Ishikawa Iterative Process with Errors for Lipschitzian and φ-Hemicontractive Mappings in Banach Spaces

本文在任意Ｂａｎａｃｈ空间中研究了Ｌｉｐｓｃｈｉｔｚφ－半压缩映象与φ－强拟增生映象的带误差项的Ｉｓｈｉｋａｗａ迭代过程，使用新的分析技巧建立了几个强收敛定理．

ITERATIVE APPROXIMATIONS OF φ-HEMICONTRACTIVEMAPPINGS WITHOUT LIPSCHITZ ASSUMPTION

Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E by Hx=f+x-Tx,and suppose that the range of H is bounded. for any x1 E let {xn}∞n=qin E be the Ishikawa iterative process defined by Under suitable comditions,the Ishikawa iterative process strongly converges to the unique solution of Tx=f.the related result deals with the problems that Ishikawa iterative process strongly converges to the unique fixed point of -hemicontractive mappings.These results generalize results of Osilike [2],Chidume[4,5]and Tan[10],Zeng[11]and several other results from the class of strongly assertive operators and the class of strongly pseudocontractive operators to the much more general class of -trongly accrtive and class of -hemicontractive maps.

ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

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.

ON THE UNIVALENCE OF CERTAIN POLYHARMONIC MAPPINGS WITH BOUNDED LENGTH DISTORTIONS

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.

A novel three-step implicit iteration process for threeΦ-hemicontractive mapping in the intermediate sense

In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.

Leveraging ROTI map derived from Indonesian GNSS receiver network for advancing study of Equatorial Plasma Bubble in Southeast/East Asia

This paper highlights the crucial role of Indonesia’s GNSS receiver network in advancing Equatorial Plasma Bubble(EPB)studies in Southeast and East Asia,as ionospheric irregularities within EPB can disrupt GNSS signals and degrade positioning accuracy.Managed by the Indonesian Geospatial Information Agency(BIG),the Indonesia Continuously Operating Reference Station(Ina-CORS)network comprises over 300 GNSS receivers spanning equatorial to southern low-latitude regions.Ina-CORS is uniquely situated to monitor EPB generation,zonal drift,and dissipation across Southeast Asia.We provide a practical tool for EPB research,by sharing two-dimensional rate of Total Electron Content(TEC)change index(ROTI)derived from this network.We generate ROTI maps with a 10-minute resolution,and samples from May 2024 are publicly available for further scientific research.Two preliminary findings from the ROTI maps of Ina-CORS are noteworthy.First,the Ina-CORS ROTI maps reveal that the irregularities within a broader EPB structure persist longer,increasing the potential for these irregularities to migrate farther eastward.Second,we demonstrate that combined ROTI maps from Ina-CORS and GNSS receivers in East Asia and Australia can be used to monitor the development of ionospheric irregularities in Southeast and East Asia.We have demonstrated the combined ROTI maps to capture the development of ionospheric irregularities in the Southeast/East Asian sector during the G5 Geomagnetic Storm on May 11,2024.We observed simultaneous ionospheric irregularities in Japan and Australia,respectively propagating northwestward and southwestward,before midnight,whereas Southeast Asia’s equatorial and low-latitude regions exhibited irregularities post-midnight.By sharing ROTI maps from Indonesia and integrating them with regional GNSS networks,researchers can conduct comprehensive EPB studies,enhancing the understanding of EPB behavior across Southeast and East Asia and contributing significantly to ionospheric research.

Stability analysis of approximately multidimensional additive mappings on fuzzy spaces

The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.

HB-Continuous Mappings in L-Topological Space

In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.

A New Kind of Pre-Mean-Type Mappings and Its Gauss Iteration

A function which is reflexive is called by pre-mean, a more generalized definition of a mean. In this paper, we define a new pre-mean and study its properties, and then using the given invariant curve we consider the problem of convergence of Gauss iteration of a kind of pre-mean type mappings generated by the exponential and logarithmic functions.

Landslide Susceptibility Mapping Using RBFN-Based Ensemble Machine Learning Models

This study was aimed to prepare landslide susceptibility maps for the Pithoragarh district in Uttarakhand,India,using advanced ensemble models that combined Radial Basis Function Networks(RBFN)with three ensemble learning techniques:DAGGING(DG),MULTIBOOST(MB),and ADABOOST(AB).This combination resulted in three distinct ensemble models:DG-RBFN,MB-RBFN,and AB-RBFN.Additionally,a traditional weighted method,Information Value(IV),and a benchmark machine learning(ML)model,Multilayer Perceptron Neural Network(MLP),were employed for comparison and validation.The models were developed using ten landslide conditioning factors,which included slope,aspect,elevation,curvature,land cover,geomorphology,overburden depth,lithology,distance to rivers and distance to roads.These factors were instrumental in predicting the output variable,which was the probability of landslide occurrence.Statistical analysis of the models’performance indicated that the DG-RBFN model,with an Area Under ROC Curve(AUC)of 0.931,outperformed the other models.The AB-RBFN model achieved an AUC of 0.929,the MB-RBFN model had an AUC of 0.913,and the MLP model recorded an AUC of 0.926.These results suggest that the advanced ensemble ML model DG-RBFN was more accurate than traditional statistical model,single MLP model,and other ensemble models in preparing trustworthy landslide susceptibility maps,thereby enhancing land use planning and decision-making.

Compiling molecular evidence from a tetraploid rose genome into a near-saturated map for the identification of pigment-related genes

With their high economic value and cultural significance,modern roses are one of the most important ornamental plants.Because of their complicated genetic background and tetraploid nature,the creation of high-density genetic maps of roses has been a challenge that has slowed the pace of molecular breeding for modern roses.The current construction of tetraploid genetic maps based on existing diploid rose genomes could lead to inaccurate marker information and genotyping results.Therefore,we generated the first high-quality tetraploid genome of Rosa chinensis‘Yunzheng Xiawei.'Utilizing Illumina,PacBio,and Hi-C sequencing technologies,we assembled a genome of 858.59 Mb with 14pseudo-chromosomes.Mode of inheritance analysis using PolyOrigin indicated that modern roses show both quadrivalent and bivalent pairing.Based on this reference genome,high-density genetic maps were constructed using MSTmap with nearly saturated markers.Quantitative trait locus(QTL)analysis was conducted using WinQTLCart and R/qtl for flavonoids and carotenoids,and 11 QTL clusters were identified.By combining the genome annotation,phylogenetic analyses,and gene expression analyses,we were able to identify several key genes related to flavonoid and carotenoid biosynthesis.This study provides the basis for further genetic analyses of highly heterozygous tetraploid roses and could facilitate the progress of marker-assisted selection in modern roses.

Identification of long InDels through whole genome resequencing to fine map qIF05-1 for seed isoflavone content in soybean(Glycine max L. Merr.)

Soybean seed isoflavones are a type of secondary metabolites that can provide health and nutrition benefits for humans. In our previous study, a stable quantitative trait locus(QTL) qIF05-1 controlling the seed isoflavone content in soybean was detected on chromosome(Chr.) 05 in a recombinant inbred line(RIL) population from a cross of Huachun 2×Wayao. In this study, the parental lines were re-sequenced using the Illumina Solexa System with deep coverage. A total of 63,099 polymorphic long insertions and deletions(InDels)(≥15 bp)were identified between the parents Huachun 2 and Wayao. The InDels were unevenly distributed on 20chromosomes of soybean, varying from 1,826 in Chr. 12 to 4,544 in Chr. 18. A total of 10,002 long InDels(15.85% of total) were located in genic regions, including 1,139 large-effect long InDels which resulted in truncated or elongated protein sequences. In the qIF05-1 region, 68 long InDels were detected between the two parents. Using a progeny recombination experiment and genotype analysis, the qIF05-1 locus was mapped into a 102.2 kb genomic region, and this region contained 12 genes. By RNA-seq data analysis, genome sequence comparison and functional validation through ectopic expression in Arabidopsis thaliana, Glyma.05G208300(described as GmEGL3), which is a basic helix-loop-helix(bHLH) transcription factor in plants, emerged as the most likely confirmed gene in qIF05-1. These long InDels can be used as a type of complementary genetic method for QTL fine mapping, and they can facilitate genetic studies and molecular-assisted selection breeding in soybean.

DTI联合T2 mapping在神经根型颈椎病神经根损伤定量评价中的应用

目的:探讨弥散张量成像(DTI)联合T2 mapping技术在定量评价神经根型颈椎病患者神经根损伤中的应用价值。方法:对82例神经根型颈椎病患者与30例健康志愿者进行颈椎间盘常规MRI、DTI、T2 mapping及T1 Vibe检查。测量所有受试者神经根的各序列参数,包括FA(各向异性分数)、ADC(表观扩散系数)、AD(轴向扩散系数)、RD(径向扩散系数)及T2值。利用VAS评分对患者进行疼痛学评分。比较患者受压神经根与健康志愿者神经根的各序列参数值差异,并分析各序列参数值与VAS评分的相关性。结果:神经根型颈椎病患者的患侧神经根较健侧及健康志愿者神经根FA值显著减低,ADC、AD、RD、T2值显著升高(P<0.05)。患侧神经根FA平均值与VAS评分呈中度负相关(r=-0.544),ADC、AD、RD、T2平均值与VAS呈正相关(ADC:r=0.457;AD:0.249;RD:0.390;T2:r=0.497)(P<0.05)。ROC曲线分析显示,当DTI所有参数与T2值联合时,曲线下面积(AUC)最大,为0.980,对应的敏感度为95.3%,特异度为94.6%。结论:DTI及T2 mapping技术可以用于评价神经根型颈椎病患者颈神经根损伤,且当DTI与T2 mapping联合使用时可获得最佳诊断效能。

The Growth Theorem for Almost Starlike Mappings of Order α on Bounded Starlike Circular Domains

In this paper,we extend the definition of almost starlike mappings of order 1/2 on B n to the almost starlike mappings of order α on the bounded starlike circular domains in C n,and give the growth theorem of it. This type of domain on which we discuss is rather general,in the sense that the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it.

融合Mind Map优势助力完善线上线下教学衔接--以园林树木学树种识别教学为例

疫情当前,线上线下混合式教学已经成为课程教学新模式。树种识别是园林树木学教学的重点和难点,也是教学目的之一。由于课程涉及的树种种类繁多,知识点琐碎,专业术语抽象,再加上课时少任务重,使得教师在教学过程中无法将所有树种的特征逐一讲解到,学生在学习过程中也容易混淆,无法有效吸收知识点。因此,在课程的教学改革中,通过引入Mind Map帮助厘清知识框架,优化知识结构,搭建知识关联,不仅使教师授课过程更顺畅,而且能够激发学生在线学习的兴趣,促使学生养成“整理知识点”的良好习惯,使学习效率大幅度提高,从而创建高效的线上课堂,有效巩固混合式教学的教学效果。

磁共振T1rho序列、T2 mapping技术在膝关节早期软骨退变早期诊断中的评估价值

目的探讨磁共振T1rho序列、T2 mapping技术在膝关节早期软骨退变早期诊断中的评估价值。方法选取2020年1月至2022年11月在我院治疗的110例膝关节早期软骨退变患者(观察组),按照疾病严重程度分为轻度退变组及重度退变组,另选取同期在我院进行体检的64例健康者为对照组,受试者均行磁共振T1rho序列、T2 mapping技术扫描,测量受试者T2值及T1ρ值,探讨磁共振T1rho序列、T2 mapping技术在膝关节早期软骨退变早期诊断中的评估价值。结果观察组股骨外侧面、股骨内侧面、胫骨外侧面、胫骨内侧面、髋骨面T2值均明显高于对照组(P<0.05),重度退变亚组患者股骨外侧面、股骨内侧面、胫骨外侧面、胫骨内侧面、髋骨面T2值显著高于轻度退变者(P<0.05);观察组股骨内踝负重区、股骨内踝非负重区、股骨外踝负重区、股骨外踝非负重区、胫骨外侧平台区、胫骨内侧平台区、髌后软骨区磁共振T1ρ值明显高于对照组(P<0.05),重度退变亚组患者股骨内踝负重区、股骨内踝非负重区、股骨外踝负重区、股骨外踝非负重区、胫骨外侧平台区、胫骨内侧平台区、髌后软骨区磁共振T1ρ值明显高于轻度退变亚组患者(P<0.05);磁共振T1rho序列在膝关节早期软骨退变中早期诊断及严重程度评估中的的诊断ROC值及特异度明显高于T2 mapping技术(P<0.05),但后者具有更高的敏感度(P<0.05)。结论磁共振T1rho序列、T2 mapping技术均能有效反映膝关节早期软骨退变中软骨组织学成分变化情况,还可为膝关节软骨退变严重程度评估提供客观依据,二者具有一定互补价值。

Several Results on the Number of Zeroes of Nonlinear Mappings on Bounded Regions

With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.

MR T2^(*)mapping成像技术定量评价腰椎小关节炎软骨损伤

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。

The Growth Theorem for Strongly Starlike Mappings of Order α on Bounded Starlike Circular Domains

The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it.

MOLLI T1 mapping定量技术在儿童脑发育评估中的应用可行性探讨

目的探讨改良回顾反转恢复(modified Look-Locker inversion recover,MOLLI)序列T1 mapping定量技术在定量评价儿童脑部发育中的价值。材料与方法纳入头部磁共振检查正常的儿童53例,使用优化后的MOLLI及磁化准备2快速采集梯度回波(magnetization prepared 2 rapid acquisition gradient echoes,MP2RAGE)序列对每例受检者的36个脑区进行T1 mapping定量分析。评价两个序列所得各脑区T1值的一致性,比较两个序列各脑区T1值的差异,分析两个序列各脑区T1值与年龄之间的相关性。结果MOLLI序列和MP2RAGE序列除在双侧脑桥背侧、大脑脚组内相关系数(intra-class correlation coefficient,ICC)<0.8(P<0.001)外,其余脑区ICC均>0.8(P<0.001)。两个序列各脑区的T1值差异均有统计学意义(P<0.05,FDR校正),MOLLI组各脑区T1值高于MP2RAGE组。两个序列各脑区的T1值均与年龄呈负相关(P均<0.001)。结论优化后的MOLLI序列可用于儿童脑部发育的定量评价,与MP2RAGE序列一致性好,可较准确地量化脑区的T1值,为儿童神经系统的研究提供了新的方法选择。