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
In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided...In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.展开更多
In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the compl...In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result.展开更多
In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged ...In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.展开更多
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo...Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.展开更多
In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the d...In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works.展开更多
The study integrates both the geological and geophysical mapping techniques for groundwater potential studies at Ekwegbe-Agu and the environs, Enugu state, Nigeria for optimal citing of borehole. Located in the Anambr...The study integrates both the geological and geophysical mapping techniques for groundwater potential studies at Ekwegbe-Agu and the environs, Enugu state, Nigeria for optimal citing of borehole. Located in the Anambra Basin between latitudes 6˚43'N and 6˚47'N and longitudes 7˚28'E and 7˚32'E, it is stratigraphycally underlain by, from bottom to top, the Enugu/Nkporo, Mamu and Ajali Formation respectively, a complex geology that make citing of productive borehole in the area problematic leading to borehole failure and dry holes due to inadequate sampling. The study adopted a field and analytic sampling approach, integrating field geological, electrical resistivity and self-potential methods. The software, SedLog v3.1, InterpexIx1Dv.3, and Surfer v10 were employed for the data integration and interpretation. The result of the geological field and borehole data shows 11 sedimentary facies consisting of sandstone, shales and heterolith of sandstone/shale, with the aquifer zone mostly prevalent in the more porous sand-dominated horizons. Mostly the AK and HK were the dominant curve types. An average of 6 geo-electric layers were delineated across all transects with resistivity values ranging from 25.42 - 105.85 Ωm, 186.38 - 3383.3 Ωm, and 2992 - 6286.4 Ωm in the Enugu, Mamu and Ajali Formations respectively. The resistivity of the main aquifer layer ranges from 1 to 500 Ωm. The aquifer thickness within the study area varies between 95 and 140 m. The western and northwestern part of the study area which is underlain mainly by the Ajali Formation showed the highest groundwater potential in the area and suitable for citing productive boreholes.展开更多
A new variant,JN.1,stemming from the omicron subvariant BA.2.86,garnered the attention of the World Health Organization(WHO)as a"variant of interest."Despite its rapid global spread,especially in the US,Cana...A new variant,JN.1,stemming from the omicron subvariant BA.2.86,garnered the attention of the World Health Organization(WHO)as a"variant of interest."Despite its rapid global spread,especially in the US,Canada,France,Singapore,Sweden[1],and the UK,JN.1 is considered to pose minimal danger.Current vaccinations are believed to remain effective against it.The WHO underscores the importance of maintaining immunization records amid co-occurring respiratory illnesses,and epidemiologists recommend monitoring hospitalizations,particularly in areas with low vaccination rates.展开更多
Amyotrophic lateral sclerosis(ALS)is a rare neurological disease,featuring gradual loss of muscle controls due to degeneration of motor neurons.Unfortunately,there is currently no cure for ALS.The available therapies ...Amyotrophic lateral sclerosis(ALS)is a rare neurological disease,featuring gradual loss of muscle controls due to degeneration of motor neurons.Unfortunately,there is currently no cure for ALS.The available therapies only offer a limited extension of survival by several months,begging for more options of therapeutics.展开更多
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.
文摘背景:腰椎小关节炎是引起下腰痛的一个主要原因,目前主要依靠MRI进行初步定性诊断,但仍有一定漏诊、误诊的概率发生,因此MR T2^(*)mapping成像技术有望成为定量检查腰椎小关节炎软骨损伤的重要检测手段。目的:探讨MR T2^(*)mapping成像技术在定量分析腰椎小关节炎软骨损伤退变中的应用价值。方法:收集南京医科大学第四附属医院2020年4月至2022年3月门诊或住院合并下腰痛共110例患者,设为病例组;同时招募无症状志愿者80例,设为对照组。对所有纳入对象L1-S1的小关节行3.0 T MR扫描,获取T2^(*)mapping横断位图像和T2WI图像,分别对所有小关节软骨进行Weishaupt分级及T2^(*)值测量,收集数据并行统计学分析。不同小关节Weishaupt分级之间小关节软骨T2^(*)值比较采用单因素方差分析。结果与结论:①经统计分析发现,病例组腰椎小关节软骨T2^(*)值(17.6±1.5)ms明显较对照组(21.4±1.3)ms降低,差异有显著性意义(P<0.05);②在病例组中,随着腰椎小关节Weishaupt分级增加,小关节软骨T2^(*)值也呈逐渐下降趋势,且这种差异有显著性意义(P<0.05);③提示T2^(*)mapping能够较好地显示腰椎小关节软骨损伤的早期病理变化,腰椎小关节软骨的T2^(*)值能够定量评估腰椎小关节的软骨损伤程度;T2^(*)mapping成像技术能为影像学诊断腰椎小关节炎软骨早期损伤提供很好的理论依据,具有重要的临床应用价值。
文摘In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.
文摘In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result.
文摘In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.
基金Supported by the NNSF of China(11971165)the Natural Science Foundation of Zhejiang Province(LY21A010003)。
文摘Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.
基金the National Natural Science Foundation of China(12071354)XIONG was the National Natural Science Foundation of China(12061035)+2 种基金the Jiangxi Provincial Natural Science Foundation(20212BAB201012)the Research Foundation of Jiangxi Provincial Department of Education(GJJ201104)the Research Foundation of Jiangxi Science and Technology Normal University(2021QNBJRC003)。
文摘In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works.
文摘The study integrates both the geological and geophysical mapping techniques for groundwater potential studies at Ekwegbe-Agu and the environs, Enugu state, Nigeria for optimal citing of borehole. Located in the Anambra Basin between latitudes 6˚43'N and 6˚47'N and longitudes 7˚28'E and 7˚32'E, it is stratigraphycally underlain by, from bottom to top, the Enugu/Nkporo, Mamu and Ajali Formation respectively, a complex geology that make citing of productive borehole in the area problematic leading to borehole failure and dry holes due to inadequate sampling. The study adopted a field and analytic sampling approach, integrating field geological, electrical resistivity and self-potential methods. The software, SedLog v3.1, InterpexIx1Dv.3, and Surfer v10 were employed for the data integration and interpretation. The result of the geological field and borehole data shows 11 sedimentary facies consisting of sandstone, shales and heterolith of sandstone/shale, with the aquifer zone mostly prevalent in the more porous sand-dominated horizons. Mostly the AK and HK were the dominant curve types. An average of 6 geo-electric layers were delineated across all transects with resistivity values ranging from 25.42 - 105.85 Ωm, 186.38 - 3383.3 Ωm, and 2992 - 6286.4 Ωm in the Enugu, Mamu and Ajali Formations respectively. The resistivity of the main aquifer layer ranges from 1 to 500 Ωm. The aquifer thickness within the study area varies between 95 and 140 m. The western and northwestern part of the study area which is underlain mainly by the Ajali Formation showed the highest groundwater potential in the area and suitable for citing productive boreholes.
文摘A new variant,JN.1,stemming from the omicron subvariant BA.2.86,garnered the attention of the World Health Organization(WHO)as a"variant of interest."Despite its rapid global spread,especially in the US,Canada,France,Singapore,Sweden[1],and the UK,JN.1 is considered to pose minimal danger.Current vaccinations are believed to remain effective against it.The WHO underscores the importance of maintaining immunization records amid co-occurring respiratory illnesses,and epidemiologists recommend monitoring hospitalizations,particularly in areas with low vaccination rates.
基金supported by the TARCC,Welch Foundation Award(1-1724)the Decherd Foundation,the Pope Adarms FoundationNIH grants NS092616,NS127375,NS117065,and NS111776(to CLZ)。
文摘Amyotrophic lateral sclerosis(ALS)is a rare neurological disease,featuring gradual loss of muscle controls due to degeneration of motor neurons.Unfortunately,there is currently no cure for ALS.The available therapies only offer a limited extension of survival by several months,begging for more options of therapeutics.
