo almost automorphic solutions to abstract partial neutral functional differential equations with infinite delay

In this article, we introduce and investigate the concept of $\mu$-Stepanov-like pseudo almost automorphic functions of class $h$ and class infinity via measure theory. We present new results on completeness and composition theorems for the space of such functions. To illustrate our main results, we provide some applications to an abstract partial neutral functional differential equation with infinite delay.     

带有长期趋势的近似周期时间序列的刻度变换估计

近似周期时间序列具有近似的周期趋势,即近似周期性.所谓近似周期性是指它看起来有周期性,但是每个周期的长度不是常数,比如太阳黑子数序列.近似周期时间序列在社会经济现象建模中有着广泛的应用前景.对于近似周期时间序列,关键在于刻画它的近似周期趋势,因为一旦近似周期趋势被刻画出来它就可以作为一个普通的时间序列来处理.然而,关于近似周期趋势刻画的研究却很少. 本文首先建立一些必要的理论,特别地,提出了带长度压缩的保形变换概念,并且得到了带长度压缩的线性保形变换的充分必要,然后基于此理论作者提出了一种估计尺度变换的方法,该方法可以很好地估计出近似周期趋势.最后,对一个仿真实例进行了分析.结果表明,本文所提出的方法强力有效.     

Generalized solutions in systems with active unilateral constraints

The concept of the generalized solution that admits well-posed representation of controlled complex behavior in systems with active unilateral phase constraints is proposed. Based on this concept, the definition of the generalized solution for this class of problems is introduced that encompasses Zeno type behavior and sliding modes along the constraint boundary. The general representation of such solutions in terms of nonlinear differential equations with a measure is derived. The latter is shown to solve a long-standing problem of providing unique extensibility of a trajectory beyond accumulation points in systems with Zeno-type behavior. An example is given, showing that the representation proposed completely captures Zeno-type behavior and provides unique extensibility of solutions without the need to truncate infinite sequences and/or switch system coefficients depending on system motion relative to the generalized coordinates of the accumulation point.