In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bou...In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.展开更多
In this research work, we consider the below inequalities: (1.1). The researchers attempt to find an answer as to what are the best possible parameters <i><i>α</i></i>, <i><i&...In this research work, we consider the below inequalities: (1.1). The researchers attempt to find an answer as to what are the best possible parameters <i><i>α</i></i>, <i><i>β</i></i> that (1.1) can be held? The main tool is the optimization of some suitable functions that we seek to find out. Without loss of generality, we have assumed that <i>a</i> > <i>b</i> and let <img src="Edit_26c0f99b-93dd-48ff-acdb-f1c8047744f1.bmp" alt="" /> for 1) and <i>a</i> < <i>b</i>, <img src="Edit_15c32a7a-e9ae-41d3-8f49-c6b9c01c7ece.bmp" alt="" />(<i>t</i> small) for 2) to determine the condition for <i><i>α</i></i> and <i><i>β</i></i> to become <i>f</i>(<i>t</i>) ≤ 0 and <i>g</i>(<i>t</i>) ≥ 0.展开更多
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
幸存者平均因果效应(Survivor Average Causal Effect,SACE)可以用来度量任何处理下都能存活的受试者接受不同处理的影响差异,是因果推断中的一个重要研究方向。由于处理组和对照组中总是存活的受试者样本不能直接观测,SACE通常是不可...幸存者平均因果效应(Survivor Average Causal Effect,SACE)可以用来度量任何处理下都能存活的受试者接受不同处理的影响差异,是因果推断中的一个重要研究方向。由于处理组和对照组中总是存活的受试者样本不能直接观测,SACE通常是不可识别的,只能得到SACE的边界。已有文献中SACE尖锐边界的主流求解方法依赖于多参数线性规划,通过枚举对偶问题的约束多边形的所有顶点来产生封闭形式的解。如果单调性和随机占优等条件不成立,则无法采用枚举法求解该多参数线性规划问题。文章基于主分层框架考虑了“死亡截断”、稳定个体处理效应和可忽略性假设下SACE的尖锐边界问题,其中,优化问题的求解是基于一阶KKT(Kraush-Kuhn-Tucker)条件所对应的多项式方程组。实证选取美国国家支持工作示范项目(National Supported Work Demonstration,NSW)中的Lalonde数据集,计算了“永远幸存者”(always-survivor)在完整协变量情形下的SACE尖锐边界。展开更多
It was conjectured by Escobar(J Funct Anal 165:101–116,1999)that for an ndimensional(n≥3)smooth compact Riemannian manifold with boundary,which has nonnegative Ricci curvature and boundary principal curvatures bound...It was conjectured by Escobar(J Funct Anal 165:101–116,1999)that for an ndimensional(n≥3)smooth compact Riemannian manifold with boundary,which has nonnegative Ricci curvature and boundary principal curvatures bounded below by c>0,the first nonzero Steklov eigenvalue is greater than or equal to c with equality holding only on isometrically Euclidean balls with radius 1/c.In this paper,we confirm this conjecture in the case of nonnegative sectional curvature.The proof is based on a combination of Qiu-Xia’s weighted Reilly-type formula with a special choice of the weight function depending on the distance function to the boundary,as well as a generalized Pohozaev-type identity.展开更多
We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly de...We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.展开更多
图G的顶点集V(G)划分为一些子集,使得每个子集的导出子图是0线森林(即每个分支是路)的最小子集数叫图G的点线荫度,记为v|a(G).Poh K S证明了任何平面图的点线荫度最多是3.Matsumato M给出了图的点线荫度的上界,即v|a(G)≤[△(G)/2].这里...图G的顶点集V(G)划分为一些子集,使得每个子集的导出子图是0线森林(即每个分支是路)的最小子集数叫图G的点线荫度,记为v|a(G).Poh K S证明了任何平面图的点线荫度最多是3.Matsumato M给出了图的点线荫度的上界,即v|a(G)≤[△(G)/2].这里△(G)是G的最大度.本文给出了完全n部图的点线荫度计算公式,同时也给出了任意图的点线荫度的精确上下界．展开更多
Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and cov...Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S^＊k＋1（B）.展开更多
We obtain the operator norms of the n-dimensional fractional Hardy operator Hα（0 〈 α 〈 n） from weighted Lebesgue spaces Lp｜x｜p（R^n） to weighted weak Lebesgue spacesLq,∞｜x｜β（R^n）.
Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate...Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate is sharp for eachλ.In this article,we establish the corresponding inequality for a normalized convex function f on U such that z=0 is a zero of order k+1 of f(z)−z,and then we extend this result to higher dimensions.These results generalize some known results.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11871452)Beijing Information Science and Technology University Foundation (Grant No.2025031)+1 种基金Natural Science Foundation of Henan Province (Grant No.202300410338)the Nanhu Scholar Program for Young Scholars of Xinyang Normal University.
文摘In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.
文摘In this research work, we consider the below inequalities: (1.1). The researchers attempt to find an answer as to what are the best possible parameters <i><i>α</i></i>, <i><i>β</i></i> that (1.1) can be held? The main tool is the optimization of some suitable functions that we seek to find out. Without loss of generality, we have assumed that <i>a</i> > <i>b</i> and let <img src="Edit_26c0f99b-93dd-48ff-acdb-f1c8047744f1.bmp" alt="" /> for 1) and <i>a</i> < <i>b</i>, <img src="Edit_15c32a7a-e9ae-41d3-8f49-c6b9c01c7ece.bmp" alt="" />(<i>t</i> small) for 2) to determine the condition for <i><i>α</i></i> and <i><i>β</i></i> to become <i>f</i>(<i>t</i>) ≤ 0 and <i>g</i>(<i>t</i>) ≥ 0.
基金Research supported by Council of Scientific and Industrial Research, India under award no.9/143(163)/91-EER-
文摘Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
文摘幸存者平均因果效应(Survivor Average Causal Effect,SACE)可以用来度量任何处理下都能存活的受试者接受不同处理的影响差异,是因果推断中的一个重要研究方向。由于处理组和对照组中总是存活的受试者样本不能直接观测,SACE通常是不可识别的,只能得到SACE的边界。已有文献中SACE尖锐边界的主流求解方法依赖于多参数线性规划,通过枚举对偶问题的约束多边形的所有顶点来产生封闭形式的解。如果单调性和随机占优等条件不成立,则无法采用枚举法求解该多参数线性规划问题。文章基于主分层框架考虑了“死亡截断”、稳定个体处理效应和可忽略性假设下SACE的尖锐边界问题,其中,优化问题的求解是基于一阶KKT(Kraush-Kuhn-Tucker)条件所对应的多项式方程组。实证选取美国国家支持工作示范项目(National Supported Work Demonstration,NSW)中的Lalonde数据集,计算了“永远幸存者”(always-survivor)在完整协变量情形下的SACE尖锐边界。
基金supported by NSFC(Grant nos.11871406,12271449)supported by Australian Laureate Fellowship FL150100126 of the Australian Research CouncilNational Key R and D Program of China 2021YFA1001800 and NSFC(Grant no.12171334).
文摘It was conjectured by Escobar(J Funct Anal 165:101–116,1999)that for an ndimensional(n≥3)smooth compact Riemannian manifold with boundary,which has nonnegative Ricci curvature and boundary principal curvatures bounded below by c>0,the first nonzero Steklov eigenvalue is greater than or equal to c with equality holding only on isometrically Euclidean balls with radius 1/c.In this paper,we confirm this conjecture in the case of nonnegative sectional curvature.The proof is based on a combination of Qiu-Xia’s weighted Reilly-type formula with a special choice of the weight function depending on the distance function to the boundary,as well as a generalized Pohozaev-type identity.
基金supported by the Faculty Research Project grant of DTU(DTU/Council/BOM-AC/Notification-/31/2018/5738)Research Fellowship from the Department of Science and Technology,New Delhi(IF170272)。
文摘We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.
基金supported by the Key Laboratory on Mathematics and Complex System (at Beijing Normal University) from the Ministry of Education,Chinasupported by NSFC(No.10931001)
文摘图G的顶点集V(G)划分为一些子集,使得每个子集的导出子图是0线森林(即每个分支是路)的最小子集数叫图G的点线荫度,记为v|a(G).Poh K S证明了任何平面图的点线荫度最多是3.Matsumato M给出了图的点线荫度的上界,即v|a(G)≤[△(G)/2].这里△(G)是G的最大度.本文给出了完全n部图的点线荫度计算公式,同时也给出了任意图的点线荫度的精确上下界．
基金Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Nos.19540205,200717540138,2007).
文摘Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S^＊k＋1（B）.
基金National Natural Science Foundation of China(11971165,11561030)。
文摘Let K be the familiar class of normalized convex functions in the unit disk.In[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈C.The above estimate is sharp for eachλ.In this article,we establish the corresponding inequality for a normalized convex function f on U such that z=0 is a zero of order k+1 of f(z)−z,and then we extend this result to higher dimensions.These results generalize some known results.
