Related papers: A Note on the Lalescu Sequence
This note presents an interesting counterexample to a basic covering problem.
We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.
The following note proves that conditional entropy of a sequence is almost time-reversal invariant, specifically they only differ by a small constant factor dependent only upon the forward and backward models that the entropies are being…
We give a simple proof of a strengthened version of a theorem of Lieb that played a key role in the proof of strong subadditivity of the quantum entropy.
The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x+1), which leads to the log-concavity of…
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.
In the note, two alternative proofs are provided for a monotonicity result that the function $\psi(x)+\ln\bigl(e^{1/x}-1\bigr)$ is strictly increasing on $(0,\infty)$, where $\psi(x)$ is the psi function.
We prove that a compact space is monotonically Sokolov if and only if it is monotonically $\omega$-monolithic. This gives answers to several questions of R. Rojas-Hernandez and V. V. Tkachuk.
In this short note we prove a conjecture for the interval $(0,1)$, related to a logarithmically completely monotonic function, presented in \cite{BG}. Then, we extend by proving a more generalized theorem. At the end we pose an open problem…
In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.
It is proved that every normalized weakly null \sq\ has a sub\sq\ which is convexly unconditional. Further, an Hierarchy of summability methods is introduced and with this we give a complete classification of the complexity of weakly null…
In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem.
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
In this note, we prove some new stability results for plethysm coefficients. As special cases, we verify a conjecture of Wildon, and show the stability of sequences recently predicted by Bessenrodt, Bowman and Paget to be weakly increasing.
A very short proof of Kneser's theorem via transversal is given.
We prove the log-concavity of the Fennessey-Larcombe-French sequence based on its three-term recurrence relation, which was recently conjectured by Zhao. The key ingredient of our approach is a sufficient condition for log-concavity of a…
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
We establish monotone bijections between the Farey sequences of order m and the halfsequences of Farey subsequences associated with the rank m elements of the Boolean lattice of subsets of a 2m-set. We also present a few related…