Self-adjointness of Schrödinger-type operators with locally integrable potentials on manifolds of bounded geometry

We consider a Schrödinger-type differential expression , where ∇ is a C^∞-bounded Hermitian connection on a Hermitian vector bundle E of bounded geometry over a manifold of bounded geometry (M,g) with metric g and positive C^∞-bounded measure dμ, and V∈L_loc¹(EndE) is a linear self-adjoint bundle map. We define the maximal operator H_V,max associated to H_V as an operator in L²(E) given by H_V,maxu=H_Vu for all , where ∇∗∇u in is understood in distributional sense. We give a sufficient condition for the self-adjointness of H_V,max. The proof adopts Kato's technique to our setting, but it requires a more general version of Kato's inequality for Bochner Laplacian operator as well as a result on the positivity of u∈L²(M) satisfying the equation (Δ_M+b)u=ν, where Δ_M is the scalar Laplacian on M, b>0 is a constant and ν?0 is a positive distribution on M. For local estimates, we use a family of cut-off functions constructed with the help of regularized distance on manifolds of bounded geometry.     

N = 4 Superconformal Algebra in Curved Space and Pseudo-Hyper-Kähler Geometry

We construct the representation of the small N=4 superconformal algebra in curved space under the minimal interaction assumption. We find that the structure relations of the algebra are satisfied within our assumption in the background of the metric of a pseudo-hyper-Kähler manifold.     

Study of upper bound problem of heilbronn type

A set of n points in the plane determines a total Cn^2 distances (some of them may be the same). Let rn be the ratio of the maximum distance to the minimum distance, and Rn be the greatest lower bound for rn.By using the mathematical software Mathematica,the author gets the following results in this paper.R12≤2.99496…,R13≤cscπ/10.     

A new extension theorem for linear codes

For an [n,k,d]_q code with k3, gcd(d,q)=1, the diversity of is defined as the pair (Φ₀,Φ₁) with

All the diversities for [n,k,d]_q codes with k3, d−2 (mod q) such that A_i=0 for all i0,−1,−2 (mod q) are found and characterized with their spectra geometrically, which yields that such codes are extendable for all odd q5. Double extendability is also investigated.     

Zero-Point Energy of Quantum Fields in a Schwarzschild Geometry

The effective Lagrangian and the zero-point (or Casimir) energy is calculated from the zeta-function which is obtained by the heat kernel method using the expansion of (Bormann and Antonsen, 1995). Calculated this way this unavoidable energy contribution is automatically regularised and ready for further investigation. Interesting observations include a large energy contribution (from scalar field and fermionic zero-point fluctuations) that is non-zero as the mass goes to zero, perhaps indicating a topological origin. Also, plots of the contribution of gauge boson fields to the zero-point energy, as a function of radial distance (gravitational field strength) and the size of the gauge boson coupling (gauge field strength) shows great variation, notably the occurrence of resonances.     

Connections and Distributions on Quantum Hyperplane

In this paper we introduce basic notions from noncommutative geometry to the quantum hyperplane: linear connections, submanifolds, distributions and we give a Frobenius type theorem for the quantum hyperplane.     

Some geometric aspects of maps

In this talk we introduce a Weierstrass-like system of equations corresponding to CP N -1 fields in two dimensions. Then using this representation we introduce a vector in R N 2-1 and treating this vector as the radius vector of a surface immersed in R N 2-1 we discuss to what extent the associated metric describes the geometry of the CP N -1 maps. We show that for the holomorphic maps - the correspondence is exact; while for the more general fields we have to go beyond the Weierstrass system and add extra terms. Received 1st August 2001 / Received in final form 18 October 2001 Published online 2 October 2002 RID="a" ID="a"Work done in collaboration with M. Grundland e-mail: w.j.zakrzewski@durham.ac.uk     

1,4,8,11-tetrakis(2-pyridylmethyl)-1,4,8,11-tetraazacyclotetradecane

The crystal structure of the ligand 1,4,8,11-tetrakis(2-pyridylmethyl)-1,4,8,11-tetraazacyclotetradecane (tpmc) has been determined. The compound crystallizes in triclinic space group P with a = 6.1927(3), b = 11.3771(3), c = 11.8229(3) Å = 84.368(2), = 98.77(1), = 78.533(2)° V = 810.84(5) ų; and Z = 1.     

基于SIFT算法的移动机器人同时定位与地图创建

研究了基于尺度不变特征变换（SIFT）算法的移动机器人同时定位与地图创建（SLAM）方法,即在视角改变情况下,用SIFT算法对不同图像进行特征匹配,根据极线几何原理得到摄像头的旋转角度,将之与里程计的角度信息融合,从而实现较准确的自我定位与地图创建.实验表明：本方法利用电荷耦合器件（CCD）摄像头和里程计间内在的几何关系来实现SLAM,提高了低成本移动机器人的定位精度.     

Chain spaces with many reflections

We consider chain spaces that possess a group of automorphisms containing many reflections. Such a chain space can be coordinatized by a commutative algebra, if the group satisfies a 3-reflection theorem, or if the chain space has additional geometric properties. Received 7 February 2000; in revised form 26 June 2000.