We propose a class of sharing schemes for the distribution of the gains from cooperation for coalition games with externalities. In the context of the partition function, it is shown that any member of this class of sharing schemes leads to the same set of stable coalitions in the sense of...

The statistical proprieties of complex systems can differ deeply for those of classical systems governed by Boltzmann–Gibbs entropy. In particular, the probability distribution function observed in several complex systems shows a power-law behavior in the tail which disagrees with the standard...

Fractional oscillator process can be obtained as the solution to the fractional Langevin equation. There exist two types of fractional oscillator processes, based on the choice of fractional integro-differential operators (namely Weyl and Riemann-Liouville). An operator identity for the...

We present a new method based on genetic algorithms which permits to determine efficiently the partition function and the excitation spectrum of few-body quantum systems. In our approach, we use a variational formulation for the partition function Z of the system as a functional of its...

This paper investigates the stability of agreements for sharing fish stocks among coastal states when migrations patterns change — a heretofore largely unexplored topic. The case investigated is the agreement on sharing the mackerel stock (<italic>Scomber scombrus</italic>) in the North-east Atlantic Ocean....

We present a method for calculating transfer matrices for the q-state Potts model partition functions Z(G,q,v), for arbitrary q and temperature variable v, on strip graphs G of the square (sq), triangular (tri), and honeycomb (hc) lattices of width Ly vertices and of arbitrarily great length Lx...

The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On L×L self-dual lattices studied (L⩽8), no Fisher zero lies on the unit circle p0=eiθ in the complex...

We study the dissipative dynamics of a charged oscillator in a magnetic field by coupling (a la Caldeira and Leggett) it to a heat bath consisting of non-interacting harmonic oscillators. We derive here the autocorrelation functions of the position and momentum and study its behavior at various...

The Yang–Lee zeros of the Q-state Potts model are investigated in one, two and three dimensions. Analytical results derived from the transfer matrix for the one-dimensional model reveal a systematic behavior of the locus of zeros as a function of Q. For 1<Q<2 the zeros in the complex x=exp(βHq) plane lie inside the unit circle, while for Q>2 they lie outside the unit circle for...</q<2>

This paper revisits the fundamental statistical properties of the crucial model in critical phenomena i.e., the Ising model, guided by our knowledge of the energy values of the Ising Hamiltonian and aided by numerical estimation techniques. We have obtained exact energies in 2D and 3D and nearly...