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SOME PROPERTIES OF FUZZY convex SETS

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Chinese Science Bulletin 1982年第9期27卷 926-929页

作者：刘应明 Institute of Mathematics Sichuan University Chengdun the fundamental paper where the important concept of fuzzy set was first introduced L. A. Zadeh developed a basic framework to treat mathematically the fuzzy phenomena. He paid special attention to the investigation on fuzzy convex sets which cover nearly half of the space of the paper. The results on fuzzy convex

In the fundamental paper, where the important concept of fuzzy set was first introduced, L. A. Zadeh developed a basic framework to treat mathematically the fuzzy phenomena. He paid special attention to the investigat... 详细信息

关键词： convex FUZZY ordinaryunion smallest hence topology subset 加名冲阳

On Certain Properties of Trigonometrically <i>ρ</i>-convex Functions

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Advances in Pure Mathematics 2012年第5期2卷 337-340页

作者： Mohamed Sabri Salem Ali Department of Mathematics Faculty of Basic Education PAAET Shamiya Kuwait

The aim of this paper is to prove that the average function of a trigonometrically ρ-convex function is trigonometrically ρ-convex. Furthermore, we show the existence of support curves implies the trigonometric ρ-c... 详细信息

关键词： Generalized convex Functions Trigonometrically ρ-convex Functions Supporting Functions Average Functions Extremum Problems

Distributed Majorization-Minimization for Laplacian Regularized Problems

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IEEE/CAA Journal of Automatica Sinica 2019年第1期6卷 45-52页

作者： Jonathan Tuck David Hallac Stephen Boyd IEEE the Department of Electrical Engineering Stanford University

We consider the problem of minimizing a block separable convex function(possibly nondifferentiable, and including constraints) plus Laplacian regularization, a problem that arises in applications including model fitting, regularizing stratified models, and multi-period portfolio optimization. We develop a distributed majorization-minimization method for this general problem, and derive a complete, self-contained, general,and simple proof of convergence. Our method is able to scale to very large problems, and we illustrate our approach on two applications, demonstrating its scalability and accuracy.

关键词： convex optimization distributed optimization graphical networks Laplacian regularization

ON AN EXTENSION OF HADAMARD INEQUALITIES OF convex FUNCTIONS

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Chinese Science Bulletin 1981年第8期26卷 763-764页

作者：王中烈王兴华 Department of Mathematics and Statistics University of Regina Canada Department of Mathematics

In 1893, J. Hadamard pointed out that for any continuous convex function f(x) on a closed interval [a, b] (a≠b) the following inequalities hold. In 1974 and 1976, P. M. Vasi and I. B. Lackovi and in 1976 A. Lupas int... 详细信息

关键词： Hadamard convex pointed 上互刁云

机器设计选择、工程平衡及convex C2系列的决策过程

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计算机工程与科学 1989年第4期11卷 1-6页

作者：沈雁金士尧

计算机界普遍认为,计算机结构还没有形成一种科学,只是一种工艺,至多在某些部分可称为科学,大部分只是一种科学的方法。从广义上讲计算机重要的不是发明什么,而是要形成一种别人肯买它的产品。买的人越多,应用就越广;应用越广,它本身的... 详细信息

计算机界普遍认为,计算机结构还没有形成一种科学,只是一种工艺,至多在某些部分可称为科学,大部分只是一种科学的方法。从广义上讲计算机重要的不是发明什么,而是要形成一种别人肯买它的产品。买的人越多,应用就越广;应用越广,它本身的改进也就越快。在开始设计一种新机器时,必须要考虑到预算,元器件的现状水平,需要消耗多少人年,技术的提前量与实际实施的可能性等综合因素,在诸多因素中力求取得最佳平衡点。由于我们只考虑机器本身,故在此不考虑市场前景等非技术性的因素。

关键词：机器设计决策过程 convex C2 现状水平非技术性计算机结构计算机界并行处理计算机市场结构效率

ON THE convex SUM OF STARLIKE FUNCTIONS

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Chinese Science Bulletin 1983年第1期28卷 133-134页

作者：吴卓人 Tongji University Shanghai

Let f（z）=z+a1z2 +… be analytic and univalent in the unit disc U={z||z|

Let f（z）=z+a1z2 +… be analytic and univalent in the unit disc U={z||z|convex set, then we say that f is a convex function in U. If f（U） is starshaped with respect to the origin, then f is said to be a starlike function. A function f（z）=z+…is starlike of order ρ in U if and only if there is a constant ρ, 0≤ρ

关键词： convex analytic 从一

Extracting hand articulations from monocular depth images using curvature scale space descriptors

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Frontiers of Information Technology & Electronic Engineering 2016年第1期17卷 41-54页

作者： Shao-fan WANG Chun LI De-hui KONG Bao-cai YIN Beijing Key Laboratory of Multimedia and Intelligent Software Technology College of Metropolitan Transportation Beijing University of Technology Beijing 100124 China School of Software Technology Dalian University of Technology Dalian 116024 China Collaborative Innovation Center of Electric Vehicles in Beijing Beijing 100081 China

We propose a framework of hand articulation detection from a monocular depth image using curvature scale space(CSS) descriptors. We extract the hand contour from an input depth image, and obtain the fingertips and finger-valleys of the contour using the local extrema of a modified CSS map of the contour. Then we recover the undetected fingertips according to the local change of depths of points in the interior of the contour. Compared with traditional appearance-based approaches using either angle detectors or convex hull detectors, the modified CSS descriptor extracts the fingertips and finger-valleys more precisely since it is more robust to noisy or corrupted data;moreover, the local extrema of depths recover the fingertips of bending fingers well while traditional appearance-based approaches hardly work without matching models of hands. Experimental results show that our method captures the hand articulations more precisely compared with three state-of-the-art appearance-based approaches.

关键词： Curvature scale space (CSS), Hand articulation, convex hull, Hand contour

Influence of a multi-step process on the thickness reduction error of sheet metal in a flexible rolling process

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International Journal of Minerals,Metallurgy and Materials 2019年第1期26卷 76-85页

作者： Yi Li Ming-zhe Li Kai Liu Dieless Forming Technology Center Roll Forging Institute Jilin University College of Materials Science and Engineering Jilin University

Flexible rolling is a forming process based on thickness reduction, and the precision of thickness reduction is the key factor affecting bending deformation. The major purpose of the present work is to solve the problem of bending deformation error caused by insufficient thickness reduction. Under the condition of different rolling reductions with the same sheet thickness and the same thickness reduction with different sheet thicknesses, the thickness reduction error of sheet metal is analyzed. In addition, the bending deformation of sheet metal under the same conditions is discussed and the influence of the multi-step forming process on the thickness reduction error is studied. The results show that, under the condition of the same sheet thickness, the thickness reduction error increases with increasing rolling reduction because of an increase in work hardening. As rolling reduction increases, the longitudinal bending deformation decreases because of the decrease of the maximum thickness difference. Under the condition with the same thickness reduction, the thickness reduction error increases because of the decrease of the rolling force with increasing sheet thickness. As the sheet thickness increases, the longitudinal bending deformation increases because of the increase in the maximum thickness difference. A larger bending deformation is divided into a number of small bending deformations in a multi-step forming process, avoiding a sharp increase in the degree of work hardening; the thickness reduction error is effectively reduced in the multi-step forming process. Numerical simulation results agree with the results of the forming experiments.

关键词： flexible rolling convex surface numerical simulation thickness reduction error multi-step forming process

How to Select the Best Sensors for TDOA and TDOA/AOA Localization?

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China Communications 2019年第2期16卷 134-145页

作者： Yue Zhao Zan Li Benjian Hao Pengwu Wan Linlin Wang State Key Laboratory of Integrated Service Networks Xidian University Collaborative Innovation Center of Information Sensing and Understanding

This paper focuses on the sensor subset optimization problem in time difference of arrival(TDOA) passive localization scenario. We seek for the best sensor combination by formulating a non-convex optimization problem, which is to minimize the trace of covariance matrix of localization error under the condition that the number of selected sensors is given. The accuracy metric is described by the localization error covariance matrix of classical closed-form solution, which is introduced to convert the TDOA nonlinear equations into pseudo linear equations. The non-convex optimization problem is relaxed to a standard semi-definite program(SDP) and efficiently solved in a short time. In addition, we extend the sensor selection method to a mixed TDOA and angle of arrival(AOA) localization scenario with the presence of sensor position errors. Simulation results validate that the performance of the proposed sensor selection method is very close to the exhaustive search method.

关键词： sensor selection localization TDOA/AOA non-convex convex relaxation