相关论文: Some Applications of Lie Groups in Theory of Techn…

A Lie group is an old mathematical abstract object dating back to the XIX century, when mathematician Sophus Lie laid the foundations of the theory of continuous transformation groups. As it often happens, its usage has spread over diverse…

This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.

There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…

The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the…

This paper is devoted to the development and applications of some (new) basic concepts in Lie theory, both from `computational" and "observability" viewpoint. We specify set of all "G-equivariant" maps from a given Lie group G to the…

In this paper we extend the work by Ryuzo Sato devoted to the development of economic growth models within the framework of the Lie group theory. We propose a new growth model based on the assumption of logistic growth in factors. It is…

In the first, mostly expository, part of this paper, a graded Lie algebra is associated to every group G given with an N-series of subgroups. The asymptotics of the Poincare series of this algebra give estimates on the growth of the group…

The quest for accurate economic forecasting has traditionally been dominated by econometric models, which most of the times rely on the assumptions of linear relationships and stationarity in of the data. However, the complex and often…

The detection of political fake statements is crucial for maintaining information integrity and preventing the spread of misinformation in society. Historically, state-of-the-art machine learning models employed various methods for…

The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

Forecasting technological progress is of great interest to engineers, policy makers, and private investors. Several models have been proposed for predicting technological improvement, but how well do these models perform? An early…

The increasing reliance on AI-driven solutions, particularly Large Language Models (LLMs) like the GPT series, for information retrieval highlights the critical need for their factuality and fairness, especially amidst the rampant spread of…

Bayesian models of group learning are studied in Economics since the 1970s. and more recently in computational linguistics. The models from Economics postulate that agents maximize utility in their communication and actions. The Economics…

Today, the economy is greatly influenced by Artificial General Intelligence (AGI). The purpose of this paper is to determine the impact of the quantitative relations of AGI on the country's economic parameters. The authors use the analysis…

Let G be a semisimple Lie group with associated symmetric space D, and let Gamma subset G be a cocompact arithmetic group. Let L be a lattice inside a Z Gamma-module arising from a rational finite-dimensional complex representation of G.…

Our paper illustrates how the theory of Lie systems allows recovering known results and provide new examples of piecewise deterministic processes with phase-type jumps for which the corresponding first-time passage problems may be solved…

This paper aims to explore the application of machine learning in forecasting Chinese macroeconomic variables. Specifically, it employs various machine learning models to predict the quarterly real GDP growth of China, and analyzes the…

In this paper we study estimating Generalized Linear Models (GLMs) in the case where the agents (individuals) are strategic or self-interested and they concern about their privacy when reporting data. Compared with the classical setting,…

Doctoral Thesis, year 2002, about Lie systems and applications in Physics and Control Theory. The text is in English. Advisor: Jos\'e F. Cari\~nena