Related papers: On the squeezing function for finitely connected p…
We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with weight the modulus squared of a meromorphic function in the case that the meromorphic function has a finite number of…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.
The purpose of this paper has twofold. The first is to establish a second main theorem for meromorphic functions on annuli and meromorphic function targets (may not be small functions) with truncated counting functions (truncation level 1)…
We construct "large" Cantor sets whose complements resemble the unit disk arbitrarily well from the point of view of the squeezing function, and we construct "large" Cantor sets whose complements do not resemble the unit disk from the point…
In this note, we provide an explicit formula for computing the quasiconvex envelope of any real-valued function $W\colon\operatorname{SL}(2)\to\mathbb{R}$ with $W(RF)=W(FR)=W(F)$ for all $F\in\operatorname{SL}(2)$ and all…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
Let $U$ be a bounded open subset of the complex plane. Let $0<\alpha<1$ and let $A_{\alpha}(U)$ denote the space of functions that satisfy a Lipschitz condition with exponent $\alpha$ on the complex plane, are analytic on $U$ and are such…
We demonstrate an angular momentum-enhanced protocol that permits an angular displacement estimation by using tunable squeezed Bell state and parity detection. We consider the resolution and the sensitivity, super-resolution is presented…
Using the functional associated with the optimal Wente inequality for pairs of functions on 2-dimensional domains, we show the existence of solutions to the H-system on an annulus satisfying Neumann boundary conditions.
The intention of this survey to collect in one paper many recent results and advances related with Bergman type projection acting in various spaces of analytic functions in several complex variables in the unit ball, tubular domains over…
We found that the two-dimensional Schr\"odinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency $\omega_0$) has exact analytical solutions in the…
Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers.…
In this paper, we concern trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary. This kind of inequalities were extensively studied by Osgood-Phillips-Sarnak [24], Liu [20], Li-Liu [17], Yang [31, 32] and…
We provide a new direct proof of the $\ell^2$-boundedness of the Discrete Spherical Maximal Function that neither relies on abstract transference theorems (and hence Stein's Spherical Maximal Function Theorem) nor on delicate asymptotics…
A new characterization of harmonic functions is obtained. It is based on quadrature identities involving mean values over annular domains and over concentric spheres lying within these domains or on their boundaries. The analogous result…
We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals…
Conformal mapping may be the best-known topic in complex analysis. Any simply connected nonempty domain $\Omega$ in the complex plane ${{\mathbb{C}}}$ (assuming $\Omega\ne {{\mathbb{C}}}$) can be mapped bijectively to the unit disk by an…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…