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uniqueness OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN

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Acta Mathematica Scientia 2023年第1期43卷 450-468页

作者：向建立严国政 Three Gorges Mathematical Research Center College of ScienceChina Three Gorges UniversityYichang443002China School of Mathematics and Statistics Central China Normal UniversityWuhan430079China

In this paper,we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed *** is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field,so it is impossible to reconstruct the location of the underlying *** on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium,we consider different types of superpositions of incident waves to break the translation invariance property.

关键词： conductive boundary condition uniqueness phaseless far field data inverse scattering

uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems Ⅱ: Case of Multiple Feedback Dampings

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Chinese Annals of Mathematics,Series B 2022年第5期43卷 659-684页

作者： Tatsien LI Bopeng RAO School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematic Nonlinear Mathematical Modeling and Methods Laboratory Shanghai 200433China Institut de Recherche Mathematique Avancee Universitede Strasbourg67084 StrasbourgFrance

In this paper,the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback *** first show that under the observability of a scalar equation,Kalman’s rank condition is sufficient for the uniqueness of solution to a complex system of elliptic equations with *** authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various *** classic models are presented to illustrate the field of applications of the abstract theory.

关键词： Kalman rank condition uniqueness Asymptotic synchronization Kelvin-Voigt damping

THE REGULARITY AND uniqueness OF A GLOBAL SOLUTION TO THE ISENTROPIC NAVIER-STOKES EQUATION WITH ROUGH INITIAL DATA

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Acta Mathematica Scientia 2023年第4期43卷 1675-1716页

作者：王海涛张雄韬 Institute of Natural Sciences and School of Mathematical Sciences LSC-MOEShanghai Jiao Tong UniversityShanghai 200240China School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed *** key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time *** these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong ***,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.

关键词： compressible Navier-Stokes equation BV initial data regularity uniqueness

uniqueness of Meromorphic Solutions for a Class of Complex Linear Differential-Difference Equations

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Journal of Mathematical Research with Applications 2022年第4期42卷 331-348页

作者： Hongjin LIN Junfan CHEN Shuqing LIN School of Mathematics and Statistics Fujian Normal University

In this paper,we mainly study the uniqueness of transcendental meromorphic solutions for a class of complex linear differential-difference ***,suppose that f（z）is a finite order transcendental meromorphic solution of complex linear differential-difference equation:W1（z）f'（z+1）+W2（z）f（z）=W3（z）,where W1（z）,W2（z）,W3（z） are nonzero meromorphic functions,with their orders of growth being less than one,such that W1（z）+W2（z）■*** f（z） and a meromorphic function g（z） share 0,1,∞ CM,then either f（z）≡g（z） or f（z）+g（z）≡f（z）g（z） or f2（z）(g（z）-1)2+g2（z）(f（z）-1)2≡f（z）g（z）(f（z）g（z）-1) or there exists a polynomial φ（z）=az+b0such that ■ where a（≠0）,a0,b0are constants with ea0≠eb0.

关键词： meromorphic solution complex differential-difference equation shared value uniqueness finite order

The Chinese path to modernisation: Its universality and uniqueness

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Economic and Political Studies 2023年第1期11卷 1-16页

作者： Shouying Liu Xuefeng Xiong School of Economics Renmin University of ChinaBeijingChina School of Agricultural Economics and Rural Development Renmin University of ChinaBeijingChina

Modernisation is a worldwide *** marks a revolution-ary transformation in all fields of human endeavour,including politics,society,culture,thought,and *** many ways,China’s modernisation has the common characteristics of modern-isation,including the nature of being developmental and trans-formative,institutional innovation,the guiding role of values,consciousness of material exchange between man and nature,and global *** also has the unique characteristics of catching up with and surpassing the modernisation of other countries through institutional construction and reform under the leadership of the Communist Party of China(CPC).In the new era,China will build itself into a strong and modernised country through the Chinese path to modernisation.

关键词： Chinese path to modernisation universality uniqueness strong and modernised country

uniqueness RESULTS OF MEROMORPHIC FUNCTIONS WHOSE DERIVATIVES SHARE FOUR SMALL FUNCTIONS

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Acta Mathematica Scientia 2012年第4期32卷 1593-1606页

作者：李效敏仪洪勋胡海燕 Department of Mathematics Ocean University of ChinaQingdao 266100China Department of Physics and Mathematics University of Eastern FinlandP.O.Box 11180101 JoensuuFinland Department of Mathematics Shandong UniversityJinan 250100China

We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.

关键词： Nevanlinna theory meromorphic function shared value uniqueness orderof growth

uniqueness of admissible meromorphic functions in the unit disc

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Science China Mathematics 1999年第4期42卷 367-381页

作者：方明亮 Institute of Mathematics Chinese Academy of Sciences Beijing China Department of Mathematics Nanjing Normal University Nanjing China

The uniqueness of admissible meromorphic functions in the unit disc is

关键词： admissible meromorphic function uniqueness unit disc.

uniqueness Theorems of Entire Functions with Shared-set in an Angular Domain

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Acta Mathematica Sinica,English Series 2008年第11期24卷 1925-1934页

作者： Wei Chuan LIN Seiki MORI Hong Xun YI Department of Mathematics Fujian Normal University Fuzhou 350007 P. R. China Department of Mathematical Sciences Faculty of Science Yamagata University Yamagata990-8560 Japan Department of Mathematics Shandong University Ji'nan 250100 P. R. China

There have been lots of papers on the uniqueness theory of entire functions concerning shared-sets in the whole complex plane. However, it seems that the uniqueness theory in an angular domain is not widely investigated. In this paper, we study the uniqueness of entire functions concerning shared-sets in an angular domain instead of the whole complex plane, and we supply examples to show that Theorem 1 is sharp.

关键词： shared-set uniqueness entire function angular domain

uniqueness, scale, and resolution issues in groundwater model parameter identification

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Water Science and Engineering 2015年第3期8卷 175-194页

作者： Tian-chyi J.Yeh De-qiang Mao Yuan-yuan Zha Jet-chau Wen Li Wan Kuo-chin Hsu Cheng-haw Lee Department of Hydrology and Water Resources The University of Arizona Department of Resources Engineering National Cheng Kung University Department of Geophysics Colorado School of Mines State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Department of Safety Health and Environmental Engineering National Yunlin University of Science and Technology Research Center for Soil & Water Resources and Natural Disaster Prevention National Yunlin University of Science and Technology

This paper first visits uniqueness, scale, and resolution issues in groundwater flow forward modeling problems. It then makes the point that non-unique solutions to groundwater flow inverse problems arise from a lack of information necessary to make the problems well defined. Subsequently, it presents the necessary conditions for a well-defined inverse problem. They are full specifications of （1） flux boundaries and sources/sinks, and （2） heads everywhere in the domain at at least three times （one of which is t = 0）, with head change everywhere at those times being nonzero for transient flow. Numerical experiments are presented to corroborate the fact that, once the necessary conditions are met, the inverse problem has a unique solution. We also demonstrate that measurement noise, instability, and sensitivity are issues related to solution techniques rather than the inverse problems themselves. In addition, we show that a mathematically well-defined inverse problem, based on an equivalent homogeneous or a layered conceptual model, may yield physically incorrect and scenario-dependent parameter values. These issues are attributed to inconsistency between the scale of the head observed and that implied by these models. Such issues can be reduced only if a sufficiently large number of observation wells are used in the equivalent homogeneous domain or each layer. With a large number of wells, we then show that increase in parameterization can lead to a higher-resolution depiction of heterogeneity if an appropriate inverse methodology is used. Furthermore, we illustrate that, using the same number of wells, a highly parameterized model in conjunction with hydraulic tomography can yield better characterization of the aquifer and minimize the scale and scenario-dependent problems. Lastly, benefits of the highly parameterized model and hydraulic tomography are tested according to their ability to improve predictions of aquifer responses induced by independent stresses not u

关键词： uniqueness Scale Resolution Forward and inverse problems Hydraulic tomography