Related papers: Separable functions: symmetry, monotonicity, and a…
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex…
In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…
We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory,…
The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502…
We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is…
Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
The fundamental measure density functional theory for hard spheres is generalized to binary mixtures of arbitrary positive and moderate negative non-additivity between unlike components. In bulk the theory predicts fluid-fluid phase…
We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we…
Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly…
In this paper we study the property of separability of functional space with the open-point and bi-point-open topologies.
This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We…
Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the $j^*$-metric, and the distance ratio metric defined in the unit ball domain. Several sharp results are proven and a conjecture about the…
We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.
In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be…
In this paper, using 1+1D models as examples, we study symmetries and anomalous symmetries via multi-component partition functions obtained through symmetry twists, and their transformations under the mapping class group of spacetime. This…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
We introduce and develop the notion of spherical polyharmonics, which are a natural generalisation of spherical harmonics. In particular we study the theory of zonal polyharmonics, which allows us, analogously to zonal harmonics, to…