相关论文: A natural occurrence of shift equivalence
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…
In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…
We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a…
We discuss C$^*$-algebras associated with several different natural shifts on the Hilbert space of the $s$-adic tree, that is, the tree of balls in the space of $s$-adic integers.
In the scientific literature, the term emergent phenomena is invoked in the context of a collective behavior observed in a complex adaptive system that exhibits no correspondence with the behavior of the system constituents. Although this…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
The work lays the foundations of the theory of changeable sets. In author opinion, this theory, in the process of it's development and improvement, can become one of the tools of solving the sixth Hilbert problem least for physics of…
The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…
This thesis focuses on algebraic shifting and its applications to f-vector theory of simplicial complexes and more general graded posets. In particular, several approaches and partial results concerning the g-conjecture for simplicial…
We propose a model theoretic interpretation of the theorems about the equivalence between mixed characteristic perfectoid spaces and their tilts.
I give a short proof of the following algebraic statement: if a vertex algebra is simple, then its underlying Lie conformal algebra is either abelian, or it is an irreducible central extension of a simple Lie conformal algebra.
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
We establish results about algebraic shifting of simplicial complexes and use them to compare different shifting operations. In particular, we show that each shifting operation does not decrease the number of facets, and that the exterior…
Equivalencies of many basic elementary inequalities are given
In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the…