Related papers: A note on an Counter Example of Dacorogna
D\'ungal's letter to Charlemagne on the double solar eclipse in the year 810 is extremely interesting both for its form and for its subject matter. Part I of the present study deals with the epistula as a literary work (genre, language,…
Another counter-example to Dirac's Conjecture is presented, which resembles the Cawley model but is so modified as to include second class constraints. The arbitrary function in the general solution to the defining equations of momenta…
The note corrects the aforementioned paper (also, arXiv:0902.4716). The consequences of the correction are traced and the examples updated.
Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly)…
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
Corrections are brought to an article of Friesen on continued fractions of a given period.
This note presents an application of the quasi-conform transformation in surveying.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
The paper has been withdrawn by the author due to a crucial error.
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
We give some new refinements and reverses Young inequalities in both additive-type and multiplicative-type for two positive numbers/operators. We show our advantages by comparing with known results. A few applications are also given. Some…
In this note we show that the only result of [Rocky Mountain J. Math. 54 (2024), no. 4, 995--1004] is nothing more than a misformulated version of an exercise from classical texts, presented with a flawed proof. To place the matter on…
This article contains counterexamples to theorems and claims in Brams, Jones and Klamler's article "Better Ways to Cut a Cake" in the December 2006 Notices of the American Mathematical Society.
The paper titled "Cremona problem in dimension 2" by W. Bartenwerfer presented a flawed attempt at proving the Jacobian Conjecture. Our aim is to provide a thorough analysis of the author's approach, highlighting the errors that were made…
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
The note is dedicated to refining a theorem by Diaconis, Evans, and Graham concerning successions and fixed points of permutations. This refinement specifically addresses non-adjacent successions, predecessors, excedances, and drops of…
In this note, we provide with a simple example to show a defect in the definition of the geometric mixing scale, and then introduce an improved scale, called as the strong geometric mixing scale. The main theorem in this note is the…
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…
The purpose of this note is to verify that the archimedean multiplicity one theorems shown for orthogonal groups (as well as general linear and unitary groups) in a previous paper of the authors remain valid for special orthogonal groups.…
We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum…