Sufficient conditions are given for a mapping to be γ -G inverse differentiable. Constrained implicit function theorems for γ -G inverse differentiable mappings are obtained, where the constraint is taken to be either a closed convex cone or a closed subset. A theorem without assuming the γ -G inverse differentiability in a finite-dimensional space is also presented.

The purpose of this paper is to provide a modified open mapping theorem, which also applies to maps which are not open, but whose intersection with a convex cone is relatively open. We give a constructive proof, which for the special maps considered here may be seen as an alternative to the indirect proof of Frankowska’s more general open mapping principle. Open mapping theorems are of utmost i...

We show that the mapping cone of a morphism of differential graded Lie algebras χ : L → M can be canonically endowed with an L∞-algebra structure which at the same time lifts the Lie algebra structure on L and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of L∞-algebras. The associated deformation functor coincides with the one introduced by t...

Cone-shaped volcanoes have important research significance and application value due to their typical cone shape unique structural features. The existing methods for recognizing are mainly morphological feature matching machine learning. In general, the former has low recognition accuracy, while latter requires a large number of training samples. contour lines cone-shaped distributed in concent...

We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2+1) dimensions (QED_{3}) with N=1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surfa...

In this note we consider a method of generating functions for systems with constraints and, as an example, we prove that the billiard mappings for billiards on the Euclidean space, sphere, and the Lobachevsky space are sympletic. Further, by taking a quadratic generating function we get the skew-hodograph mapping introduced by Moser and Veselov, which relates the ellipsoidal billiards in the Eu...

We show here that tubulin is the major in vivo substrate of the tyrosine-specific protein kinase pp60c-src in nerve growth cone membranes. Phosphotyrosine antibodies were used to demonstrate phosphotyrosyl residues in a subpopulation of alpha- and beta-tubulin that was highly enriched in a subcellular fraction of growth cone membranes from fetal rat brain. The presence of phosphotyrosine-modifi...

PURPOSE The purpose of this study was to identify the causative gene defect in two siblings with an uncharacterized cone-rod dysfunction and to describe the clinical characteristics. METHODS Genome-wide homozygosity mapping, with a 250K SNP-array followed by a search for candidate genes, was performed. The patients underwent ophthalmic examination, including elaborate electroretinography. R...

Purpose: To evaluate anterior surface topographic technologies and display algorithms in mapping keratoconus. Materials and methods: A total of 27 eyes of 17 subjects clinically diagnosed with keratoconus were imaged on six topographers: EyeSys, Alcon EyeMap, Keratron, TMS-1, Orbscan and PAR corneal topography system. Axial distance (AD) and instantaneous radius of curvature (IROC) algorithms w...

Carriers of blue cone monochromacy have fewer cone photoreceptors than normal. Here we examine how this disruption at the level of the retina affects visual function and cortical organization in these individuals. Visual resolution and contrast sensitivity was measured at the preferred retinal locus of fixation and visual resolution was tested at two eccentric locations (2.5° and 8°) with spect...