Autonomous and Mobile Prototype of Curvature Sensor with Remote Reliable Communication of Spectral Curvature

Through the creation and construction of a curvature sensor of accelerometer type, using the spectral curvature concept or curvature energy that measures curvature in Volts/m3, an autonomous and mobile censorship of curvature sensing with reliable data transmission/reception in real time and remote position is designed and constructed considering the spectra of curvature of the measured curvature energy during the advance of the prototype as the normed measure by with β , a constant rationalized parameter according with the required advance of the mobile device in the control scale of their velocity. Likewise, the sensed curvature data are digitalized through wireless interconnectivity using a HC-05 Module with a programmable device that includes logic blocks whose interconnection and functionality can be configured according to the sensor measure in situs. Also an application is planted to the obtaining of an energy plus due to the curvature that could be used in the displacement of a vehicle.

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.

Experimental Study on Full-Surface Buckling of Variable Curvature Cylindrical Shell Using Multi-camera 3D-DIC System

To achieve full-surface strain measurement of variable curvature objects,a 360°3D digital image correlation(DIC)system is proposed.The measurement system consists of four double-camera systems,which capture the object’s entire surface from multiple angles,enabling comprehensive full-surface measurement.To increase the stitching quality,a hierarchical coordinate matching method is proposed.Initially,a 3D rigid body calibration auxiliary block is employed to track motion trajectory,which enables preliminary matching of four 3D-DIC sub-systems.Subsequently,secondary precise matching is performed based on feature points on the test specimen’s surface.Through the hierarchical coordinate matching method,the local 3D coordinate systems of each double-camera system are unified into a global coordinate system,achieving 3D surface reconstruction of the variable curvature cylindrical shell,and error analysis is conducted on the results.Furthermore,axial compression buckling experiment is conducted to measure the displacement and strain fields on the cylindrical shell’s surface.The experimental results are compared with the finite element analysis,validating the accuracy and effectiveness of the proposed multi-camera 3D-DIC measuring system.

Gradient Estimate of Solutions to a Class of Mean Curvature Equations with Prescribed Contact Angle Boundary Problem

This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation.Applying the maximum principle and the moving frame method and based on the location of the maximum point,the boundary gradient estimation of the solutions to the equation is obtained.

HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

Let Mn be an n-dimensional complete connected and oriented hypersurface in a hyperbolic space H（n＋1）（c） with non-zero constant mean curvature H and two distinct principal curvatures. In this paper, we show that （1） if the multiplicities of the two distinct principal curvatures are greater than 1,then Mn is isometric to the Riemannian product Sk（r）×H（n-k）（-1/（r2 ＋ ρ2））, where r 〉 0 and 1 〈 k 〈 n - 1;（2）if H2 〉 -c and one of the two distinct principal curvatures is simple, then Mn is isometric to the Riemannian product S（n-1）（r） × H1（-1/（r2 ＋ρ2）） or S1（r） × H（n-1）（-1/（r2 ＋ρ2））,r 〉 0, if one of the following conditions is satisfied （i） S≤（n-1）t22＋c2t（-2）2 on Mn or （ii）S≥ （n-1）t21＋c2t（-2）1 on Mn or（iii）（n-1）t22＋c2t（-2）2≤ S≤（n-1）t21＋c2t（-2）1 on Mn, where t_1 and t_2 are the positive real roots of （1.5）.

DEFORMING CONVEX HYPERSURFACES BY THE LINEAR COMBINATION OF THE MEAN CURVATURE AND THE N-TH ROOT OF THE GAUSS-KRONECKER CURVATURE

In this paper a flow of convex hypersurfaces in the Euclidean space by the linear-combination of the mean curvature and the n-th root of the Gauss-Kronecker curvature is considered. It is proved that such deforming convex hypersurfaces converge to a round sphere in the Huisken's sense.

ON(α,β)-METRICS OF CONSTANT FLAG CURVATURE

In this paper,we study the(α,β)-metrics of constant flag curvature.We characterize almost regular(α,β)-metrics of constant flag curvature under the condition that β is a homothetic 1-form with respect to a.Furthermore,we prove that if a regular(α,β)-metric is of constant flag curvature and β is a Killing 1-form with constant length,then it must be a Riemannian metric or locally Minkowskian.

The algorithm of 3D multi-scale volumetric curvature and its application

To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. We also propose a fast algorithm for computing 3D volumetric curvature. In comparison to conventional volumetric curvature attributes, its main improvements and key algorithms introduce multi-frequency components expansion in time-frequency domain and the corresponding multi-scale adaptive differential operator in the wavenumber domain, into the volumetric curvature calculation. This methodology can simultaneously depict seismic multi-scale features in both time and space. Additionally, we use data fusion of volumetric curvatures at various scales to take full advantage of the geologic features and anomalies extracted by curvature measurements at different scales. The 3D MSVC can highlight geologic anomalies and reduce noise at the same time. Thus, it improves the interpretation efficiency of curvature attributes analysis. The 3D MSVC is applied to both land and marine 3D seismic data. The results demonstrate that it can indicate the spatial distribution of reservoirs, detect faults and fracture zones, and identify their multi-scale properties.

Creep age forming of 2124 aluminum alloy with single/double curvature

In order to investigate the springback rules, the variation characteristics of physical property and microstructure in bending creep age forming process, a series of creep forming tests of 2124 aluminum alloy were conducted based on three kinds of single and double curvature forming tools. The results show that the spingback rate would be the minimum under the optimal coupling conditions among the temperature, aging time and internal stress state of material. Difference exists in the two directions of the formed sample with double curvature, but the curvature variation keeps the same. Yield strength, ultimate tensile strength and fracture toughness of the double curvature formed sample appear to be higher than those of the single curvature formed sample under the same aging condition, but the elongation and the anisotropy are opposite.

A Near-1V 10ppm/℃ CMOS Bandgap Reference with Curvature Compensation

A low voltage bandgap reference with curvature compensation is presented. Using current mode structure, the proposed bandgap circuit has a minimum voltage of 900mV. Compensated through the VEB linearization technique, this bandgap reference can reach a temperature coefficient of 10ppmFC from 0 to 150℃. With a 1.1V supply voltage,the supply current is 43μA and the PSRR is 55dB at DC frequency. This bandgap reference has been verified in a UMC 0.18μm mixed mode CMOS technology and occupies 0. 186mm^2 of chip area.

FEM analysis of workpiece curvature influence on groove deformation during plough process

To investigate the workpiece curvature influence on groove deformation,numerical studies with curvature varying from negative to positive were conducted on copper material.Groove deformations were analyzed,including groove geometry,effective stress distribution and plough force.The curled groove shape whose workpiece curvature was 0.133 mm-1 was validated by experiments.Moreover,a series of geometry models with various curvatures were introduced to analyze the change of groove deformation.The results show that positive curvatures influence groove deformation more intensively than negative or zero curvature.It is mainly due to the action of the tool forming face during plough process.

Water Manipulation through Curvature Energy on Humidity Microparticles

The electric field created in a curvature energy sensor on air microparticles is used to obtain a temperature-humidity map G:M→SO(2)∪F,by stereo-radially of the sensor design to detect and measure the temperature and humidity of certain local region of the environment space.Likewise,considering the curvature energy as the deviation of any field interaction,even the obstruction to its proper flow,is designed and created a humidity-resistor sensor to the control and optimization of humidity in a space with different gradients of humidity,pressure and temperature in a radial detection and measuring.Then the sensing problem is a problem of free boundary conditions where is satisfied an energy functional of norm ||ξ||_(2),to curvature functions κ,that satisfy in the temperature and humidity function ξ,the change limit condition ξ|_(∂Ω)≤2πξ(r).This carries to that the temperature-humidity sensor must be designed on a length gauge to measure the changes of humidity and temperature in the space.

一类Curvature方程的两种边值问题解的存在性

利用含有伪单调算子的变分不等式解的存在性定理,证明一类具有Dirichlet边值条件的Curvature方程在W1,p(Ω)空间中存在唯一解.深入研究具有Dirichlet边值条件的Curvature方程和具有Neumann边值条件的Curvature方程之间的关系,利用极大单调算子值域的扰动理论,给出具有Neumann边值条件的Curvature方程在W1,p(Ω)空间中存在解的充分条件.文中采用一些新的证明技巧,推广和补充了以往的相关研究成果.

The Submanifolds with Parallel Mean Curvature Vector in a Locally Symmetric and Conformally Flat Riemannian Manifold

In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).

无穷个增生映射和的半隐式算法、Ergodic收敛及Curvature系统（英文）

在实一致凸且q一致光滑Banach空间中,构造无穷个m增生映射和μ_i逆强增生映射和的公共零点的半隐式迭代算法.证明ergodic收敛性.与近期研究成果相比,限定条件更弱.此外,还研究了一类curvature系统并证明其解恰好是无穷个m增生映射和μ_i逆强增生映射和的公共零点,进而验证了迭代算法的有效性.

A rigidity theorem for submanifolds in S^(n+p) with constant scalar curvature

Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of Mn, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mn immersed in Sn +pwith parallel nor- malized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.

Curvatures estimation on triangular mesh

Curvatures are important geometric attributes of surfaces. There are many applications that require as a first step the accurate estimation of curvatures at arbitrary vertices on a triangulated surface. Chen and Schmitt (1992) and Taubin (1995) presented two simple methods to estimate principal curvatures. They used circular arcs to approximate the normal curvature. We find this may cause large error in some cases. In this paper, we describe a more accurate method to estimate the normal curvature, and present a novel algorithm to estimate principal curvatures by simplifying the Chen and Schmitt’s method. Some comparison results are also shown in this paper.

PROJECTIVELY FLAT FINSLER METRICS WITH ALMOST ISOTROPIC S-CURVATURE

This article characterizes projectively fiat Finsler metrics with almost isotropic S-curvature.