where ω̃ = ( √ −1/2)g̃ij̄dz ∧ dz and Σ̃ = ( √ −1/2)R̃ij̄dz ∧ dz are the Kähler form, the Ricci form of the metric g̃ respectively, while c1(M) denotes the first Chern class. Under the normalized initial condition (2), the first author [3] (see also Proposition 1.1 in [4]) showed that the solution g(x, t) = ∑ gij̄(x, t)dz dz to the normalized flow (1) exists for all time. Furthermore by the work of Mok ...

This paper addresses one major aspect of a project aimed at the design of an image database query engine, where the images are searched at the 3D object-level. This approach is a novelty since image databases are usually searched by comparing colours, textures and 2D shapes of regions in the images. The main topic and contribution of this paper is a new method for object part segmentation, from...

: Investigations on control and optimization of continuum manipulators have resulted in a number of kinematic and dynamic modeling approaches each having their own advantages and limitations in various applications. In this paper, a comparative study of five main methods in the literature for kinematic, static and dynamic modeling of continuum manipulators is presented in a unified mathematical...

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability densi...

In [12], we treated the Christoffel-Minkowski problem as a convexity problem of a spherical hessian equation on S via Gauss map. In this paper, we study the curvature equations of radial graphs over Sn. Our main concern is the existence of hypersurface with prescribed Weingarten curvature on radial directions. For a compact hypersurface M in Rn+1, the kth Weingarten curvature at x ∈ M is define...

In this paper, we propose a new scheme for anisotropic motion by mean curvature in R. The scheme consists of a phase-field approximation of the motion, where the nonlinear diffusive terms in the corresponding anisotropic Allen-Cahn equation are linearized in the Fourier space. In real space, this corresponds to the convolution with a specific kernel of the form Kφ,t(x) = F−1 [ e−4π 2tφo(ξ) ] (x...

In this paper, we give several applications of the discrete game approach to partial differential equations (PDEs). We first present a rigorous game-theoretic proof of fattening phenomenon for motion by curvature with figure-eight–shaped initial curves without using parabolic PDE theory. The proof is based on a comparison between the game value and its inverse. Accompanied by the example of fig...

INTRODUCTION This study investigated the fatigue and fracture modes of RaCe and ProTaper rotary instruments. MATERIALS AND METHODS Fatigue resistance was evaluated by rotating the files 30° or 60° and with 2 or 5mm radius of curvature. RaCe taper 06 size 25 and ProTaper F1 files (n=40) were used. The number of rotations to failure was analyzed by two-way ANOVA and independent sample t-test. F...

Classical general relativity from quantum gravity and the generalized Kodama states. Abstract In this paper we investigate the relation between the CDJ matrix used for construction of the generalized Kodama states and the Weyl curvature tensor. By exploiting special self-duality relations unique to four dimensional spacetime, we show that the effects of quantum gravity in Ashtekar variables are...

Many information fusion tasks involve the processing of Gaussian mixtures with simple underlying shape, but many components. This paper addresses the problem of reducing the number of components, allowing for faster density processing. The proposed approach is based on identifying components irrelevant for the overall density’s shape by means of the curvature of the density’s surface. The key i...