The work proposes a general background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza– Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on highe...

We study O(N+1) nonlinear σ-model in (p+1+N)-dimensional curved spacetime with a negative cosmological constant, and find a new σ-lump solution with half-integer winding and divergent energy. When the spatial structure of N extra-dimensions is determined by this global defect, a black σp-brane surrounded by the degenerated horizon is formed and its near-horizon geometry is identified as a warp ...

Abstract: We first calculate the heat capacities of the nonlinear electrodynamics (NED) black hole for fixed mass and electric charge, and the electric capacitances for fixed mass and entropy. Then, we study the properties of the Ruppeiner thermodynamic geometry of the NED black hole. Lastly, some discussions on the thermal stability of the NED black hole and the implication to the flatness of ...

A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conver...

We consider the nonlinear eigenvalue problem −u′′(t) = f(λ, u(t)), u > 0, u(0) = u(1) = 0, where λ > 0 is a parameter. It is known that under some conditions on f(λ, u), the shape of the solutions associated with λ is almost ‘box’ when λ 1. The purpose of this paper is to study precisely the asymptotic shape of the solutions as λ → ∞ from a standpoint of L1-framework. To do this, we establish t...

Geometric wavelet-like transforms for univariate and multivariate manifold-valued data can be constructed by means of nonlinear stationary subdivision rules which are intrinsic to the geometry under consideration. We show that in an appropriate vector bundle setting for a general class of interpolatory wavelet transforms, which applies to Riemannian geometry, Lie groups and other geometries, Hö...

We study the Cauchy problem for a strictly hyperbolic n×n system of conservation laws in one space dimension: ut + f(u)x = 0, u(0, x) = ū(x). The initial data ū is a small BV perturbation of a single rarefaction wave with an arbitrary strength. All characteristic fields are assumed to be genuinely nonlinear or linearly degenerate in the vicinity of the reference rarefaction curve. We prove that...

Møller’s energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a “generalized Schwarzschild” geometry in (3+1)-dimensions on a noncommutative curved D3brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and dep...

This article introduces a methodology for designing the geometry of diffuse-walled radiant enclosures through nonlinear programming. In this application, the enclosure is represented parametrically using B-spline curves, while the radiosity distribution is solved by infinitesimal-area analysis. The enclosure geometry is repeatedly adjusted with a gradientbased minimization algorithm until a nea...

where ν is the outward unit normal vector on ∂Ω; ν exists a.e. for Lipschitz domains. The goal of this paper is to understand the asymptotic behavior of Λ(γ) as γ → ∞ when ∂Ω ∈ C1. Since Λ(γ) → ∞ when γ → ∞, (2) can be viewed as a singularly perturbed linear eigenvalue problem. The asymptotic behavior of Λ(γ) was first studied by Lacey, Ockendon and Sabina in [3], where they investigated some r...