The symmetric projective varieties of rank one are all smooth and Fano by a classic result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric G-varieties of rank 2 which are Fano. When G is semisimple we classify also the locally factorial (respectively smooth) projective symmetric G-varieties of rank 2 which are only quasi-Fano. Moreover, we classify the ...

Rydberg spin-waves are optically excited in a quasi-one-dimensional atomic sample of Rb atoms. Pairwise spin-wave correlations are observed by a spatially selective transfer of the quantum state onto a light field and photoelectric correlation measurements of the light. The correlations are interpreted in terms of the dephasing of multiply excited spin-waves by long-range Rydberg interactions.

In this section, we derive in detail the closed form solution of problem (12) for binary pairwise factors (Sect. 4.1). Recall that the marginal polytope M(G a) is given by:

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

We define the notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the Drinfeld double D(H) of any finite dimensional quasi-Hopf algebra H is factorizable, and we characterize D(H) when H itself is factorizable. Finally, we prove that any finite dimensional factorizable quasi-Hopf algebra is unimodular. In particular, we obtain that the Drinfeld double D(...

This paper presents H∞ control problem for input-delayed systems. A neutral system approach is considered to the design of PD controller for input delay systems in presence of uncertain time-invariant delay. Using this approach, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed coeff...

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise th...

Scott conjectured in [6] that the class of graphs with no induced subdivision of a given graph is χ-bounded. We verify his conjecture for maximal triangle-free graphs. Let F be a graph. We denote by Forb∗(F ) the class of graphs with no induced subdivision of F . A class G of graphs is χ-bounded if there exists a function f such that every graph G of G satisfies χ(G) ≤ f(ω(G)), where χ and ω re...

Let d be a positive integer. A graph G is called d-divisible if d divides the degree of each vertex of G. G is called nowhere d-divisible if no degree of a vertex of G is divisible by d. For a graph H, gcd(H) denotes the greatest common divisor of the degrees of the vertices of H. The H-packing number of G is the maximum number of pairwise edge disjoint copies of H in G. The H-covering number o...