This motivates the following definition. Definition 1.2. A conserved quantity in a Hamiltonian system is a smooth function f ∈ C∞(M) such that {f,H} = 0. Remark 1.3. If you’re familiar with the Lagrangian model of classical mechanics, you can derive the above setup from a Lagrangian field theory on the real line R, i.e. from classical Lagrangian mechanics. There’s a classical procedure for doin...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

Random walk methods and diffusion theory pervaded ecological sciences as methods to analyze and describe animal movement. Consequently, statistical physics was mostly seen as a toolbox rather than as a conceptual framework that could contribute to theory on evolutionary biology and ecology. However, the existence of mechanistic relationships and feedbacks between behavioral processes and statis...

The volume brings together contributions in the spirit embodied by Marek J. Siemek († 2011) and Jakub Kloc-Konkołowicz 2021), two Warsaw philosophers truly devoted to Classical German Philosophy. They were simultaneously a relationship between thinker adept, thinker. both taught philosophy, with strong emphasis on classic at University. Under theme “Ethical Theory Classic Philosophy Then Now,” ...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...