Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.

Weak and Strong Convergence for Fixed Points of Asymptotically Non-expansive Mappings

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).

Fixed Points for Mean Non-expansive Mappings

For a Banach Space X Garcia-Falset introduced the coefficient R（X） and showed that if R（X） 〈 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ｜｜Tx - TY｜｜ ≤ a｜｜x - y｜｜ ＋ b｜｜x - Ty｜｜ for any x,y E X, where a,b ≥ 0, a ＋ b ≤ 1. We show that if R（X） 〈 1/1＋b then T has a fixed point in X.

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED OINTS FOR ASYMPTOTICALLY NON-EXPANSIVE TYPE MAPPINGS IN BANACH SPACES

Some iterative approximation theorems of fixed points for asymptotically nonexpansive type mappings in Banach spaces are obtained.

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.

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.

基于MAP法的线路板重金属铜氨废水处理研究

随着线路板的广泛应用,其在印刷过程中产生的铜氨废水的排放问题日益突出。铜氨废水中氨氮和铜离子对环境的危害较大,为了解决该问题,提出了一种MAP法和折点氯化法相结合的方法。该方法首先向铜氨废水中加入镁盐和磷酸盐,将氨氮转化为MAP沉淀,降低铜氨废水中氨氮的浓度,同时可以将MAP回收再利用;然后向剩余浓液中加入过量的NaClO溶液,进一步将溶液中的氨氮浓度降低,随着NaClO溶液的增加,反应液会逐渐呈碱性,而Cu^(2+)在碱性环境中会与OH-生成Cu(OH)_(2)沉淀,进而降低Cu^(2+)的浓度,从而使铜氨废水中的氨氮和Cu2+的浓度均符合《中华人民共和国环境保护法》的排放要求;最后通过纳氏试剂分光光度法和火焰原子吸收光度法检验反应后浓液中氨氮和Cu^(2+)的浓度。经过验证得知,该方法可以显著降低氨氮和Cu^(2+)的浓度。

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.

GPU-Enabled Isogometric Topology Optimization with Bezier Element Stiffness Mapping

Due to the high-order B-spline basis functions utilized in isogeometric analysis(IGA)and the repeatedly updating global stiffness matrix of topology optimization,Isogeometric topology optimization(ITO)intrinsically suffers from the computationally demanding process.In this work,we address the efficiency problem existing in the assembling stiffness matrix and sensitivity analysis using B˙ezier element stiffness mapping.The Element-wise and Interaction-wise parallel computing frameworks for updating the global stiffness matrix are proposed for ITO with B˙ezier element stiffness mapping,which differs from these ones with the traditional Gaussian integrals utilized.Since the explicit stiffness computation formula derived from B˙ezier element stiffness mapping possesses a typical parallel structure,the presented GPU-enabled ITO method can greatly accelerate the computation speed while maintaining its high memory efficiency unaltered.Numerical examples demonstrate threefold speedup:1)the assembling stiffness matrix is accelerated by 10×maximumly with the proposed GPU strategy;2)the solution efficiency of a sparse linear system is enhanced by up to 30×with Eigen replaced by AMGCL;3)the efficiency of sensitivity analysis is promoted by 100×with GPU applied.Therefore,the proposed method is a promising way to enhance the numerical efficiency of ITO for both single-patch and multiple-patch design problems.

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.