相关论文: The Auxiliary Mass Method beyond the Local Potenti…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
Using the auxiliary field method, we give an analytical expression for the eigenenergies of a system composed of two non-relativistic particles interacting via a potential of type $\sqrt{a^2 r^2 + b}$. This situation is usual in the case of…
We derive a new result for exponential approximation using Stein's method of exchangeable pairs. As an application, an exponential limit theorem with error term is derived for |Tr(U)|^2, where Tr(U) denotes the trace of a matrix chosen from…
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of the effective potentials deduced under su(1,1) algebra can be brought back to the general Natanzon hypergeometric…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
Unconventional way of handling the perturbative series is presented with the help of Heaviside transformation with respect to the mass. We apply Heaviside transform to the effective potential in the massive Gross-Neveu model and carry out…
The paper contributes to strengthening the relation between machine learning and the theory of differential equations. In this context, the inverse problem of fitting the parameters, and the initial condition of a differential equation to…
The spectrum of masses from a lattice QCD simulation may be found by fitting exponential functions to correlators of operators possessing the quantum numbers of the particles of interest. The ability of evolutionary algorithms to find…
We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
We determine the nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
In this paper we prove a stochastic representation for solutions of the evolution equation $ \partial_t \psi_t = {1/2}L^*\psi_t $ where $ L^* $ is the formal adjoint of an elliptic second order differential operator with smooth coefficients…
This letter is about effective approximation for a stochastic parabolic equation with a large potential in a periodic medium. Under a condition on the spectral properties of the associated cell problem, we prove that the solution can be…
We apply the string inspired worldline formalism to the calculation of the higher derivative expansion of one-loop effective actions in non-Abelian gauge theory. For this purpose, we have completely computerized the method, using the…
We study models of quintessence consisting of a number of scalar fields coupled to several dark matter components. In the case of exponential potentials the scaling solutions can be described in terms of a single field. The corresponding…