In this paper we develop a way to count zero momentum modes in front-form quantization and apply it to several such approaches: canonical light-cone quantization; Dirac light-cone quantization; reduced phase space quantization ; and Penrose quantization. We also examine which of these light-cone methods are consistent with the Atiyah-Singer index theorem.

By constructing a special cone and applying the fixed index theory in the cone, we prove the existence of positive solutions for a class of singular m-point boundary-value problems.

the aim of this study was to investigate the effect of tillage methods to obtain suitable seedbed for monogerm seed. therefore, a split plot experiment based on a randomized complete block design (rcbd) with three replicatians was conducted at darab station of fars province. the main plot was seedbed prepration at two levels including fall and spring season. subplot included 1) moldboard plow a...

Owing to optical refraction, external rays that are incident upon a high-refractive-index medium fall within a small internal cone angle. A one-dimensionally periodic Bragg structure can reflect over an angular acceptance range that is greater than the small internal refraction cone, if the internal refractive-index contrast is sufficient. Thus Winn et al. [Opt. Lett. (to be published)] charted...

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Zero index materials where sound propagates without phase variation, holds a great potential for wavefront and dispersion engineering. Recently explored electromagnetic double zero index metamaterials consist of periodic scatterers whose refractive index is significantly larger than that of the surrounding medium. This requirement is fundamentally challenging for airborne acoustics because the ...

The Morrison-Kawamata cone conjecture predicts that the actions of the automorphism group on the effective nef cone and the pseudo-automorphism group on the effective movable cone of a klt Calabi-Yau pair (X,∆) have finite, rational polyhedral fundamental domains. Let Z be an n-dimensional Fano manifold of index n − 1 such that −KZ = (n − 1)H for an ample divisor H. Let Γ be the base locus of a...