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.

某平面凹凸不规则且带错层和通高墙的超限高层建筑结构设计

针对某平面凹凸不规则且带错层和通高墙的超限高层建筑结构,首先分析了结构在小震和风荷载作用下的各项指标;其次对凹凸不规则弱连接处楼板应力进行了详细分析;再次对错层处剪力墙设计、底部通高墙体平面外计算长度进行了重点分析;最后采用大震弹塑性时程分析方法验算了结构薄弱层层间塑性位移角。分析结果表明:对于单肢正交形式的凹凸不规则结构,应加强单肢与中心区连接范围的楼板厚度及配筋,中震作用下,楼板满足钢筋抗拉弹性,混凝土抗剪不屈服;中震作用下,错层处剪力墙会受到上下层楼面错位而产生的平面外和平面内附加剪力及弯矩,墙肢段竖向配筋应取平面外和平面内计算结果的包络值;通高墙体平面外计算长度不能盲目套用规范计算公式,应从结构整体来考察其计算长度;对于平面凹凸不规则的复杂超限高层建筑,应采用弹性动力时程补充验算层间位移角是否满足规范要求。

A novel image segmentation approach for wood plate surface defect classification through convex optimization

Detection of wood plate surface defects using image processing is a complicated problem in the forest industry as the image of the wood surface contains different kinds of defects. In order to obtain complete defect images, we used convex optimization(CO) with different weights as a pretreatment method for smoothing and the Otsu segmentation method to obtain the target defect area images. Structural similarity(SSIM) results between original image and defect image were calculated to evaluate the performance of segmentation with different convex optimization weights. The geometric and intensity features of defects were extracted before constructing a classification and regression tree(CART) classifier. The average accuracy of the classifier is 94.1% with four types of defects on Xylosma congestum wood plate surface: pinhole, crack,live knot and dead knot. Experimental results showed that CO can save the edge of target defects maximally, SSIM can select the appropriate weight for CO, and the CART classifier appears to have the advantages of good adaptability and high classification accuracy.

A Comprehensive Model for Structural Non-Probabilistic Reliability and the Key Algorithms

It is very difficult to know the exact boundaries of the variable domain for problems with small sample size,and the traditional convex set model is no longer applicable.In view of this,a novel reliability model was proposed on the basis of the fuzzy convex set(FCS)model.This new reliability model can account for different relations between the structural failure region and variable domain.Key computational algorithms were studied in detail.First,the optimization strategy for robust reliability is improved.Second,Monte Carlo algorithms(i.e.,uniform sampling method)for hyper-ellipsoidal convex sets were studied in detail,and errors in previous reports were corrected.Finally,the Gauss-Legendre integral algorithm was used for calculation of the integral reliability index.Three numerical examples are presented here to illustrate the rationality and feasibility of the proposed model and its corresponding algorithms.

Convex Set Theory for Reliability Assessment of Steel Beam with Bounded Uncertainty

Probabilistic reliability model established by insufficient data is inaccessible. The convex model was applied to model the uncertainties of variables. A new non-probabilistic reliability model was proposed based on the robustness of system to uncertainty. The non-probabilistic reliability model,the infinite norm model,and the probabilistic model were used to assess the reliability of a steel beam,respectively. The results show that the resistance is allowed to couple with the action effect in the non-probabilistic reliability model. Additionally,the non-probabilistic reliability model becomes the same accurate as probabilistic model with the increase of the bounded uncertain information. The model is decided by the available data and information.

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。

基于“凸节”结构的超声温度传感器设计

温度参数是航空发动机在燃烧稳定性试验中的重要参数,基于单晶氧化物的超声测温相对于其他测温方法具有范围广、稳定性好的优点。首先,分析并设计传感器参数,通过COMSOL有限元仿真模拟“凸节”结构在不同直径及曲率下声波的传输及传感器工作状态,其结果表明“凸节”模型具有良好的声速-温度特性;然后,采用激光加热基座法生长新型“凸节”结构的蓝宝石声波导杆,制作与仿真参数一致的超声温度传感器并搭建测温系统,在工作温度1 600℃的高温炉完成传感器静态标定,其测试结果验证传感器可在1 600℃高温环境连续工作5 h,重复性达95.43%,单位灵敏度为12.57~35.72 ns·(℃·m)^(-1)。与激光刻蚀“凹槽”结构相比,这种“凸节”结构表现出卓越的结构稳定性和抗氧化性,更能满足高温测试需求,为解决高温环境监测和新型材料的结构研究提供了新方法。