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For a real-valued one dimensional diffusive strict local martingale,, we provide a set of smooth functions in which the Cauchy problem has a unique classical solution under a local H\"older condition. Under the weaker Engelbert-Schmidt…
We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a…
According to quantum field theory, the inflaton equation of motion does not have the local form that is generally assumed for cosmological purposes. In particular, earlier investigations of the nonequilibrium dynamics of an inflaton that…
We consider a possibility that one of the flat directions in the minimal supersymmetric standard model plays the role of the inflaton field and realizes large-field inflation. This is achieved by introducing a generalized shift symmetry on…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
It is known that the price of call options in the Heston model is determined in a non-unique way. In this paper, this problem is analyzed from the point of view of the existing mathematical theory of uniqueness classes for degenerate…
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…
Using a classical technique introduced by Achi E. Brandt for elliptic equations, we study a general class of nonlocal equations obtained as a superposition of classical and fractional operators in different variables. We obtain that the…
In this paper, we consider the 3-D compressible isentropic MHD equations with infinity electric conductivity. The existence of unique local classical solutions is firstly established when the initial data is arbitrarily large, contains…
This paper develops the approach to special relativity put forward by John S. Bell. The classical dynamics of an electron orbiting a nucleus in uniform motion is solved analytically and compared to numerical simulations for an accelerated…
This paper gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms…
Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate…
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
We continue to study the local well-posedness for higher order Benjamin-Ono type equations, especially fourth order equations. The proof is based on the energy methods with correction terms. Although one of correction terms can eliminate…
We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions proved that, when the damping term is bounded in space and time, the equation is well posed in the class of…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
In this paper, an idea to solve nonlinear equations is presented. During the solution of any problem with Newton's Method, it might happen that some of the unknowns satisfy the convergence criteria where the others fail. The convergence…
In this paper we present a new local Lagrangian approximation to the gravitational dynamics of cold matter. We describe the dynamics of a Lagrangian fluid element through only one quantity, the deformation tensor. We show that this tensor…