Related papers: A simple proof of Tong's theorem
In this paper we present a surprisingly short proof of Minkowski's second theorem. The author hopes there is no mistake in it, though the argument seems to be too plain to contain one. Also, we apply the main construction of the proof to…
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
Recently a new proof was given for Beurling's Ingham type theorem on one-dimensional nonharmonic Fourier series, providing explicit constants. We improve this result by applying a short elementary method instead of the previous complex…
A two-component generalization of the Camassa-Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. {\bf 146} (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian…
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
We prove direct quantum coding theorem for random quantum codes. The problem is separated into two parts: proof of distinguishability of codewords by receiver, and that of indistinguishability of codewords by environment (privacy). For a…
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
We summarize the proofs for the s-injectivity of the tensor tomography problem on compact Riemannian manifolds with boundaries in [Dairbekov, Inverse Problems, 22: 431, 2006] and [Paternain-Salo-Uhlmann, Math. Ann., 363: 305-362, 2015]…
We give a direct proof of the local $Tb$ Theorem, in the Euclidean setting, and under the assumption of dual exponents. This Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator, supposing the…
We show that, under some mild hypotheses, the Gowers uniformity norms (both in the additive and in the hypergraph setting) are essentially equivalent to certain weaker norms which are easier to understand. We present two applications of…
We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.
The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.
A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…
It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…
We present a short and completely elementary proof for a double sum studied by Brent and Osburn in arXiv:1309.2795v2.
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
It is well known that the strong subadditivity theorem is hold for classical system, but it is very difficult to prove that it is hold for quantum system. The first proof of this theorem is due to Lieb by using the Lieb's theorem. Here we…
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.
We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.