The goal of this paper is to generalize a theorem of Fujiwara (formerly Deligne’s conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is much simpler than the original one and applies to more general situations like algebraic spaces or Deligne–Mumford stacks without any changes. We also i...

In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.

We introduce several color image restoration algorithms based on the Mumford-Shah model and nonlocal image information. The standard Ambrosio-Tortorelli and Shah models are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, textures are not local in nature and require semi-local/non-local information to be denoised effic...

In this paper a novel region-merging image segmentation approach is presented. This approach is based on a two-step procedure: a distance metric is learned from some features on the image, then a piecewise approximation function for the Mumford-Shah model is optimized by this metric. The global optimum of the approximation function is inductively achieved under high polynomial terms of the Maha...

A new graph algorithm for multiscale segmentation of threedimensional medical data sets is presented. It is a threedimensional generalisation of an existing two-dimensional Mumford-Shah region-merging segmentation algorithm. The Mumford-Shah functional formulation leads to improved segmentation results compared to alternative approaches; the graph theoretic approach yields improved performance ...

ferromagnetism: Co–ZnO versus Co–CeO2 Lubna R. Shah, Weigang Wang, Hao Zhu, Bakhtyar Ali, Y. Q. Song, H. W. Zhang, S. I. Shah, and J. Q. Xiao Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA School of Microelectronic and Solid-State Electronic, University of Electronic Science and Technology of China, Chengdu 610054, People’s Republic of China Materials Science and Eng...

1 DOI: 10.1002/smll.201102350 The Removal of Single Layers from Multi-Layer Graphene by Low Energy Electron Stimulation Jason D. Jones, Rakesh K. Shah, Guido F. Verbeck, and Jose M. Perez* [*] Prof. J. M. Perez Department of Physics University of North Texas Denton, TX 76203 (USA) E-mail: [email protected] J. D. Jones, R. K. Shah Department of Physics University of North Texas Denton, TX 76203 (US...

A climate dependent model is proposed to simulate the population of Aedes aegypti mosquito. In developing the model, average temperature of Shah Alam, Malaysia was used to determine the development rate of each stage of the life cycle of mosquito. Rainfall dependent function was proposed to simulate the hatching rate of the eggs under several assumptions. The proposed transition matrix was obta...

As recently discussed by Bar, Kiryati, and Sochen in [3], the Ambrosio-Tortorelli approximation of the Mumford-Shah functional defines an extended line process regularization where the regularizer has an additional constraint introduced by the term ρ|∇v|. This term mildly forces some spatial organization by demanding that the edges are smooth. However, it does not force spatial coherence such a...