Analytic, explicit and non-empirical equations of state for the double Yukawa and hard core double Yukawa fluids are presented. They are based on a second-order inverse temperature expansion of the free energy within the mean spherical approximation. These equations of state yield good results...

The divergence of the perturbation series in quantum field theory is reviewed and an argument presented showing that, at least in the unrenormalised theory, it must be asymptotic in the Poincaré sense. Some basic concepts of asymptotic series are reviewed. By combining momentum analyticity with...

For an optimization problem with a composed objective function and composed constraint functions we determine, by means of the conjugacy approach based on the perturbation theory, some dual problems to it. The relations between the optimal objective values of these duals are studied. Moreover,...

The single-impurity specific heat ci(T) and impurity susceptibility χi(T) of an extended s–d Hamiltonian H are derived and examined in the vicinity of the transition temperature Tc. ci(T) is found by exploiting the single-impurity solution of H due to Andrei et al., whereas χi(T) by applying...

The RKKY perturbation scheme for the spin 12 s–d exchange model is reexamined in the case of a finite number of electrons per impurity. The distribution of impurities is assumed to be random. The free electron gas representing the unperturbed system in the RKKY approach is replaced by a...

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The series for the exact moments, if not the distribution...

For an optimization problem with a composed objective function and composed constraint functions we determine, by means of the conjugacy approach based on the perturbation theory, some dual problems to it. The relations between the optimal objective values of these duals are studied. Moreover,...

Given a row-stochastic matrix describing pairwise similarities between data objects, spectral clustering makes use of the eigenvectors of this matrix to perform dimensionality reduction for clustering in fewer dimensions. One example from this class of algorithms is the Robust Perron Cluster...

We study the dynamics of atomic Bose–Einstein condensates (BECs), when the quadrupole mode is excited. Within the Thomas–Fermi approximation, we derive an exact first-order system of differential equations that describes the parameters of the BEC wave function. Using perturbation theory...