相关论文: Potpourri, 3
We investigate the norms appearing in the forcing from combinatorial point of view. We make first steps towards building a catalog of the norms appearing in multiple settings and sources, reviewing four norms from Bartoszy\'nski and Judah…
In this note we collect some known facts concerning central projection correspondances and time parametrizations of Kepler problems in Euclidean spaces and on Spheres.
In this article we obtain the classification of the congruences of lines with one-dimensional focal locus. It turns out that one can restrict to study the case of $\mathbb{P}^3$.
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
The predictions of $U_{e3}$ are discussed. Typical models which lead to the large, the seizable and the tiny $U_{e3}$ are also studied.
We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will allow us to obtain a canonical way in which to assign ideals…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent…
The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.
We consider compositions of natural numbers when there are different types of each natural number. Several recursions as well as some closed formulas for the number of compositions is derived. We also find its relationships with some known…
One of the key skills of a researcher is noticing what's going on. Both in the experiment one's performing and in one's data: is there something interesting, reason to doubt one's data or suspect that one's theoretical description is…
Some notes and observations on analytic functions defined on an annulus
For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and `real harmonic functions' with respect to A. We also consider certain groups…
The aim of the present note is to enhance groups $G_{n}^{3}$ and to construct new invariants of classical braids. In particular, we construct invariants valued in $G_{N}^{2}$ groups. In groups $G_{n}^{2}$, the identity problem is solved,…
These are the preparatory notes for a Science & Music essay, "Playing by numbers", appeared in Nature 453 (2008) 988-989.
Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being…
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work we continue this program, with a focus on the two smallest…
We study the Modular Isomorphism Problem applying a combination of existing and new techniques. We make use of the small group algebra to give a positive answer for two classes of groups of nilpotency class 3. We also introduce a new…
These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.