Related papers: Some Estimates for a Generalized Abreu's Equation

We provides some useful estimates for solving martingale representation problem under G-expectations. We also study the corresponding conditions for the existence and uniqueness.

We solve Abreu's equation with periodic right hand side, in any dimension. This can be interpreted as prescribing the scalar curvature of a torus invariant metric on an Abelian variety.

We show that a general estimate in the $\dib$-Neumann problem implies a upper bound on the order of contact of a complex curve with the boundary and a lower bound on the rate of the Levi form of a bounded family of weights.

I discuss generalized spin-1/2 equations for neutrinos. They have been obtained by means of the Gersten's method for derivation of arbitrary-spin relativistic equations. Possible physical consequences are discussed.

In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…

The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given.

We analyze a system of linear algebraic equations whose solutions lead to a proof of a generalization of Boole's formula. In particular, our approach provides an elementary and short alternative to Katsuura's proof of this generalization.

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

We study particular solutions of the inner equation associated to the splitting of separatrices on generalized standard maps. An exponentially small complete expression for their difference is obtained. We also provide numerical evidence…

We establish derivative estimates of solution of elliptic system in narrow regions.

The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…

The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation.…

In this work we carry out a complete group classification of Burgers' equations.

We consider a fourth order partial differential equation in n-dimensional space introduced by Abreu in the context of K\"{a}hler metrics on toric orbifolds. Similarity solutions depending only on the radial coordinate in R^n are determined…

This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE)…

In this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic solution, in some cases one might need to…

In this very short note we slightly generalize some relations for one-part double Hurwitz numbers from math.AG/0209282.

We consider general subordination and obtain the formula of the subordinated predictable compensator. An example of application is given.