Related papers: A Realization of Discrete Geometry by String Model
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
String vibration represents an active field of research in acoustics. Small-amplitude vibration is often assumed, leading to simplified physical models that can be simulated efficiently. However, the inclusion of nonlinear phenomena due to…
The elements of $O(d,d,\Z)$ are shown to be discrete symmetries of the space of curved string backgrounds that are independent of $d$ coordinates. The explicit action of the symmetries on the backgrounds is described. Particular attention…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
We explore gauge fields - strings duality by means of the loop equations and the zigzag symmetry. The results are striking and incomplete. Striking - because we find that the string ansatz proposed in [A.M. Polyakov, hep-th/9711002]…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
We present a method for numerical computation of conformal mappings from simply or doubly connected domains onto so-called canonical domains, which in our case are rectangles or annuli. The method is based on conjugate harmonic functions…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
The gauge gravity action for general relativity in any dimension using a connection for the Euclidean or Poincar\'e group and a symmetry-breaking scalar field is written using a particularly simple matrix technique. A discrete version of…
We derive a class of solutions to the string sigma-model equations for the closed bosonic string. The tachyon field is taken to form a constant condensate and the beta-function equations at one-loop level are solved for the evolution of the…
In this article I first give an abbreviated history of string theory and then describe the recently-conjectured field-string duality. This suggests a class of nonsupersymmetric gauge theories which are conformal (CGT) to leading order of…
In string theory the coupling parameters are functions of moduli fields. The actual values of the coupling constants are then dynamically determined through the vacuum expextation values of these fields. We review the attempts to connect…
A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.
Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…
We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these…
It is shown that the string concept results naturally from considerations of gravitation. This paper describes a derivation of linearized general relativity based upon the hypotheses of special covariance and the existence of a…
We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter. The ground states of these models can be thought of as…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
In this work we prove uniqueness result for an implicit discrete system defined on connected graphs. Our discrete system is motivated from a certain class of spatial segregation of reaction-diffusion equations.
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…