Related papers: A short proof of the irreflexivity conjecture
The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented…
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
Short proof of the aperiodicity of the Robinson tile set.
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
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.
We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to $\approx \exp(1.96 \times 10^{19})$, which is significantly below the conjectured value of $\approx \exp(5.15 \times…
We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique…
We present new short proofs to both the exact and the stability results of two extremal problems. The first one is the extension of Tur\'{a}n's theorem in hypergraphs, which was firstly studied by Mubayi $\cite{MU06}$. The second one is…
We prove that the well-rounded retract of SO_n\SL_n(R) is a minimal SL_n(Z)-invariant spine.
We report a simple rigidity theorem for certain Euler products.
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
Beben and Theriault proved a theorem on the homotopy fiber of an extension of a map with respect to a cone attachment, which has produced several applications. We give a short and elementary proof of this theorem.
We prove a result about extension of a minimal AF-equivalence relation R on the Cantor set X, the extension being `small' in the sense that we modify R on a thin closed subset Y of X. We show that the resulting extended equivalence relation…
Watson proved Kirkman's hypothesis (partially solved by Cayley). Using Lagrange Inversion, we drastically shorten Watson's computations and generalize his results at the same time.
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
A simple heuristic proof of an integral identity recently derived (Glasser ML 2011 J. Phys. A: Math. Theor. 44 225202) is presented.
The Fourier extension conjecture of E. Stein was proved in the plane in 1970 by C. Fefferman, see also Zygmund and Carleson and Sj\"olin, with simplifications given by other authors later on, in particular by L. H\"ormander and T. Tao. We…
A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of…