[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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Convex Analysisの二,三の進展について

Fractional Differential Equations

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.

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Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan.

The Classical Calculus of Variations Fractional Calculus of Variations via Riemann - Liouville Operators Fractional Calculus of Variations via Caputo Operators Other Approaches to the Fractional Calculus of Variations Towards a Combined Fractional Mechanics and Quantization.

Introduction to the Fractional Calculus of Variations

A formulation of Noether's theorem for fractional problems of the calculus of variations

Discrete-time fractional variational problems

Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler–Lagrange equations, we prove a Noether-like theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define anymore a conservation law. Instead, it is proved that the fractional conservation law adds to the Hamiltonian a new term which depends on the fractional-order of differentiation, the generalized momentum and the fractional derivative of the state variable.

Delfim F. M. Torres

Papers

Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan.

Introduction to the Fractional Calculus of Variations

A formulation of Noether's theorem for fractional problems of the calculus of variations

Discrete-time fractional variational problems

Fractional conservation laws in optimal control theory