Related papers: Structural Properties of ${\cal R}_2$ Part I
We give an introduction to the theory of initial ideals and initial algebras with emphasis on the transfer of structural properties.
We describe the ring of modular forms of degree 2 in characteristic 2 using its relation with curves of genus 2.
By using the concept of duality between direct channel resonances and Regge exchanges we relate the small- and large-$x$ behavior of the structure functions. We show that even a single resonance exhibits Bjorken scaling at large $Q^2$.
This is a work in progress, far from being in its final form whose purpose is to investigate thoroughly the structure of Berkovich analytic curves and its relation with the semi-stable reduction theorem (of which a new proof is given here,…
This is a survey paper of Shelah's pcf theory. In this part the theory is developed up to the pcf theorem.
This is a pedagogical review on polarized structure functions .
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…
A complete structure theorem of Sally modules of $\fkm$-primary ideals $I$ in a Cohen-Macaulay local ring $(A, \m)$ satisfying the equality $\e_1(I)=\e_0(I)-\ell_A(A/I)+1$ is given, where $\e_0(I)$ and $\e_1(I)$ denote the first two Hilbert…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
Using factorization properties, we give several characterizations for an algebraic number ring to have class number 2.
This article is Part I in a series of three papers devoted to determining the minimal complexity of scales in the inner model $K(\mathbb{R})$. Here, in Part I, we shall complete our development of a fine structure theory for $K(\mathbb{R})$…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considered in part I are also highest weight categorifications in the…
Companion matrices of the second type are characterized by properties that involve bilinear maps.
Structure and properties of two-dimensional spiral textures in helical ferromagnets have been studied. In these magnetic mediums have been predicted new types of periodical structures - spiral lattices.
The Poisson structures on two-dimensional Galilei group, classified in the author previous paper are quantized. The dual quantum Galilei Lie algebras are found.
Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.
Small three-dimensional strongly coupled charged particles in a spherical confinement potential arrange themselves in a nested shell structure. By means of experiments, computer simulations and theoretical analysis, it is shown that their…
Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are…
A pedagogical review of the past 50 years of study of resonances, leading to our understanding of the quark content of baryons and mesons. The level of this review is intended for undergraduates or first-year graduate students. Topics…