利用有限域上的向量空间构作带仲裁的认证码

This paper is devoted to constructing an authentication code with arbitration using subspaces of vector spaces over finite fields.Moreover,if we choose the encoding rules of the transmitter and the decoding rules of the receiver according to a uniform probability distribution,then some parameters and the probabilities of successful attacks are computed.     

Boundary Stabilization of the Korteweg-de Vries Equation and the Korteweg-de Vries-Burgers Equation

In this article, we continue our study of a system described by a class of initial boundary value problem (IBVP) of the Korteweg-de Vries (KdV) equation and the KdV Burgers (KdVB) equation posed on a finite interval with nonhomogeneous boundary conditions. While the system is known to be locally well-posed (Kramer et al. , [2010]; Rivas et al. in Math. Control Relat. Fields 1:61–81, [2011]) and its small amplitude solutions are known to exist globally, it is not clear whether its large amplitude solutions would blow up in finite time or not. This problem is addressed in this article from control theory point of view: look for some appropriate feedback control laws (with boundary value functions as control inputs) to ensure that the finite time blow-up phenomena would never occur. In this article, a simple, but nonlinear, feedback control law is proposed and the resulting closed-loop system is shown not only to be globally well-posed, but also to be locally exponentially stable for the KdV equation and globally exponentially stable for the KdVB equation.     

Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (?1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.     

Symbolic algorithm for solving cyclic penta-diagonal linear systems

In this paper, by using a special matrix factorization, a symbolic computational algorithm is developed to solve the cyclic penta-diagonal linear system. The algorithm is suitable for implementation using Computer Algebra Systems (CASs) such as MATLAB, MATHEMATICA and MAPLE. In addition, an efficient way of evaluating the determinant of a cyclic penta-diagonal matrix is also discussed. Two numerical examples are given for the purpose of illustration.     

Assessing the diagnostic power of variables measured with a detection limit

The phenomenon of the limit of detection (LoD) often happens in many practical situations because of technique and instrument limitations. In the literature, some reports show that, in general, to apply conventional methods to evaluate the diagnostic power of variables while ignoring LoD could be seriously biased. Although the area under the receiver operating characteristic (ROC) curve can be estimated consistently if the distribution of variables are known. In practical situation, such information is usually not available. On the other hand, it has been proved that the area under ROC curve of a variable with a LoD and no distribution assumptions is usually biased no matter what kinds of replacement strategies are used. However, there is a lack of similar studies on the partial area under ROC curve (pAUC), and because this measure is usually preferred in practice, it is of interest to examine whether the estimate of pAUC of a variable measured with a LoD behaves the same. In this study, we found that for some LoD scenarios, and even without distribution assumption, consistent estimate of pAUC can be constructed. When the consistent estimate of pAUC cannot be obtained, the bias can be ineffectual in practical situations, and the proposed estimator can be a good approximation of pAUC. Numerical studies using simulated data sets and real data examples are reported.     

On the distribution of αp modulo one (II)

Suppose that α is an irrational number and β is a real number. It is proved that there are infinitely many prime numbers p such that ‖ αp-β‖ <p ^-9/28.     

Discrete-time models for releases of sterile mosquitoes with Beverton–Holt-type of survivability

In this paper, we formulate discrete-time mathematical models for the interactive wild and sterile mosquitoes. Instead of the Ricker-type of nonlinearity for the survival functions, we assume the Beverton–Holt-type in these models. We consider three different strategies for the releases of sterile mosquitoes and investigate the model dynamics. Threshold values for the releases of sterile mosquitoes are derived for all of the models that determine whether the wild mosquitoes are wiped out or coexist with the sterile mosquitoes. Numerical examples are given to demonstrate the dynamics of the models.     

基于正态分布的逐批抽样检验贝叶斯控制图控制限研究

在生产条件受控的状态下,先验分布与后验分布应服从同一分布,在假设该分布为正态分布的前提下,根据贝叶斯理论推导出均值、极差和标准差的迭代计算公式,并依此计算控制图的控制限,使有效的先验批检验信息得到充分运用,弥补传统控制图在小批量生产环境下样本信息不足的缺点。研究发现,基于贝叶斯原理的统计控制图控制限随着检验批次的逐渐增加,更接近控制界限的实际值,比传统控制图的控制效果更加可靠、有效。