相关论文: Algebraic structure of aromatic B-series
In this paper we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to…
This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…
In this paper we give a generalization of the main results in \cite{ab,ab1} about $b$-ary expansions of algebraic numbers. As a byproduct we get a large class of new transcendence criteria. One of our corollaries implies that $b$-ary…
Kleisli bicategories are a natural environment in which the combinatorics involved in various notions of algebraic theory can be handled in a uniform way. The setting allows a clear account of comparisons between such notions. Algebraic…
A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the…
This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VIII), we construct the braided…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
In this paper we give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequence for every simple set Q. We characterize sequences of real numbers which…
The aim of this paper is to gather and (try to) unify several approaches for the modular representation theory of Hecke algebras of type $B$. We attempt to explain the connections between Geck's cellular structures (coming from…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.
In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
We decribe the correspondence between normalised $\omega$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category.…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
Sampling formulas describe probability laws of exchangeable combinatorial structures like partitions and compositions. We give a brief account of two known parametric families of sampling formulas and add a new family to the list.
Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and…
The aim of the present paper is to generalize the concept of residuated poset, by replacing the usual partial ordering by a generic binary relation, giving rise to relational systems which are residuated. In particular, we modify the…
For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…
Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…