TWO-PARAMETER

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Convex PBW-type Lyndon Bases and Restricted Two-parameter Quantum Group of Type F_(4)
《Acta Mathematica Sinica,English Series》2023年第6期1053-1084,共32页Xiao Yu CHEN Nai Hong HU Xiu Ling WANG 
Nai Hong Hu is supported by the NNSF of China(Grant Nos.12171155,12071094);in part by Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)。
The convex PBW-type Lyndon basis for two-parameter quantum group U_(r,s)(F_(4))is given.Assume thatrs^(-1)is a primitive l-th root of unity with l odd,then the restricted quantum group u_(r,s)(F_(4))as a quotient of U...
关键词：Convex PBW-type Lyndon basis restricted 2-parameter quantum groups INTEGRALS ribbon Hopf algebra 
Derivations of the Positive Part of the Two-parameter Quantum Group of Type G_(2)
《Acta Mathematica Sinica,English Series》2021年第9期1471-1484,共14页Yong Yue ZHONG Xiao Min TANG 
Supported by National Natural Science Foundation of China(Grant No.11771069);Natural Science Foundation of Heilongjiang Province(Grant No.LH2020A020)。
In this paper,we compute the derivations of the positive part of the two-parameter quantum group of type G_(2) by embedding it into a quantum torus.We also show that the first Hochschild cohomology group of this algeb...
关键词：Two-parameter quantum group DERIVATION Hochschild cohomology group 
Derivations and Automorphisms of the Positive Part of the Two-parameter Quantum Group U_(r,s)(B_3)被引量：1
《Acta Mathematica Sinica,English Series》2017年第2期235-251,共17页Min LI Xiu Ling WANG 
supported by Specialized Research Fund for the Doctoral Program of Highter Education(Grant No.20130031110005);supported by NSFC(Grant No.11271131)
We compute the derivations of the positive part of the two-parameter quantum group Ur,s（B3） and show that the Hochschild cohomology group of degree 1 of this algebra is a three- dimensional vector space over the bas...
关键词：Two-parameter quantum group ore extension hochschild cohomology group （Hopf） al- gebra automorphism 
Quasi-sure Product Variation of Two-parameter Smooth Martingales on the Wiener Space被引量：1
《Acta Mathematica Sinica,English Series》2006年第4期1103-1114,共12页Ji Cheng LIU 
Project 973 and NSF(No.10526020)of China
In this paper, we prove that the process of product variation of a two-parameter smooth martingale admits an ∞ modification, which can be constructed as the quasi-sure limit of sum of the corresponding product variat...
关键词：quasi-sure ∞-modification smooth martingale product variation Kolmogorov＇s criterion 
A. S. Convergence of Two-Parameter Banach Space Valued Martingales and the Radon-Nikodym Property of Banach Spaces
《Acta Mathematica Sinica,English Series》1999年第2期187-196,共10页Shixin Gan, Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China 
Project supported by the National Natural Science Foundation of China;the State Education Commission Ph. D. Station Foundation
In this paper, we prove that under the F4 condition, any L log+ L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable...
关键词：Two-parameter Banach space valued martingale A. S. convergence Radon-Nikodym property F4 condition Local F4 condition 
Uniqueness Theorem of Solutions for Stochastic Differential Equation in the Plane被引量：1
《Acta Mathematica Sinica,English Series》1998年第4期495-500,201+502-506,共12页Liang Zongxia, Department of Applied Mathematics, Tsinghua University Beijing 100084, China 
Supported by the National Science Foundation;the Postdoctoral Science Foundation of China
Let M = {Mz, z∈R+2} be a continuous square integrable martingale and A = {Az, z∈ R+2} be a continuous adapted increasing process. Consider the follow...
关键词：Two-parameter S. D. E.  Two-parameter martingale ITO’s formula Pathwise uniqueness Gronwall’s-Bellman lemma 
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