S. Schmidt,1 D. Gerace,2 A. A. Houck,3 G. Blatter,1 and H. E. Türeci3,4 1Institute for Theoretical Physics, ETH-Zurich, CH-8093 Zurich, Switzerland 2Dipartimento di Fisica “Alessandro Volta,” Università di Pavia, 27100 Pavia, Italy 3Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA 4Institute for Quantum Electronics, ETH-Zurich, CH-8093 Zurich, Switzer...

Museo di Storia Naturale e del Territorio, Università di Pisa, via Roma 79, I-56011 Calci (Pisa), Italy Dipartimento di Biologia Animale, Università di Pavia, p.za Botta 9, I-27100 Pavia, Italy Centre d’Etudes Biologiques de Chizé, CNRS, F-79360 Villiers en Bois, France FIZV (Ecology), via Olona 7, I-00198 Rome, Italy Dipartimento di Biologia (Unità di ProtistologiaZoologia), Università di Pisa...

In this expository article, which is a slightly expanded version of the lecture given at the All Ireland Algebra Days (Belfast, 16–19 May, 2001), we first recall a technique recently developed by F. Dalla Volta and A. Lucchini to study generation properties of finite groups. We then discuss some problems in permutation groups, linear groups and profinite groups where this technique has proved u...

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

Resolving the incompleteness of Weil-Petersson metric on Teichmüller spaces by taking metric and geodesic completion results in two distinct spaces, where the Hopf-Rinow theorem is no longer relevant due to the singular behavior of the Weil-Petersson metric. We construct a geodesic completion of the Teichmüller space through the formalism of Coxeter complex with the Teichmüller space as its non...

S2 (|∇u| + 2u)}, and the equality holds if and only if eg is a metric of constant curvature. In the study of deforming metrics and prescribing curvatures on S, this inequality is often used to control the size and behavior of a new metric eg0 near a concentration point. With certain “balance” condition on the metric one would guess that if the metric concentrates, it should concentrate at more ...

Non-rigid shapes are ubiquitous in Nature and are encountered at all levels of life, from macro to nano. The need to model such shapes and understand their behavior arises in many applications in imaging sciences, pattern recognition, computer vision, and computer graphics. Of particular importance is understanding which properties of the shape are attributed to deformations and which are invar...

The NVIDIA Volta GPU microarchitecture introduces a specialized unit, called Tensor Core that performs one matrix-multiplyand-accumulate on 4×4 matrices per clock cycle. The NVIDIA Tesla V100 accelerator, featuring the Volta microarchitecture, provides 640 Tensor Cores with a theoretical peak performance of 125 Tflops/s in mixed precision. In this paper, we investigate current approaches to pro...

In this paper, we introduce the notion of an extended metric space ($p$-metric space) as a new generalization of the concept of $b$-metric space. Also, we present the concept of $(psi ,varphi )_{Omega}$-contractive mappings and we establish some fixed point results for this class of mappings in ordered complete $p$-metric spaces. Our results generalize several well...