Related papers: On a generalized conjecture by Alzer and Matkowski
We study the distribution of partial sums of Rademacher random multiplicative functions $(f(n))_n$ evaluated at polynomial arguments. We show that for a polynomial $P\in \mathbb Z[x]$ that is a product of at least two distinct linear…
Hille in 1959 gave a stronger form for the classical implicit function theorem of Cauchy for equations of the type $y = \psi(x,y)$, $x,y$ real or complex, $\psi$ analytic with a condition which determines a radius of convergence of the…
For a matrix $A$ which satisfies Crouzeix's conjecture, we construct several classes of matrices from $A$ for which the conjecture will also hold. We discover a new link between cyclicity and Crouzeix's conjecture, which shows that…
We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…
A conjectural generalization of the McKay correspondence in terms of stringy invariants to arbitrary characteristic, including the wild case, was recently formulated by the author in the case where the given finite group linearly acts on an…
This work develops some technology for accessing the loop expansion of the Kontsevich integral of a knot. The setting is an application of the LMO invariant to certain surgery presentations of knots by framed links in the solid torus. A…
In this work, using a new geometrical approach we study to the existence of the fixed-point of mappings that independence of the smoothness, and also of their single-values or multi-values. This work proved the theorems that generalize in…
In this paper, the $q$-th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the $q$-th dual curvature measure of convex bodies which defined by Huang, Lutwak, Yang…
In our previous work, we introduced the Generalised Nonvanishing Conjecture, which generalises several central conjectures in algebraic geometry. In this paper, we derive some surprising nonvanishing results for pluricanonical bundles which…
Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…
In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary…
Brief account of results on the Cauchy problem for the Einstein equations starting with early the works of Darmois and Lichnerowicz and going up to the proofs of the existence and uniqueness of solutions global in space and local in time,…
In this article, which is dedicated to my friend and colleague Boris Zilber on the occasion of his 75th birthday, I put forward a strategy for proving his quasiminimality conjecture for the complex exponential field. That is, for showing…
In 2005, B\"ottcher and Wenzel raised the conjecture that if $X,Y$ are real square matrices, then $||XY-YX||^2\leq 2||X||^2||Y||^2$, where $||\cdot||$ is the Frobenius norm. Various proofs of this conjecture were found in the last few years…
In this paper we introduce Hausdorff locally convex algebra topologies on subalgebras of the whole algebra of nonlinear generalized functions. These topologies are strong duals of Fr\'echet-Schwartz space topologies and even strong duals of…
An abstract formulation of a duality principle established by Krasnoselskii is presented. Under appropriate conditions, it shall be shown that, if the solutions of a nonlinear functional equation can be obtained by finding fixed points of…
Menger's basis property is a generalization of $\sigma$-compactness and admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct non $\sigma$-compact sets of reals with Menger's property.…
Given a real number $q$ and a star body in the $n$-dimensional Euclidean space, the generalized dual curvature measure of a convex body was introduced by Lutwak-Yang-Zhang [43]. The corresponding generalized dual Minkowski problem is…
In this paper, we investigate the uniqueness problem of entire functions that share an entire function with their higher-order difference operators. We obtain two results that confirm the conjectures posed by Liu and Laine \cite{LL1} and by…
We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…