Related papers: A Note on the Lalescu Sequence

The branching random walk is shown to be monotone decreasing in ascending direction of integer lattices as a corollary of an observation in regard to the lineage of particles from antisymmetric initial states, and a related property of…

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

Given k>1, let a_n be the sequence defined by the recurrence a_n=c_1a_{n-1}+c_2a_{n-2}+...+c_ka_{n-k} for n>=k, with initial values a_0=a_1=...=a_{k-2}=0 and a_{k-1}= 1. We show under a couple of assumptions concerning the constants c_i…

We present theoretical and numerical evidence for a random matrix theoretic approach to a conjecture about vanishings of quadratic twists of certain L-functions

We obtain some results related to Romanoff's theorem.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

In this paper we introduce a localized and relativized generalization of the usual concept of Fej\'er monotonicity together with uniform and quantitative versions thereof and show that the main quantitative results obtained by the 1st…

We prove that for every planar convex set $\Omega$, the function $t\in (-r(\Omega),+\infty)\longmapsto \sqrt{|\Omega_t|}h(\Omega_t)$ is monotonically decreasing, where $r$, $|\cdot|$ and $h$ stand for the inradius, the measure and the…

We prove the the multipole Lempert function is monotone under inclusion of pole sets.

In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the authors verify…

We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In this paper, we give some $l_p$-type inequalities about sequences satisfying certain quasi monotone type properties. As special cases, reverse $l_p$-type inequalities for non-negative decreasing sequences are obtained. The inequalities…

We obtain necessary and sufficient conditions on a function in order that it be the Laplace transform of an absolutely monotonic function. Several closely related results are also given.

We prove some new results related to Tanaka's formula.

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

We develop techniques to deal with monotonicity of sequences z_{n+1}/z_n and \sqrt[n]{z_n}. A series of conjectures of Zhi-Wei Sun and of Amdeberhan et al. are verified in certain unified approaches.

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of…

The paper presents a counterexample to the Hodge conjecture.