Operads of compatible structures and weighted partitions

In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large class of algebraic structures by using the poset method of B. Vallette. In particular we show that this is true for the operads of compatible Lie, associative and pre-Lie algebras.     

Minimal free resolutions of monomial curves in P3k

Minimal free resolutions for prime ideals with generic zero (tn3,tn3?n10tn11,tn3?n20tn2, tn31), n1<n2<n3 positive integers, (n1,n2,n3)=1, are determined.     

Berry’s Phase in Pilot-Wave Theory

The projective-geometric derivation of Berry's adiabatic geometric phase for a single trajectory in the de Broglie-Bohm pilot-wave theory is given. The relation between this phase and the first order nature of pilot-wave theory is discussed. It is shown, in the case where the electromagnetic vector potential is a gradient, that the phase can be given in a locally phase invariant form. The appearance of the Berry connection is justified and its physical significance in pilot-wave theory is discussed.     

Magnetotransport in simple metals. An exactly soluble model

The magnetoconductivity tensors of a metal with a weakly anisotropic Fermi surface are determined from analytic solutions to the Boltzmann equation without any restrictions on the magnitude of the cyclotron frequency compared to the collision rate. Results are given for both a two- and a three-dimensional model, the former being analytically simpler to handle. The Hall coefficient and magnetoresistance are obtained as functions of the magnetic field, and we show by explicit calculation how the thermoelectric coefficients at high magnetic fields are determined by the thermodynamic entropy.     

Synthesis and characterisation of Gd2O3 nanocrystals functionalised by organic acids

Nanocrystals of Gd2O3 have been prepared by various methods, using, e.g., trioctylphosphine oxide (TOPO), diethylene glycol (DEG) or glycine. The crystalline particles were of sizes 5 to 15 nm. Different carboxylic acids, e.g., oleic acid or citric acid, were adsorbed onto the surface of the particles made with DEG. IR measurements show that the molecules coordinate to the Gd2O3 surface via the carboxylate group in a bidentate or bridging manner. The organic-acid/particle complexes were characterised by XRPD, TEM, FTIR, Raman, and XPS.     

A dimerization "switch" in the internalization mechanism of a cell-penetrating peptide

The internalization mechanism of a cell-penetrating peptide has been explored through combinatorial selection of a phage-displayed peptide dimer library, chemical synthesis, and biophysical characterization. Both energy-dependent and energy-independent modes for peptide uptake by the target mammalian cells were observed, suggesting a role for higher-order structure in modulating the action of this novel cell-penetrating peptide.     

Microporous organic crystals: an unusual case for L-leucyl-L-serine

Cocrystallized acetonitrile solvent molecules located inside 5.2 A channels in the crystal structure of L-leucyl-L-serine have been replaced by I2 molecules with full retention of the peptide scaffold.