Related papers: A note on lower bounds for numerical series
Here, we give upper and lower bounds on the count of positive integers $n\le x$ dividing the $n$th term of a nondegenerate linearly recurrent sequence with simple roots.
This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…
These notes explore three amazing formulas proved by Abel in his 1826 Paris memoir on what we now call Abelian integrals. We discuss the first two formulas from the point of view of symbolic computation and explain their connection to…
We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers $1,\Theta_1,...,\Theta_m\in\mathbb{C}^*$ over the ring $\mathbb{Z}_{\mathbb{I}}$ of an imaginary quadratic field $\mathbb{I}$. This work deals…
An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…
In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower…
Lower bounds for some explicit decision problems over the complex numbers are given.
We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The note complements topological aspects of the theory of chiral algebras.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.
Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences…
In this note we would like to give an explicit lower bound by using a lower saturated subset of \mathbb{R}_{\geq 0}^n.
We are interested to bound from below the number of distinct dot products determined by a finite set of points $P$ in the Euclidean plane. In this paper, we build on the work of B. Hanson, O. Roche-Newton, and S. Senger, to obtain the…
In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…