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Several Expressions of Dirichlet L-function at Positive Integers
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作者 Yuan HE 《数学学报:英文版》 SCIE CSCD 2019年第9期1549-1562,共14页
In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers... In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered. 展开更多
关键词 Dirichlet L-FUNCTION trigonometric SUMS GAUSS SUMS BERNOULLI POLYNOMIALS combinatorial IDENTITIES
Properties of Toeplitz Operators on the Dirichlet Space Over the Ball
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作者 Yin Yin HU Yu Feng LU Liu LIU 《数学学报:英文版》 SCIE CSCD 2019年第10期1617-1628,共12页
On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. B... On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero. 展开更多
关键词 TOEPLITZ OPERATOR pluriharmonic SYMBOLS DIRICHLET SPACE
Fundamental Solution of Dirichlet Boundary Value Problem of Axisymmetric Helmholtz Equation 预览
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作者 Zhang Kang-qun Yuan Hong-jun 《数学研究通讯:英文版》 CSCD 2019年第1期21-26,共6页
Fundamental solution of Dirichlet boundary value problem of axisymmetric Helmholtz equation is constructed via modified Bessel function of the second kind,which unified the formulas of fundamental solution of Helmholt... Fundamental solution of Dirichlet boundary value problem of axisymmetric Helmholtz equation is constructed via modified Bessel function of the second kind,which unified the formulas of fundamental solution of Helmholtz equation,elliptic type Euler-Poisson-Darboux equation and Laplace equation in any dimensional space. 展开更多
关键词 Axisymmetic HELMHOLTZ equation FUNDAMENTAL solution DIRICHLET boundary value problem SIMILARITY method
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On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin
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作者 Patrick J. Fitzsimmons Liping Li 《中国科学:数学英文版》 SCIE CSCD 2019年第8期1477-1492,共16页
Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to C_c^∞(R^3\{0}).We will prove that this energy form is a regular Diric... Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to C_c^∞(R^3\{0}).We will prove that this energy form is a regular Dirichlet form with core C_c^∞(R^3).The associated diffusion X behaves like a 3-dimensional Brownian motion with a mild radial drift when far from 0,subject to an ever-stronger push toward 0 near that point.In particular,{0}is not a polar set with respect to X.The diffusion X is rotation invariant,and admits a skew-product representation before hitting{0}:its radial part is a diffusion on(0,∞)and its angular part is a time-changed Brownian motion on the sphere S^2.The radial part of X is a"reflected"extension of the radial part of X^0(the part process of X before hitting{0}).Moreover,X is the unique reflecting extension of X^0,but X is not a semi-martingale. 展开更多
关键词 DIRICHLET form reflected EXTENSION rotationally INVARIANT process Fukushima’s DECOMPOSITION
Interior gradient and Hessian estimates for the Dirichlet problem of semi-linear degenerate elliptic systems: A probabilistic approach
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作者 Jun Dai Shanjian Tang Bingjie Wu 《中国科学:数学英文版》 SCIE CSCD 2019年第10期1851-1886,共36页
In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equ... In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equations and quasi-derivatives. 展开更多
关键词 SEMI-LINEAR DEGENERATE ELLIPTIC systems quasi-derivatives BACKWARD stochastic differential equations DIRICHLET problems
RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE 预览
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作者 梁载涛 杨艳娟 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第2期395-402,共8页
In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theo... In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature. 展开更多
关键词 RADIAL CONVEX SOLUTIONS SINGULAR Dirichlet problem mean CURVATURE OPERATOR fixed point theorem in cones
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Behaviour of the Stokes operators under domain perturbation Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday
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作者 Sylvie Monniaux 《中国科学:数学英文版》 SCIE CSCD 2019年第6期1167-1174,共8页
Depending on the geometry of the domain, one can define—at least—three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to... Depending on the geometry of the domain, one can define—at least—three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging sequence of domains. 展开更多
关键词 domain PERTURBATION STOKES operator DIRICHLET boundary conditions
Incorporating travel time reliability in predicting the likelihood of severe crashes on arterial highways using non-parametric random-effect regression
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作者 Emmanuel Kidando Ren Moses +1 位作者 Eren Erman Ozguven Thobias Sando 《交通运输工程学报(英文版)》 CSCD 2019年第5期470-481,共12页
Travel time reliability(TTR) modeling has gain attention among researchers’ due to its ability to represent road user satisfaction as well as providing a predictability of a trip travel time.Despite this significant ... Travel time reliability(TTR) modeling has gain attention among researchers’ due to its ability to represent road user satisfaction as well as providing a predictability of a trip travel time.Despite this significant effort,its impact on the severity of a crash is not well explored.This study analyzes the effect of TTR and other variables on the probability of the crash severity occurring on arterial roads.To address the unobserved heterogeneity problem,two random-effect regressions were applied;the Dirichlet random-effect(DRE)and the traditional random-effect(TRE) logistic regression.The difference between the two models is that the random-effect in the DRE is non-parametrically specified while in the TRE model is parametrically specified.The Markov Chain Monte Carlo simulations were adopted to infer the parameters’ posterior distributions of the two developed models.Using four-year police-reported crash data and travel speeds from Northeast Florida,the analysis of goodness-of-fit found the DRE model to best fit the data.Hence,it was used in studying the influence of TTR and other variables on crash severity.The DRE model findings suggest that TTR is statistically significant,at 95 percent credible intervals,influencing the severity level of a crash.A unit increases in TTR reduces the likelihood of a severe crash occurrence by 25 percent.Moreover,among the significant variables,alcohol/drug impairment was found to have the highest impact in influencing the occurrence of severe crashes.Other significant factors included traffic volume,weekends,speed,work-zone,land use,visibility,seatbelt usage,segment length,undivided/divided highway,and age. 展开更多
关键词 Travel time reliability CRASH severity NON-PARAMETRIC DISTRIBUTED random-effect Gaussian DISTRIBUTED random-effect Dirichlet process prior
Lipschitz continuity for solutions of the ?-Poisson equation
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作者 Xingdi Chen 《中国科学:数学英文版》 SCIE CSCD 2019年第10期1935-1946,共12页
In this paper, we study the Lipschitz continuity for solutions of the ?-Poisson equation. After characterizing the boundary conditions for the Lipschitz continuity of ?-harmonic mappings, we present four equivalent co... In this paper, we study the Lipschitz continuity for solutions of the ?-Poisson equation. After characterizing the boundary conditions for the Lipschitz continuity of ?-harmonic mappings, we present four equivalent conditions for the(K, K′)-quasiconformal solutions of the ?-Poisson equation with a nonhomogeneous term to be Lipschitz continuous. 展开更多
关键词 weighted LAPLACIAN operator LIPSCHITZ CONTINUITY DIRICHLET boundary problem HARMONIC MAPPING (K K′)-quasiconformal MAPPING
On Scattering of Poles for Schrodinger Operator from the Point of View of Dirichlet Series
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作者 Xiangdong YANG Bijun ZENG 《数学研究及应用:英文版》 CSCD 2019年第2期160-170,共11页
In this article, we are concerned with the scattering problem of Schr?dinger operators with compactly supported potentials on the real line. We aim at combining the theory of Dirichlet series with scattering theory. N... In this article, we are concerned with the scattering problem of Schr?dinger operators with compactly supported potentials on the real line. We aim at combining the theory of Dirichlet series with scattering theory. New estimate on the number of poles is obtained under the situation that the growth of power series which is related to the potential is not too fast by using a classical result of Littlewood. We propose a new approach of Dirichlet series such that significant upper bounds and lower bounds on the number of poles are obtained. The results obtained in this paper improve and extend some related conclusions on this topic. 展开更多
关键词 RESONANCES SCHRODINGER OPERATORS DIRICHLET SERIES
The Fourth Power Mean of the General 3-dimensional Kloostermann Sums mod p
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作者 Wen Peng ZHANG Xing Xing LV 《数学学报:英文版》 SCIE CSCD 2019年第3期369-377,共9页
The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the gen... The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 3-dimensional Kloostermann sums mod p, and give a sharp asymptotic formula for it. 展开更多
关键词 The general 3-dimensional Kloostermann SUMS the FOURTH power mean DIRICHLET CHARACTER ASYMPTOTIC FORMULA
A New Elliptic Measure on Lower Dimensional Sets
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作者 Guy DAVID Joseph FENEUIL Svitlana MAYBORODA 《数学学报:英文版》 SCIE CSCD 2019年第6期876-902,共27页
The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of n-1 dimensional sets across analysis, geometric measure theory, and PDEs. The p... The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of n-1 dimensional sets across analysis, geometric measure theory, and PDEs. The present paper surveys the first steps of a program recently launched by the authors and aimed at the new PDE approach to sets with lower dimensional boundaries. We define a suitable class of degenerate elliptic operators, explain our intuition, motivation, and goals, and present the first results regarding absolute continuity of the emerging elliptic measure with respect to the surface measure analogous to the classical theorems of C. Kenig and his collaborators in the case of co-dimension one. 展开更多
关键词 ELLIPTIC MEASURE in higher CODIMENSION DEGENERATE ELLIPTIC operators absolute continuity Dahlberg’s theorem DIRICHLET SOLVABILITY
ON THE HEAT FLOW OF EQUATION OF H-SURFACE 预览
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作者 吴国春 谭忠 许建开 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第5期1397-1405,共9页
We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique gl... We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H^1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1. 展开更多
关键词 H-surface non-zero DIRICHLET BOUNDARY SINGULARITY global solutions
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Extrapolation for the L^p Dirichlet Problem in Lipschitz Domains
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作者 Zhongwei Shen 《数学学报:英文版》 SCIE CSCD 2019年第6期1074-1084,共11页
Let L be a second-order linear elliptic operator with complex coefficients. It is shown that if the Lp Dirichlet problem for the elliptic system L(u) = 0 in a fixed Lipschitz domain Ω in Rd is solvable for some 1 <... Let L be a second-order linear elliptic operator with complex coefficients. It is shown that if the Lp Dirichlet problem for the elliptic system L(u) = 0 in a fixed Lipschitz domain Ω in Rd is solvable for some 1 < p = p0 <2(d-1)/(d-2), then it is solvable for all p satisfying ■ The proof is based on a real-variable argument. It only requires that local solutions of L(u) = 0 satisfy a boundary Cacciopoli inequality. 展开更多
关键词 DIRICHLET PROBLEM LIPSCHITZ DOMAIN EXTRAPOLATION
WEIGHTED COMPOSITION OPERATORS ON THE HILBERT SPACE OF DIRICHLET SERIES 预览
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作者 王茂发 姚兴兴 邓方文 《数学物理学报:B辑英文版》 SCIE CSCD 2018年第4期1427-1440,共14页
关键词 DIRICHLET HILBERT 操作员 加权 DIRICHLET HILBERT 空间 操作符
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BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS 预览
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作者 林勇 吴艺婷 《数学物理学报:B辑英文版》 SCIE CSCD 2018年第3期843-856,共14页
让 G=(V, E ) 是一张局部地有限的连接的加权的图,并且是平常的图拉普拉斯算符。在这篇文章,我们为非线性的寓言的方程 u <sub 学习发作问题 > G 上的 t </sub>=u + f (u) 。为 u <sub 的发作现象 > t </sub>... 让 G=(V, E ) 是一张局部地有限的连接的加权的图,并且是平常的图拉普拉斯算符。在这篇文章,我们为非线性的寓言的方程 u <sub 学习发作问题 > G 上的 t </sub>=u + f (u) 。为 u <sub 的发作现象 > t </sub>=u + f (u) 以二个盒子被讨论:一个起始的条件被给的(i) ;(ii ) 一个 Dirichlet 边界条件被给。我们证明如果 f 满足适当条件,那么,相应答案将在一有限时间骤起。 展开更多
关键词 非线性 方程 寓言 DIRICHLET 拉普拉斯算符 边界条件 有限时间 加权
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Stochastic Variational Inference-Based Parallel and Online Supervised Topic Model for Large-Scale Text Processing
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作者 Yang Li Wen-Zhuo Song Bo Yang 《计算机科学技术学报:英文版》 SCIE EI CSCD 2018年第5期1007-1022,共16页
话题建模是一种主流、有效的技术处理文章数据,用在文章分析的宽应用,自然语言,个性化的建议,计算机视觉,等等。在所有已知的话题模型之中,监督了潜伏的 Dirichlet 分配(sLDA ) 作为一个流行、竞争的监督话题模型被承认。然而,... 话题建模是一种主流、有效的技术处理文章数据,用在文章分析的宽应用,自然语言,个性化的建议,计算机视觉,等等。在所有已知的话题模型之中,监督了潜伏的 Dirichlet 分配(sLDA ) 作为一个流行、竞争的监督话题模型被承认。然而,数据集的规模的渐渐的增加使 sLDA 越来越低效、费时间,并且在一个很狭窄的范围限制它的应用程序。解决它,平行联机 sLDA,命名 PO-sLDA (平行、联机的 sLDA ) ,在这研究被建议。它使用使训练过程更快速、有效的学习方法,和并行计算机制经由 MapReduce 框架实现了的随机的变化推理被建议支持云计算并且大数据处理的能力。PO-sLDA 支持的联机训练能力扩展这条途径的申请范围,为有高即时的需求的真实应用使它有帮助。当 sLDA 和罐头高效地加速训练过程,用有不同尺寸的二数据集的确认证明建议途径有比较精确性。而且,它的好集中和联机训练能力为分析并且处理的大规模文章数据使它赚钱。 展开更多
关键词 文本处理 监督 平行 推理 随机 模特儿 DIRICHLET 计算机视觉
A NEW BOUNDARY CONDITION FOR RATE-TYPE NON-NEWTONIAN DIFFUSIVE MODELS AND THE STABLE MAC SCHEME
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作者 Kun Li Youngju Lee Christina Starkey 《计算数学:英文版》 SCIE CSCD 2018年第4期605-626,共22页
关键词 边界条件 MAC 稳定性 DIRICHLET 模型 牛顿 类型 NEUMANN
Predicting compositional time series via autoregressive Dirichlet estimation
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作者 Ganbin ZHOU Ping LUO Qing HE 《中国科学:信息科学(英文版)》 SCIE EI CSCD 2018年第9期268-270,共3页
关键词 DIRICHLET 时间 预言 评价 数据分析方法 数据建模 列数据 水文学
Event Detection and Identification of Influential Spreaders in Social Media Data Streams
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作者 Leilei Shi Yan Wu +2 位作者 Lu Liu Xiang Sun Liang Jiang 《大数据挖掘与分析(英文)》 2018年第1期34-46,共13页
Microblogging, a popular social media service platform, has become a new information channel for users to receive and exchange the most up-to-date information on current events. Consequently, it is a crucial platform ... Microblogging, a popular social media service platform, has become a new information channel for users to receive and exchange the most up-to-date information on current events. Consequently, it is a crucial platform for detecting newly emerging events and for identifying influential spreaders who have the potential to actively disseminate knowledge about events through microblogs. However, traditional event detection models require human intervention to detect the number of topics to be explored, which significantly reduces the efficiency and accuracy of event detection. In addition, most existing methods focus only on event detection and are unable to identify either influential spreaders or key event-related posts, thus making it challenging to track momentous events in a timely manner. To address these problems, we propose a Hypertext-Induced Topic Search(HITS) based Topic-Decision method(TD-HITS), and a Latent Dirichlet Allocation(LDA) based Three-Step model(TS-LDA). TDHITS can automatically detect the number of topics as well as identify associated key posts in a large number of posts. TS-LDA can identify influential spreaders of hot event topics based on both post and user information.The experimental results, using a Twitter dataset, demonstrate the effectiveness of our proposed methods for both detecting events and identifying influential spreaders. 展开更多
关键词 event detection MICROBLOGGING Hypertext-Induced Topic Search(HITS) Latent Dirichlet Allocation(LDA) IDENTIFICATION of influential SPREADER
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