In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequal...In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequalities.展开更多
Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-...Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.展开更多
The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.I...The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.展开更多
By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antino...By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.展开更多
We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by...We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.展开更多
目的龙江医派知名医家陈景河先生的益脑通络方在临床上治疗缺血性中风效果明显,但是其治疗机制方面的研究尚浅。文章基于中医药整合药理学研究平台(Integrative Pharmacology-based Research Platform of Traditional Chinese Medicine,...目的龙江医派知名医家陈景河先生的益脑通络方在临床上治疗缺血性中风效果明显,但是其治疗机制方面的研究尚浅。文章基于中医药整合药理学研究平台(Integrative Pharmacology-based Research Platform of Traditional Chinese Medicine,TCMIP)探讨益脑通络方治疗缺血性中风的分子机制。方法利用该平台筛选方剂的活性成分并预测其靶点;基于方剂靶点与疾病靶点的匹配结果筛选方剂-疾病的关键靶点,并对关键靶点进行基因本体论(gene ontology,GO)功能、生物过程(Reactome)富集分析;通过构建蛋白互作网络(protein-protein interaction network,PPI)、构建“中药-成分-靶点-通路”网络,分析并筛选益脑通络方治疗缺血性中风的主要活性成分和核心靶点;进一步对核心靶点与主要活性成分进行分子对接,以虚拟验证其结合能力并分析其结合模式。对核心活性成分和核心靶点进行分子对接验证。结果获得益脑通络方治疗缺血性中风的主要活性成分40种,关键靶点18个,包括了APP、PIK3CA等,GO功能分析主要富集在对凋亡的调控上,Reactome信号通路涉及了凋亡途径、炎症途径、基因调控、血管通路、神经再生、突触传导、细胞自噬等多途径。分子对接结果显示主要活性成分与核心靶蛋白具有结合力,川芎的萘呋内酯结合能力最强。结论益脑通络方中的萘呋内酯等多种活性成分能够作用于APP、PIK3CA等多靶点、通过促红细胞生成素(erythropietin,EPO)激活的PI3K等多通路,在缺血性中风中主要发挥抗凋亡等作用。展开更多
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan...Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.展开更多
基金supported by the Natural Science Foundation of China(11901005,12071003)the Natural Science Foundation of Anhui Province(2008085QA20)。
文摘In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequalities.
基金Supported by the National Natural Science Foundation of China(11871191)the Science Foundation of Hebei Province(A2023205006,A2019106037)+2 种基金the Key Development Foundation of Hebei Normal University in2024(L2024ZD08)the Graduate Student Innovation Project Fund of Hebei Province(CXZZBS2022066)the Key Foundation of Hebei Normal University(L2018Z01)。
文摘Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.
基金Supported by National Nature Science Foundation in China(12101564,11971425,11801508)Nature Science Foundation of Zhejiang province(LY22A010013)Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。
文摘The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)
文摘By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.
基金＊Supported by the National Natural Science Foundation of China under Grant No. 10775097, and the Natural Science Foundation of Heze University of Shandong Province, under Crant No. XY07WL01
文摘We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product （IWOP） of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.
文摘目的龙江医派知名医家陈景河先生的益脑通络方在临床上治疗缺血性中风效果明显,但是其治疗机制方面的研究尚浅。文章基于中医药整合药理学研究平台(Integrative Pharmacology-based Research Platform of Traditional Chinese Medicine,TCMIP)探讨益脑通络方治疗缺血性中风的分子机制。方法利用该平台筛选方剂的活性成分并预测其靶点;基于方剂靶点与疾病靶点的匹配结果筛选方剂-疾病的关键靶点,并对关键靶点进行基因本体论(gene ontology,GO)功能、生物过程(Reactome)富集分析;通过构建蛋白互作网络(protein-protein interaction network,PPI)、构建“中药-成分-靶点-通路”网络,分析并筛选益脑通络方治疗缺血性中风的主要活性成分和核心靶点;进一步对核心靶点与主要活性成分进行分子对接,以虚拟验证其结合能力并分析其结合模式。对核心活性成分和核心靶点进行分子对接验证。结果获得益脑通络方治疗缺血性中风的主要活性成分40种,关键靶点18个,包括了APP、PIK3CA等,GO功能分析主要富集在对凋亡的调控上,Reactome信号通路涉及了凋亡途径、炎症途径、基因调控、血管通路、神经再生、突触传导、细胞自噬等多途径。分子对接结果显示主要活性成分与核心靶蛋白具有结合力,川芎的萘呋内酯结合能力最强。结论益脑通络方中的萘呋内酯等多种活性成分能够作用于APP、PIK3CA等多靶点、通过促红细胞生成素(erythropietin,EPO)激活的PI3K等多通路,在缺血性中风中主要发挥抗凋亡等作用。
基金supported by the NSF of Hebei Province(A2022208007)the NSF of China(11571089,11871191)the NSF of Henan Province(222300420397)。
文摘Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
