We prove a Hitchin-Kobayashi correspondence for affine vortices generalizing a result of Jaffe-Taubes [19] for the action of the circle on the complex line. Namely, suppose a compact connected Lie group K acts on a Kähler manifold X with proper moment map so that stable=semistable for the action of the complexified Lie group G and X is equivariantly convex at infinity. Then, for some sufficient...

To reduce to resolving Cohen–Macaulay singularities, Faltings initiated the program of “Macaulayfying” a given Noetherian scheme X. For wide class X, Kawasaki built sought-for modifications, with crucial drawback that his blowups did not preserve locus CM(X)?X, where X is already Cohen–Macaulay. We extend Kawasaki’s methods show every quasi-excellent, has X˜ proper map X˜?X an isomorphism over ...

A map merging component is crucial for the proper functionality of a multi-robot system performing exploration, since it provides the means to integrate and distribute the most important information carried by the agents: the explored/covered space and its exact (depending on the SLAM accuracy) morphology. Map merging is a prerequisite for an intelligent multi-robot team aiming to deploy a smar...

Navigation services for pedestrians are spreading in recent years. Our approach to provide personal navigation is to build a multiagent system that assigns one guiding agent to each human. This paper attempts to demonstrate a design implication of the guiding agent. In the navigation experiment where a pedestrian using a map on a GPScapable cellular phone was guided by a distant navigator, we o...

of the Dissertation The Ahlfors Iteration for Conformal Mapping by Christopher Michael Green Doctor of Philosophy in Mathematics Stony Brook University 2011 The Riemann Mapping Theorem states that for any proper, simply connected planar domain there exists a conformal mapping from the disk onto the domain. But can this map be explicitly described? For general domains, there is no obvious answer...

Among the results of Part Two there is the following: Proposition B. Let J be a C-smooth almost complex structure defined in R. Let v be a continuous map from the unit disc D ⊂ C into (R, J). Let u be either a constant map from D into R or a proper J-holomorphic and C2-smooth map from D into an open subset Ω of R. Assume that v is J-holomorphic near z if v(z) 6∈ u(D). If u ≡ u(0) then v is J-ho...

The goal of color image segmentation is to divide the image into homogeneous regions. Thresholding is a commonly used technique for image segmentation. Thresholding assumes that image present a number of components, each of a nearly homogeneous value, and that one can separate the components by a proper choice of intensity threshold. In this paper, we present an efficient iterative algorithm fo...

Asymmetric disassembly of the synaptonemal complex (SC) is crucial for proper meiotic chromosome segregation. However, the signaling mechanisms that directly regulate this process are poorly understood. Here we show that the mammalian Rho GEF homolog, ECT-2, functions through the conserved RAS/ERK MAP kinase signaling pathway in the C. elegans germline to regulate the disassembly of SC proteins...

Grothendieck duality theory assigns to essentially-finite-type maps f of noetherian schemes a pseudofunctor f× right-adjoint to Rf∗, and a pseudofunctor f ! agreeing with f× when f is proper, but equal to the usual inverse image f∗ when f is étale. We define and study a canonical map from the first pseudofunctor to the second. This map behaves well with respect to flat base change, and is taken...

In this article, the Four Color Conjecture has been discussed from a standpoint outside the graph theoretic realm. It has first been shown that in a map with four regions, every region connected to every other, at least one of the regions would be enveloped. With the help of this result, it has been shown that at most three colors are needed to color the boundary regions of a planar map. Finall...