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Poincaré Inequalities on a Countable Set E and Ω={x:0≤x_i≤a, i=1,2,…,n}
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作者 陈文英 《Journal of Southwest Jiaotong University(English Edition)》 2005年第1期92-94,共3页
In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accord... In the study of Poincaré inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space Rn, while the method in this paper is based on a countable set E and accordingly the accurate expressions of Poincaré inequalities JB(=(f-μ(f))nJB)=_B≤cD(f, f) is presented to expand the research and application scope. As to inequalities for Ω={DK(x:0DK)≤x_i≤a, i=1,2,…,n}, the existing studies was usually made for n=2, but such an inequality was not the best. Therefore, the different values of n is discussed in this paper, and accordingly the accurate expressions of Poincaré inequalities is presented. 展开更多
关键词 Countable set poincaré inequalities Weight function
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Poincaré Inequalities for Bounded Jump Processes
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作者 陈文英 《Journal of Southwest Jiaotong University(English Edition)》 2009年第2期174-176,共3页
A lot of forms and applications have been found in Poincar6 inequality, but the optimum constants satisfying Poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfyi... A lot of forms and applications have been found in Poincar6 inequality, but the optimum constants satisfying Poincar6 inequality have not been estimated. This paper estimates the optimum constants λ0 and λ1 satisfying Poincaré inequality by using isoperimetric constants. It is λ0≥k0^2/(2R) and λ1 ≥k1^2/(2R). 展开更多
关键词 Non-trivial probability space poincaré inequality Isoperimetric constants Bounded jump processes
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Understanding the educational inequalities in suicide attempts and their mediators:a Mendelian randomisation study
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作者 Jiahao Zhu Houpu Liu +5 位作者 Rui Gao Lilu Ding Jing Wang Ye Yang Dan Zhou Yingjun Li 《General Psychiatry》 CSCD 2024年第1期133-142,共10页
Background Educational inequalities in suicide have become increasingly prominent over the past decade.Elucidating modifiable risk factors that serve as intermediaries in the impact of low educational attainment on su... Background Educational inequalities in suicide have become increasingly prominent over the past decade.Elucidating modifiable risk factors that serve as intermediaries in the impact of low educational attainment on suicide has the potential to reduce health disparities.Aims To examine the risk factors that mediate the relationship between educational attainment and suicide attempts and quantify their contributions to the mediation effect.Methods We conducted a two-sample Mendelian randomisation(MR)analysis to estimate the causal effect of educational attainment on suicide attempts,utilising genome-wide association study summary statistics from the Integrative Psychiatric Research(iPSYCH;6024 cases and 44240 controls)and FinnGen(8978 cases and 368299 controls).We systematically evaluated 42 putative mediators within the causal pathway connecting reduced educational attainment to suicide attempts and employed two-step and multivariable MR to quantify the proportion of the mediated effect.Results In the combined analysis of iPSYCH and FinnGen,each standard deviation(SD)decrease in genetically predicted educational attainment(equating to 3.4 years of education)was associated with a 105%higher risk of suicide attempts(odds ratio(OR):2.05;95%confidence interval(Cl):1.81 to 2.31).0f the 42 risk factors analysed,the two-step MR identified five factors that mediated the association between educational attainment and suicide attempts.The respective proportions of mediation were 47%(95%Cl:29%to 66%)for smoking behaviour,36%(95%Cl:0%to 84%)for chronic pain,49%(95%Cl:36%to 61%)for depression,35%(95%Cl:12%to 59%)for anxiety and 26%(95%Cl:18%to 34%)for insomnia.Multivariable MR implicated these five mediators collectively,accounting for 68%(95%Cl:40%to 96%)of the total effect.Conclusions This study identified smoking,chronic pain and mental disorders as primary intervention targets for attenuating suicide risk attributable to lower educational levels in the European population. 展开更多
关键词 effect. RANDOM inequalities
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Mapping and measuring urban-rural inequalities in accessibility to social infrastructures
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作者 Chenmeng Guo Weiqi Zhou +1 位作者 Chuanbao Jing Dawa Zhaxi 《Geography and Sustainability》 CSCD 2024年第1期41-51,共11页
Equal access to social infrastructures is a fundamental prerequisite for sustainable development,but has long been a great challenge worldwide.Previous studies have primarily focused on the accessibility to social inf... Equal access to social infrastructures is a fundamental prerequisite for sustainable development,but has long been a great challenge worldwide.Previous studies have primarily focused on the accessibility to social infras-tructures in urban areas across various scales,with less attention to rural areas,where inequality can be more severe.Particularly,few have investigated the disparities of accessibility to social infrastructures between urban and rural areas.Here,using the Changsha-Zhuzhou-Xiangtan urban agglomeration,China,as an example,we investigated the inequality of accessibility in both urban and rural areas,and further compared the urban-rural difference.Accessibility was measured by travel time of residents to infrastructures.We selected four types of social infrastructures including supermarkets,bus stops,primary schools,and health care,which were funda-mentally important to both urban and rural residents.We found large disparities in accessibility between urban and rural areas,ranging from 20 min to 2 h.Rural residents had to spend one to two more hours to bus stops than urban residents,and 20 min more to the other three types of infrastructures.Furthermore,accessibility to multiple infrastructures showed greater urban-rural differences.Rural residents in more than half of the towns had no access to any infrastructure within 15 min,while more than 60%of the urban residents could access to all infrastructures within 15 min.Our results revealed quantitative accessibility gap between urban and rural areas and underscored the necessity of social infrastructures planning to address such disparities. 展开更多
关键词 ACCESSIBILITY Social infrastructures Urban-rural difference inequALITY Regional sustainability
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STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES
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作者 姚永红 Abubakar ADAMU Yekini SHEHU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期551-566,共16页
This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inerti... This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature. 展开更多
关键词 forward-backward-forward algorithm inertial extrapolation variational inequality on-line rule
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Global prevalence and gender inequalities in at least 60 min of self-reported moderate-to-vigorous physical activity 1 or more days per week:An analysis with 707,616 adolescents
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作者 Raphael H.O.Araujo AndrúO.Werneck +13 位作者 Clarice L.Martins Luciana L.Barboza Rafael M.Tassitano Nicolas Aguilar-Farias Gilmar M.Jesus Robinson Ramírez-Véelez Riki Tesler Adewale L.Oyeyemi Ellen C.M.Silva Robert G.Weaver Mark S.Tremblay Javier Brazo-Sayavera Grégore I.Mielke Danilo R.P.Silva 《Journal of Sport and Health Science》 SCIE CAS CSCD 2024年第5期709-716,共8页
Background:Guidelines recommend that adolescents should accumulate an average of 60 min per day of moderate-to-vigorous physical activity(MVPA).However,using only this cut-off could hide important information.For inst... Background:Guidelines recommend that adolescents should accumulate an average of 60 min per day of moderate-to-vigorous physical activity(MVPA).However,using only this cut-off could hide important information.For instance,from a population-level point of view,increasing physical activity for those with no or low physical activity could provide more health benefits than increasing physical activity for those with intermediate levels.Also,including a more sensitive cut-point of≥1 days per week could be an additional strategy for identifying those with low access/opportunities for physical activity practice.Thus,the current study aims to estimate the prevalence of≥60 min of MVPA≥1 days per week among adolescents globally,and to describe any relevant gender inequalities.Methods:We used representative datasets from 146 countries/territories collected between 2003 and 2019.MVPA was self-reported.Participants were grouped into younger(≤14 years old)and older(>14 years old)adolescents.Crude Poisson regression models were used to identify the relative differences in≥60 min of MVPA≥1 days per week between boys and girls,and random-effects meta-analysis models were used to identify the pooled estimates.Analyses were stratified by country and region.Results:Approximately 80%of both younger and older adolescents reported≥60 min of MVPA≥1 days per week.This prevalence was≥94%in Europe and Central Asia and North America,while the estimates for the other regions were<77%.The prevalence of≥60 min of MVPA≥1 days per week was higher among boys than girls,with the largest differences occurring among the oldest adolescents(Prevalence ratio_(≤14y)=1.04(95%confidence interval(95%CI)):1.03-1.04)vs.Prevalence ratio_(>14y)=1.09(95%CI:1.08-1.10)).Conclusion:Approximately 8 out of 10 adolescents reported accumulating≥60 min of MVPA≥1 days per week,with notable differences between regions.Gender differences were observed in several countries,especially among the oldest adolescents.Priorities for physical activity promotion among adolescents should include increasing access/opportunities for physical activity among those who do not achieve≥60 min of MVPA≥1 days per week and reducing gender inequalities. 展开更多
关键词 Global School-based Student Health Survey Health Behaviour Among School-aged Children survey inequality Surveillance Youth
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Does digitalization mitigate regional inequalities?Evidence from China
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作者 Haimeng Liu Xinyang Wang +1 位作者 Zheye Wang Yu Cheng 《Geography and Sustainability》 CSCD 2024年第1期52-63,共12页
Regional inequality significantly influences sustainable development and human well-being.In China,there exists pronounced regional disparities in economic and digital advancements;however,scant research delves into t... Regional inequality significantly influences sustainable development and human well-being.In China,there exists pronounced regional disparities in economic and digital advancements;however,scant research delves into the interplay between them.By analyzing the economic development and digitalization gaps at regional and city levels in China,extending the original Cobb-Douglas production function,this study aims to evaluate the impact of digitalization on China's regional inequality using seemingly unrelated regression.The results indicate a greater emphasis on digital inequality compared to economic disparity,with variable coefficients of 0.59 for GDP per capita and 0.92 for the digitalization index over the past four years.However,GDP per capita demonstrates higher spatial concentration than digitalization.Notably,both disparities have shown a gradual reduction in recent years.The southeastern region of the Hu Huanyong Line exhibits superior levels and rates of economic and digital advancement in contrast to the northwestern region.While digitalization propels economic growth,it yields a nuanced impact on achieving balanced regional development,encompassing both positive and negative facets.Our study highlights that the marginal utility of advancing digitalization is more pronounced in less developed regions,but only if the government invests in the digital infrastructure and education in these areas.This study's methodology can be utilized for subsequent research,and our findings hold the potential to the government's regional investment and policy-making. 展开更多
关键词 Regional inequality Regional disparities Digital divide DIGITALIZATION Sustainable development Economic growth Seemingly unrelated regression
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A Note on Sharp Affine Poincaré-Sobolev Inequalities and Exact in Minimization of Zhang’s Energy on Bounded Variation and Exactness
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作者 Salih Yousuf Mohamed Salih 《Journal of Applied Mathematics and Physics》 2023年第3期804-822,共19页
As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* ... As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities. 展开更多
关键词 Affine Energy Affine Sobolev inequality Compactness of Affine Immersion Constrained Minimization
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Global Poincaré Inequalities on the Heisenberg Group and Applications 被引量:1
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作者 Yu Xin DONG Guo Zhen LU Li Jing SUN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第4期735-744,共10页
Let f be in the localized nonisotropic Sobolev space Wloc^1,p (H^n) on the n-dimensional Heisenberg group H^n = C^n ×R, where 1≤ p ≤ Q and Q = 2n + 2 is the homogeneous dimension of H^n. Suppose that the sub... Let f be in the localized nonisotropic Sobolev space Wloc^1,p (H^n) on the n-dimensional Heisenberg group H^n = C^n ×R, where 1≤ p ≤ Q and Q = 2n + 2 is the homogeneous dimension of H^n. Suppose that the subelliptic gradient is gloablly L^p integrable, i.e., fH^n |△H^n f|^p du is finite. We prove a Poincaré inequality for f on the entire space H^n. Using this inequality we prove that the function f subtracting a certain constant is in the nonisotropic Sobolev space formed by the completion of C0^∞(H^n) under the norm of (∫H^n |f| Qp/Q-p)^Q-p/Qp + (∫ H^n |△H^n f|^p)^1/p. We will also prove that the best constants and extremals for such Poincaré inequalities on H^n are the same as those for Sobolev inequalities on H^n. Using the results of Jerison and Lee on the sharp constant and extremals for L^2 to L(2Q/Q-2) Sobolev inequality on the Heisenberg group, we thus arrive at the explicit best constant for the aforementioned Poincaré inequality on H^n when p=2. We also derive the lower bound of the best constants for local Poincaré inequalities over metric balls on the Heisenberg group H^n. 展开更多
关键词 Heisenberg group Sobolev inequalities poincaré inequalities best constants
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A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES 被引量:1
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作者 Duong Viet THONG Vu Tien DUNG 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期184-204,共21页
In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient ext... In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis. 展开更多
关键词 subgradient extragradient method inertial method variational inequality problem pseudomonotone mapping strong convergence convergence rate
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Criteria for Super-and Weak-Poincaré Inequalities of Ergodic Birth-Death Processes 被引量:2
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作者 Jian WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第2期357-370,共14页
Criteria for the super-Poincare inequality and the weak-Pincare inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 ... Criteria for the super-Poincare inequality and the weak-Pincare inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 (p. 15) of Prof. Mu-Fa Chen's book "Eigenvalues, Inequalities and Ergodic 展开更多
关键词 Super-poincare inequality weak-poincare inequality Nash inequality ergodic birth-deathprocesses capacity
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Coupling,convergence rates of Markov processes and weak Poincaré inequalities 被引量:2
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作者 王凤雨 《Science China Mathematics》 SCIE 2002年第8期975-983,共9页
Some analytic and probabilistic properties of the weak Poincaré inequality are obtained. In particular, for strong Feller Markov processes the existence of this inequality is equivalent to each of the following: ... Some analytic and probabilistic properties of the weak Poincaré inequality are obtained. In particular, for strong Feller Markov processes the existence of this inequality is equivalent to each of the following: (i)the Liouville property (or the irreducibility); (ii) the existence of successful couplings (or shift-couplings); (iii)the convergence of the Markov process in total variation norm; (iv) the triviality of the tail (or the invariant)σ-field; (v) the convergence of the density. Estimates of the convergence rate in total variation norm of Markov processes are obtained using the weak Poincaré inequality. 展开更多
关键词 WEAK poincarÉ inequality harmonic function Markov process TAIL σ-fleld coupling.
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Weak Poincaré Inequalities,Decay of Markov Semigroups and Concentration of Measures 被引量:3
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作者 Feng Yu WANG Qi Zhi ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第4期937-942,共6页
For a reasonable class of weak Poincaré inequalities, the decay of the corresponding Markov semigroups obtained earlier by Rockner and the first named author is improved by removing an extra L^2-norm. Next, a con... For a reasonable class of weak Poincaré inequalities, the decay of the corresponding Markov semigroups obtained earlier by Rockner and the first named author is improved by removing an extra L^2-norm. Next, a concentration estimate of the reference measure is presented for the weak Poincaré inequality, which is sharp as illustrated by some examples of one-dimensional diffusion processes. 展开更多
关键词 Weak poincaré inequality Markov semigroup Concentration of measures
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NEW DOOB'S MAXIMAL INEQUALITIES FOR MARTINGALES
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作者 郝志伟 李丽波 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期531-538,共8页
Let 1≤q≤∞,b be a slowly varying function and letΦ:[0,∞)■[0,∞)be an increasing convex function withΦ(0)=0 and■Φ(r)=∞.In this paper,we present a new class of Doob’s maximal inequality on Orlicz-Lorentz-Karam... Let 1≤q≤∞,b be a slowly varying function and letΦ:[0,∞)■[0,∞)be an increasing convex function withΦ(0)=0 and■Φ(r)=∞.In this paper,we present a new class of Doob’s maximal inequality on Orlicz-Lorentz-Karamata spaces LΦ,q,b.The results are new,even for the Lorentz-Karamata spaces withΦ(t)=tp,the Orlicz-Lorentz spaces with b≡1,and weak Orlicz-Karamata spaces with q=∞in the framework of LΦ,q,b-Moreover,we obtain some even stronger qualitative results that can remove the△2-condition of Liu,Hou and Wang(Sci China Math,2010,53(4):905-916). 展开更多
关键词 MARTINGALES Doob's inequality Orlicz-Lorentz-Karamata spaces convex functions
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Generalization of Inequalities in Metric Spaces with Applications
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作者 Eltigani I. Hassan 《Journal of Applied Mathematics and Physics》 2023年第10期2923-2931,共9页
In this paper, which serves as a continuation of earlier work, we generalize the idea of inequalities in metric spaces and use them to demonstrate that the incomplete metric space can be used to obtain a Banach space.
关键词 Metric Spaces Banach Space inequalities
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What in Fact Proves the Violation of the Bell-Type Inequalities?
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作者 Sofia Wechsler 《Journal of Quantum Information Science》 CAS 2023年第1期24-32,共9页
A. Peres constructed an example of particles entangled in the state of spin singlet. He claimed to have obtained the CHSH inequality and concluded that the violation of this inequality shows that in a measurement in w... A. Peres constructed an example of particles entangled in the state of spin singlet. He claimed to have obtained the CHSH inequality and concluded that the violation of this inequality shows that in a measurement in which some variables are tested, other variables, not tested, have no defined value. In the present paper is proved that the correct conclusion of the violation of the CHSH inequality is different. It is proved that the classical calculus of probabilities of test results, obeying the Kolmogorov axioms, is unfit for the quantum formalism, dominated by probability amplitudes. 展开更多
关键词 CHSH inequalities Kolmogorov Axioms Photon Singlet of Polarization Malus Law
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HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING
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作者 裴雯熠 闫理坦 陈振龙 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1403-1414,共12页
In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H... In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented. 展开更多
关键词 stochastic differential equations Harnack type inequalities fractional Brownian motion Markovian switching
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Regularization Methods to Approximate Solutions of Variational Inequalities
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作者 Nguyen Van Kinh 《Open Journal of Optimization》 2023年第2期34-60,共27页
In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regul... In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data  satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones. 展开更多
关键词 Ill-Posed Problem Variational inequality Regularization Method Monotone Operator Hemi-Continuous Operator Lower Semi-Continuous Function
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POINCARE INEQUALITIES IN WEIGHTED SOBOLEV SPACES
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作者 王万义 孙炯 郑志明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第1期125-132,共8页
The weighted Poincare inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincare inequalities hold if, and only if, the ball me... The weighted Poincare inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincare inequalities hold if, and only if, the ball measure of non-compactness of the natural embedding of weighted Sobolev spaces is less than 1. 展开更多
关键词 weighted sobolev spaces poincare inequalities EMBEDDINGS
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THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE
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作者 东瑜昕 林和子 陆琳根 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期189-194,共6页
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality... In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature. 展开更多
关键词 asymptotically nonnegative sectional curvature logarithmic Sobolev inequality ABP method
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