scholarly journals New Characterizations of Simple Points, Minimal Non-simple Sets and P-Simple Points in 2D, 3D and 4D Discrete Spaces

Author(s):  
Michel Couprie ◽  
Gilles Bertrand
Author(s):  
Roze Hentschell

St Paul’s Cathedral Precinct in Early Modern Literature and Culture: Spatial Practices is a study of London’s cathedral, its immediate surroundings, and its everyday users in early modern literary and historical documents and images, with a special emphasis on the late sixteenth and early seventeenth centuries. Hentschell discusses representations of several of the seemingly discrete spaces of the precinct to reveal how these spaces overlap with and inform one another spatially. She argues that specific locations—including the Paul’s nave (also known as Paul’s Walk), Paul’s Cross pulpit, the bookshops of Paul’s Churchyard, the College of the Minor Canons, Paul’s School, the performance space for the Children of Paul’s, and the fabric of the cathedral itself—should be seen as mutually constitutive and in a dynamic, ever-evolving state. To support this argument, she attends closely to the varied uses of the precinct, including the embodied spatial practices of early modern Londoners and visitors, who moved through the precinct, paused to visit its sacred and secular spaces, and/or resided there. This includes the walkers in the nave, sermon-goers, those who shopped for books, the residents of the precinct, the choristers—who were also schoolboys and actors—and those who were devoted to church repairs and renovations. By attending to the interactions between place and people and to the multiple stories these interactions tell—Hentschell attempts to animate St Paul’s and deepen our understanding of the cathedral and precinct in the early modern period.


2007 ◽  
Vol 40 (8) ◽  
pp. 2301-2314 ◽  
Author(s):  
Christophe Lohou ◽  
Gilles Bertrand

2017 ◽  
Vol 15 (07) ◽  
pp. 1750049 ◽  
Author(s):  
Y. Akbari-Kourbolagh

We present sufficient criteria for the entanglement of three-qubit states. For some special families of states, the criteria are also necessary for the entanglement. They are formulated as simple sets of inequalities for the mean values of certain observables defined as tensor products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with positive partial transpositions. Furthermore, they improve the best known result for the case of W state mixed with the white noise. The efficiency of the criteria is illustrated through several examples.


Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 975-984 ◽  
Author(s):  
Vladimir Vasilyev

We introduce discrete pseudo-differential operators in appropriate discrete Sobolev-Slobodetskii spaces. Using discrete Fourier transform and factorization concept we study invertibility of such operators in some discrete spaces. Some examples for discrete Calderon-Zygmund operators and difference operators are considered.


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