We discuss several geometric PDEs and their relationship with Hydrodynamics and classical Electrodynamics. We start from the Euler equations of ideal incompressible fluids that, geometrically speaking, describe geodesics on groups of measure preserving maps with respect to the L metric. Then, we introduce a geometric approximation of the Euler equation, which involves the Monge-Ampère equation ...

We prove C regularity of c-convex weak Alexandrov solutions of a Monge-Ampère type equation in dimension two, assuming only a bound from above on the Monge-Ampère measure. The Monge-Ampère equation involved arises in the optimal transport problem. Our result holds true under a natural condition on the cost function, namely non-negative cost-sectional curvature, a condition introduced in [7], th...

This paper describes some of the major contributions to metrology and physics made by the NIST Electricity Division, which has existed since 1901. It was one of the six original divisions of the National Bureau of Standards. The Electricity Division provides dc and low-frequency calibrations for industrial, scientific, and research organizations, and conducts research on topics related to elect...

A unified, Bayesian inference of midplane electron temperature and density profiles using both Thomson scattering (TS) and interferometric data is presented. Beyond the Bayesian nature of the analysis, novel features of the inference are the use of a Gaussian process prior to infer a mollification length-scale of inferred profiles and the use of Gauss-Laguerre quadratures to directly calculate ...

It is proved that if 0 < λ ≤ f(x) ≤ Λ for x ∈ Ω, where Ω ⊂ R is a bounded convex domain, and f is L-Dini continuous on Ω, then there exist infinitely many biLipschitz maps F : Ω → R such that detDF (x) = f(x) for a.e. x ∈ Ω. Moreover, these mappings can be chosen to have convex potentials. We relate our result to a classical theorem by H. M. Reimann; however, the emphasis is on the novel use of...

We show a stability estimate for the degenerate complex Monge-Ampère operator that generalizes a result of Ko lodziej [11]. In particular, we obtain the optimal stability exponent and also treat the case when the right hand side is a general Borel measure satisfying certain regularity conditions. Moreover our result holds for functions plurisubharmonic with respect to a big form generalizing th...

The linear system of equations Ax = b where A = [aij ] in Cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. In this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as Drazin inverse andpseudo-inverse are investigated.