The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge symmetries. In this work we continue to study the structure of graphs obtained from CY3 reflexive polyhedra. The objective is to describe the “simply laced” cases...

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...

We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various spaces: the disc algebra, subspaces of C(K) with reflexive annihilator and subspaces of the Morse-TransueOrlicz space Mq (Ω, μ) with q > 2.

The discovery that real-world large networks from many different domains (sociology, biology, computer science. . . ) share the same characteristics has raised an interest in their studying ([17, 2, 15]). The associated graphs of such networks are rather sparse (the mean degree stays roughly constant when the number of nodes increases), highly clustered, and there exists short paths that can be...

Let Γ = (V,E) be a point-transitive reflexive relation. Let v ∈ V and put r = |Γ(v)|. Also assume Γ(v) ∩ Γ−(v) = {v}. Then |Γ(v) \ Γ(v)| ≥ r − 1. In particular we have |Γ(v)| ≥ 1 + (r − 1)j. The last result confirms a recent conjecture of Seymour in the case vertex-transitive graphs. Also it gives a short proof for the validity of the Caccetta-Häggkvist conjecture for vertex-transitive graphs a...

The main result is that a Banach space X is not super-reflexive if and only if the diamond graphs Dn Lipschitz embed into X with distortions independent of n. One of the consequences of that and previously known results is that dimension reduction a-la Johnson–Lindenstrauss fails in any non super reflexive space with non trivial type. We also introduce the concept of Lipschitz (p, r)-summing ma...