Related papers: On Rugina's System of Thought
Three classical systems, the Kelvin gyrostat, the Maclaurin spheroids, and the Ziegler pendulum have directly inspired development of the theory of Pontryagin and Krein spaces with indefinite metric and singularity theory as independent…
A family of special cases of the integrable Euler equations on $so(n)$ introduced by Manakov in 1976 is considered. The equilibrium points are found and their stability is studied. Heteroclinic orbits are constructed that connect unstable…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
This paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the Lotka-Volterra model, the Goodwin model. We provide a characterization of orbits in the deterministic highly…
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as…
We consider the unexploited/exploited logistic equation and study the stability of equilibrium points through Lyapunov functions. Then, we apply first and second order optimality conditions for the optimal control of the total biomass…
Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and which has no statically stable near-standing configurations can walk stably. We show here that a…
In this work, we leverage the 2-contraction theory, which extends the capabilities of classical contraction theory, to develop a global stability framework. Coupled with powerful geometric tools such as the Poincare index theory, the…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
There exists in nature many examples of systems presenting self-limiting behaviour: population dynamics, structure engineering, Townsend's electron breakdown, nuclear decay in radioactive equilibrium, histeresis process, meteorological…
Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a…
An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open-loop control solving…
The recursive logit (RL) model provides a flexible framework for modeling sequential decision-making in transportation and choice networks, with important applications in route choice analysis, multiple discrete choice problems, and…
We argue that Ulam-Hyers stability concept is quite significant in realistic problems in numerical analysis, biology and economics. A generalization to nonlinear systems is proposed and applied to the logistic equation (both differential…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
This paper characterizes equilibrium properties of a broad class of economic models that allow multiple heterogeneous agents to interact in heterogeneous manners across several markets. Our key contribution is a new theorem providing…
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
Logical rules are a popular knowledge representation language in many domains, representing background knowledge and encoding information that can be derived from given facts in a compact form. However, rule formulation is a complex process…
Let G be one of the groups SL_n C, Sp_2n C, SO_m C, O_m C, or G_2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G x P^N is rational. In this paper we improve known bounds for the…