This paper presents a parametric and feature-based methodology for the design of solids with local composition control (LCC). A suite of composition design features are conceptualized and implemented. The designer can use them singly or in combination, to specify the composition of complex components. Each material composition design feature relates directly to the geometry of the design, often...

Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation literature is that methods have not been developed for manifolds with boundary, except in simple cases of linear manifolds where the location of the boundary is a...

We discuss the ‘continuity correction’ that should be applied to connect the prices of discretely sampled American put options (i.e. Bermudan options) and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we compute the correction and relate it to that discussed by Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) for barrier options. In the Ber...

We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter ...

We investigate how the mass correction appears in 5-D with Scherk-Schwarz compactification and clarify whether the KK regularization is reliable method or not. In the extremely sharp cutoff limit of the 5-D regulator which preserves 5-D Lorentz invariance, we prove that the one loop correction to the mass does not depend on the ultraviolet physics for the Scherk-Schwarz breaking of supersymmetr...

Consider the steady neutron transport equation with diffusive boundary condition. In [17] and [18], it was discovered that geometric correction is necessary for the Milne problem of Knudsen-layer construction in a disk or annulus. In this paper, we establish diffusive limit for a 2D convex domain. Our contribution relies on novel weighted W 1,∞ estimates for the Milne problem with geometric cor...

We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter ...