Related papers: A note on arclength null quadrature domains
In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous…
In this work we prove that certain entire $q$-functions have infinitely many nonzero roots $\left\{ \rho_{n}\right\} _{n=1}^{\infty}$, as $n\to+\infty$ the moduli $\left|\rho_{n}\right|$ grow at least exponentially. Applications to entire…
We present new rectification theorems of degenerate quasi-conformal structures that give a meaning to quotients of Riemann surfaces with empty interior "fundamental domains". These techniques are used to define the unique renormalization of…
Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument…
The problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions is addressed by considering a particular nonlocal correlation function, called row configuration probability. This correlation…
We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and…
The Akbari-Cameron-Khosrovshahi (ACK) conjecture, which appears to be unresolved, states that for any simple graph $G$ with at least one edge, there exists a nonzero {$\{0,1\}$}-vector in the row space of its adjacency matrix that is not a…
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two projective bundle structures. Given a general hyperplane section on such a variety, we consider…
Using Laurent decomposition and Mergelyan's theorem combined with Baire's category theorem, we prove generic nowhere differentiability on the distinguished boundary of functions of analytic type on products of planar domains bounded by…
We present a one-parameter family $F_\lambda$ of transcendental entire functions with zeros, whose Newton's method yields wandering domains, coexisting with the basins of the roots of $F_\lambda$. Wandering domains for Newton maps of…
We show that wandering domains can exist in the Fatou set of a polynomial type quasiregular mapping of the plane. We also give an example of a quasiregular mapping of the plane, with an essential singularity at infinity, which has a…
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara's quantity $A(\ell)$, for $\ell = p^n$ with $p$…
In this study we find height bounds for polynomial rings over integral domains. We apply nonstandard methods and hence our constants will be ineffective. Then we find height bounds in the polynomial ring over algebraic numbers to test…
The aim of this study is to understand to what extent a 1-convex domain with Levi-flat boundary is capable of holomorphic functions with slow growth. This paper discusses a typical example of such domain, the space of all the geodesic…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
We gave an alternative short proof on the finite generation of holomorphic functions with polynomial growth on Riemann surfaces with nonnegative curvature. The first proof was due to Li and Tam.
We prove that a bounded domain in $\mathbb{C}^n$ admitting a complete K\"ahler metric with negatively pinched holomorphic bisectional curvature near the boundary, admits a complete K\"ahler metric with negatively pinched holomorphic…
Abstract. In this work we use an elementary method to derive an upper bound on the right half-plane for genus 0 entire functions if it has only negative zeros. The bound only uses information of the function on the positive real axis.…
In this paper we will investigate the global properties of complete Hilbert manifolds with upper and lower bounded sectional curvature. We shall prove the Focal Index Lemma that we will allow us to extend some classical results of finite…
We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.