In this paper, we study the moment map image of algebraic curves in toric surfaces. We are particularly interested in the situations that we are able to perturb the moment map so that the moment map image of the algebraic curve is a graph. To put our problem into proper context, let’s start with CP. Consider the natural real n-torus (T ) action on CP given by e(x) = (ex1, e x2, · · · , exn). Pa...

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimiz...

With the development of chaos theory, many image encryption algorithmshave been designed using the properties associated withthechaotic map. The chaotic map shows high sensitivity to initial conditions and the sequence generated using chaotic map are unpredictable making it a good choice for performing encryption operation. But, without proper encryption algorithm design, encryption scheme desi...

We show that any separated essentially finite-type map f of noetherian schemes globally factors as f = hi where i is an injective localization map and h a separated finite-type map. In particular, via Nagata’s compactification theorem, h can be chosen to be proper. We apply these results to Grothendieck duality. We also obtain other factorization results and provide essentialized versions of ma...

This paper describes an experiment where dialogue-based learning is applied to map acquisition of a mobile O ce-Conversant robot. The system learns the map of environment through simple dialogue with human teachers. A formal probabilistic model is introduced as a representation of map. The importance and the e ectiveness of proper segmentation of spatial-action space and statistical inference u...

Convergence-accommodation, one of several cross-linkages in the oculomotor system is manifested by opening the accommodative feedback loop and increasing the vergence input. We elicited this response in human infants aged 3-6 months by placing a 15 delta prism (base-out) before one eye while they viewed a diffuse patch of light. Accommodation was measured and ocular alignment was confirmed with...

Substantial evidence indicates that the hippocampus plays a critical role in long-term declarative memory. In contrast, the role of the human hippocampus in working memory, particularly when information needs to be maintained only for a few seconds, remains controversial. Using PET, we show robust activation of the right anterior hippocampus proper during the performance of both object and spat...

The r-fold analogues of Whitney trick were ‘in the air’ since 1960s. However, only in this century they were stated, proved and applied to obtain interesting results, most notably by Mabillard and Wagner. Here we prove and apply a version of the r-fold Whitney trick when general position r-tuple intersections have positive dimension. Theorem. Assume that D = D1 ⊔ . . . ⊔ Dr is disjoint union of...

We consider a planar Poisson process and its associated Voronoi map. We show that there is a proper coloring with 6 colors of the map which is a deterministic isometry-equivariant function of the Poisson process. As part of the proof we show that the 6-core of the corresponding Delaunay triangulation is empty. Generalizations, extensions and some open questions are discussed.