应用两种设备测量翼状胬肉患者角膜曲率一致性评价

目的分析Oculus Keratograph眼表综合分析仪与IOLMaster 5.2.1两种仪器测量翼状胬肉患者角膜曲率结果的一致性。方法前瞻性自身对照试验。收集2018年5~9月我院诊断初发性翼状胬肉患者68例(75只眼),采用图像处理和分析软件(Image-Pro Plus V.6.0)测量并计算翼状胬肉面积≤4 mm 2、4.1~7 mm 2、>7.1 mm 2在分别使用眼表综合分析仪与IOLMaster进行角膜曲率(水平角膜曲率K1、垂直角膜曲率K2)测量,比较两种方法测量结果的相关性、一致性及检出率。结果眼表综合分析仪与IOLMaster分别测量翼状胬肉面积≤4 mm 2者的K1平均值(44.40±1.93)D,(44.20±1.90)D,差异无统计学意义(t=1.07,P>0.05),K2平均值(44.36±1.83)D、(44.21±1.69)D,差异无统计学意义(t=1.18,P>0.05),一致性分别r=0.912、0.932,两组设备检出率100%。两组设备测量翼状胬肉面积4.1~7 mm 2,K1平均值分别(45.32±1.73)D、(43.96±1.75)D、差值为(1.39±0.22)D,差异有统计学意义(t=3.07,P<0.05),K2平均值分别(44.72±1.64)D、(44.26±1.91)D、差异无统计学意义(t=-2.24,P>0.05),一致性r=0.611、0.866,两组设备检出率分别为97.33%,100%,差异无统计学意义(χ2=2.014,t>0.248)。两组设备测量翼状胬肉面积>7.1 mm 2,K1平均值分别(44.12±1.93)D、(43.21±2.25)D,差值为(0.91±0.02)D,差异有统计学意义(t=4.07,P<0.01),K2平均值分别(44.24±1.65)D、(45.15±1.41)D,差值为(-0.91±0.34)D,差异有统计学意义(t=-6.272,P<0.01),一致性分别为r=0.732、0.542,两组设备检出率分别为77.33%,98.66%(χ2=16.054,t=0.000)。Bland-Altman分析95%一致性界限K1(-2.241,3.474),K2(-4.170,2.132)。结论眼表综合分析仪与IOLMaster在翼状胬肉面积≤7 mm 2测量角膜曲率相关程度较高,临床上两者间测量的一致性较好,两组设备检出率近乎相同;当翼状胬肉面积>7 mm 2时,两者间测量一致性较差并且IOLMaster检出率更高一些。

CONTOUR EXTRACTION AND FEATURE POINT DETECTION FOR 3-D FRAGMENT REASSEMBLY

An approach to contour extraction and feature point detection in the 3-D fragment reassembly is proposed. A simple and effective technique is used for building the intrinsic topology of the fragment data suitable for contour extraction. For the scanned data in which the topology is difficult to be achieved, the corresponding solutions are given to manage this problem. A robust approach is used for the curvature and torsion calculation of the discrete contour in a 3-D space. Finally, a method is developed for detecting feature points of the fragment contour based on total curvature. Therefore, the contour description combines the simple global information with local feature points. Experiments with real contour curves extracted from 3-D fragments demonstrate that the proposed method is robust and efficient.

复杂非限定约束曲面造型

文章介绍了两种曲面建构方法,并阐述了使用ISDX构造自由曲面模型的特点、方法和注意事项,指出了构造自由曲面模型和参数化曲面模型的最大区别是对曲率表的使用方式。

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.

A New CKP Hierarchy with Two Generalized Time Series and Its Reduction

A new C-type subhierarchy for KP hierarchy with two new time series γn and σk （ （Tn,crk ）-CKPH）, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The zero-curvature representation for the （γn, σk ）-CKPH is derived. The reduction and constrained flows of （γn, σk ）-CKPH are studied.

Integrable Properties Associated with a Discrete Three-by-Three Matrix Spectral Problem

Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that the hierarchy possesses a HamiItonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.

Isospectral and Nonisospectral Lattice Hierarchies Associated with a Discrete Spectral Problem and Their Infinitely Many Conservation Laws

In this paper, based on the discrete zero curvature representation, isospectrai and nonisospectrai lattice hierarchies are proposed. By means of solving corresponding discrete spectral equations, we demonstrate the existence of infinitely many conservation laws for this two hierarchies and obtain the formulae of the corresponding conserved densities and associated fluxes.

A Note on Special Functions Related to Lotka / Negative Volterra Equations

We study special functions related to Lotka-Volterra equations and negative Volterra equation intro-duced from zero curvature representations . At first we show the relationships between Lotka-Volterra equations introduced from zero curvature representations and symmetric orthogonal polynomials. Sec-ondarily, we describe the relationships between negative Volterra equations with a special solutions and cylinder functions.

A Family of Integrable Rational Semi-Discrete Systems and Its Reduction

Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.

The Bonnesen isoperimetric inequality in a surface of constant curvature

We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.

Curvature estimates for the level sets of spatial quasiconcave solutions to a class of parabolic equations

We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations ut = F(▽2u,▽u,u,t) under a structural condition,and give a geometric lower bound of the principal curvature of the spatial level surfaces.

Interaction potential between micro/nano curved surface and a particle located inside the surface (I):driving forces induced by curvatures

This paper focuses on the interaction between a micro/nano curved surface and a particle located inside the surface (hereafter abbreviated as in-surface-particle).Based on the exponential pair potential (namely 1/R2k) between particles,the interaction potential between the micro/nano curved surface and the in-surface-particle is derived.The following results are shown:(a) For an even number of exponents in the pair potential,the interaction potential between the micro/nano curved surface and the in-surface-particle can be expressed as a unified function of the mean curvature and Gaussian curvature of the curved surface;(b) the curvatures and the gradients of curvatures of the micro/nano curved surface are the essential factors that dominate the driving force acting on the particle.

Two Hierarchies of New Differential-Difference Equations Related to the Darboux Transformations of the Kaup–Newell Hierarchy

Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newe11 hierarchy of equations. Their integrable properties such as recursion operator, zero-curvature representations, and bi-Hamiltonian structures are stud- ied. In addition, the hierarchy of equations obtained by Wu and Geng is identified with the hierarchy of two-component modified Volterra lattice equations.

Reverse Bonnesen style inequalities in a surface X_∈~2 of constant curvature

We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema＇s result in the Euclidean plane E2.

CONVEXITY AND SYMMETRY OF TRANSLATING SOLITONS IN MEAN CURVATURE FLOWS

This paper proves that any rotationally symmetric translating soliton of mean curvature flow in R3 is strictly convex if it is not a plane and it intersects its symmetric axis at one point. The authors also study the symmetry of any translating soliton of mean curvature flow in Rn.

The semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly

A new method to solve the Gauss-Codazzi system is given in which we transform the linearized system to a partial differential equation of second order, and by the method we solve the problem of semi-global isometric embedding of surfaces with Gaussian curvature changing sign cleanly.

Investigation on Cooling Effectiveness and Aerodynamic Loss of a Turbine Cascade with Film Cooling

This paper describes the numerical study on film cooling effectiveness and aerodynamic loss due to coolant and main stream mixing for a turbine guide vane. The effects of blowing ratio, mainstream Mach number, surface curvature on the cooling effectiveness and mixing loss were studied and discussed. The numerical results show that the distributions of film cooling effectiveness on the suction surface and pressure surface at the same blowing ratio(BR) are different due to local surface curvature and pressure gradient. The aerodynamic loss features for film holes on the pressure surface are also different from film holes on the suction surface.

Lax Triad Approach to Symmetries of Scalar Modified Kadomtsev–Petviashvili Hierarchy

By means of Lax triads we reconstruct isospectral and nonisospectral scalar modified Kadomtsev–Petviashvili(mKP) hierarchies. In this approach the argument y is treated as an independent variable which is independent of time parameters {t_1, t_2,...}. Consequently, the isospectral and nonisospectral scalar mKP flows can have clear zero curvature representations, which enables us to handle investigation of symmetries of the scalar isospectral mKP hierarchy as freely as for(1+1)-dimensional systems. As a result, we obtain Lie algebraic structures of the scalar mKP flows and construct symmetries for the scalar isospectral mKP hierarchy.

Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.

LOCAL ISOMETRIC EMBEDDINGS OF SURFACES INTO A 3-SPACE

In the paper, the authors show that any abstract smooth surface can be locally isometricallyembedded into a class of 3-dimensional spaces Nρ0 (ρ0>0) with the non-positively sectionalcurvature being fixed sufficiently small.