Abstract In this note, we investigate some regularity aspects for solutions of degenerate complex Monge–Ampère equations (DCMAE) on singular spaces. First, study the Dirichlet problem DCMAE Stein spaces, showing a general continuity result. A consequence our results is that Kähler–Einstein potentials are continuous at isolated singularities. Next, establish global to when reference class belong...

We study adiabatic limits of Ricci-flat Kähler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampère equation, we show that the Ricci-flat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metri...

In the present paper, we discuss Monge-Ampère equations from viewpoint of differential geometry. It is known that a Monge--Ampère equation corresponds to special exterior system on 1-jet space. this generalize and prove $(k+1)$st order generalized $k$-jet space its solution naturally an integral manifold corresponding system. Moreover, show Korteweg-de Vries (KdV) Cauchy--Riemann are examples o...

This study developed a real-time remote monitoring system (RTRMS) to receive the vibration frequency of bridge pier. The system included a front station and a middle station. A multi-hop wireless routing is employed to transmit the data from the front to the middle station. The front station includes a receiver equipped to receive the vibration frequency, and a wireless sensor network to transm...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

Einstein-Weyl geometry is a triple (D,g,w), where D symmetric connection, [g] conformal structure and w covector such that: (i) connection preserves the class [g], that is, Dg=wg; (ii) trace-free part of symmetrised Ricci tensor vanishes. Three-dimensional structures arise naturally on solutions second-order dispersionless integrable PDEs in 3D. In this context, coincides with characteristic th...

This paper studies the Vlasov-Monge-Ampère system (VMA), a fully non-linear version of the Vlasov-Poisson system (V P ) where the (real) Monge-Ampère equation det ∂ Ψ ∂xi∂xj = ρ substitutes for the usual Poisson equation. This system can be derived as a geometric approximation of the Euler equations of incompressible fluid mechanics in the spirit of Arnold and Ebin. Global existence of weak sol...

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...