Related papers: A Note on the Lalescu Sequence
In this article, we reduce the unsolved problem of convergence of Collatz sequences to convergence of Collatz sequences of odd numbers that are divisible by 3. We give an elementary proof of the fact that a Collatz sequence does not…
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
We prove a version of adelic descent for continuous localizing invariants.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We confirm Sun's conjecture that $(\root{n+1}\of{F_{n+1}}/\root{n}\of{F_n})_{n\ge 4}$ is strictly decreasing to the limit 1, where $(F_n)_{n\ge0}$ is the Fibonacci sequence. We also prove that the sequence…
We prove that, for every decreasing sequence {a \sb k} of natural numbers, there exists a map f: X --> X with cat (f\sp k)=a\sb k.
In this note we obtain a new convergence result for the Adomian decomposition method.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.
Let $\Omega_n$ stand for the volume of the unit ball in $\mathbb{R}^n$ for $n\in\mathbb{N}$. In the present paper, we prove that the sequence $\Omega_{n}^{1/(n\ln n)}$ is logarithmically convex and that the sequence…
In this note we provide a simple formula of general term of recurrent sequence.
We survey the classical results of the Dirichlet Approximation Theorem.
We give a new proof of Lucas' Theorem in elementary number theory.
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
We show that aperiodic linearly repetitive Delone sets are densely repetitive. This confirms a conjecture of Lagarias and Pleasants.
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
We prove Union-Closed sets conjecture.
The Collatz conjecture is explored using polynomials based on a binary numeral system. It is shown that the degree of the polynomials, on average, decreases after a finite number of steps of the Collatz operation, which provides a weak…
In this paper, we primarily deal with approximately monotone and convex sequences. We start by showing that any sequence can be expressed as the difference between two nondecreasing sequences. One of these two monotone sequences act as the…