The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main r...The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.展开更多
In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition...In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.展开更多
Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on ...Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on Herz-Morrey spaces on spaces of homogeneous type are obtained.展开更多
Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article ex...Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.展开更多
Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the cov...Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an adequate covering Lemma of Calderon-Zygmund type is shown, but also the boundedness of fractional maximal operators M α(0<α≤1) on some of homogeneous groups with respect to a given pair of weight functions (u,v) as above is proved. Moreover, a sufficient and necessary condition for M α∈B(u^qdx, v~~pdx), 0<α<1, 1<p<1α, and 1q=1p-α is also given. Finally, an application of the results is also obtained.展开更多
In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-ha...In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.展开更多
Let Ф be a Young function and MФ be the maximal operator associated with in the space of homogeneous type. In this paper, the composition of the maximal operators of type MФ is considered, and the result establishe...Let Ф be a Young function and MФ be the maximal operator associated with in the space of homogeneous type. In this paper, the composition of the maximal operators of type MФ is considered, and the result established by Carrozza and Passarelli Di Napoli is generalized to the space of homogeneous type.展开更多
In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our metho...In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.展开更多
In this paper, we study the convergence rates of solutions for second order elliptic equations with rapidly oscillating periodic coefficients in two-dimensional domain. We use an extension of the "mixed formulati...In this paper, we study the convergence rates of solutions for second order elliptic equations with rapidly oscillating periodic coefficients in two-dimensional domain. We use an extension of the "mixed formulation" approach to obtain the representation formula satisfied by the oscillatory solution and homogenized solution by means of the particularity of solutions for equations in two-dimensional case. Then we utilize this formula in combination with the asymptotic estimates of Green or Neumann functions for operators and uniform regularity estimates of solutions to obtain convergence rates in L^p for solutions as well as gradient error estimates for Dirichlet or Neumann problems respectively.展开更多
The phosphine-functionalized phosphonium-based ionic liquids(dppm-Q, dppe-Q, dppp-Q and dppb-Q) as the bi-functional ligands enable the efficient one-pot tandem hydroformylationeacetalization. It was found that, in dp...The phosphine-functionalized phosphonium-based ionic liquids(dppm-Q, dppe-Q, dppp-Q and dppb-Q) as the bi-functional ligands enable the efficient one-pot tandem hydroformylationeacetalization. It was found that, in dppm-Q, dppe-Q, dppp-Q and dppb-Q, the incorporated phosphino-fragments were responsible for Rh-catalyzed hydroformylation and the phosphoniums were in charge of the subsequent acetalization as the Lewis acid catalysts. Moreover, the diphosphonium-based ionic liquid of dppb-DQ could be applied as a co-solvent to immobilize the Rh/dppb-Q catalytic system with the advantages of the improved catalytic performance, the available catalyst recyclability, and the wide generality for the substrates.展开更多
In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed poi...In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.展开更多
目的基于静息态功能磁共振技术探究脑安滴丸治疗偏头痛的中枢机制。方法纳入19例偏头痛患者作为观察组,16例健康受试者作为对照组。观察组给予12周的脑安滴丸治疗,对照组不予任何干预。观察组在治疗前后进行静息态功能磁共振(resting st...目的基于静息态功能磁共振技术探究脑安滴丸治疗偏头痛的中枢机制。方法纳入19例偏头痛患者作为观察组,16例健康受试者作为对照组。观察组给予12周的脑安滴丸治疗,对照组不予任何干预。观察组在治疗前后进行静息态功能磁共振(resting state function magnetic resonance imaging,rs-fMRI)扫描,对照组仅在入组当天进行1次扫描。记录观察组治疗前后、随访4周头痛发作天数、头痛发作次数、头痛持续时间、视觉模拟评分(visual analogue scale,VAS)及患者报告的结局(patients-reported outcomes,PRO)量表评分。分析治疗前两组间的低频振幅(amplitude of low frequency fluctuation,ALFF)、局部一致性(regional homogeneity,ReHo)差异脑区,以ALFF、ReHo的共同差异脑区为感兴趣脑区(region of interest,ROI),分析计算观察组治疗前后ROI与全脑体素的功能连接(functional connectivity,FC)变化,并将FC的变化值与临床数据的改善值进行Pearson相关分析。结果观察组治疗后、随访4周的头痛发作天数、头痛发作次数、头痛持续时间及PRO量表评分均显著低于治疗前(P<0.05),且观察组随访4周的VAS评分亦显著降低(P<0.05);与对照组比较,治疗前观察组左侧背外侧额上回、右侧前扣带和旁扣带脑回、右侧岛叶、双侧内侧额上回、双侧额中回和左侧楔前叶的ALFF值显著降低(P<0.05),右侧中央前回的ReHo值显著升高(P<0.05),左侧楔前叶的ReHo值显著降低(P<0.05)。以左侧楔前叶为ROI,治疗后左侧楔前叶与左侧壳核的FC值较治疗前降低(P<0.05),未发现治疗前后FC的变化值与临床数据的相关性(P>0.05)。结论偏头痛患者存在认知、情感、感觉等多个脑区的功能活动异常,而脑安滴丸可能是通过调控楔前叶—壳核的FC达到治疗偏头痛的作用。展开更多
目的探讨心因性勃起功能障碍(pED)患者脑功能的改变以及其与异常社会心理状态之间的关系。方法选取10例pED患者(pED组)以及同期20例健康受试者(健康组)进行大脑静息态功能磁共振扫描,采用局部一致性技术(ReHo)和低频振幅(ALFF)分析,通...目的探讨心因性勃起功能障碍(pED)患者脑功能的改变以及其与异常社会心理状态之间的关系。方法选取10例pED患者(pED组)以及同期20例健康受试者(健康组)进行大脑静息态功能磁共振扫描,采用局部一致性技术(ReHo)和低频振幅(ALFF)分析,通过双样本t检验比较组间差异。通过Pearson相关分析评估差异脑区与临床特征之间的相关性。另外,以中央前回、中央后回作为感兴趣区(region of interest ROI),计算全脑FC值,并对结果进行多重比较校正。结果1)IIEF-5、SAS、SDS评分差异有统计学意义(P<0.01),pED患者IIEF-5显著低于健康受试者,SAS、SDS评分高于健康受试者;2)pED患者右侧辅助运动区(supplementary motor area,SMA)和左侧尾状核的ALFF值升高;3)pED患者壳核和SMA的ReHo值上升,右侧小脑皮质区的ReHo值降低;4)中央前回与右侧小脑后叶、右侧额中回、右侧角回及右侧楔前叶之间FC值升高;5)中央后回与右侧眶部额中回、右侧中央沟盖、右侧楔前叶FC值升高;6)pED患者左侧尾状核、SMA ALFF值与IIEF-5、自尊心和性关系问卷(SEAR)、勃起功能质量表(QEQ)呈正相关。壳核与SMA呈正相关,而右侧小脑皮质Crus2区ReHo值与IIEF-5、SEAR、QEQ评分为负相关。结论pED患者在SMA、尾状核和壳核脑区活动异常,并与性功能和心理状态密切相关。另外pED患者异常的中央前回、中央后回-DMN连接可能是导致pED的重要因素。展开更多
基金Supported by the NNSF of China (10371092)the Foundation of Wuhan University.
文摘The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.
基金Supported by the National Nature Science Foundation of China(10671009,60534080,10871149)
文摘In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.
基金Supported by Natural Science Foundation of Xinjiang University Supported by the NNSF of Chlna（10861010） Supported by Research Starting Foundation for Doctors of Xinjiang University（BS090102）
文摘Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on Herz-Morrey spaces on spaces of homogeneous type are obtained.
基金Supported by Chinese Universities Scientific Fund(2009RC0703 of BUPT)the NNSF of China (10871024)
文摘Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.
文摘Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an adequate covering Lemma of Calderon-Zygmund type is shown, but also the boundedness of fractional maximal operators M α(0<α≤1) on some of homogeneous groups with respect to a given pair of weight functions (u,v) as above is proved. Moreover, a sufficient and necessary condition for M α∈B(u^qdx, v~~pdx), 0<α<1, 1<p<1α, and 1q=1p-α is also given. Finally, an application of the results is also obtained.
基金supported by National Natural Science Foundation of China(11401310)Natural Science Foundation of Jiangsu Province(BK20140965)+2 种基金High level talent research fund of Nanjing Forestry University(G2014022)supported by the overseas research program of Jiangsu Provincesponsored by Qing Lan Project of Jiangsu Province
文摘In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.
基金Supported by the NSF from the Education Department of Henan Province(2007110006)
文摘Let Ф be a Young function and MФ be the maximal operator associated with in the space of homogeneous type. In this paper, the composition of the maximal operators of type MФ is considered, and the result established by Carrozza and Passarelli Di Napoli is generalized to the space of homogeneous type.
基金partly supported by Natural Science Foundation of China(11471332 and 11071246)
文摘In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.
基金Supported by the NNSF of Chian（11626239, 11626238） Supported by the Natural Science Foundation of Henan Province（152300410227）
文摘In this paper, we study the convergence rates of solutions for second order elliptic equations with rapidly oscillating periodic coefficients in two-dimensional domain. We use an extension of the "mixed formulation" approach to obtain the representation formula satisfied by the oscillatory solution and homogenized solution by means of the particularity of solutions for equations in two-dimensional case. Then we utilize this formula in combination with the asymptotic estimates of Green or Neumann functions for operators and uniform regularity estimates of solutions to obtain convergence rates in L^p for solutions as well as gradient error estimates for Dirichlet or Neumann problems respectively.
基金financially supported by the National Natural Science Foundation of China(Nos.21673077,21473058,and 21273077)
文摘The phosphine-functionalized phosphonium-based ionic liquids(dppm-Q, dppe-Q, dppp-Q and dppb-Q) as the bi-functional ligands enable the efficient one-pot tandem hydroformylationeacetalization. It was found that, in dppm-Q, dppe-Q, dppp-Q and dppb-Q, the incorporated phosphino-fragments were responsible for Rh-catalyzed hydroformylation and the phosphoniums were in charge of the subsequent acetalization as the Lewis acid catalysts. Moreover, the diphosphonium-based ionic liquid of dppb-DQ could be applied as a co-solvent to immobilize the Rh/dppb-Q catalytic system with the advantages of the improved catalytic performance, the available catalyst recyclability, and the wide generality for the substrates.
基金Supported by the Youth Science Foundation of China（l1201272） Supported by the Youth Science Foundatioa of Shanxi Province（2010021002-1）
文摘In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.
文摘目的基于静息态功能磁共振技术探究脑安滴丸治疗偏头痛的中枢机制。方法纳入19例偏头痛患者作为观察组,16例健康受试者作为对照组。观察组给予12周的脑安滴丸治疗,对照组不予任何干预。观察组在治疗前后进行静息态功能磁共振(resting state function magnetic resonance imaging,rs-fMRI)扫描,对照组仅在入组当天进行1次扫描。记录观察组治疗前后、随访4周头痛发作天数、头痛发作次数、头痛持续时间、视觉模拟评分(visual analogue scale,VAS)及患者报告的结局(patients-reported outcomes,PRO)量表评分。分析治疗前两组间的低频振幅(amplitude of low frequency fluctuation,ALFF)、局部一致性(regional homogeneity,ReHo)差异脑区,以ALFF、ReHo的共同差异脑区为感兴趣脑区(region of interest,ROI),分析计算观察组治疗前后ROI与全脑体素的功能连接(functional connectivity,FC)变化,并将FC的变化值与临床数据的改善值进行Pearson相关分析。结果观察组治疗后、随访4周的头痛发作天数、头痛发作次数、头痛持续时间及PRO量表评分均显著低于治疗前(P<0.05),且观察组随访4周的VAS评分亦显著降低(P<0.05);与对照组比较,治疗前观察组左侧背外侧额上回、右侧前扣带和旁扣带脑回、右侧岛叶、双侧内侧额上回、双侧额中回和左侧楔前叶的ALFF值显著降低(P<0.05),右侧中央前回的ReHo值显著升高(P<0.05),左侧楔前叶的ReHo值显著降低(P<0.05)。以左侧楔前叶为ROI,治疗后左侧楔前叶与左侧壳核的FC值较治疗前降低(P<0.05),未发现治疗前后FC的变化值与临床数据的相关性(P>0.05)。结论偏头痛患者存在认知、情感、感觉等多个脑区的功能活动异常,而脑安滴丸可能是通过调控楔前叶—壳核的FC达到治疗偏头痛的作用。
文摘目的探讨心因性勃起功能障碍(pED)患者脑功能的改变以及其与异常社会心理状态之间的关系。方法选取10例pED患者(pED组)以及同期20例健康受试者(健康组)进行大脑静息态功能磁共振扫描,采用局部一致性技术(ReHo)和低频振幅(ALFF)分析,通过双样本t检验比较组间差异。通过Pearson相关分析评估差异脑区与临床特征之间的相关性。另外,以中央前回、中央后回作为感兴趣区(region of interest ROI),计算全脑FC值,并对结果进行多重比较校正。结果1)IIEF-5、SAS、SDS评分差异有统计学意义(P<0.01),pED患者IIEF-5显著低于健康受试者,SAS、SDS评分高于健康受试者;2)pED患者右侧辅助运动区(supplementary motor area,SMA)和左侧尾状核的ALFF值升高;3)pED患者壳核和SMA的ReHo值上升,右侧小脑皮质区的ReHo值降低;4)中央前回与右侧小脑后叶、右侧额中回、右侧角回及右侧楔前叶之间FC值升高;5)中央后回与右侧眶部额中回、右侧中央沟盖、右侧楔前叶FC值升高;6)pED患者左侧尾状核、SMA ALFF值与IIEF-5、自尊心和性关系问卷(SEAR)、勃起功能质量表(QEQ)呈正相关。壳核与SMA呈正相关,而右侧小脑皮质Crus2区ReHo值与IIEF-5、SEAR、QEQ评分为负相关。结论pED患者在SMA、尾状核和壳核脑区活动异常,并与性功能和心理状态密切相关。另外pED患者异常的中央前回、中央后回-DMN连接可能是导致pED的重要因素。
