The Feynman–Kac theorem and Bogolyubov inequality are applied to obtain a lower bound and an upper bound to the free energy of the s–d Hamiltonian with locally smeared interactions between electrons and impurities. The two bounds, which express in terms of the free energy of impurities in a...

Stochastic volatility option pricing has become popular in financial mathematics due to its theoretical and empirical consistencies. However, stochastic volatility models generally suffer from analytical and calibration intractability, except for regime switching stochastic volatility. However,...

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,...

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...

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...

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,...

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...

The equilibrium state of a triangular pile of particles, interconnected by linear springs and subjected to the force of gravity, is explored algebraically. A subset of the springs is treated as weak in relation to the others and perturbation theory is used to obtain the zero order and first...

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...

A simple expression for the first coordination shell of the radial distribution function of the reference hard-sphere fluid is used in combination with Barker–Henderson perturbation theory to obtain the thermodynamic properties of triangular-well fluids. These properties are expressed...