Related papers: A note on an Counter Example of Dacorogna
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
Remarks on mathematical proof and the practice of mathematics.
In this short note, we derive an upper-bound for the sum of two comparison functions, namely for the sum of a class K and an extended class K function. To the best of our knowledge, the relations derived in this note have not been…
This paper is withdrawn. We found a mistake in Lemma 4.1
We improve constants in the Rademacher-Menchov inequality.
In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.
Known or essentially known results about duals of interpolation spaces are presented, taking a point of view sometimes slightly different from the usual one. Particular emphasis is placed on Alberto Calderon's theorem describing the duals…
The present note is an answer to complains of E.Weitz on [Sh:371]. We present a corrected version of a part of chapter VIII of " Cardinal Arithmetic".
In the paper [3] the value of the invariant denoted by d and often called "rank" was misstated for a narrow class of examples of ECS manifolds: they were identified as having d = 1 instead of the correct value d = 2. The error was repeated,…
The purpose of this letter is to point out an argument which may ultimately lead to a rigorous proof of the Penrose inequality in the general case. The argument is a variation of Geroch's original proposal for a proof of the positive energy…
It was conjectured that the augmentation ideal of a dihedral quandle of even order $n>2$ satisfies $|\Delta^k(\text{R}_n)/\Delta^{k+1}(\text{R}_{n})|=n$ for all $k\geq 2$. In this article we provide a counterexample against this conjecture.
The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a common and naturally occurring class of Cantorvals.
The note complements topological aspects of the theory of chiral algebras.
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
Telegraphic notes on the historical bibliography of the Gamma function and Eulerian integrals. Correction to some classical references. Some topics of the interest of the author. We provide some extensive (but not exhaustive) bibliography.…
In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.
This paper presents high-resolution images of the original document of the 24 February 1616 condemnation of the Copernican system, as being "foolish and absurd in philosophy", by a team of consultants for the Roman Inquisition. Secondary…
We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in representing partial derivatives in Lagrangian and Hamiltonian…
Let WO$(\omega^\omega)$ be the statement that the ordinal number $\omega^\omega$ is well ordered. WO$(\omega^\omega)$ has occurred several times in the reverse-mathematical literature. The purpose of this expository note is to discuss the…
A brief introduction is given to the methods and spirit of effective lagrangians. The emphasis is on a summary of the overall picture, using a simple model as the vehicle to motivate and illustrate the main points. Powercounting is…