Unbounded parallel batch scheduling with job delivery to minimize makespan

We consider unbounded parallel batch scheduling with job delivery to minimize makespan. When the jobs have identical size, we provide a polynomial-time algorithm. When the jobs have non-identical sizes, we provide a heuristic with a worst-case performance ratio 7/4.     

Missing information and an optimal one-step plan in a Type II progressive censoring scheme

In this paper, we consider the missing information in determining the optimal allocation of removals in a Type II progressive censoring scheme. We provide a simple expression and a recurrence relation for the missing information. Then we provide a simple way of determining an optimal censoring scheme among a class of one-step censoring by using the missing information. Finally we give some examples to illustrate our results.     

A secondary semantics for Second Order Intuitionistic Propositional Logic

In this paper we propose a Kripke‐style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of an inverse source problem for time‐fractional diffusion equation with random noise

In this paper, we consider an inverse source problem for a time fractional diffusion equation. In general, this problem is ill posed, therefore we shall construct a regularized solution using the filter regularization method in the random noise case. We will provide appropriate conditions to guarantee the convergence of the approximate solution to the exact solution. Then, we provide examples of filters in order to obtain error estimates for their approximate solutions. Finally, we present a numerical example to show efficiency of the method.     

Mechanisms with learning for stochastic multi-armed bandit problems

The multi-armed bandit (MAB) problem is a widely studied problem in machine learning literature in the context of online learning. In this article, our focus is on a specific class of problems namely stochastic MAB problems where the rewards are stochastic. In particular, we emphasize stochastic MAB problems with strategic agents. Dealing with strategic agents warrants the use of mechanism design principles in conjunction with online learning, and leads to non-trivial technical challenges. In this paper, we first provide three motivating problems arising from Internet advertising, crowdsourcing, and smart grids. Next, we provide an overview of stochastic MAB problems and key associated learning algorithms including upper confidence bound (UCB) based algorithms. We provide proofs of important results related to regret analysis of the above learning algorithms. Following this, we present mechanism design for stochastic MAB problems. With the classic example of sponsored search auctions as a backdrop, we bring out key insights in important issues such as regret lower bounds, exploration separated mechanisms, designing truthful mechanisms, UCB based mechanisms, and extension to multiple pull MAB problems. Finally we provide a bird’s eye view of recent results in the area and present a few issues that require immediate future attention.     

半直线上随机环境中的随机游动的常返性

本文讨论半直线上随机环境中的随机游动的常返性。在独立环境下，主要通过强大数定律，找到了非常返和正常返的一个充分条件下，并将这一结果推广到一些特殊情情形。在一般的随机环境下，主要通过数列的有界性，给出了常返与零常返的一个充分条件。     

Subsmooth semi-infinite and infinite optimization problems

We first consider subsmoothness for a function family and provide formulas of the subdifferential of the pointwise supremum of a family of subsmooth functions. Next, we consider subsmooth infinite and semi-infinite optimization problems. In particular, we provide several dual and primal characterizations for a point to be a sharp minimum or a weak sharp minimum for such optimization problems.     

Stationary,completely mixed and symmetric optimal and equilibrium strategies in stochastic games

In this paper, we address various types of two-person stochastic games—both zero-sum and nonzero-sum, discounted and undiscounted. In particular, we address different aspects of stochastic games, namely: (1) When is a two-person stochastic game completely mixed? (2) Can we identify classes of undiscounted zero-sum stochastic games that have stationary optimal strategies? (3) When does a two-person stochastic game possess symmetric optimal/equilibrium strategies? Firstly, we provide some necessary and some sufficient conditions under which certain classes of discounted and undiscounted stochastic games are completely mixed. In particular, we show that, if a discounted zero-sum switching control stochastic game with symmetric payoff matrices has a completely mixed stationary optimal strategy, then the stochastic game is completely mixed if and only if the matrix games restricted to states are all completely mixed. Secondly, we identify certain classes of undiscounted zero-sum stochastic games that have stationary optima under specific conditions for individual payoff matrices and transition probabilities. Thirdly, we provide sufficient conditions for discounted as well as certain classes of undiscounted stochastic games to have symmetric optimal/equilibrium strategies—namely, transitions are symmetric and the payoff matrices of one player are the transpose of those of the other. We also provide a sufficient condition for the stochastic game to have a symmetric pure strategy equilibrium. We also provide examples to show the sharpness of our results.     

Forward dynamic utility functions: A new model and new results

A major obstacle in the existing models of forward dynamic utilities and investment performance evaluation is to establish the existence and uniqueness of the optimal solutions. Consequently, we present a new model of forward dynamic utilities. In doing so, we establish the existence and uniqueness of the solutions for a general (smooth) utility function, and we show that the assumptions needed for such solutions are similar to those under the backward formulation. Moreover, we provide unique viscosity solutions. We also provide discontinuous viscosity solutions. In addition, we introduce Hausdorff-continuous viscosity solutions to the portfolio model.     

A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel

In this paper we provide a unified treatment of half-discrete Hilbert-type inequalities with a general homogeneous kernel. The main results are proved for the case of non-conjugate exponents. A special emphasis is given to determining conditions under which these inequalities include the best possible constants. As an application, we consider some operator expressions closely connected to established inequalities. Finally, we also provide improvements of derived half-discrete inequalities by virtue of the Hermite-Hadamard inequality.     

Ideal Triangulations of Link Complements and Hyperbolicity Equations

Using standard spines and their graphic presentation, we provide an algorithm which produces an ideal triangulation of a link complement starting from an arbitrary projection of the link. Then we provide another algorithm which computes the hyperbolicity equations of the ideal triangulation of a manifold bounded by tori, where the triangulation corresponds to an arbitrary graphic presentation of the manifold.     

General construction of symmetric parabolic structures

First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth systems of involutive symmetries can be obtained in this way. Further, we investigate the case of parabolic contact geometries in great detail and we provide the full classification of those with semisimple groups of symmetries without complex factors. Finally, we explicitly construct all non-trivial contact geometries with non-complex simple groups of symmetries. We also indicate geometric interpretations of some of them.     

云计算模式下SLA中的补偿策略及风险

本文基于云计算的特性,首次提出了服务水平协议(Service Level Agreement,SLA)中的三种补偿策略(分别为基于服务失败数量、基于长服务中断数量和基于累积中断时间的补偿策略),通过在SLA中约定客户容忍阀值,针对服务失败等级对客户进行分级补偿。针对三种策略的补偿成本,本文对云服务提供商造成的损失风险进行了测量和分析,得到了风险价值(Value-at-Risk,VaR)变化的特征和规律。在平均损失相同情况下,基于累积中断时间补偿策略的VaR值大于基于服务失败数量补偿策略的VaR值,因此采取基于中断时间的补偿策略风险更大。实例数据分析表明,本文提出的补偿策略是合理可行的。本文结论对于云服务提供商的补偿策略制定具有指导意义。     

A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.     

Asymptotic analysis of the optimal cost in some transportation problems with random locations

In this paper we provide an asymptotic analysis of the optimal transport cost in some matching problems with random locations. More precisely, under various assumptions on the distribution of the locations and the cost function, we prove almost sure convergence, and large and moderate deviation principles. In general, the rate functions are given in terms of infinite-dimensional variational problems. For a suitable one-dimensional transportation problem, we provide the expression of the large deviation rate function in terms of a one-dimensional optimization problem, which allows the numerical estimation of the rate function. Finally, for certain one-dimensional transportation problems, we prove a central limit theorem.     

Rigid Rings and Makar-Limanov Techniques

A ring is rigid if it admits no nonzero locally nilpotent derivation. Although a “generic” ring should be rigid, it is not trivial to show that a ring is rigid. We provide several examples of rigid rings and we outline two general strategies to help determine if a ring is rigid, which we call “parametrization techniques.” and “filtration techniques.” We provide many tools and lemmas which may be useful in other situations. Also, we point out some pitfalls to beware when using these techniques. Finally, we give some reasonably simple rings for which the question of rigidity remains unsettled.     

The effect of rounding errors on Newton methods

In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newtonlike methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitztype hypotheses on the second Fréchet-derivative instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover, we show that the ratio of convergence improves under our conditions. Furthermore, we provide a wider choice of initial guesses than before. Finally, a numerical example is provided to show that our results compare favorably with earlier ones.     

Algebraic zero mean curvature hypersurfaces in de Sitter and anti de Sitter spaces

In this paper we provide a family of algebraic space-like surfaces in the three dimensional anti de Sitter space that shows that this Lorentzian manifold admits algebraic maximal examples of any order. Then, we classify all the space-like order two algebraic maximal hypersurfaces in the anti de Sitter N-dimensional space. Finally, we provide two families of examples of Lorentzian order two algebraic zero mean curvature hypersurfaces in the de Sitter space.     

BSDEs under partial information and financial applications

In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square-integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a BSDE under full information. In particular, we provide a suitable version of the Föllmer–Schweizer decomposition of a square-integrable random variable working under partial information and we use this achievement to investigate the local risk-minimization approach for a semimartingale financial market model.     

A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.