Search results for "equation"
showing 10 items of 4219 documents
A remark on infinite initial values for quasilinear parabolic equations
2020
Abstract We study the possibility of prescribing infinite initial values for solutions of the Evolutionary p -Laplace Equation in the fast diffusion case p > 2 . This expository note has been extracted from our previous work. When infinite values are prescribed on the whole initial surface, such solutions can exist only if the domain is a space–time cylinder.
Radial growth of solutions to the poisson equation
2001
We establish a radial growth estimate of the type of the iterated law of the logarithm for solutions to the Poisson equation in the unit ball.
Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators
2016
When modelling systems with a dispersed phase involving elliptic operators, as is the case of the Stokes or Navier-Stokes problem or the heat equation in a bounded domain, the geometrical structure of the space occupied by the dispersed phase enters in the homogenization process through its capacity, a quantity which can be used to define the equivalence classes in \(H^1\). We shall review the relationship between capacity and homogenization terms in the limit when the number of inclusions becomes large, focusing in particular on the situation where the distribution of inclusions is not necessarily too regular (i.e. it is not periodic).
Optimal control of the inversion of two spins in Nuclear Magnetic Resonance
2012
International audience; We investigate the optimal control of the inversion of two spin 1/2 particles in Nuclear Magnetic Resonance. The two spins, which differ by their resonance offset, are controlled by the same radio frequency magnetic field. Using the Pontryagin Maximum Principle, we compute the optimal control sequence which allows to reach the target state in a given time, while minimizing the energy of the magnetic field. A comparison with the time-optimal solution for bounded control amplitude realizing the same control in the same time is made. An experimental illustration is done using techniques of Nuclear Magnetic Resonance.
Socio-Demographic Variables, Fear of COVID-19, Anxiety, and Depression: Prevalence, Relationships and Explanatory Model in the General Population of …
2021
The COVID-19 pandemic has gravely impacted Latin America. A model was tested that evaluated the contribution of socio-demographic factors and fear of COVID-19 on anxiety and depression in samples of residents in seven Latin American countries (Argentina, Ecuador, Mexico, Paraguay, Uruguay, Colombia, and El Salvador). A total of 4,881 individuals, selected by convenience sampling, participated in the study. Moderate and severe levels of depressive symptoms and anxiety were identified, as well as a moderate average level of fear of COVID-19. In addition, it was observed that about a quarter of the participants presented symptoms of generalized anxiety disorder and a major depressive episode. …
Asymptotic Behaviour of a Logistic Lattice System
2014
In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we study a system of in nite ordinary di erential equations which can be obtained after the spatial discretization of a logistic equation with di usion. We prove that a global attractor exists in suitable weighted spaces of sequences.
On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems
2014
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation in a Banach space by assuming that the nonlinear term is in some sense weakly continuous. We then apply this result to a lattice dynamical system with delay, proving also the existence of a global compact attractor for such system.
Discrete KP Equation and Momentum Mapping of Toda System
2003
Abstract A new approach to discrete KP equation is considered, starting from the Gelfand-Zakhharevich theory for the research of Casimir function for Toda Poisson pencil. The link between the usual approach through the use of discrete Lax operators, is emphasized. We show that these two different formulations of the discrete KP equation are equivalent and they are different representations of the same equations. The relation between the two approaches to the KP equation is obtained by a change of frame in the space of upper truncated Laurent series and translated into the space of shift operators.
GROUP ANALYSIS AND SOME EXACT SOLUTIONS FOR THE THERMAL BOUNDARY LAYER
2006
We perform the group analysis of the thermal boundary layer in laminar flow. We obtain the classification of the solutions in terms of the asymptotic velocity. Some solutions of the boundary layer equations, for some distributions of outer flow velocity, are obtained also.
Explainable Reinforcement Learning with the Tsetlin Machine
2021
The Tsetlin Machine is a recent supervised machine learning algorithm that has obtained competitive results in several benchmarks, both in terms of accuracy and resource usage. It has been used for convolution, classification, and regression, producing interpretable rules. In this paper, we introduce the first framework for reinforcement learning based on the Tsetlin Machine. We combined the value iteration algorithm with the regression Tsetlin Machine, as the value function approximator, to investigate the feasibility of training the Tsetlin Machine through bootstrapping. Moreover, we document robustness and accuracy of learning on several instances of the grid-world problem.