Related papers: Accessory Parameters for Four-Punctured Spheres
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a surface is discrete conformal to a constant curvature…
We derive an exact, analytic expression for the fourth virial coefficient of a system of polydisperse spheres under the constraint that the smallest sphere has a radius smaller than a given function of the radii of the three remaining…
We study the isoperimetric problem in product spaces equipped with the uniform distance. Our main result is a characterization of isoperimetric inequalities which, when satisfied on a space, are still valid for the product spaces, up a to a…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
For the Heun differential equation and all of its confluent equations, we derive formal series expansions of the accessory parameters using the Voros periods. We then compare these expansions with the classical conformal blocks recently…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
Using the Observable form of Maxwell's equations, we reveal that effective parameters at materials boundaries emerge naturally as anisotropic transfer functions. The complexity of the boundary dictates the order of these functions.…
In this work, we introduce a new difference equation which is discrete analogue of Diffusion differential equation and analyze some essential spectral properties, Diffusion difference operator is self-adjoint, eigenvalues of this problem…
A geometric interpretation of the spontaneous symmetry breaking effect, which plays a key role in the Standard Model, is developed. The advocated approach is related to the effective use of the momentum 4-spaces of the constant curvature,…
The transfer equation in spherical geometry with central symmetry, which is a partial differential equation in two variables r and m, is reduced to a one-dimensional transfer equation in r parametric in m. This is done by dropping the…
In this article we study the two dimensional singularly perturbed heat equation in a circular domain. The aim is to develop a numerical method with a uniform mesh, avoiding mesh refinement at the boundary thanks to the use of a relatively…
A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. This formalism also…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
We study the second quantization of field theory on the q-deformed fuzzy sphere for real q. This is performed using a path-integral over the modes, which generate a quasiassociative algebra. The resulting models have a manifest U_q(su(2))…
In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.
We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).
We consider the problem of varying conformally the metric of a four dimensional manifold in order to obtain constant $Q$-curvature. The problem is variational, and solutions are in general found as critical points of saddle type. We show…
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…