In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) i...In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.展开更多
In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point res...In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.展开更多
In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,...In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.展开更多
The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappin...The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappings with bounded length distortions.Then,using these results,we establish five Landau-type theorems for subclasses of polyharmonic mappings F and L(F),where F has bounded length distortion and L is a differential operator.展开更多
目的基于T2^(*)mapping定量分析业余马拉松运动员足踝部关节软骨的T2^(*)值,并分析其与性别、年龄、身体质量指数(body mass index,BMI)、跑龄、跑量之间的相关性。材料与方法于2023年7月份至2023年9月份招募重庆市长跑运动爱好者48名,...目的基于T2^(*)mapping定量分析业余马拉松运动员足踝部关节软骨的T2^(*)值,并分析其与性别、年龄、身体质量指数(body mass index,BMI)、跑龄、跑量之间的相关性。材料与方法于2023年7月份至2023年9月份招募重庆市长跑运动爱好者48名,其中跑量<300 km/月的36例(中低跑量组),跑量≥300 km/月的12例(高跑量组)。所有受试者均进行单侧无症状踝关节的MRI扫描,扫描序列包括T2^(*)mapping多回波自旋回波(spin echo,SE)序列矢状位、质子密度加权成像脂肪抑制(proton density-weighted imaging fat-saturated,PDWI-FS)序列矢状位、冠状位、横轴位以及T1加权脂肪抑制成像(T1-weighted imaging fat-saturated,T1WI-FS)序列横轴位。沿关节软骨轮廓边缘勾画距骨穹窿、跟骰关节跟骨面、骰骨面及后距下关节跟骨面、距骨面软骨作为感兴趣区(region of interest,ROI),获得相应的T2^(*)值。采用线性回归分析软骨T2^(*)值与年龄、BMI、跑龄的相关性,采用独立样本t检验分析不同跑量及不同性别间的软骨T2^(*)值差异。结果(1)距骨穹窿、跟骰关节跟骨面及骰骨面、后距下关节跟骨面及距骨面软骨T2^(*)值在性别上的差异均具有统计学意义(P=0.001、P<0.001、P=0.002、P=0.008、P=0.004);(2)高跑量组的距骨穹窿、后距下关节跟骨面软骨T2^(*)值高于中低跑量组(P=0.014、0.023),不同跑量的跟骰关节跟骨面及骰骨面、后距下关节距骨面软骨T2^(*)值的差异均无统计学意义(P=0.987、0.072、0.724);(3)距骨穹窿、跟骰关节跟骨面及骰骨面、后距下关节跟骨面、距骨面软骨T2^(*)值均与BMI呈正相关(r=0.376、0.384、0.300、0.422、0.455,P=0.005、0.004、0.019、0.001、0.001)。结论在业余马拉松运动员这一跑步群体中,与中低跑量相比,高跑量更有可能导致距骨穹窿、后距下关节跟骨面软骨损伤;而与较低的BMI相比,高BMI增加了距骨穹窿、跟骰关节跟骨面、骰骨面及后距下关节跟骨面、距骨面软骨损伤的风险。展开更多
In this paper,we study a subclass of close-to-convex harmonic mappings whose analytic parts are starlike mappings.We derive some properties and characteristics for this class,such as the bounds of Toeplitz determinant...In this paper,we study a subclass of close-to-convex harmonic mappings whose analytic parts are starlike mappings.We derive some properties and characteristics for this class,such as the bounds of Toeplitz determinants,bounds of Hankel determinants,Zalcman functional and Bohr's inequality.展开更多
【目的】探究丝裂原活化蛋白激酶激酶6(mitogen-activated protein kinase kinase6,MAP2K6)基因在湖羊不同发育阶段背最长肌组织中的表达水平,分析该基因的多态性与湖羊生长性状之间的相关性,以期为湖羊的生长性状分子育种提供新的标记...【目的】探究丝裂原活化蛋白激酶激酶6(mitogen-activated protein kinase kinase6,MAP2K6)基因在湖羊不同发育阶段背最长肌组织中的表达水平,分析该基因的多态性与湖羊生长性状之间的相关性,以期为湖羊的生长性状分子育种提供新的标记资源。【方法】利用实时荧光定量PCR检测MAP2K6基因在湖羊(n=15)不同发育阶段背最长肌组织中的表达情况;通过Illumina OvineSNP 50K BeadChip检测湖羊(n=3024)MAP2K6基因的单核苷酸多态性(SNP),利用一般线性模型分析MAP2K6基因SNP位点与湖羊(n=1974)生长性状间的关联性,并使用R语言corrplot包计算湖羊体重与各体尺指标的相关系数。【结果】实时荧光定量PCR检测结果显示,湖羊背最长肌组织中MAP2K6基因表达量在初生到4月龄阶段逐渐升高,且3、4月龄的表达量均极显著高于初生、45日龄和6月龄(P<0.01)。湖羊MAP2K6基因中共检测到2个位点:rs414959578G>A和rs426057803A>G。关联分析结果显示,MAP2K6基因rs414959578G>A位点对湖羊5月龄体重、体高、体斜长、胸围、胸深、胸宽、十字部高、腰角宽,以及6月龄胸围、背膘厚有显著或极显著影响(P<0.05;P<0.01);rs426057803A>G位点对湖羊3月龄管围,5月龄胸围、管围和十字部高以及6月龄背膘厚有显著或极显著影响(P<0.05;P<0.01)。相关性分析结果显示,湖羊体重与体尺指标间存在显著正相关(P<0.05),但6月龄湖羊体斜长与6月龄胸宽、腰角宽,5月龄管围与6月龄腰角宽均不存在显著相关(P>0.05)。【结论】MAP2K6基因与湖羊背最长肌的发育相关,rs414959578G>A和rs426057803A>G位点对湖羊生长性状有显著影响。研究结果可为湖羊生长性状分子标记的挖掘和利用提供一定的理论依据。展开更多
In this paper,we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings.Meanwhile,we introduce a concept of I-Hurewicz boundedness,study some basic topological operati...In this paper,we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings.Meanwhile,we introduce a concept of I-Hurewicz boundedness,study some basic topological operations of them.Finally,we obtain an equivalent characterization of I-Hurewicz boundedness in uniform spaces.展开更多
基金supported by the National Natural Science Foundation of China(12061035)the Research Foundation of Jiangxi Science and Technology Normal University of China(2021QNBJRC003)supported by the Graduate Innovation Fund of Jiangxi Science and Technology Normal University(YC2024-X10).
文摘In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.
基金funded by National Science,Research and Innovation Fund(NSRF)King Mongkut's University of Technology North Bangkok with Contract No.KMUTNB-FF-68-B-46.
文摘In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)。
文摘In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)supported by the Youth Innovation Foundation of Shenzhen Polytechnic University(6024310023K)。
文摘The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappings with bounded length distortions.Then,using these results,we establish five Landau-type theorems for subclasses of polyharmonic mappings F and L(F),where F has bounded length distortion and L is a differential operator.
基金Supported by the Natural Science Foundation of Hunan Province(Grant No.2022JJ30185)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.KYCX230410)+2 种基金the China Scholarship Council(Grant No.202306840137)the National Natural Science Foundation of China(Grant No.62063029)the Science and Technology Support Project of Pingxiang City(Grant No.2020C0102)。
文摘In this paper,we study a subclass of close-to-convex harmonic mappings whose analytic parts are starlike mappings.We derive some properties and characteristics for this class,such as the bounds of Toeplitz determinants,bounds of Hankel determinants,Zalcman functional and Bohr's inequality.
基金Supported by the National Natural Science Foundation of China(Grant No.12171015)the Natural Science Foundation of Fujian Province(Grant Nos.2023J011078+1 种基金2020J05230)the Project of Innovation Groups of Ningde Normal University(Grant No.2023T01)。
文摘In this paper,we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings.Meanwhile,we introduce a concept of I-Hurewicz boundedness,study some basic topological operations of them.Finally,we obtain an equivalent characterization of I-Hurewicz boundedness in uniform spaces.
