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Initial-irregular oblique derivative problems for nonlinear parabolic systems of second order equations with measurable coefficients

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Science China Mathematics 1999年第7期42卷 681-690页

作者：闻国椿 1. Department of Mathematics Peking University 100871 Beijing China

The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The uniqueness theorem of solutions for the above problems and some a priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem, the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding theorems in literature.

关键词： initial-irregular oblique derivative problems nonlinear parabolic systems measurable coefficients uniqueness and existence of solutions.

Existence of the optimal measurable coupling and ergodicity for Markov processes

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Science China Mathematics 1999年第1期42卷 58-67页

作者：张绍义 1. Department of Mathematics Beijing Normal University 100875 Beijing China2. Department of Mathematics Hubei Normal University 435002 Huangshi China

The existence theorem of the optimal measurable coupling of two probability kernels on a complete separable metric measurable space is proved. Then by this theorem, a general ergodicity theorem for Markov processes is obtained. And as an immediate application to particle systems the uniqueness theorem of the stationary distribution is supplemented, i.e. the uniqueness theorem also implies the existence of the stationary distribution.

关键词： probability kernel optimal measurable coupling Markov process.

THE DIRICHLET PROBLEM AND NEUMANN PROBLEM FOR NONLINEAR PARABOLIC SYSTEMS OF SECOND ORDER EQUATIONS WITH measurable COEFFICIENTS IN A HIGHER DIMENSIONAL DOMAIN

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Journal of Systems Science & Complexity 2001年第3期14卷 239-246页

作者： WEN Guochun (Department of Mathematics, Peking University, Beijing 100871, China) HUANG Sha QIAO Yuying (Department of Mathematics, Hebei Teacher’s University, Shijiazhuang 050016, China) 北京大学北京 100871 河北师范大学河北石家庄 050016

In 1988, Yu . A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for linear uniformly parabolic equations with measurable coefficients where the coefficients satisfy the condition In this paper, we try to generalize the results of Alkhutov and Mamedov to nonlinear uni- formly parabolic systems of second order equations with measurable coefficients; moreover, we also discuss the solvability of the Neumann problem for the above systems.

关键词： Neumann problem parabolic systems measurable coefficients.

A GENERALIZATION OF CHOQUET'S THEOREM TO measurable SPACES

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Chinese Science Bulletin 1987年第23期32卷 1596-1601页

作者：张连文汪培庄 Department of Mathematics Beijing Normal University

Ⅰ. PREREQUISITES AND MAIN RESULTS A class of subsets of X is called a multi-class if it is closed for finite intersections, and a multi-class containing both X and φ is called an abundant multi-class. A function Be... 详细信息

关键词： abundant belief inclusion integer 二汉 relate satisfying measurable holds complement

ON FUZZY σ-ALGEBRAS AND FUZZY measurable SPACES

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Chinese Science Bulletin 1982年第8期27卷 818-821页

作者：王戈平 Department of Mathematics Xuzhou Teachers Collegelement first gave an axiomatic definition of a fuzzy σ-algebra which is a generalization of the family of fuzzy events considered by Zadeh. Following the method adopted by Lowen in studying fuzzy topology Klement defined two important mappings ζ and κ and proved some of their corresponding properties in the research of the relationship between classical and fuzzy σ-algebra. This note attempts: (ⅰ) to

Klement first gave an axiomatic definition of a fuzzy σ-algebra which is a generalization of the family of fuzzy events considered by Zadeh. Following the method adopted by Lowen in studying fuzzy topology, Klement defined two important mappings ζ and κ, and proved some of their corresponding properties in the research of the relationship between classical and fuzzy σ-algebra. This note attempts: (ⅰ)

关键词： algebra FUZZY topology measurable generalization quotient nonempty Cartesian Borel smallest

measurable:投放效果评估的关键点

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商学院 2012年第2期 32-32页

从入门到聚焦训练,广告主很可能已经对这项投资心中有数,却未必胜算在握。投资有风险,永远只赚不赔那是神话。对于一直绷着预算这根弦的广告主来讲,抵御这项投资的风险却是必选项,目标是防止前期的广告投入沦为消费开支。

关键词：效果评估关键点投资尚德财政管理广告主搜索引擎广告 measurable 实力传播

Unraveling the nature of sensing in electrostatic MEMS gas sensors

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Microsystems & Nanoengineering 2024年第3期10卷 109-117页

作者： Yasser S.Shama Sasan Rahmanian Hamza Mouharrar Rana Abdelrahman Alaaeldin Elhady Eihab M.Abdel-Rahman Systems Design Engineering University of Waterloo200 University Ave WWaterloo N2L 3G1 ONCanada Mechanical Engineering Benha Faculty of EngineeringBenha UniversityBenha 13511Egypt

This paper investigates the fundamental sensing mechanism of electrostatic MEMS gas *** compares among the responsivities of a set of MEMS isopropanol sensors before and after functionalization,and in the presence and absence of electrostatic fields when operated in static and dynamic detection *** the static mode,we found that the sensors do not exhibit a measurable change in displacement due to added *** the other hand,bare sensors showed a clear change in displacement in response to isopropanol *** the dynamic mode,functionalized sensors showed a measurable frequency shift due to the added mass of isopropanol *** the presence of strong electrostatic fields,the measured frequency shift was found to be threefold larger than that in their absence in response to the same concentration of isopropanol *** enhanced responsivity of dynamic detection allows the sensors to measure the vapor mass captured by the functional material,which is not the case for static *** detection of isopropanol by bare sensors in static mode shows that change in the medium permittivity is the primary sensing *** enhanced responsivity of dynamic mode sensors when operated in strong electrostatic fields shows that their sensing mechanism is a combination of a weaker added mass effect and a stronger permittivity *** findings show that electrostatic MEMS gas sensors are independent of the direction of the gravitational field and are,thus,robust to changes in *** is erroneous to refer to them as‘gravimetric’sensors.

关键词： mechanism electrostatic measurable

Generalized Uncertainty Principle in the Presence of Extra Dimensions

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Chinese Physics Letters 2011年第9期28卷 76-79页

作者： MU Ben-Rong WU Hou-Wen YANG Hai-Tang School of Physical Electronics University of Electronic Science and Technology of ChinaChengdu 610054

We argue that in the generalized uncertainty principle(GUP)model,the parameterβ0 whose square root,multiplied by Planck lengthℓp,approximates the minimum measurable distance,varies with energy *** the minimal measurable length and extra dimensions are both suggested by quantum gravity theories,we investigate the models based on the GUP and one extra dimension,compactified with radiusρ.We obtain an inspiring relation√β0ℓp/ρ∼O(1).This relation is also consistent with the predictions at Planck scale and the usual quantum mechanics *** also estimate the application range of the GUP *** turns out that the minimum measurable length is exactly the compactification radius of the extra dimension.

关键词： measurable radius quantum

CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES

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Acta Mathematica Scientia 2017年第4期37卷 1019-1032页

作者： Inomjon GANIEV Farrukh MUKHAMEDO V Department of Science in Engineering Faculty of EngineeringInternational Islamic University MalaysiaP.O.Box 1050728 Kuala-LumpurMalaysia Department of Mathematical Sciences College of ScienceUnited Arab Emirates UniversityAl Ain15551Abu DhabiUAE

In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.

关键词： noncommutative Lp (M, Ф)-space Banach-Kantorovich space measurable con-ditional expectation measurable bundle martingale