Analogues of hadwiger's theorem in space ℝ n —Sufficient conditions for a convex domain to enclose another

We estimate the kinematic measure of one convex domain moving to another under the groupG of rigid motions in ⁿ . We first estimate the kinematic formula for the total scalar curvature D ₀gD ₁ Rdv of then–2 dimensional intersection submanifold D ₀gD ₁. Then we use Chern and Yen's kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in ⁿ (4). Forn=4, we directly obtain another sufficient condition in ⁴.     

A global pinching theorem for compact surfaces inS 3 with constant mean curvature

LetM be a compact minimal surface inS ³. Y. J. Hsu^[5] proved that if S₂22, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·₂ denotes theL ²-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS ³ with constant mean curvature.Supported by NSFH.     

De Sitter空间中紧致类空超曲面的积分公式及其Goddard猜想的应用

本文对ｄｅＳｉｔｅｒ空间Ｓｎ＋１１（１）中紧致类空超曲面建立Ｍｉｎｋｏｗｓｋｉ型公式，并给出其到ｒ－次（ｒ＝１，２，…，ｎ－１）平均曲率为常数超曲面的应用．当ｒ＝１时，我们得到Ｍｏｎｔｉｅｌ的结果．     

The Conjugate Nets, Cartan Submanifolds, and Laplace Transformations in Space Forms

In this paper we establish the geometric theory of conjugate nets, Cartan submanifolds, and Laplace transformations in sphere and pseudo-sphere spaces. The corresponding theory in cases of projective and Euclidean spaces has been established by Chern, Kamran and Tenenblat.     

New Examples of Willmore Surfaces in S n

A surface x: M S ⁿ is called a Willmore surface if it is a criticalsurface of the Willmore functional _M (S – 2H ²)dv, where H isthe mean curvature and S is the square of the length of the secondfundamental form. It is well known that any minimal surface is aWillmore surface. The first nonminimal example of a flat Willmoresurface in higher codimension was obtained by Ejiri. This example whichcan be viewed as a tensor product immersion of S ¹(1) and a particularsmall circle in S ²(1), and therefore is contained in S ⁵(1) gives anegative answer to a question by Weiner. In this paper we generalize theabove mentioned example by investigating Willmore surfaces in S ⁿ (1)which can be obtained as a tensor product immersion of two curves. We inparticular show that in this case too, one of the curves has to beS ¹(1), whereas the other one is contained either in S ²(1) or in S ³(1). In the first case, we explicitly determine the immersion interms of elliptic functions, thus constructing infinetely many newnonminimal flat Willmore surfaces in S ⁵. Also in the latter casewe explicitly include examples.     

Mechanically tunable broadband terahertz modulator based on high-aligned Ni nanowire arrays

We present a mechanically tunable broadband terahertz(THz) modulator based on the high-aligned Ni nanowire(NW)arrays. The modulator is a sandwich structure consisting of two polydimethylsiloxane layers and a central layer of highaligned Ni NW arrays. Our experimental measurements reveal the transmittance of THz wave can be effectively modulated by mechanical stretching. The NW density in arrays increases with the strain increasing, which induced an enhancement in the absorption of THz wave. When the strain increases from 0 to 6.5%, a linear relationship is observed for the variation of modulation depth(MD) of THz wave regarding the strain, and the modulated range is from 0 to 85% in a frequency range from 0.3 THz to 1.8 THz. Moreover, the detectable MD is about 15% regarding the 1% strain change resolution. This flexible Ni NW-based modulator can be promised many applications, such as remote strain sensing, and wearable devices.     

Analytical modeling and experimental investigation of laser induction hybrid rapid cladding for Ni-based WC composite coatings

Laser induction hybrid rapid cladding (LIHRC) cannot only increase the cladding efficiency, but can also eliminate porosity and cracking of ceramic–metal composite coatings. In order to obtain a deep understanding of LIHRC with rapid cladding speed and high powder deposition rate, an analytical model of LIHRC for Ni-based WC composite coatings is proposed in the paper. The predictions of cladding height and powder efficiency obtained with this model are in good agreement with experimental results. Injection angles at which the attenuation rate of laser power is relatively low are identified and crack-free composite coatings with smooth surface, good profile and metallurgical bonding to substrate can be obtained. The calculated results for the temperature of the powder particles are compared to experimental data of the microhardness profiles and show a similar trend.     

Embedded Rotational Hypersurfaces with Constant Scalar Curvature in Sn: A Correction to a Statement in M. L. Leite, Manuscripta Math. 67 (1990), 285-304.

We prove that there exist (n − 1)-dimensional compact embedded rotational hypersurfaces with constant scalar curvature (n − 1)(n − 2)S (S > 1) of S ⁿ other than product of spheres for 4 ≤ n ≤ 6. As a result, we prove that Leite’s Assertion was incorrect.The project is supported by the grant No. 10531090 of NSFC.     

连通无向图Rabin数的一个界

可靠性和有效性是互连网络设计的重要标准,而Rabin数是度量网络容错性和传输延迟的重要参数.将通过图的容错直径给出2- 连通无向图和~3- 连通无向图的~Rabin 数r_2(G)和r_3(G)的界;同时也得到r_2(G) = D_2(G)成立的一个条件.