Shape inverse problem for Stokes–Brinkmann equations

In this paper, we propose an imaging technique for the detection of porous inclusions in a stationary flow governed by Stokes–Brinkmann equations. We introduce the velocity method to perform the shape deformation, and derive the structure of shape gradient for the cost functional based on the continuous adjoint method and the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape inverse problem. The numerical results demonstrate the proposed algorithm is feasible and effective for the quite high Reynolds numbers problems.     

The Divergence of the Special Linear Group over a Function Ring

We compute the divergence of the finitely generated group SL _n (𝒪_𝒮), where 𝒮 is a finite set of valuations of a function field and 𝒪_𝒮 is the corresponding ring of 𝒮-integer points. As an application, we deduce that all its asymptotic cones are without cut-points.     

A Discrete Approach to the Prime Number Theorem

An elementary proof of the fundamental theorem on prime numbers is obtained. The result is obtained by defining a new sieve which permits to estimate the number of primes less than an arbitrary N by solving a simple difference equation.     

Covariational reasoning and invariance among coordinate systems

Researchers continue to emphasize the importance of covariational reasoning in the context of students’ function concept, particularly when graphing in the Cartesian coordinate system (CCS). In this article, we extend the body of literature on function by characterizing two pre-service teachers’ thinking during a teaching experiment focused on graphing in the polar coordinate system (PCS). We illustrate how the participants engaged in covariational reasoning to make sense of graphing in the PCS and make connections with graphing in the CCS. By foregrounding covariational relationships, the students came to understand graphs in different coordinate systems as representative of the same relationship despite differences in the perceptual shapes of these graphs. In synthesizing the students’ activity, we provide remarks on instructional approaches to graphing and how the PCS forms a potential context for promoting covariational reasoning.     

图像的多层次模糊增强与边缘提取

在单层次模糊增强算法中,某个灰度层次附近的边缘得到了增强,同时其它的一些边缘受到了抑制。为了同时增强图像中不同灰度层次的边缘信息,提出一种多层次模糊增强算法,并且给出了快速实现算法。此外,把多层次模糊增强算法应用于图像边缘提取中,取得了优于单层次模糊增强的效果。     

Secant algorithms with nonmonotone trust region that employs fletcher penalty function for constrained optimization

In this paper, we present a family of secant algorithms in association with nonmonotone trust region strategy for nonlinear equality constrained optimization problems. The proposed algorithms are globally convergent while keeping the local superlinear rate by introducing Fletcher's penalty function as merit function.     

A Mixed Boundary Value Problem for Generalized Polyanalytic Functions of Order n in the Sobolev Space W n,p ( D )

Given is the following boundary value problem for a generalized polyanalytic differential equation of order n in a domain D : $${{\partial ^n w} \over {\partial \bar z^n }} = F\left( {z, w, {{\partial ^{m + k} w} \over {\partial z^m \partial \bar z^k }}} \right)\quad {\rm on}\enskip D \eqno (1)$$ $$Bw = g\quad {\rm on}\enskip \gamma \cup \partial D \eqno (2)$$ $$n \ge m, k \in {\shadN}_0 \quad m + k \le n, \quad (0, 0) \ne (m, k) \ne (0, n), \quad n \in {\shadN}$$ where B is an operator acting on the boundary ‘ D of D and possibly on some closed curve n in D . First the existence of a general solution is established under certain assumptions on the right-hand side of (1). Next, a general method for solving boundary value problems or other related problems (2) is laid down. The latter is possible whenever the corresponding problem for a polyanalytic function admits a unique solution which, in addition, satisfies certain a priori estimates. The method will be illustrated for the case of a mixed boundary value problem.     

F值Choquet积分（I）：F值函数关于F测度的Choquet积分

本文为取值于F数的Choquet积分系列之一,探讨了F值函数关于F测度的Choquet积分。我们以区间分析为工具,在定义区间值函数Choquet积分的基础上,给出了F值函数Choquet积分的定义,得到了各种性质和收敛定理。     

Markov chains in random environments and random iterated function systems

We consider random iterated function systems giving rise to Markov chains in random (stationary) environments. Conditions ensuring unique ergodicity and a ``pure type' characterization of the limiting ``randomly invariant' probability measure are provided. We also give a dimension formula and an algorithm for simulating exact samples from the limiting probability measure.

     

二元函数极值充要条件的简便证明

本采用变级王换分析的方法给出二元函数极值的充分必要条件的一个简便证明。