相关论文: On the relation between algebraic and configuratio…

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and…

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.

A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…

Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…

We discuss a symmetry-adapted algebraic (or vibron) model for molecular spectroscopy. The model is formulated in terms of tensor operators under the molecular point group. In this way, we have identified interactions that are absent in…

We apply a symmetry-adapted algebraic model to the vibrational excitations in D_3h and T_d molecules. A systematic procedure is used to establish the relation between the algebraic and configuration space formulations. In this way we have…

We present an algebraic approach to the internal structure of baryons in terms of three constituents. We investigate a collective model in which the nucleon is regarded as a rotating and vibrating oblate top with a prescribed distribution…

An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the…

We present an overview of the rapidly evolving field of dynamics of algebraic correspondences, with a focus on matings between rational maps and Kleinian groups. These correspondences exhibit rich dynamics, both within the Sullivan…

We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.

Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.

In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…

We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…

This paper is devoted to the comparison of the notions of regularity for algebraic connections and (holonomic) regularity for algebraic $\mathcal D$-modules.

This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the…

A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.

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…