Trees, wreath products and finite Gelfand pairs

We present a new construction of finite Gelfand pairs by looking at the action of the full automorphism group of a finite spherically homogeneous rooted tree of type r on the variety V(r,s) of all spherically homogeneous subtrees of type s.This generalizes well-known examples as the finite ultrametric space, the Hamming scheme and the Johnson scheme.We also present further generalizations of these classical examples. The first two are based on Harary's notions of composition and exponentiation of group actions. Finally, the generalized Johnson scheme provides the inductive step for the harmonic analysis of our main construction.     

A simple separable exact C*-algebra not anti-isomorphic to itself

We give an example of an exact, stably finite, simple, separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^∞ UHF algebra. We can also explicitly compute the K-theory of D, namely ${K_0 (D) \cong {\mathbb{Z}} [ \tfrac{1}{3}]}$ with the standard order, and K ₁ (D) =  0, as well as the Cuntz semigroup of D, namely ${W (D) \cong {\mathbb{Z}} [ \tfrac{1}{3} ]_{+} \sqcup (0, \infty).}$      

Cell protection from Ca2+-overloading by bioactive molecules extracted from olive pomace

We are reporting in the present study that molecules extracted from olive pomace prevent cell death induced by Ca²⁺-overloading in different cell types. Exposure of cells to these molecules counteracts the Ca²⁺-induced cell damages by reducing the activation of the Ca²⁺-dependent protease calpain, acting possibly through the modification of the permeability to Ca²⁺ of the plasma membrane. The purification step by RP-HPLC suggests that effective compound(s), differing from the main biophenols known to be present in the olive pomace extract, could be responsible for this effect. Our observations suggest that bioactive molecules present in the olive pomace could be potential candidates for therapeutic applications in pathologies characterised by alterations of intracellular Ca²⁺ homeostasis.     

A semi-analytical finite element formulation for modeling stress wave propagation in axisymmetric damped waveguides

A semi-analytical finite element (SAFE) method is presented for analyzing the wave propagation in viscoelastic axisymmetric waveguides. The approach extends a recent study presented by the authors, in which the general SAFE method was extended to account for material damping. The formulation presented in this paper uses the cylindrical coordinates to reduce the finite element discretization over the waveguide cross-section to a mono-dimensional mesh. The algorithm is validated by comparing the dispersion results with viscoelastic cases for which a Superposition of Partial Bulk Waves solution is known. The formulation accurately predicts dispersion properties and does not show any missing root. Applications to viscoelastic axisymmetric waveguides with varying mechanical and geometrical properties are presented.     

Characterizing the structure of preserved information in quantum processes

We introduce a general operational characterization of information-preserving structures-encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes-by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every information-preserving structure is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schr?dinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process.     

Halogen bonding in supramolecular chemistry

Halogen bonding is the noncovalent interaction where halogen atoms function as electrophilic species. The energetic and geometrical features of the interaction are described along with the atomic characteristics that confer molecules with the specific ability to interact through this interaction. Halogen bonding has an impact on all research fields where the control of intermolecular recognition and self-assembly processes plays a key role. Some principles are presented for crystal engineering based on halogen-bonding interactions. The potential of the interaction is also shown by applications in liquid crystals, magnetic and conducting materials, and biological systems.     

Mutual induced coordination in halogen-bonded anionic assemblies with (6,3) cation-templated topologies

We describe the use of halogen bonding for the deliberate construction of cation-templated anionic (6,3) networks thanks to a strategy based on the mutual induced fitting of the valences of the building blocks.     

Superfluorinated Ionic Liquid Crystals Based on Supramolecular,Halogen‐Bonded Anions

Unconventional ionic liquid crystals in which the liquid crystallinity is enabled by halogen‐bonded supramolecular anions [C_nF_{2 n+1}‐I⋅⋅⋅I⋅⋅⋅I‐C_nF_{2 n+1}]⁻ are reported. The material system is unique in many ways, demonstrating for the first time 1) ionic, halogen‐bonded liquid crystals, and 2) imidazolium‐based ionic liquid crystals in which the occurrence of liquid crystallinity is not driven by the alkyl chains of the cation.