Longitudinal profiled plate straightening process based on curvature integral method

Considering the variable cross section thickness of longitudinal profiled plate and the dynamic reductions of straightening rolls,an analytical model combining curvature integral method with linear decreasing straightening scheme was proposed to investigate the longitudinal profiled plate straightening process.Moreover,the calculation flow and solution algorithm of longitudinal profiled plate straightening process were presented.To verify the proposed model,calculated straightening forces were compared with the measured values,and very good agreements were achieved.Then,the reduction,contact angle,reverse bending curvature,residual curvature,straightening force and straightening moment of longitudinal profiled plate in the straightening process were calculated and analyzed,and the calculated results show that the curvature integral method can be used to reveal the mechanism of longitudinal profiled plate straightening.

A DIFFERENTIABLE SPHERE THEOREM WITH PINCHING INTEGRAL RICCI CURVATURE

In this article, we introduce the Hausdorff convergence to derive a differentiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.

EXISTENCE OF AREA MINIMIZING TANGENT CONES OF INTEGRAL CURRENTS WITH PRESCRIBED MEAN CURVATURE

Given an integral M-currrent To in Rm+k and a tensor H of type(m.l)on Rn+k with values orthogonal to each of its arguments we proved in a previous peper[3]the sxistence of anintegral m-current T =γ(M,θ.ζ)with boundary T0 and mean curvature vector H by minimizing an appropriate functional on suitable subclasses of the set of all integral currents.In thes paperwe discuss the existence and structure of oriented tangent cones C of T at points x∈spt(T) spt(T),especially we show that C is locally mass minimizing.

Boundary determination of leveling capacity for plate roller leveler based on curvature integration method

Leveler is widely used to improve the quality of defective mild steel plates.Its typical ranges of the leveling capacity are constrained by three criteria,namely the maximum stroke of rollers,allowable total leveling force and motor power.In this work,an optimization model with equality and inequality constraints was built for the maximum yield stress search of each thickness of plates.The corresponding search procedure with three loops was given.The approximate range by the simplification model could be used as the initial value for the actual range search of the leveling capacity.Therefore,the search speed could be accelerated compared with a global search.The consistency of the analytical results and field data demonstrates the reliability of the proposed model and procedure.The typical ranges of the leveling capacity are expressed by several boundary curves which are helpful to judge whether the incoming plate can be leveled quickly or not.Also,these curves can be used to find the maximum yield stress for a specific thickness or the maximum thickness for a yield stress for plates.

SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

Given a family of smooth immersions of closed hypersurfaces in a locally symmetric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quantities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case

The extension for mean curvature flow with finite integral curvature in Riemannian manifolds

We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature at a finite time interval [0,T) can be extended over time T. Moreover,we show that the condition is optimal in some sense.

Integral curvature bounds and diameter estimates on Finsler manifolds

In this paper, we study the integrals of the Ricci curvature over metric balls in a Finsler manifold,which can be viewed as an L^(q)-norm of the Ricci curvature. By bounding such integrals from above, we obtain several Myers type theorems.

Geometric Estimates of the First Eigenvalue of(p,q)-elliptic Quasilinear System Under Integral Curvature Condition

Consider(M,g)as a complete,simply connected Riemannian manifold.The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of(p,q)-elliptic quasilinear system in both Dirichlet and Neumann conditions on Riemannian manifold.In some cases we add integral curvature condition and maybe we prove some theorems under other conditions.

Integral Formula of Minkowski Type and New Characterization of the Wulff Shape

Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n＋1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n＋1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results.

VARIATIONAL PROPERTIES OF THE INTEGRATED MEAN CURVATURES OF TUBES IN SYMMETRIC SPACES

Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.