Viscous flow past a porous sphere with an impermeable core : effect of stress jump condition

An arbitrary flow of a viscous, incompressible fluid past a porous sphere of radius `a' with an impermeable core of radius `b', using Brinkman's equation in the porous region is discussed. At the interface of the clear fluid and porous region, stress jump boundary condition for the tangential stresses along with the continuity of normal stresses and the velocity components are used. On the surface of the impermeable core no slip condition is used. The corresponding Faxen's laws are derived to compute the drag and torque acting on the surface r=a. It is found that the drag and torque not only change with the change of the permeability, but also a significant effect of the stress jump co-efficient is observed. The variation of drag and torque with permeability for different thickness (a-b) of the porous region as well as for different values of stress jump coefficient is discussed when the basic flow is due to uniform flow, two dimensional irrotational flow, doublet in a uniform flow, stokeslet, rotlet. In case of uniform flow the flow field has been plotted. In all the cases, a significant effect of the stress jump coefficient has been realized.     

Parameter Estimation for Periodically Stationary Time Series

Abstract. The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper, we compute the asymptotic distribution for these estimates in the case, where the innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule–Walker estimates.     

Controller synthesis with guaranteed closed-loop phase constraints

In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval [−α,α] for a given α>0 at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where , we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function.     

数据加密技术刍议

数据加密是保证信息安全的基本措施之一.本文介绍了数据加密的概念,同时阐述了对称型加密算法和公钥加密算法.并对两种算法的优劣进行了比较.     

On mesh restrictions to satisfy comparison principles,maximum principles,and the non-negative constraint: Recent developments and new results

This article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.     

基于逆数据包络分析法的中医方药评价与药量计算研究

针对中医组方的药量推算建模问题,提出了基于证候上下文分析的逆数据包络分析（IDEA）算法。该算法以证侯的典型方剂为依据,以数据包络分析为评价工具,建立起反映证候演化的方药评价模型;依据代表证候状态的评价值,给相应的证型症状信息赋值,以完成“词计算”过程。最后,把具体的辨证过程植入到证侯发展的上下文环境中,以典型证型的“词计算”为依据,给出具体案例的证侯状态评价,再采用IDEA算法推算出药量数据。该模型的推算结果表明,它能够反映中医的一般用药规律,这将对辨证论治组方环节的数值化、客观化研究提供一种可能的思路。     

Some fixed point theorems in 1-M-complete fuzzy metric-like spaces

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept of fuzzy metric-like space and proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results.     

Input-output properties of the Page-Hinkley detector

We consider the stochastic input-output properties of a simple non-linear dynamical system, the so-called Page-Hinkley detector, playing a key role in change detection, and also in queuing theory. We show that for L-mixing inputs with negative expectation the output process of this system is L-mixing. The result is applied to get an upper bound for the false alarm rate. The proof is then adapted to get a similar result for the case of random i.i.d. inputs. Possible extensions and open problems are given in the discussion.     

一种基于IDEA和ECC算法的数字化防伪认证新方案的研究与实现

商品防伪是一项系统工程，现有防伪措施在有效性和易操作性之间不能达到很好的统一，本文在研究商品防伪机制的基础上提出了一种有效解决上述问题的新方案．该方案通过IDEA比特流重组的加密算法对商品信息进行加密，以主密钥机制采用椭圆曲线密码算法ECC实现对IDEA密钥的自动化安全管理，而客户可依据加密产生的防伪码通过电话或网站快速准确认证其对应商品的真伪．理论分析和系统的实际运行表明该方案是一种有效、安全的新型实用方案．