Given a sequence tending to , we consider the set of Abel universal functions consisting of holomorphic functions f in the open unit disk such that for any compact set K included in the unit circle , different from , the set is dense in the space …
We apply capacities to explore the space–time fractional dissipative equation: (0.1)where and . In this paper, we focus on the regularity and the blow-up set of mild solutions to (0.1). First, we establish the Strichartz-type estimates for the homogen…
We derive three critical exponents for Bernoulli site percolation on the uniform infinite planar triangulation (UIPT). First, we compute explicitly the probability that the root cluster is infinite. As a consequence, we show that the off-critical expon…
We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form for some -space X. In our investigations, we also uncover new properties that th…
We consider two sequences and , , generated by Dirichlet series satisfying a familiar functional equation involving the gamma function . Two general identities are established. The first involves the modified Bessel function , and can be thought of as…
First, we build a computational procedure to reconstruct the convex body from a pre-given surface area measure. Nontrivially, we prove the convergence of this procedure. Then, the sufficient and necessary conditions of a Sobolev binary function to be a…
We use tools from free probability to study the spectra of Hermitian operators on infinite graphs. Special attention is devoted to universal covering trees of finite graphs. For operators on these graphs, we derive a new variational formula for the spe…
We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area, and total spherical curvature. These results can be viewed as…
A multivariate, formal power series over a field K is a Bézivin series if all of its coefficients can be expressed as a sum of at most r elements from a finitely generated subgroup ; it is a Pólya series if one can take . We give explicit structural de…
In the past years, the enumeration of plane lattice walks confined to a convex cone—normalized into the first quadrant—has received a lot of attention, stimulated the development of several original approaches, and led to a rich collection of results….