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Convergences of Random Variables Under sublinear Expectations

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 39-54页

作者： Zechun HU Qianqian ZHOU College of Mathematics Sichuan University School of Mathematical Sciences Nankai University Department of Mathematics Nanjing University

In this note, the authors survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that convergence in capacity is stronger than convergence in distribution,and give some equivalent characterizations of convergence in distribution. In addition,they give a dominated convergence theorem under sublinear expectations, which may have its own interest.

关键词： sublinear expectation Capacity The dominated convergence theorem

POSITIVE SOLUTIONS OF SINGULAR sublinear SECOND ORDER BOUNDARY VALUE PROBLEMS

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Systems Science and Mathematical Sciences 1998年第1期11卷 82-88页

作者： WEI Zhongli(Department of Fundamental Courses, Shandong Arehitectuml andCivil Engineering Institute, Ji’nan 250014, China) 山东建筑工程学院基础部山东济南

This paper mainly studies the existence of positive solutions of singular sub-linear boundary value problems concerning the generalized Emden-Fowler equations. Anecessary and sufficient condition for the existence of positive solutions to this problemhas been obtained by using the method of lower and upper solutions with the fixed poilltt heorems.

关键词： Singular sublinear boundary value problem positive solution lower andupper soplutions.

A REMARK ON PERIODIC SOLUTIONS OF SINGULAR HAMILTONIAN SYSTEMS WITH sublinear TERMS

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Systems Science and Mathematical Sciences 1992年第2期5卷 121-126页

作者： DING Yanheng LI Shujie (Institute of Mathematics,Academia Sinica,Beijing 100080,China)

In this paper,we prove the existence of multiple periodic solutionsfor a class of singular Hamiltonian systems with sublinear terms via variationalmethods.

关键词： Singular Hamiltonian system sublinear periodic solution

ON INDEFINITE sublinear ELLIPTIC EQUATIONS

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Systems Science and Mathematical Sciences 2000年第1期13卷 48-58页

作者： YANG Hai tao WU Shao ping (Department of Mathematics, Zhejiang University, Hangzhou 310027, China) 浙江大学数学系浙江杭州 310027 浙江大学数学系浙江杭州

***,N23,beasmoothboundeddomainandconsiderthesemilinearellipticequationswhereatbELoc(Q),***eaction-diffusionprocessess(seethereferencesof[1]).Bytheresultsof[... 详细信息

***,N23,beasmoothboundeddomainandconsiderthesemilinearellipticequationswhereatbELoc(Q),***eaction-diffusionprocessess(seethereferencesof[1]).Bytheresultsof[...

关键词： sublinear elliptic equation critical point theory sub-sup-solution.

ON AN ELLIPTIC PROBLEM INVOLVING CRITICAL AND sublinear GROWTH

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Journal of Systems Science & Complexity 2002年第3期15卷 329-336页

作者： YANG Haitao (Department of Mathematics, Zhejiang University, Hangzhou 310027, China) Department of Mathematics Zhejiang University Hangzhou 310027

In this paper,the author considers an elliptic problem with critical and sublinear *** results about the multiplicity and uniqueness of the positive solutions are given by making use of variational method and bifurcat... 详细信息

关键词： Critical exponent sublinear critical point bifurcation.

OSCILLATION CRITERION FOR A CLASS OFSECOND ORDER sublinear DIFFERENTIALEQUATIONS

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Annals of Differential Equations 1997年第3期13卷 228-231页

作者：董莹云南工业大学 650051

In this paper some oscillation criteria are established for equation [q(t)y'] +a(t)f(y) = 0, where a(t) is not assumed to be non-negative and f(y) is nodecreasing in y, and yf(y) > 0 for y≠0, f(y) also satisfics a sublinear condition, q(t) is a positive function on [0, ). These results extend earlier oscillation theorems of Philos and Wong.

关键词： sublinear Differential equation Oscillation

OSCILLATION CRITERIA FOR A FOURTH ORDER sublinear DYNAMIC EQUATION ON TIME SCALE

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Annals of Differential Equations 2011年第3期27卷 361-366页

作者： Said R.Grace Ravi P.Agarwal Sandra Pinelas Dept. of Engineering Math. Faculty of EngineeringCairo University Dept. of Mathematical Sciences Florida Institute of Technology Dept. of Math. Azores University

Some new criteria for the oscillation of a fourth order sublinear and/or linear dynamic equation on time scale are established. Our results are new for the corresponding fourth order differential equations as well as ... 详细信息

关键词： fourth order sublinear dynamic equations oscillation

A New Demonstration of a Theorem for sublinear Approximations

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Journal of Mathematical Research and Exposition 2000年第2期20卷 211-212页

作者：林贵华冯恩民大连理工大学应用数学系 116024

The demonstration of a theorem for sublinear approximations, due to Demyanov and Rubinov, is modified as a new one in this paper.

关键词： sublinear superlinear approximation.

Loss of energy dissipation capacity from the deadzone in linear and nonlinear viscous damping devices

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Earthquake Engineering and Engineering Vibration 2007年第1期6卷 11-20页

作者： Mai Tong Thomas Liebner Multidisciplinary Center for Earthquake Engineering Research State University of New York at Buffalo USA Department of Mechanical Engineering Pennsylvania State University

In a viscous damping device under cyclic loading, after the piston reaches a peak stroke, the reserve movement that follows may sometimes experience a short period of delayed or significantly reduced device force output. A similar delay or reduced device force output may also occur at the damper＇s initial stroke as it moves away from its neutral position. This phenomenon is referred to as the effect of ＂deadzone＂. The deadzone can cause a loss of energy dissipation capacity and less efficient vibration control. It is prominent in small amplitude vibrations. Although there are many potential causes of deadzone such as environmental factors, construction, material aging, and manufacture quality, in this paper, its general effect in linear and nonlinear viscous damping devices is analyzed. Based on classical dynamics and damping theory, a simple model is developed to capture the effect ofdeadzone in terms of the loss of energy dissipation capacity. The model provides several methods to estimate the loss of energy dissipation within the deadzone in linear and sublinear viscous fluid dampers. An empirical equation of loss of energy dissipation capacity versus deadzone size is formulated, and the equivalent reduction of effective damping in SDOF systems has been obtained. A laboratory experimental evaluation is carried out to verify the effect of deadzone and its numerical approximation. Based on the analysis, a modification is suggested to the corresponding formulas in FEMA 3 5 6 for calculation of equivalent damping if a deadzone is to be considered.

关键词： viscous damping device stroke deadzone sublinear viscous fluid dampers