A remark on Bony maximum principle

0 Remark on the Second Principle of Thermodynamics

All presently available results lead to the conclusion that nonextensivity, in the sense of nonextensive statistical mechanics (i.e., q = 1), does not modify anything to the second principle of thermodynamics, which therefore holds in the usual way. Moreover, some claims in the literature that this principle can be violated for specific anomalous systems (e.g., granular materials) can be shown ...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

The Strong Maximum Principle on Infinite Networks

We study the strong maximum principle for the heat equation associated with the Dirichlet form on an infinite network. We prove that the strong maximum principle is equivalent to the underlying graph being connected after deletion of the nodes with infinite degree. Using this result, we prove that the multiplicity of the eigenvalue 0 of a generalization of the Laplace matrix equals the number o...

On the Maximum Principle for Harmonic Functions

Some generalizations of the maximum principle for harmonic functions are discussed. §

The Pontryagin Maximum Principle

Theorem (PontryaginMaximum Principle). Suppose a final time T and controlstate pair (û, x̂) on [τ, T ] give the minimum in the problem above; assume that û is piecewise continuous. Then there exist a vector of Lagrange multipliers (λ0, λ) ∈ R × R with λ0 ≥ 0 and a piecewise smooth function p: [τ, T ] → R n such that the function ĥ(t) def =H(t, x̂(t), p(t), û(t)) is piecewise smooth, and one has ̇̂ ...