We address the problem of surface inpainting, which aims to fill in holes or missing regions on a Riemann surface based on its surface geometry. In practical situation, surfaces obtained from range scanners often have holes or missing regions where the 3D models are incomplete. In order to analyze the 3D shapes effectively, restoring the incomplete shape by filling in the surface holes is neces...

We review the construction of braided tensor categories and modular tensor categories from representations of vertex operator algebras, which correspond to chiral algebras in physics. The extensive and general theory underlying this construction also establishes the operator product expansion for intertwining operators, which correspond to chiral vertex operators, and more generally, it establi...

The goal of this paper is to express the Bach tensor of a four– dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang–Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach t...

We take advantage of the Shiromizu et al. covariant formalism to find out brane properties originating from five dimensional bulk spacetime. Making a different choice for conformal factor $e^{-2b(z)}$ compared Estrada [24], we reach new solution with lot interesting properties, where $b(z) = ln(1/\sqrt{cosh2\mu z})$. The non-local tensor $E_{ab}$ rooted 5-dimensional Riemann gives an anisotropi...

Motivated by optimal control of affine systems stemming from mechanics, metrics on the two-sphere of revolution are considered; these metrics are Riemannian on each open hemisphere whereas one term of the corresponding tensor becomes infinite on the equator. Length minimizing curves are computed and structure results on the cut and conjugate loci are given, extending those in [11]. These result...

The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in the quantum corrections; depending on the values of quantization parameters, they obey an exact or perturbed power-law expansion in conformal time. The comov...

A method which uses a generalized ζ-function to compute the renormalized (Euclidean) stress tensor of a quantum field propagating in a curved background is presented. The method does not use point-splitting procedures or off-diagonal ζ functions but employs an analytic continuation of a generalized ζ-function. The starting point of the method is the direct computation of the functional derivati...

Many researches attempt to improve the efficiency of the usual quasi-Newton (QN) methods by accelerating the performance of the algorithm without causing more storage demand. They aim to employ more available information from the function values and gradient to approximate the curvature of the objective function. In this paper we derive a new QN method of this type using a fourth order tensor m...

Representation and comparison of shapes is a problem with many applications in computer vision and imaging, including object recognition and medical diagnosis. We will discuss some constructions from the theory of conformal mapping which provide ways to represent and compare planar shapes. It is a remarkable fact that conformal maps from the unit disk to a planar domain encode the geometry of t...