New Unique Common Fixed Point Results for Four Mappings with Ф-Contractive Type in 2-Metric Spaces

In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.

Uniqueness of Common Fixed Points for a Family of Mappings with <i>Φ</i>-Contractive Condition in 2-Metric Spaces

In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.

Four Mappings Satisfying Ψ-Contractive Type Condition and Having Unique Common Fixed Point on 2-Metric Spaces

In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.

An Improvement of a Known Unique Common Fixed Point Result for Four Mappings on 2-Metric Spaces

In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four mappings with γ-contractive condition instead of Ψ-contractive condition on 2-metric spaces.

Unique Common Fixed Points for Two Weakly C~*-contractive Mappings on Partially Ordered 2-metric Spaces

In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.

Common Fixed Points for Two Mappings with Implicit-linear Contractions on Partially Ordered 2-metric Spaces

In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.

Common Fixed Point Theorems for Generalized Cyclic Contraction Pairs in b2-metric Spaces

In this paper,we introduce the notion of generalized cyclic contraction pairs in b2-metric spaces and establish some fixed point theorems for such pairs.Then,we give an example to illustrate our results.

3D MERGE与3D SPACE STIR序列在腰椎间盘突出症检查中的应用比较

目的:对比三维多回波恢复梯度回波(3D MERGE)、三维可变反转角快速自旋回波(3D SPACE STIR)序列在腰椎间盘突出症(LDH)检查中的应用效果。方法:选择2020年1月~2022年11月收治的135例LDH患者,回顾性分析患者临床和磁共振成像(MRI)资料,所有患者均接受常规MRI扫描及3D MERGE、3D SPACE STIR序列扫描,对比3D MERGE、3D SPACE STIR序列测量神经根直径的一致性,评价两种序列的图像质量参数[信噪比(SNR)、对比噪声比(CNR)]、图像清晰度评分。结果:3D MERGE和3D SPACE STIR序列测量的L3~S1神经根直径比较差异无统计学意义(P>0.05),且两组序列测量的L3、L4、L5和S1直径均显示出较高相关性(r=0.957,0.986,0.975,0.972,P<0.05);3D MERGE序列的SNR及CNR均高于3D SPACE STIR序列,神经根显示分级、图像清晰度评分优于3D SPACE STIR序列,差异有统计学意义(P<0.05)。结论:3D MERGE、3D SPACE STIR序列在LDH神经根直径测量中具有极高一致性,3D MERGE序列较3D SPACE STIR序列能够更清晰显示神经跟的解剖形态,图像质量更好。

UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE

In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.

μ-Separations in generalized topological spaces

This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relations among these spaces are established.

3D printing in space:from mechanical structures to living tissues

3D printing stands at the forefront of transforming space exploration,offering unprecedented on-demand and rapid manufacturing capabilities.It adeptly addresses challenges such as mass reduction,intricate component fabrication,and resource constraints.Despite the obstacles posed by microgravity and extreme environments,continual advancements underscore the pivotal role of 3D printing in aerospace science.Beyond its primary function of producing space structures,3D printing contributes significantly to progress in electronics,biomedicine,and resource optimization.This perspective delves into the technological advantages,environmental challenges,development status,and opportunities of 3D printing in space.Envisioning its crucial impact,we anticipate that 3D printing will unlock innovative solutions,reshape manufacturing practices,and foster self-sufficiency in future space endeavors.

GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES

In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces.

Penrose Transform on <i>D</i>-Modules, Moduli Spaces and Field Theory

We consider a generalization of the Radon-Schmid transform on coherent D-modules of sheaves of holomorphic complex bundles inside a moduli space, with the purpose of establishing the equivalences among geometric objects (vector bundles) and algebraic objects as they are the coherent D-modules, these last with the goal of obtaining conformal classes of connections of the holomorphic complex bundles. The class of these equivalences conforms a moduli space on coherent sheaves that define solutions in field theory. Also by this way, and using one generalization of the Penrose transform in the context of coherent D-modules we find conformal classes of the space-time that include the heterotic strings and branes geometry.

1.5T磁共振3D-SPACE序列与3D-TSERT序列在MRCP成像中的应用对比

目的:通过MR可变翻转角的三维快速自旋回波(3D sampling perfertion with application optimized contrasts using deifferent flip angle evolutions,3D-SPACE)序列与三维快速恢复快速自旋回波(3D-TSE Retore,3D-TSERT)序列对胰胆管水成像(MR cholangiopancreatgrapgy,MRCP)中的成像质量进行对比,优化MRCP的成像序列。方法:对48位受检者分别用3D-SPACE序列与3D-TSERT序列行MRCP检查,将采集到的影像利用siemens 3D软件进行MIP(maxium intensity projection)重建,并对2种图像的显示情况进行分析比较。结果:3D-SPACE序列的MRCP显示肝段胆管、胰管的效果明显优于3D-TSERT-MRCP序列(P﹤0.05),2种成像序列显示左右肝管、肝总管、胆囊、胆总管的效果差异无显著性意义(P>0.05)。结论:在1.5TMRI检查中,应用3D-SPACE序列的MRCP在检查时间及成像质量上都优于3D-TSE序列,应成为常规MRCP的首选序列。

MR 3D FLASH-WE结合3D SPACE技术在颅神经疾病中的应用

目的:研究MR 3D FLASH-WE结合3D SPACE序列对颅神经疾病微血管减压术(MVD)指导价值。方法:106例经显微血管减压术治疗颅神经疾病患者。其中HFS(面肌痉挛)68例,TN(三叉神经痛)34例,GPN(舌咽神经痛)4例。术前均行常规磁共振及3D FLASH WE、3D SPACE、3D TOF序列检查。单独并联合应用以上序列分析颅神经与血管关系,并与手术结果对照。结果:3D FLASH-WE序列对面神经及三叉神经REZ(出脑干区)段的显示明显优于3D TOF序列,对其周围血管的显示与3D TOF序列差异无统计学意义;3D FLASH-WE结合3D SPACE序列较3D TOF结合3D SPACE序列显示神经与血管关系更清晰,对神经与血管是否存在接触的情况判断更准确,但与手术比较无明显差异(P<0.05)。结论:3D FLASH-WE结合3D SPACE序列能清晰显示颅神经与血管关系,准确判断责任血管,对显微血管减压术有重要的指导意义。

3D MEDIC和3D SPACE磁共振神经成像在腰骶丛神经根的一致性对比研究

目的验证三维多回波数据联合成像(three dimensional multi-echo data imagine combination with selective water excitation,3D MEDIC WE)和三维快速自旋回波成像(three dimensional sampling perfection with application optimized contrasts by using different flip angle evolution,3D SPACE STIR)序列在腰骶丛神经根成像中的可行性和重复性。方法将55例受试者分为腰椎无异常表现的正常对照组(20例)、单纯性腰椎间盘突出症(lumbar disc herniation,LDH)组(20例)和慢性炎性脱髓鞘性多发性神经根神经病症(chronic inflammatory demyelinating polyradiculoneuropathy,CIDP)组(15例),分别应用两种腰骶丛神经根成像,评价图像质量参数信噪比(signal to noise ratio,SNR)、对比噪声比(contrast to noise ratio,CNR)和对比度(contrast ratio,CR),并验证正常对照组、CIDP组和LDH组测量神经根直径的一致性。结果两序列测得神经根直径的一致性较高(正常组r=0.95,CIDP组r=0.99,LDH组r=0.97,P<0.001),图像质量评价指标显示,3D SPACE STIR序列在SNR、CNR和CR三项指标中占优,3D MEDIC WE定性评估图像质量评分较高。两序列均能清晰显示正常腰骶丛神经根、病变所致的弥漫性形态增粗神经根以及间盘突出受挤压变形的神经根。结论3D MEDIC WE和3D SPACE STIR序列可应用于腰骶丛神经根成像,两序列对正常和异常形态、走行的神经根评估具备很高的可行性和重复性。综合考量临床图像的定性、定量评价,可择优选择恰当的序列为腰骶丛神经根成像提供影像支持。

3D SPACE序列及后处理在显示大脑中动脉硬化中的临床价值

目的:探讨高分辨率MRI脑血管壁成像3D SPACE序列及后处理技术在显示大脑中动脉硬化中的价值。方法:对行MRI常规序列和3D SPACE序列检查、符合脑动脉硬化诊断标准的40例患者进行观察和分析。采用3D SPACE序列行冠状面T1WI-FS、T2WI-FS和T1WI-FS增强扫描、曲面重建(CPR),在CPR图像上行大脑中动脉的硬化斑块断面重建。分析动脉硬化斑块的以下MRI表现:病变数目、狭窄长度、断面血管形态、信号强度、强化程度、内膜的完整性。计算血管狭窄程度和测量增强的信号值。根据T2WI、DWI等表现等将患者分为急性脑梗死组(组1)、非急性脑梗死组(组2)和无脑梗死组(组3),比较各组病变MRI表现的差异。结果:40例患者CPR显示共61处位于大脑中动脉的硬化性病变。MRI表现为节段性或局限性狭窄,多为偏心性管壁增厚,T1WI和T2WI呈高、稍高或等信号,强化程度主要为明显、中度,血管内膜多不完整。急性脑梗死组(组1)19例,非急性脑梗死组(组2)11例,无脑梗死组(组3)10例。组1狭窄长度、T1WI-FS和T2WI-FS的信号强度、强化程度均高于组2和组3,组2、组3依次降低。急性脑梗死组的管腔狭窄程度为0.729±0.209,明显高于组2和组3(分别为0.482±0.232和0.406±0.194),差异有统计学意义(P<0.05)。3组增强的信号值分别为408.83±137.56、306.65±114.05、201.24±42.31,差异有统计学意义(P<0.05)。结论:3D SPACE序列及后处理技术显示大脑中动脉及其管壁硬化性病变具有一定优势,能显示动脉硬化斑块的多种MRI表现,且急性脑梗死、非急性脑梗死和无脑梗死患者各种MRI表现的严重程度也不相同,3D SPACE序列对大脑中动脉硬化性病变的显示具有一定价值。

对比增强3D STIR SPACE序列对子宫内膜异位症患者骶丛神经异常的显示

【目的】探讨增强3D STIR SPACE序列对盆腔子宫内膜异位症患者骶丛神经异常的显示价值,并与增强3D VIBE序列进行对比。【方法】病例组包括30名子宫内膜异位症患者,对照组包括20名健康女性,均接受盆腔MRI检查,包括对比增强3D STIR SPACE序列和增强3D VIBE序列。评估骶丛神经显示的图像质量以及子宫内膜异位症患者中的骶丛神经侵犯。【结果】对照组和病例组中,3D STIR SPACE序列和3D VIBE序列均能很好地显示骶丛神经纤维(P<0.001)。阅片者应用3D-STIR-SPACE序列对病变的诊断信心分数一致性较强(Kappa=0.684,P<0.001),应用3D-VIBE序列的诊断信心分数一致性一般(Kappa=0.130,P=0.386)。【结论】对比增强T2-SPACE序列和3D VIBE序列能够清晰显示骶丛神经,前者对盆腔子宫内膜异位症患者骶丛神经异常的显示更有优势。

基于dSPACE的“硬件在回路”导弹控制系统设计与仿真

基于d SPACE实时仿真系统提供的强大运算能力及各种成熟的硬件接口电路,文中研究了导弹控制系统的“硬件在回路”设计与仿真方法。给出系统架构及设计流程,介绍了执行机构舵机测试及模型辨识方法,将舵机实物引入导弹控制回路的设计过程中,实现了从传统的数字离线仿真过程到“硬件在回路”的设计与仿真,克服了传统纯数字模型不能真实代表制导部件性能的缺点,提高了导弹控制系统设计的工作效率及可靠性。

2D TSE与3D SPACE序列对直肠癌术前T分期的诊断价值比较

目的比较三维可变翻转角各向同性快速自旋回波(3D SPACE)序列与传统二维快速自旋回波(2D TSE)序列对直肠癌术前T分期的诊断价值。资料与方法选取2018年1月—2019年12月青岛大学附属医院收治的直肠癌患者75例,术前进行2D TSE及3D SPACE序列扫描,计算2D TSE及3D SPACE序列图像的信噪比(SNR)、对比噪声及图像评分评估图像质量。以术后病理结果为“金标准”,比较2D TSE及3D SPACE序列诊断直肠癌术前T分期的准确度。结果2D TSE和3D SPACE序列的图像质量在显示直肠浆膜层或外膜[3.00(2.00,3.00)比3.00(3.00,3.00);Z=−0.16,P=0.990]、肠周脂肪[3.00(3.00,3.00)比3.00(3.00,3.00);Z=−0.259,P=0.800]、直肠系膜筋膜[3.00(3.00,3.00)比3.00(3.00,3.00);Z=−1.27,P=0.210]、瘤体[3.00(3.00,3.00)比3.00(3.00,3.00);Z=−0.03,P=0.990]比较,差异无统计学意义。3D SPACE序列在显示直肠黏膜层[3.00(2.00,3.00)比3.00(3.00,3.00);Z=−2.47,P=0.013]、直肠肌层[3.00(2.00,3.00)比3.00(3.00,3.00);Z=−3.21,P=0.001]方面图像质量更高。对于瘤体,3D SPACE序列的SNR优于2D TSE序列(119.95±39.83比83.94±40.34;t=−2.54,P=0.016);对于脂肪(213.56±95.26比191.22±59.47;t=0.80,P=0.430)及肌肉(41.86±19.34比40.40±15.58;t=0.24,P=0.820),2D TSE及3D SPACE序列的SNR差异无统计学意义;两序列对比噪声比差异无统计学意义(19.36±10.11比27.54±18.72;t=−1.54,P=0.140)。与术后病理结果对比,2D TSE序列的诊断一致性(Kappa=0.49,P=0.00)比3D SPACE序列低(Kappa=0.95,P=0.000),两序列对T分期的诊断准确度分别为76.00%和98.67%。结论2D TSE和3D SPACE序列显示直肠浆膜层或外膜、肠周脂肪、直肠系膜筋膜及瘤体一样可靠。3D SPACE序列对于显示直肠黏膜层及直肠肌层较2D TSE序列更优越。对于直肠癌的术前T分期,3D SPACE序列较传统高分辨2D TSE序列的诊断准确度更高,可更好地为临床制订治疗方案提供影像学依据。