Related papers: Erratum to "Generalizations of the Poincar\'e-Birk…
We correct several errors in Phys. Rev. D 66, 094011 (2002). [arXiv:hep-ph/0205210].
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…
Erratum to cond-mat 9309014
We prove a modularity lifting theorem for potentially Barostti-Tate representations over totally real fields, generalising recent results of Kisin. Unfortunately, there was an error in the original version of this paper, meaning that we can…
In this paper, theorem 3.2 and theorem 4.1 of \"{O}z\c{c}a\u{g} and Eysen [S. \"{O}z\c{c}a\u{g} and A.E. Eysen, Almost Menger property in bitopological spaces, Ukrainian Math. J., {\bf 68}, No 6, 950-958 (2016)] are proven to be incorrect.…
This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A=k[X_1, X_2, \ldots, X_n]$ is a polynomial ring over a field $k$. The Complete Intersection conjecture states that, for any ideal $I$ in $A$,…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
We sample some Poincare-Birkhoff-Witt theorems appearing in mathematics. Along the way, we compare modern techniques used to establish such results, for example, the Composition-Diamond Lemma, Groebner basis theory, and the homological…
This paper has been withdrawn due to an error, and no further revisions will be made.
A common error, originally due to Ehrenfest, is corrected.
We consist of first presenting Zeckendorf Theorem with these two versions Fibonacci and Luca. In this document we obtain results on the generalized of the Zeckendorf theorem for Fibonacci numbers (multibonacci). Such results find…
We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…
We disprove and correct some recently obtained results regarding Montgomery identity for quantum integral operator and Ostrowski type inequalities involving convex functions.
An improved estimate is given for $|\theta(x) -x|$, where $\theta(x) = \sum_{p\leq x} \log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the…
We give an explicit $O(x/T)$ error term for the truncated Riemann--von Mangoldt explicit formula. For large $x$, this provides a modest improvement over previous work, which we demonstrate via an application to a result on primes between…
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
It is demonstrated that the "generalized fluctuation-dissipation theorem" [Physica A 106, 443 (1981)] covers the later suggested "fluctuation theorems" and related statistical equalities.
We survey the classical results of the Dirichlet Approximation Theorem.
Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…
This paper has been withdrawn by the author due to a crucial error.