Related papers: A short proof of the irreflexivity conjecture
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We prove that Ma\~n\'e's conjecture, as stated in {\em Lagrangian flows: the dynamics of globally minimizing orbits}, Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), no. 2, 141--153, contains another conjecture of Ma\~n\'e, stated in {\em Generic…
In this note we build on the arguments of van Geemen and Voisin to prove a conjecture of Matsushita that a Lagrangian fibration of an irreducible hyperk\"ahler manifold is either isotrivial or of maximal variation. We also complete a…
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.
We establish a novel characterisation of the law of the convex minorant of any L\'evy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of…
This work is a continuation of what was done in a previous paper and strongly connected to the recent work of U. Abel and I. Rasa [arXiv:1707.00127]
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
We present an elementary, $L^2,$ proof of Fedi\u{\i}'s theorem on arbitrary (e.g., infinite order) degeneracy and extensions. In particular, the proof allows and shows $C^\infty,$ Gevrey, and real analytic hypoellipticity, and allows the…
Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.
Weinstein's[2] brilliant short proof of de Branges'[1] theorem can be made yet much shorter(modulo routine calculations), completely elementary (modulo L\"owner theory), self contained(no need for the esoteric Legendre polynomials' addition…
We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.
We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.
We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Koml\'os conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.
In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].