From Polyesters to Polyamides Via O?N Acyl Migration: An Original Multi‐Transfer Reaction

A new strategy for the synthesis of polyamides from polyesters of hydroxyl‐containing amino acids using a multi O N acyl transfer reaction was developed. This original approach allowed the synthesis of three generations of polymers from the same starting monomer. The polymerization of N‐benzyloxycarbonyl‐serine and its γ‐homologated derivative provided the Z‐protected polyesters; then the water‐soluble polycationic polyesters were obtained by removal of the Z‐protecting group; and finally the polyamides were obtained by a base‐induced multi O N acyl transfer, both in aqueous or organic medium. The key step transfer reaction was monitored by the disappearance and appearance of characteristic NMR proton signals and IR bands of polyesters and polyamides.

     

Scattering and Bound States of two Polaritons in an Array of Coupled Cavities

We develop an analytical approach for calculating the scattering and bound states of two polaritons in a one-dimensional (1D) infinite array of coupled cavities, with each cavity coupled to a two-level system. We find that in such a system a contact interaction between two polaritons is induced by the non-linearity of the Jaynes–Cummigs Hamiltonian. We then solve the two-polariton problem with zero center-of-mass momentum, and find 1D scattering resonances. Our results are relevant to the transport of two polaritons, and are helpful for the investigation of many-body physics in a dilute gas of polaritons in a 1D cavity array.     

Effect of nitrogen pressure on the combustion synthesis of titanium nitride

Abstract

Titanium nitride, TiN, has attractive physical and chemical properties such as hardness, chemical stability and electrical conductivity. It is a typical material with a wide range of stoichiometry. It can be synthesised by high pressure combustion synthesis. The composition and microstructures can vary with the experimental conditions especially with thermal treatment and nitrogen pressure.     

A Complexity Dichotomy for the Coloring of Sparse Graphs

Galluccio, Goddyn, and Hell proved in 2001 that in any minor‐closed class of graphs, graphs with large enough girth have a homomorphism to any given odd cycle. In this paper, we study the computational aspects of this problem. Let be a monotone class of graphs containing all planar graphs, and closed under clique‐sum of order at most two. Examples of such class include minor‐closed classes containing all planar graphs, and such that all minimal obstructions are 3‐connected. We prove that for any k and g, either every graph of girth at least g in has a homomorphism to , or deciding whether a graph of girth g in has a homomorphism to is NP‐complete. We also show that the same dichotomy occurs when considering 3‐Colorability or acyclic 3‐Colorability of graphs under various notions of density that are related to a question of Havel (On a conjecture of Grünbaum, J Combin Theory Ser B 7 (1969), 184–186) and a conjecture of Steinberg (The state of the three color problem, Quo Vadis, Graph theory?, Ann Discrete Math 55 (1993), 211–248) about the 3‐Colorability of sparse planar graphs.     

Some new properties of composition operators associated with lens maps

We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space H ². The last ones are connected with Hardy-Orlicz and Bergman-Orlicz spaces ${H^\psi }$ and ${B^\psi }$ , and provide a negative answer to the question of knowing if all composition operators which are weakly compact on a non-reflexive space are norm-compact.     

Numerical Methods for Non-Linear Black–Scholes Equations

Abstract

In recent years non-linear Black–Scholes models have been used to build transaction costs, market liquidity or volatility uncertainty into the classical Black–Scholes concept. In this article we discuss the applicability of implicit numerical schemes for the valuation of contingent claims in these models. It is possible to derive sufficient conditions, which are required to ensure the convergence of the backward differentiation formula (BDF) and Crank–Nicolson scheme (CN) scheme to the unique viscosity solution. These stability conditions can be checked a priori and convergent schemes can be constructed for a large class of non-linear models and payoff profiles. However, if these conditions are not satisfied we show that the schemes are not convergent or produce spurious solutions. We study the practical implications of the derived stability criterions on relevant numerical examples.     

RF field visualization of RF ablation at the Larmor frequency

Radio-frequency ablation (RFA) is an effective minimally invasive treatment for tumors. One primary source of difficulty is monitoring and controlling the ablation region. Currently, RFA is performed at 460 kHz, for which magnetic resonance imaging (MRI) could play a role given its capability for temperature monitoring and tumor visualization. If instead the ablation were to be performed at the MRI Larmor frequency, then the MR capability for B(1) field mapping could be used to directly visualize the radio-frequency (RF) fields created by the ablation currents. Visualizing the RF fields may enable better control of the ablation currents, enabling better control of lesion shape and size and improving repeatability. We demonstrate the feasibility of performing RFAs at 64 MHz and show preliminary results from imaging the RF fields from the ablation. The post-ablation RF fields show an increase in current density in the ablated region, consistent with an increase in conductivity of the ablated tissue.     

Characterization of circumferential guided waves in a cylindrical cortical bone-mimicking phantom

The femoral neck cortical shell was recently demonstrated to act like a waveguide for circumferential waves. Femoral neck assessment with ultrasound could be enhanced by guided waves measurement. In this study, the decomposition of the time reversal operator (DORT) method is used to measure the phase velocities of circumferential guided modes in a circular tube with dimensions characteristic of femoral neck. The tube is made of a bone-mimicking material. Five guided modes are obtained and compared to theoretical predictions. The work substantiates the feasibility of measuring guided waves in a relatively thick tube of attenuating material with the DORT method.