Related papers: Reflection theorems for number rings
This note briefly reviews the {\it Mirror Principle} as developed in the series of papers \LLYI\LLYII\LLYIII\LLYIV\LCHY. We illustrate this theory with a few new examples. One of them gives an intriguing connection to a problem of counting…
In the recently posted arXiv:2312.04495v3 [1], its authors used a computer code written by me supplied to them by the authors of Ref. [2], and claimed that the results that they obtained invalidate the results and conclusions presented in…
In this brief note we comment on the recent results presented in arXiv:1812.08736v1
The paper is being withdrawn since the results are incorporated in paper arxiv.org/abs/math.AG/0306195.
In this paper we show an index theorem for gerbes
I review some of the main results on hard diffraction, in their relation to QCD, and indicate some of the strengths and weaknesses of the arguments. I also make some suggestions for future work.
Correction to The Annals of Probability 21 (1993) 554--580 [http://projecteuclid.org/euclid.aop/1176989415]
This paper has been withdrawn - the results (with updated proofs) now appear in arXiv:0801.1627.
We study connections between recollements of the derived category D(Mod-R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature.…
This is a survey paper with some original results of the author on refined versions of the Azuma-Hoeffding inequality with some examples that are related to information theory. This work has evolved to the joint paper with Maxim Raginsky in…
We prove Dirichlet's theorem for polynomial rings: Let F be a pseudo algebraically closed field. Then for all relatively prime polynomials a(X), b(X)\in F[X] and for every sufficiently large positive integer n there exist infinitely many…
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov--Imbert transverse shift of the centers of gravity of the reflected…
This note corrects one serious mistake and several smaller mistakes from arXiv:math/0502404. The main results of that paper are unchanged.
The proof of Theorem 11 of the paper M. Scheepers, Remarks on countable tightness, Topology and its Applications 161 (2014), 407 - 432 relies on Lemma 10 of that paper. The offered proof of Lemma 10 had shortcomings, and I was recently…
We separate the Collection Principle, the Reflection Principle, and the Partial Reflection Principle in ZF with urelements (ZFU), despite their equivalence under the Axiom of Choice. In particular, Collection and the Partial Reflection…
We study the well-known Ptolemy-Alhazen problem on reflection of light at the surface of a spherical mirror in the case when the source of light is very far from the mirror.
This paper has been withdrawn by the author because there are some typos in proofs.
It has recently been shown that a minimal reversible nonsymmetric ring has order 256 answering a questioned original posed in a paper on a taxonomy of 2-primal rings. Answers to similar questions on minimal rings relating to this taxonomy…
We extend to orbifolds the quasimap theory of arXiv:0908.4446 and arXiv:1106.3724, as well as the genus zero wall-crossing results from arXiv:1304.7056 and arXiv:1401.7417. As a consequence, we obtain generalizations of orbifold mirror…
In this paper we will study an important but rather technical result which is called The Reduction Property. The result tells us how much arithmetical conservation there is between two arithmetical theories. Both theories essentially speak…