Related papers: Further study of Squeezing function Corresponding …
We first give an exposition on holomorphic isometries from the Poincar\'e disk to polydisks and from the Poincar\'e disk to the product of the Poincar\'e disk with a complex unit ball. As an application, we provide an example of proper…
We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
In this paper, we seek to explore under what conditions the periodicity of an entire function $ f(z) $ follows from the periodicity of a differential polynomial in $ f(z) $. We improve and generalize some earlier results and we give other…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
In this note, we provide a simple derivation of expressions for the restricted partition function and its polynomial part. Our proof relies on elementary algebra on rational functions and a lemma that expresses the polynomial part as an…
I review recent numerical studies of accretion disks, focusing on measurements of the turbulent shear stress, or $\alpha$, in the shearing box model. I conclude with a list of astronomically relevant open questions that can be settled via…
We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.
Broadband multimode squeezers constitute a powerful quantum resource with promising potential for different applications in quantum information technologies such as information coding in quantum communication networks or quantum simulations…
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
We prove two separate lower bounds -- one for nondegenerate convex domains and the other for nondegenerate $\mathbb{C}$-convex (but not necessarily convex) domains -- for the squeezing function that hold true for all domains in…
The so-called weighted solid Cauchy transform, from inside the unit disc into the complement of its closure, is considered and their basic properties such as boundedness is studied for appropriate probability measures. The action the disc…
In a recent paper, Ng, Tang and Tsai (Math. Ann. 2020) have found an explicit formula for the squeezing function of an annulus via the Loewner differential equation. Their result has led them to conjecture a corresponding formula for planar…
We give a rigorous proof of the approximability of the so-called Helfrich's functional via diffuse interfaces, under a constraint on the ratio between the bending rigidity and the Gauss-rigidity.
We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of…
We analyze certain compositions of rational inner functions in the unit polydisk $\mathbb{D}^{d}$ with polydegree $(n,1)$, $n\in \mathbb{N}^{d-1}$, and isolated singularities in $\mathbb{T}^d$. Provided an irreducibility condition is met,…
This paper extends our recent study on Casimir friction forces for dielectric plates moving parallel to each other [J. S. H{\o}ye and I. Brevik, Eur. Phys. J. D {\bf 68}, 61 (2014)], to the case where the plates are no longer restricted to…
In this paper, the notion of convexity of picture fuzzy multisets was introduced and some of their properties were presented after studying the concept of picture fuzzy multisets.
This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions and piecewise cubic functions are investigated and their…