Aromatic-aromatic interaction between metallacycle and phenyl ring

The X-ray crystal structure of [CuL2]ClO4 where L is the 1:1 condensate of benzil-monohydrazone and 2-pyridinecarboxalde-hyde, reveals unprecedented pi - pi interaction between the metallacycles and phenyl rings. The interaction is intramolecular. (C) 2003 Elsevier Science B.V. All rights reserved.

Self-assembly of a peptide amphiphile: transition from nanotape fibrils to micelles

A thermal transition is observed in the peptide amphiphile C16-KTTKS (TFA salt) from nanotapes at 20 degrees C to micelles at higher temperature (the transition temperature depending on concentration). The formation of extended nanotapes by the acetate salt of this peptide amphiphile, which incorporates a pentapeptide from type I procollagen, has been studied previously [V. Castelletto et al., Chem. Commun., 2010, 46, 9185]. Here, proton NMR and SAXS provide evidence for the TFA salt spherical micelles at high temperature. The phase behavior, with a Krafft temperature separating insoluble aggregates (extended nanotapes) at low temperature from the high temperature micellar phase resembles that for conventional surfactants, however this has not previously been reported for peptide amphiphiles.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Optimal infinity-quasiconformal immersions

For a Hamiltonian K ∈ C2(RN × n) and a map u:Ω ⊆ Rn − → RN, we consider the supremal functional (1) The “Euler−Lagrange” PDE associated to (1)is the quasilinear system (2) Here KP is the derivative and [ KP ] ⊥ is the projection on its nullspace. (1)and (2)are the fundamental objects of vector-valued Calculus of Variations in L∞ and first arose in recent work of the author [N. Katzourakis, J. Differ. Eqs. 253 (2012) 2123–2139; Commun. Partial Differ. Eqs. 39 (2014) 2091–2124]. Herein we apply our results to Geometric Analysis by choosing as K the dilation function which measures the deviation of u from being conformal. Our main result is that appropriately defined minimisers of (1)solve (2). Hence, PDE methods can be used to study optimised quasiconformal maps. Nonconvexity of K and appearance of interfaces where [ KP ] ⊥ is discontinuous cause extra difficulties. When n = N, this approach has previously been followed by Capogna−Raich ? and relates to Teichmüller’s theory. In particular, we disprove a conjecture appearing therein.