Related papers: Accessory Parameters for Four-Punctured Spheres
We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…
We show that the use of Sudakov variables greatly simplifies the study of the solutions to the scattering equations in the Cachazo-He-Yuan formalism. We work in the center-of-mass frame for the two incoming particles, which partially fixes…
We establish several nonuniqueness results for the problem of finding complete conformal metrics with constant (fourth-order) $Q$-curvature on compact and noncompact manifolds of dimension $\geq5$. Infinitely many branches of metrics with…
In this paper, aliasing effects are investigated for random fields defined on the d-dimensional sphere and reconstructed from discrete samples. First, we introduce the concept of an aliasing function on the sphere. The aliasing function…
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…
Using the notion of aggregation work, we construct a system of differential equations for the aggregation number of micelles which is a function of the parameters of micellization (parametric equations). There are explicit solutions for two…
In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
In this note, we exhibit a weakly holomorphic modular form for use in constructing a Fourier eigenfunction in four dimensions. Such auxiliary functions may be of use to the D4 checkerboard lattice and the four dimensional sphere packing…
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…
For Riemannian metrics of constant positive curvature on a punctured sphere with conic singularities at the punctures and co-axial monodromy of the developing map, possible angles at the singularities are completely described. This…
We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…
The problem of resolving point-like light sources not only serves as a benchmark for optical resolution but also holds various practical applications ranging from microscopy to astronomy. In this research, we aim to resolve two thermal…
The existence of numerical solutions to a fourth order singular boundary value problem arising in the theory of epitaxial growth is studied. An iterative numerical method is applied on a second order nonlinear singular boundary value…
In this exploratory article, we present a constructive method for scattering points on the surface of $d$ dimensional spheres which we believe is new and of interest. Indeed, the problem of uniformly distributing points on spheres is an…
We embark on a tour that takes us through four closely related topics: the dual concepts of independence and spanning in finite abelian groups and the analogous dual concepts of designs and distance sets on spheres. We review some of the…
Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal…
We investigate a discretization of a class of stochastic heat equations on the unit sphere with multiplicative noises. A spectral method is used for the spatial discretization and the truncation of the Wiener process, while an implicit…
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
We consider the problem of adaptive observer design in the settings when the system is allowed to be nonlinear in the parameters, and furthermore they are to satisfy additional feasibility constraints. A solution to the problem is proposed…