Related papers: Reflection theorems for number rings
The paper has been withdrawn by authors. The issues studied in this paper were changed so much that we have published a new paper considering these issues. See hep-th/0406074
Periodic multilayers of various periods were prepared according to an algorithm proposed by the authors. The reflectivity properties of these systems were investigated using neutron reflectometry.The obtained experimental results were…
This is an expository paper designed to introduce undergraduates to the Atiyah-Singer index theorem 50 years after its announcement. It includes motivation, a statement of the theorem, an outline of the easy part of the heat equation proof.…
PhD Thesis--A compilation of the papers: "Lower Bounds for Identifying Codes in Some Infinite Grids", "Improved Bounds for r-identifying Codes of the Hex Grid", and "Vertex Identifying Codes for the n-dimensional Lattics" along with some…
We review the discovery of reflection positivity. We also explain a new geometric approach and proof of the reflection positivity property.
In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtained illustrate a significant difference between the classes…
The main purpose of this paper is to correct an error in the previously submitted version [*] := arXiv:2004.13749v1. [*] had been already accepted for publication in a scientific journal, but withdrawn by the author after the discovery of…
Withdrawn by author - Superseded by arXiv:0910.5106 [math.FA].
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas,…
This paper has been withdrawn because of a gap in the proof of Lemma 3.10. The main reults in this paper have now been proved, and extended in the following papers: S. Ariki and A. Mathas, The number of simple modules of the Hecke algebras…
We present five open problems in the theory of vertex rings. They cover a variety of different areas of research where vertex rings have been, or are threatening to be, relevant. They have also been chosen because I personally find them…
The claim in \cite{Al-Badawi:2025ipr} that *"the errors in the foundational components (3) and (5) of Ref. [1] invalidate all subsequent analyses, numerical results, and physical interpretations that depend on them"* is **entirely…
The original version of this paper has been withdrawn by the authors and merged with the revised version of astro-ph/9702014.
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
We provide a certain direct-sum decomposition of reflexive modules over (one-dimensional) Arf local rings. We also see the equivalence of three notions, say, integrally closed ideals, trace ideals, and reflexive modules of rank one (i.e.,…
Two methods of refractometry in reflected light from optical surface of samples are considered and studied experimentally. Methods are grounded on results of Fresnel theory of concerning light reflectivity at near normal incidence and…
This doctoral thesis is a mathematical study of quantum computing, concentrating on two related, but independent topics. First up are dilations, covered in chapter 2. In chapter 3 "diamond, andthen, dagger" we turn to the second topic:…
This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.