NORMAL STRUCTURE AND SOME GEOMETRIC PARAMETERS RELATED TO THE MODULUS OF U-CONVEXITY IN BANACH SPACES

We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax（ε） and βx （ε）, both related to Gao＇s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.

Computer Aided Design Technology for Convex Faceted Gem Cuts Based on the Half-Edge Data Structure

Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for the implementation is presented in this work. By using object-oriented methods, geometrical elements of CFGC are classified and responding geometrical feature classes are established. Each class is implemented and embedded based on the gem process. Matrix arithmetic and analytical geometry are used to derive the affine transformation and the cutting algorithm. Based on the demand for a diversity of gem cuts, CAD functions both for free-style faceted cuts and parametric designs of typical cuts and visualization and human-computer interactions of the CAD system including two-dimensional and three-dimensional interactions have been realized which enhances the flexibility and universality of the CAD system. Furthermore, data in this CAD system can also be used directly by the gem CAM module, which will promote the gem CAD/CAM integration.

ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE

In this article, the authors study a generalized modulus of convexity, δ（α） （ε）. Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0 ≤e≤ 1, such that δ^（α）（1＋ε ） 〉 （1- α）ε.

COINCIDENCE POINT THEOREMS iN PROBABILISTIC METRIC SPACES WITH A CONVEX STRUCTURES

In lhis paper we draw some coincidence and common fixed point theorems fornonlinear hybrid contraction mappings on probabilistic metric spaces with a convexstructure.

Simulation and Experimental Study on Improving Electrochemical Machining Stability of Highly Convex Structures on Casing Surfaces Using Backwater Pressure

Casing parts are regarded as key components of aero-engines.Most casing parts are attached to convex structures of diferent shapes,whose heights range from hundreds of microns to tens of millimeters.Using profling blocky electrodes for electrochemical machining(ECM)of casing parts is a commonly adopted method,especially when highly convex structures.However,with an increase in the convex structure height,the fow felds of the machining areas become more complex,and short circuits may occur at any time.In this study,a method to improve the fow feld characteristics within a machining area by adjusting the backwater pressure is proposed and validated through simulation and experiment analyses.The simulation results demonstrated that the back-pressure method can signifcantly improve the uniformity of the fow feld around the convex structure compared with the extraction and open outlet modes.Subsequently,the back-pressure value was optimized at 0.5 MPa according to the simulation results.The experimental results showed that using the optimized back-pressure parameters,the cathode feed-rate increased from 0.6 to 0.7 mm/min,and a 16.1 mm tall convex structure was successfully machined.This indicates that the back-pressure method is suitable and efective for electrochemical machining of highly convex structures with blocky electrodes.In this study,we propose a method to improve the electrochemical machining stability of a convex structure on a casing surface using backwater pressure,which has achieved remarkable results.

Research on Optimizing Computer Network Structure based on Genetic Algorithm and Modified Convex Optimization Theory

In this paper, we report in-depth analysis and research on the optimizing computer network structure based on genetic algorithm and modified convex optimization theory. Machine learning method has been widely used in the background and one of its core problems is to solve the optimization problem. Unlike traditional batch algorithm, stochastic gradient descent algorithm in each iteration calculation, the optimization of a single sample point only losses could greatly reduce the memory overhead. The experiment illustrates the feasibility of our proposed approach.

Deployment Characteristics of Braid Coated Bi-Convex Tape and Bi-SMA Convex Tape Booms for Deployable Membrane Structures

The purpose of this paper is to demonstrate and investigate the concepts of new deployable boom systems, which consist of the BCON （braid coated bi-convex tape） boom and the SMA-BCON （braid coated bi-shape memory alloy convex tape） boom. Both booms are developed for the deployable membrane structures such as solar sails, thin membrane solar array panels, deorbit mechanisms for small satellites and reflectors of space solar power satellite, etc. BCON booms can store around polygonal or cylindrical center hub, and the booms can deploy by the stepwise manner by releasing a constraint mechanism which pins the boons into two or three points for the total length. SMA-BCON booms are mainly developed for a square center body systems, and SMA is adapted on the bent po^nts of the booms where stored around each edge of the center hub. Through the deployment experiments of both booms, the stepwise deployment behavior and its tendency are obtained. The design concept of BCON boom and SMA-BCON hnnm i~ demonstrated through this study.

A New Class of Banach Spaces with Uniform Normal Structure

Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.

Structural eigenvalue analysis under the constraint of a fuzzy convex set model

In small-sample problems, determining and controlling the errors of ordinary rigid convex set models are difficult. Therefore, a new uncertainty model called the fuzzy convex set（FCS） model is built and investigated in detail. An approach was developed to analyze the fuzzy properties of the structural eigenvalues with FCS constraints. Through this method, the approximate possibility distribution of the structural eigenvalue can be obtained. Furthermore, based on the symmetric F-programming theory, the conditional maximum and minimum values for the structural eigenvalue are presented, which can serve as nonfuzzy quantitative indicators for fuzzy problems. A practical application is provided to demonstrate the practicability and effectiveness of the proposed methods.

A NEW METHOD FOR THE UNCERTAIN RESPONSE ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS

A computing method for estimating the upper and lower bounds of the response of structures with uncertainties is presented. The uncertain parameters are described by the convex model. A numerical example of the frame structure is given to illustrate the effectiveness of this method.

Structured Sparse Coding With the Group Log-regularizer for Key Frame Extraction

Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge.In this paper,we propose a novel model of structured sparse-codingbased key frame extraction,wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error.To automatically extract key frames,a decomposition scheme is designed to separate the sparse coefficient matrix by rows.The rows enforced by the nonconvex group log-regularizer become zero or nonzero,leading to the learning of the structured sparse coefficient matrix.To solve the nonconvex problems due to the log-regularizer,the difference of convex algorithm(DCA)is employed to decompose the log-regularizer into the difference of two convex functions related to the l1 norm,which can be directly obtained through the proximal operator.Therefore,an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed,which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error.Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most Sum Me videos compared to the stateof-the-art methods.Furthermore,the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection(SMRS)and an 8% increase compared to SC-det on the VSUMM dataset.

ON A CLASS OF KTHE SEQUENCE SPACES WITH NORMAL STRUCTURE

In this note, we investigate the generalized modulus of convexity δ（λ） and the generalized modulus smoothness p（λ）. We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX（λ）. We show that, for a wide class of class the sequence spaces X, if for some ε∈（0, 9/10] holds δx（e） 〉 1/3（1- √3/2）ε, then X has normal structure.

Filtering algorithm of line structured light for long-distance obstacle detection

Since unmanned ground vehicles often encounter concave and convex obstacles in wild ground, a filtering algorithm using line structured light to detect these long distance obstacles is proposed. For the line structured light image, a ranked-order based adaptively extremum median （RAEM） filter algorithm on salt and pepper noise is presented. In the algorithm, firstly effective points and noise points in a filtering window are differentiated; then the gray values of noise points are replaced by the medium of gray values of the effective pixels, with the efficient points＇ gray values unchanged; in the end this algorithm is proved to be efficient by experiments. Experimental resuits demonstrate that the image blur, resulting into proposed algorithm can remove noise points effectively and minimize the protecting the edge information as much as possible.

团聚物与凸起结构柔性振动筛板碰撞解聚特性

为了促进潮湿细粒煤团聚物的解聚,提出将凸起结构筛板用于物料的筛分。首先,采用挤压壁面法构建了潮湿细粒团聚物模型,仿真分析了团聚物在不同筛板上的碰撞解聚过程及解聚程度;其次,通过单因素和响应面分析法研究了凸起结构参数对团聚物碰撞解聚程度的影响性能,对凸起结构参数进行了优化;最后,通过筛分试验对比了物料在普通筛板和凸起结构筛板的解聚性能。结果表明:凸起结构能提高潮湿细粒团聚物的解聚程度,其参数对团聚物的解聚性能有显著影响;平均垂直应力σyy、液桥断裂百分比DR、平均偏心距离Ad和膨胀速度Ue随凸起结构下底a、上底b的增加呈非单调变化,与高h的变化呈正比;响应面分析得到凸起结构各参数对解聚程度的影响显著性依次为h>b/a>a;通过对凸起结构参数优化,团聚物的解聚程度最高可提升13.4%。

凸台类型对离散型流道叠片过滤器水头损失的影响

离散型流道叠片过滤器是一种水头损失相对较小的新型叠片过滤器,其叠片表面均匀分布的凸台结构是影响叠片过滤器水头损失的主要因素之一。为探明凸台类型对内部流场的影响并进一步降低离散型流道叠片过滤器的水头损失,通过物理试验与数值仿真,对比分析了初始的右三角形和优化新增的菱形、椭圆形、上三角形、下三角形等共5种凸台类型的离散型流道叠片过滤器的水头损失及流场分布特征。结果表明:将离散型流道叠片过滤器凸台类型设置为下三角形有利于减小水流主流区与凸台边壁的接触长度和凸台间湍动能强度,降低离散型流道叠片过滤器的水头损失;与初始右三角形凸台相比,4种优化的凸台与主流区接触长度的降幅为9.61%~36.73%,最大湍动能的降幅为25.87%~49.96%,其中下三角形凸台降幅分别为29.99%和49.96%;根据模拟计算可得右三角形凸台流道间水头损失系数最大,下三角形凸台流道间水头损失系数最小,其能量转换效率最高;清水条件下,下三角形凸台离散型流道叠片过滤器水头损失相比初始离散型流道叠片过滤器降低了14.89%~21.93%。研究结果可为离散型流道叠片过滤器的结构优化提供参考。

Investigation of anode shaping process during co-rotating electrochemical machining of convex structure on inner surface

A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemical machining are different from traditional electrochemical machining.An equivalent kinematic model is established to analyze the novel electrodes motion,since the anode and cathode rotate in the same direction while the cathode simultaneously feeds along the line of centres.According to the kinematic equations of the electrodes and Faraday’s law,a material removal model is established to simulate the evolution of the anode profile in co-rotating electrochemical machining.The simulation results indicate that the machining accuracy of the convex structure is strongly affected by the angular velocity ratio and the radius of the cathode tool.An increase of the angular velocity ratio can improve the machining accuracy of a convex structure.A small difference in the radius of the cathode tool will cause changes in the shape of the sidewalls of the convex structure.The width of the cathode window affects only the width of the convex structure and the inclination a of the sidewall.A relation between the width of the cathode window and the width of the convex structure was obtained.The formation process for a convex structure under electrochemical dissolution was revealed.Based on the simulation results,the optimal angular velocity ratio and cathode radius were selected for an experimental verification,and 12 convex structures were simultaneously fabricated on the inner surface of a thin-walled revolving part.The experimental results are in good agreement with the simulation results,which verifies the correctness of the theoretical analysis.Therefore,inner surface co-rotating electrochemical machining is an effective method for fabricating convex structures on the inner surface of a revolving part.

具有凸包结构的风力机翼型表面减阻数值模拟

基于非光滑凸包面减阻原理,通过分析半球型凸包不同结构参数下的绕流场特性得出其最优参数,在此基础上定义流线型凸包来探讨二者结构在减阻方面的差异,并分析凸包结构对风力机的影响。对附加两种凸包的NACA0012翼型及加入了半球型凸包的风力机进行数值模拟,并对其气动特性进行分析。研究表明:当半球型凸包的高度为弦长的0.4%时,其减阻效果最佳,并在攻角为10°~16°之间具有良好的减阻效果。附加间隔比为3的凸包结构将使翼型减阻效果达到最佳。半球型和流线型凸包结构均在攻角为14°时取得最好减阻效果,其最大减阻率分别为12.69%和17.39%。与半球型凸包结构相比,流线型凸包结构的外形曲率变化较小,使流动较好地贴合在流体与物体的交界处,以致黏性阻力的能耗更小。同时考虑到加工制造的工艺难度和实际情况,将优选的凸包结构应用于风力机叶片表面,与原始风力机相比,加入凸包结构的风力机能量利用区半径增大了20.68%;叶尖涡对高速流区域的影响降低,湍动能分布更加均匀,在额定工况下其扭矩和推力分别提升了14.72%和5.41%,提高了能量利用率及运行稳定性。

类水黾脚部“凹凸沟壑”结构仿生超疏水涂层的制备与性能

以坡缕石粉为功能颜料,环氧树脂E-44和杜仲胶混合物为成膜物质,在涂有环氧/杜仲胶清漆的表面制备了一层具有类水黾脚部“凹凸沟壑”结构的仿生超疏水涂层。对涂层进行了SEM、FTIR、XRD表征,对C_(3)涂层(坡缕石粉质量分数为25%)进行了水接触角、水滚动角、自清洁性能、抗润湿性能、耐磨性能、耐水性能测试。结果表明,C_(3)涂层表面具有明显的“凹凸沟壑”结构,其静态、动态水接触角分别为153.1°、152.6°,水滚动角为8.8°,具有优异的自清洁性能;C_(3)涂层对泥土浆液、甲基橙溶液和亚甲基蓝溶液具有优良的抗润湿性,接触角均>150°;C_(3)涂层具有良好的基材适用性,涂覆于混凝土、织物棉布、纸张及塑料表面均具有超疏水性能;经过载重为100 g的A4纸循环打磨50次,C_(3)涂层水接触角仍高达151.9°,具有较好的耐磨性能;C_(3)涂层在经过18和24 h浸泡后,其水接触角分别为152.2°和144.4°。

雨水作用下缓倾角岩层露天煤矿凸边坡变形机理研究

为了揭示强降雨作用下缓倾角岩层凸边坡剪切滑动破坏机理及其控制措施。本文以宝日希勒露天煤矿边坡为例,采用牛顿力现场监测和FLAC^(3D)三维数值模拟相结合的方法,研究冻融作用下缓倾角岩层凸边坡的内部牛顿力演化规律,分析强降雨作用下无支护和高预应力锚索支护条件下凸边坡的变形规律和塑性区分布特征。研究结果表明:露天煤矿开采形成典型的凸边坡,凸边坡在局部应力集中和卸荷回弹变形共同作用下产生显著变形;在凸边坡解冻期,凸边坡北部边坡产生牛顿力降低,东部边坡产生牛顿力增加;在强降雨作用下,岩体容重增加,边坡内形成裂隙水压力,增加了边坡岩体的滑动力,同时煤层间碳质泥岩强度遇水弱化,形成缓倾角软弱结构面,从而导致边坡岩体沿软弱结构面的整体水平剪切滑动;高预应力锚索可以有效增加缓倾角边坡的整体性,减小由于降雨引起的边坡塑性变形。本文研究工作为后期宝日希勒露天煤矿凸边坡的变形控制和支护设计提供了依据。

求解一类线性等式约束凸优化问题的加速方法

具有线性约束的凸优化问题是数学规划中的一类经典问题。本文将借助对偶理论,研究求解一类具有线性等式约束的凸优化问题的加速算法。由于此类问题的对偶问题是一个具有两块可分离结构的凸优化问题,我们基于Goldstein等人在加速交替方向乘子法方面的重要工作,提出了一种在弱化条件下求解线性等式约束凸优化问题的加速方法。我们的方法与Goldstein等人的加速交替方向乘子法的不同之处为:1)目标函数仅要求具有凸性(而不必强凸);2)罚参数仅要求β>0(而不受目标函数的利普希茨常数、强单调系数的限制)。基于上述弱化的条件,我们证明了所提的加速交替方向乘子法依然具有收敛性和O(1/k^(2))的收敛率。我们将条件弱化后的加速交替方向乘子法用于求解一个图像重建问题。数值实验结果表明,条件弱化后的加速交替方向乘子法依然具有较好的数值效果。