COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

Distribution and correlation of refractive parameters in children with different corneal curvatures in southeast China

AIM:To analyze the distribution of refractive status in school-age children with different corneal curvatures(CC)and the correlation between CC and refractive status.METHODS:A total of 2214 school-aged children of grade 4 in Hangzhou who were screened for school myopia were included.Uncorrected distance visual acuity(UCDVA),non-cycloplegic refraction,axial length(AL),horizontal and vertical corneal curvature(K1,K2)were measured and spherical equivalent(SE),corneal curvature radius(CCR)and axial length/corneal radius of curvature ratio(AL/CR)were calculated.UCDVA<5.0 and SE≤-0.50 D were classified as school-screening myopia.According to the different CCRs,the patients were divided into the lower corneal curvature(LCC)group(CCR≥7.92)and the higher corneal curvature(HCC)group(CCR<7.92).Each group was further divided into the normal AL subgroup and the long AL subgroup.The refractive parameters were compared to identify any differences between the two groups.RESULTS:Both SE and AL were greater in the LCC group(P=0.013,P<0.001).The prevalence of myopia was 38% in the LCC group and 44% in the HCC group(P<0.001).The proportion of children without screening myopia was higher in the LCC group(62%)than in the HCC group(56%).Among these children without screening myopia,the proportion of long AL in the LCC group(24%)was significantly higher than that in the HCC group(0.012%;P<0.001).The change of SE in the LCC group was less affected by the increase of AL than that in the HCC group.CONCLUSION:School-aged children in the LCC group have a lower incidence of screening myopia and longer AL.Low CC can mask SE reduction and AL growth to some extent,and the change of AL growth change more in children with low CC than high CC.Before the onset of myopia,its growth rate is even faster than that after the onset of myopia.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.

RANDERS SPACES WITH SCALAR FLAG CURVATURE

Let(M, F) be an n-dimensional Randers space with scalar flag curvature. In this paper, we will introduce the definition of a weak Einstein manifold. We can prove that if(M, F) is a weak Einstein manifold, then the flag curvature is constant.

Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction.This compliance reduces the risk of damage to the manipulated object and its surroundings.However,continuum robots possess theoretically infinite degrees of freedom,and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints.Describing these complex deformations is the main challenge in modeling continuum robots.In this study,we investigated a novel variable curvature modeling method for continuum robots,considering external forces and positional constraints.The robot configuration curve is described using the developed mechanical model,and then the robot is fitted to the curve.A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model.The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load.This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.

Microcurvature landscapes induce neural stem cell polarity and enhance neural differentiation

Tissue curvature has long been recognized as an important anatomical parameter that affects intracellular behaviors,and there is emerging interest in applying cell-scale curvature as a designer property to drive cell fates for tissue engineering purposes.Although neural cells are known to undergo dramatic and terminal morphological changes during development and curvature-limiting behaviors have been demonstrated in neurite outgrowth studies,there are still crucial gaps in understanding neural cell behaviors,particularly in the context of a three-dimensional(3D)curvature landscape similar to an actual tissue engineering scaffold.In this study,we fabricated two substrates of microcurvature(curvature-substrates)that present a smooth and repeating landscape with focuses of either a concave or a convex pattern.Using these curvature-substrates,we studied the properties of morphological differentiation in N2a neuroblastoma cells.In contrast to other studies where two-dimensional(2D)curvature was demonstrated to limit neurite outgrowth,we found that both the concave and convex substrates acted as continuous and uniform mechanical protrusions that significantly enhanced neural polarity and differentiation with few morphological changes in the main cell body.This enhanced differentiation was manifested in various properties,including increased neurite length,increased nuclear displacement,and upregulation of various neural markers.By demonstrating how the micron-scale curvature landscape induces neuronal polarity,we provide further insights into the design of biomaterials utilizing the influence of surface curvature in neural tissue engineering.

GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE

In this paper,we mainly study the global rigidity theorem of Riemannian submanifolds in space forms.Let Mn(n≥3)be a complete minimal submanifold in the unit sphere Sn+p(1).Forλ∈[0,n2−1/p),there is an explicit positive constant C(n,p,λ),depending only on n,p,λ,such that,if∫MSn/2dM<∞,∫M(S−λ)n/2+dM<C(n,p,λ),then Mn is a totally geodetic sphere,where S denotes the square of the second fundamental form of the submanifold and∫+=max{0,f}.Similar conclusions can be obtained for a complete submanifold with parallel mean curvature in the Euclidean space Rn+p.

A CLASS OF INVERSE QUOTIENT CURVATURE FLOW IN THE ADS-SCHWARZSCHILD MANIFOLD

In this paper,we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold.We prove that under suitable convex conditions for the initial hypersurface,one can get the long-time existence for the inverse curvature flow.Moreover,we also get that the principal curvatures of the evolving hypersurface converge to 1 when t→+∞.

Passability test and simulation of sand control string with natural gas hydrates completion in large curvature hole

To meet the requirements of marine natural gas hydrate exploitation,it is necessary to improve the penetration of completion sand control string in the large curvature borehole.In this study,large curvature test wells were selected to carry out the running test of sand control string with pre-packed screen.Meanwhile,the running simulation was performed by using the Landmark software.The results show that the sand control packer and screen can be run smoothly in the wellbore with a dogleg angle of more than 20°/30 m and keep the structure stable.Additionally,the comprehensive friction coefficient is 0.4,under which and the simulation shows that the sand control string for hydrate exploitation can be run smoothly.These findings have important guiding significance for running the completion sand control string in natural gas hydrate exploitation.

Trimmable bandgap reference circuit with exponential curvature compensation

This paper proposes an improved exponential curvature-compensated bandgap reference circuit to exploit the exponential relationship between the current gainβof the bipolar junction transistor(BJT)and the temperature as well as reduce the influence of resistance-temperature dependency.Considering the degraded circuit performance caused by the process deviation,the trimmable module of the temperature coefficient(TC)is introduced to improve the circuit stability.The circuit has the advantages of simple structure,high linear stability,high TC accuracy,and trimmable TC.It consumes an area of 0.09 mm^(2)when fabricated by using the 0.25-μm complementary metal-oxide-semiconductor(CMOS)process.The proposed circuit achieves the simulated power supply rejection(PSR)of about-78.7 dB@1 kHz,the measured TC of~4.7 ppm/℃over a wide temperature range from-55℃to 125℃with the 2.5-V single-supply voltage,and the tested line regulation of 0.10 mV/V.Such a high-performance bandgap reference circuit can be widely applied in high-precision and high-reliability electronic systems.

Numerical simulation of a truncated cladding negative curvature fiber sensor based on the surface plasmon resonance effect

A refractive index(RI)sensor based on the surface plasmon resonance effect is proposed using a truncated cladding negative curvature fiber(TC-NCF).The influences of the TC-NCF structure parameters on the sensing performances are investigated and compared with the traditional NCF.The simulation results show that the proposed TC-NCF RI sensor has an ultra-wide detection range from 1.16 to 1.43.The maximum wavelength sensitivity reaches 12400 nm/RIU,and the corresponding R^(2)of the polynomial fitting equation is 0.9999.The maximum and minimum resolutions are 2.56×10^(-5)and 8.06×10^(-6),respectively.In addition,the maximum amplitude sensitivity can reach-379.1 RIU^(-1)when the RI is chosen as 1.43.The proposed TC-NCF RI sensor could be useful in biochemical medicine,environmental monitoring,and food safety.

基于曲率特征分析的小儿颅骨畸形重建技术

小儿颅骨畸形影响患者容貌和发育,并会导致局部触痛、易怒、不安等症状,需要通过手术重建出规则的颅骨形状。但目前手术方案设计多依据医生的经验,缺乏标准的目标形状作指导,手术时间长,重建效果需要提升。针对这一问题,利用曲面的主曲率和高斯曲率分布为依据,对正常的颅骨形状特征进行曲率分析,获得了分区域的曲率值分布范围;通过有限元及实体仿真实验,研究了不同接触结构及不同骨瓣参数对重建模型力学性能的影响;针对具体病例,基于计算机断层扫描(CT)图像重建颅骨三维模型,并进行曲率分析,与正常颅骨曲率分布进行比较,制订出重建修复方案,并设计和打印手术切割模板,临床手术时在模板引导下完成重建手术。实际应用表明,术前额骨部位高斯曲率极值为-0.05200和0.00023,术后降低至正常范围,颅骨重建的效率和形状恢复效果得到了显著提高。

拟常曲率黎曼流形中的2-调和子流形

该文讨论了拟常曲率黎曼流形Nn+p中具有平行平均曲率的2-调和子流形Mn,在ξ∈Γ(TM)时,得到这类子流形是极小子流形的一个拼挤定理.对2-调和超曲面的情形,也得到了其为极小超曲面的一个充分条件.

不同覆盖物清理状态下海底电缆打捞受力仿真

该文通过对海缆深浅水打捞过程机理的分析,确定覆盖物对打捞过程存在一定影响。通过OrcaFlex考虑水动力建立打捞过程模型,研究覆盖物厚度与覆盖物位置对海缆打捞过程中张力及曲率的影响。研究发现,覆盖段被打捞时,海缆张力会出现明显的波动;打捞过程覆盖段海缆曲率极值明显增大。随着覆盖物厚度的增加,覆盖段海缆曲率极值逐渐增大,海缆的张力波动也更加明显。覆盖物只对覆盖段曲率极值有明显影响;当吊点处覆盖物未完全清理时海缆易发生弯曲失效,远离吊点处的覆盖物对打捞过程海缆沿缆曲率极值影响不大。在实际工况下可进行针对性工作和保护,降低工作量并提高打捞效率,防止电缆在打捞过程中受到二次破坏。

多镜面大视场主动光学望远镜调控方法

为了更好地实现多镜面大视场主动光学望远镜波前像差抑制、提升望远镜探测能力极限,本文基于望远镜视场边缘内置的错位型曲率传感器进行波前感知,并利用功率谱对波前感知结果进行分析,进而基于波前像差的空间频率特征进行调控。首先,基于复光场理论分析了非瞳面对系统波前调控的影响机理。其次,分析了本方法在多镜面大视场主动光学望远镜调控过程中的精度特性。再次,利用桌面实验对多镜面大视场主动光学望远镜调控的可行性进行了验证。最终,波前重建结果与理论波前相关性高于0.85。利用功率谱对各个视场的空间频率特性进行了分析,与单纯使用均方根对多镜面影响敏感度进行分析的方法相比,灵敏度提升了20%。

OPD-ScanⅢ及IOL-Master 700测量白内障术前角膜曲率和水平角膜直径的比较

目的比较OPD-ScanⅢ与IOL-Master 700在角膜曲率(平坦曲率K1与陡峭曲率K2)及水平角膜直径(WTW)测量上的差异性及一致性。方法选取2021年10月至2022年9月在航天中心医院眼科行白内障手术的患者268例328眼(右眼164例,左眼164例)。采用OPD-ScanⅢ及IOL-Master 700仪器分别检测患者左右眼的K1、K2以及WTW值并进行分析比较。采用配对t检验进行参数比较;Pearson相关分析检测参数间的相关性;Bland-Altman以及组内相关系数(ICC)分析确定两种仪器相关参数测量的一致性。结果在左右眼参数的测量中,OPD-ScanⅢ测得的K1及K2值均大于IOL-Master 700,WTW值均低于IOL-Master 700的测量值,差异均有统计学意义(均为P<0.001)。OPD-ScanⅢ在左右眼中测得的K1、K2及WTW值与IOL-Master 700所测得的对应值均呈正相关,差异均有统计学意义(均为P<0.001)。两种仪器K1、K2及WTW值在95%一致性界限外的比例均在5%以内,但95%界限内差值绝对值均接近或超过了1.0 D,存在较大的临床偏差。ICC分析证实两种仪器左右眼测量K1及K2值一致性均极好(ICC>0.90)。两种仪器测得的WTW差值与K2值均显著相关(均为P<0.05)。WTW正偏差范围外有5例(83.33%)样本IOL-Master 700测得的K 2在47.03以上。结论OPD-ScanⅢ及IOL-Master 700在测量K1、K2及WTW上存在偏差,临床应用中不可互相替代。IOL-Master 700测得的WTW值大于OPD-ScanⅢ,当其测量的K2≥47.03时,所获得的WTW值参考价值可能有限。

S135钻杆接头螺纹三维参数化建模及力学特性分析

S135钢级钻杆在矿井勘探、探放水、瓦斯抽采等钻孔施工中得到了广泛使用。然而,由于钻杆接头螺纹承受轴向拉压、扭转、弯曲及其复合载荷的循环作用,导致接头螺纹的使用寿命远远低于其设计寿命,是整个钻杆结构中最薄弱的环节。因此,通过万能拉伸试验获得钻杆接头材料的力学性能参数,经计算转化得到其本构参数,对钻杆接头进行有限元分析。为了提高有限元分析效率,推导垂直于钻杆接头轴线的螺纹截面轮廓几何表达式,基于旋转、抬升、缩径和连接节点的设计思路,提出了一种考虑钻杆接头锥度和台肩的三维螺纹参数化建模方法,并根据单元和节点之间的关系开发了钻杆接头连接的参数化三维六面体网格建模程序,通过与交互式建模方法计算结果的对比验证了其有效性和可行性。此外,对上扣扭矩、压扭及压弯扭复合载荷作用下接头外螺纹的力学特性进行了分析。结果表明:3种工况下钻杆接头外螺纹上的应力近似呈现“浴盆”形态,第1螺纹牙上的应力最大;随着圈次的增加,螺纹牙上的应力迅速下降,最后一圈螺纹牙上的应力呈现上升趋势;在弯矩的作用下,螺纹牙上的应力具有非对称特征。在接头螺纹设计时,必须考虑井眼曲率的影响并且需要重点关注接头压缩边第1螺纹牙上的应力。

摩擦驱动焊接小车牵引力和通过性分析

针对焊接小车对变曲率半径工件适应性差的问题,进行了理论研究,改进焊接小车的驱动系统,建立了焊接小车在斜坡工况下的力学模型,分析了焊接小车运动过程中的牵引力变化规律,为焊接小车设计提供了理论支持。在此基础上,研究了焊接小车在外圆曲面和内圆曲面工况下的通过性,并计算出了2种特殊工况下特定结构和尺寸的焊接小车可以通过的最小曲率半径。基于上述分析结果设计出了一款基于摩擦传动的焊接小车,并进行了仿真验证,结果表明该焊接小车在变曲率半径轨道上具有良好的通过性,可以为焊接小车的设计提供技术保障。

覆岩导水裂隙带发育高度动态演化规律研究

为了研究覆岩导水裂隙带发育高度动态演化规律,以小保当矿区2^(-2)煤层为研究对象,通过理论分析、相似模拟实验及实例验证的方法,对导水裂隙带动态发育高度进行研究;借助概率积分法预计其上部岩层移动变形的理论公式,给出了1种基于覆岩曲率变形的导水裂隙带动态发育高度预计方法。研究表明:导水裂隙带上部岩层下沉系数是1个与挠度及下部自由空间高度相关的分段函数,上部岩层曲率变形大小是决定导水裂隙带发育高度的关键因素;导水裂隙带发育高度与工作面推进长度相关;理论预计小保当矿区2^(-2)煤层导水裂隙带发育高度为160.8 m,相似模拟实验发育高度为155 m,现场实测发育高度为152.01~175.57 m。

融合角点检测的点云配准研究

为提高点云配准效率,提出一种基于点云曲率信息的Harris角点提取算法,通过引入曲率约束,对传统Harris角点提取做出改进;计算每个点的曲率值并与整幅点云的平均曲率作比较,保留曲率值大于平均曲率的点云,实现对配准价值较低的点的剔除,为后续点云配准减少计算量;构建所提取角点之间的特征匹配,结合采样一致性(sample consensus initial alignment, SAC-IA)粗配准和正态分布变换(normal distributions transform, NDT)精配准,寻找最优的变换矩阵,实现源点云和目标点云的重合。通过比较不同算法在公开数据集上进行实验验证,结果表明该方法对复杂点云、多拐点点云都有较好的表现,对初始位置相差较大的点云也有良好的适用性。