CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY

This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.

The Isospectrum Problem of Compact Hypersurfaces on a Sphere

In this paper, we discuss the isospectrum of totally umbilical hypersurfaces with totally geodesic hypersurfaces on a sphere.

On the Compact Spacelike Hypersurfaces in de Sitter Space

In this paper, two properties of compact spacelike hypersurfaces in de Sitter space are obtained. When r =1, we recover Montiel's result.

The Effect of Benzyltetrahydropalmatine (BTHP) on Action Potentials and the Two Components of Delayed Rectifying Potassium Currents in Guinea Pig Ventricular Myocytes

The effects of BTHP on Ca 2+ independent action potential and the two components of delayed rectifier potassium currents were studied in guinea pig single ventricular myocytes by using whole cell patch clamp technique. BTHP 30 μmol·L -1 significantly prolonged APD 90 from 143±16 ms to 184±21 ms ( P 【0.01, n=5) without affecting either the RP or APA, and the APD prolonging effects of BTHP were independent of extracellular Ca 2+ . BTHP inhibited both I kr (IC 50 =7 9 μmol·L -1 ) and I ks (IC 50 =22 4 μmol·L -1 ) in a concentration dependent fashion. The results demon strated that BTHP had no obvious selectivity for I kr and I ks .

On spectral characterizations of Willmore hypersurfaces in a sphere

Let M be a closed Willmore hypersurface in the sphere S^n＋1（1） （n ≥ 2） with the same mean curvature of the Willmore torus Wm,n-m, if SpecP（M） = Spec^P（Wm,n-m ） （p = 0, 1,2）, then M is Wm,n-m.

On Laguerre Isopararmetric Hypersurfaces in R^7

Let x : M → R n be an umbilical free hypersurface with non-zero principal curvatures, then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. A classical theorem of Laguerre geometry states that M(n > 3) is characterized by g and B up to Laguerre equivalence. A Laguerre isopararmetric hypersurface is defined by satisfying the conditions that C = 0 and all the eigenvalues of B with respect to g are constant. It is easy to see that all Laguerre isopararmetric hypersurfaces are Dupin hypersurfaces. In this paper, we established a complete classification for all Laguerre isopararmetric hypersurfaces with three distinct principal curvatures in R7.

Deviation-Rectifying Control of Carbon Fiber Prepreg Slitting and Winding Machine

With the growing needs of prepreg tapes for the automated fiber placement(AFP),the deviation-rectifying of prepreg in slitting process was investigated on a self-developed 16-tow prepreg slitting and winding machine.The process of slitting and rewinding of prepreg tape was introduced,and the reason of prepreg tape deviation in slitting process was analyzed.In order to ensure the quality of the narrow prepreg slits,the application of the fuzzy PID algorithm in a closed-loop control system was discussed.A fuzzy PID algorithm was designed by combining fuzzy rules and PID controller.By applying it to precise deviation-rectifying control strategy,the automatic control of rectification could be achieved with accuracy of 0.1 mm,which satisfies the requirement of the prepreg tape both in slitting quality and layup quality for AFP.

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）.

Anchoring eccentricity features and rectifying devices for resin grouted bolt/cable bolt

The anchoring eccentricity of the bolt and cable bolt is a common problem in geotechnical support engineering and affects the ability of the bolt and cable bolt to control the rock mass to a certain extent.This paper reports on numerical simulation and laboratory experiments conducted to clarify the effect of eccentricity on the anchoring quality of the bolt and cable bolt,and to establish an effective solution strategy.The results reveal that the anchoring eccentricity causes unbalanced stress distribution and the uncoordinated deformation of the resin layer,which results in higher stress and greater deformation of the resin layer at the near side of the rod body.Additionally,as the degree of anchoring eccentricity increases,the effect becomes more significant,and the resin layer of the anchoring system becomes more likely to undergo preferential failure locally,which weakens the load-bearing performance of the anchoring system.This paper develops an innovative bolt anchoring rectifying device(B-ARD)and cable bolt anchoring rectifying device(C-ARD)on the basis of the structural characteristics of the bolt and cable bolt to better ensure the anchoring effect of them.The working effects of these two devices were verified in detailed experiments and analysis.The experimental results show that the anchoring rectifying devices(ARD)improve and ensure the anchoring concentricity of the bolt and cable bolt,which will help improve the supporting performance of them.The paper provides a convenient and effective method for improving the anchoring concentricity of the bolt and cable bolt,and provides a concept and reference for technical research on improving the effect of roof bolting.

STABILITY OF CONSTANT MEAN CURVATURE HYPERSURFACES OF REVOLUTION IN HYPERBOLIC SPACE

In this article, by solving a nonlinear differential equation, we prove the existence of a one parameter family of constant mean curvature hypersurfaces in the hyperbolic space with two ends. Then, we study the stability of these hypersurfaces.

ASYMPTOTIC EXPANSION OF DIRAC-TYPE DISTRIBUTION ASSOCIATED WITH A CLASS OF HYPERSURFACES WITH DEGENERATED CRITICAL POINTS

In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE, this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x) with degenerate critical points and proves that [F(x)](+)(lambda) is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x). Next, the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x) = 0 with A(mu) type degenerate critical point at x = 0, F-+(lambda) is a distribution-valued meromorphic function of lambda.

ON STATIONARY HYPERSURFACES IN EUCLIDEAN SPACES

Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article.

Hypersurfaces with constant mean curvature in unit sphere

The pinching of n-dimensional closed hypersurface Mwith constant mean curvature H in unit sphere S^（n＋1）（ 1） is considered. Let A = ∑i,j,k h（ijk）~2（ λi＋ nH）~2,B = ∑i,j,k h（ijk）~2（ λi＋ nH） ·（ λj＋ nH）,S = ∑i（ λi＋ nH）~2, where h（ij）= λiδ（ij）. Utilizing Lagrange＇s method, a sharper pointwise estimation of 3（A- 2B） in terms of S and ｜▽h｜~2 is obtained, here ｜▽h｜~2= ∑i,j,k h（ijk）~2. Then, with the help of this, it is proved that Mis isometric to the Clifford hypersurface if the square norm of the second fundamental form of Msatisfies certain conditions. Hence, the pinching result of the minimal hypersurface is extended to the hypersurface with constant mean curvature case.

NORMAL CRITERION FOR FAMILIES OF HOLOMORPHIC MAPS OF SEVERAL COMPLEX VARIABLES INTO P^N(C)WITH MOVING HYPERSURFACES

This article gives a normal criterion for families of holomorphic mappings of several complex variables into P N(C)for moving hypersurfaces in pointwise general position,related to an Eremenko’s theorem.

RECTIFYING EFFECT OF POLYANILINE(PANI)/N-TYPE POROUS SILICONE HETEROJUNCTION

Heterojunctions between polyaniline (PANI) and n-type porous silicon (PS), Al/PS-PANI/Au cell, were fabricated, and the rectifying parameters of this heterojunction diode were measured as a function of the preparation conditions of PANI and PS, the electronic structure of PANI as well as cell structure. The rectifying parameters of Al/PS-PANI/Au cell were determined to be gamma = 1.8x10(1) similar to 1.0x10(5) for the rectifying ratio at 3V, n = 3 similar to 12 for the ideal factor, j(0) = 8.0x10(-5) similar to 5.6x10(-2) mA/cm(2) for the reversed saturated current density, and phi(0) = 0.67 similar to 0.83 V for the barrier height, respectively. The best rectifying heterojunction diode made between PANI and n-type PS with higher rectifying factor (gamma = 1.0x10(5) at 3V), output current (>1500 mA/cm(2) at 3V) and lower ideal factor (n = 3.3) was obtained by preventing the oxidation of PS before evaporating Al electrode.

ISOPARAMETRIC HYPERSURFACES AND COMPLEX STRUCTURES

The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres.As a consequence,complex structures on S^(1)×S^(7)×S^(6),and on S^(10)×S^(3)×S(2)with vanishing first Chern class,are built.

Quasi- Einstein Hypersurfaces in a Hyperbolic Space

In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough.

ON A CURVATURE CHARACTERIZATION OF RICCI-PSEUDOSYMMETRIC HYPERSURFACES

The author presents a curvature characterization of Ricci-pseudosymmetric hypersurfaces in semi-Riemannian space forms Nsn+1(c), n>4.

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.

NEW SPECTRAL CHARACTERIZATIONS OF EXTREMAL HYPERSURFACES

Let M be a closed extremal hypersurface in S^n＋1 with the same mean curvature of the Willmore torus Wm,n-m.We proved that if Spec^p（M） = Spec^p（Wm,n-m ） for p = 0, 1, 2, then M is Wm,m.