A fractional isoperimetric problem in the Wiener space

We introduce a notion of fractional perimeter in an abstract Wiener space and show that half-spaces are the only volume-constrained minimisers.     

On certain degenerate and singular elliptic PDEs I: Nondivergence form operators with unbounded drifts and applications to subelliptic equations

We prove a Harnack inequality for nonnegative strong solutions to degenerate and singular elliptic PDEs modeled after certain convex functions and in the presence of unbounded drifts. Our main theorem extends the Harnack inequality for the linearized Monge–Ampère equation due to Caffarelli and Gutiérrez and it is related, although under different hypotheses, to a recent work by N.Q. Le.Since our results are shown to apply to the convex functions $|x{|}^p$ with $p\ge 2$ and their tensor sums, the degenerate elliptic operators that we can consider include subelliptic Grushin and Grushin-like operators as well as a recent example by A. Montanari of a nondivergence-form subelliptic operator arising from the geometric theory of several complex variables. In the light of these applications, it follows that the Monge–Ampère quasi-metric structure can be regarded as an alternative to the usual Carnot–Carathéodory metric in the study of certain subelliptic PDEs.     

Long time behavior of heat kernels of operators with unbounded drift terms

Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L²(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also proved.     

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent −2.     

Nilmanifolds with a calibrated G2-structure

We introduce obstructions to the existence of a calibrated G₂-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G₂-structure.     

On Taylor series and Kapteyn series of the first and second type

We study the relation between the coefficients of Taylor series and Kapteyn series representing the same function. We compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method.     

Evaluating cost impacts on reverse logistics using an Economic Order Quantity (EOQ) model with environmental and social considerations

Central European Journal of Operations Research - Societal awareness and legislation changes concerning sustainability have affected how organizations generate value for stakeholders, as well as...     

Inhomogeneous Universe Models with Varying Cosmological Term

The evolution of a class of inhomogeneous spherically symmetric universe models possessing a varying cosmological term and a material fluid, with an adiabatic index either constant or not, is studied.     

Newtonian Dynamics from the Principle of Maximum Caliber

The foundations of Statistical Mechanics can be recovered almost in their entirety from the principle of maximum entropy. In this work we show that its non-equilibrium generalization, the principle of maximum caliber (Jaynes, Phys Rev 106:620–630, 1957), when applied to the unknown trajectory followed by a particle, leads to Newton’s second law under two quite intuitive assumptions (both the expected square displacement in one step and the spatial probability distribution of the particle are known at all times). Our derivation explicitly highlights the role of mass as an emergent measure of the fluctuations in velocity (inertia) and the origin of potential energy as a manifestation of spatial correlations. According to our findings, the application of Newton’s equations is not limited to mechanical systems, and therefore could be used in modelling ecological, financial and biological systems, among others.