In the present paper using homotopy analysis method (HAM), we approximate a special case of fuzzy integral equations. The fuzzy integral and integro-differential equations have a wide range of applications in science and engineering. In this paper HAM can be to find the exact solution or an approximate solution of the problem. Within this paper the HAM is used to obtain A series solution of int...

The Floreanini-Jackiw formulation of the chiral quantum-mechanical system oscillator is a model of constrained theory with only secondclass constraints. in the Dirac’s classification.The covariant quantization needs infinite number of auxiliary variables and a Wess-Zumino term. In this paper we investigate the path integral quatization of this model using Gülers canonical formalism. All variabl...

The authors have recently proposed a “microcanonical functional integral” representation of the density of quantum states of the gravitational field. The phase of this real–time functional integral is determined by a “microcanonical” or Jacobi action, the extrema of which are classical solutions at fixed total energy, not at fixed total time interval as in Hamilton’s action. This approach is fu...

Path integral Monte Carlo is an exact simulation method for calculating thermodynamic properties of bosonic systems. Properties such as superfluidity and bose condensation are directly related to multiparticle exchange cycles of individual particle paths. Such calculations of bosonic systems in confined geometries, such as helium and hydrogen on surfaces and in droplets are reviewed. © 2001 Ame...

In present paper we elaborated the numerical schemes of iterative methods for an approximate solution of weak singular integral equations with logarithmic Kernel. The equation is examined in a pair of spaces. The results obtained could be used for any pair of the functional spaces where the problem of finding the solution of weak singular integral equations is correctly formulated problem by Ti...

In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vecto...

This identity allows to map interacting fermion system onto the system of noninteracting fermions coupled with fluctuating auxilary field. One uses a path integral formulation of a problem to eliminate the interaction term. We divide the imaginary time interbal [0, β] into Lequal subintervals of width ∆τ : L∆τ = β. After doing that we can rewrite equation for the partitionfunction Z as: Z = Tre...

We develop an optimization technique to compute local solutions to synthesis problems subject to integral quadratic constraints (IQCs). We use the fact that IQCs may be transformed into semi-infinite maximum eigenvalue constraints over the frequency axis and approach them via nonsmooth optimization methods. We develop a suitable spectral bundle method and prove its convergence in the sense that...

The Hamiltonian treatment of constrained systems in Gülers formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a Jacobi system. The main aim of this paper is to investigate the quantization of the finite dimensional systems with constraints using the canonical formalism introduc...

We recalculate the amplitude for photon splitting in a strong magnetic eld below the pair production threshold, using the worldline path integral variant of the Bern{Kosower formalism. Numerical comparison (using programs that we have made available for public access on the Internet) shows that the results of the recalculation are identical to the earlier calculations of Adler and later of Ston...