The k‐piece packing problem

A k‐piece of a graph G is a connected subgraph of G all of whose nodes have degree at most k and at least one node has degree equal to k. We consider the problem of covering the maximum number of nodes of a graph by node disjoint k‐pieces. When k = 1 this is the maximum matching problem, and when k = 2 this is the problem, recently studied by Kaneko [ 19 [, of covering the maximum number of nodes by disjoint paths of length greater than 1. We present a polynomial time algorithm for the problem as well as a Tutte‐type existence theorem and a Berge‐type min‐max formula. We also solve the problem in the more general situation where the “pieces” are defined in terms of lower and upper bounds on the degrees. © 2006 Wiley Periodicals, Inc. J Graph Theory     

On rational Drinfeld associators

We prove an estimate on denominators of rational Drinfeld associators. To obtain this result, we prove the corresponding estimate for the p-adic associators stable under the action of suitable elements of Gal([`(\mathbbQ)]/\mathbbQ){{\rm Gal}(\bar{\mathbb{Q}}/\mathbb{Q})} . As an application, we settle in the positive Duflo’s question on the Kashiwara–Vergne factorizations of the Jacobson element J _p (x, y) = (x + y) ^p − x ^p − y ^p in the free Lie algebra over a field of characteristic p. Another application is a new estimate on denominators of the Kontsevich knot invariant.     

Λc enhancement from strongly coupled QGP

We propose the enhancement of Λ _c yield in heavy ion collisions at RHIC and LHC as a novel signal for the existence of diquarks in the strongly coupled quark-gluon plasma produced in these collisions as well as in the Λ _c . Assuming that stable bound diquarks can exist in the quark-gluon plasma, we argue that the yield of Λ _c would be increased by two-body collisions between [ud] diquarks and c quarks, in addition to normal three-body collisions among u, d and c quarks. A quantitative study of this effect based on the coalescence model shows that including the contribution of diquarks to Λ _c production indeed leads to a substantial enhancement of the Λ _c /D ratio in heavy ion collisions.     

In-process ZnO thin films alloying during pulsed laser deposition

Alloyed ZnO:Al thin films were prepared by a pulsed laser deposition by the altering of two pure targets (ZnO and Al) during the deposition process. Two deposition temperatures (?197 °C and 400 °C) were applied and differences of diffusion dynamics were compared. As-grown layered films were annealed and aluminium distribution was homogenized. The results revealed that the amorphous structure (samples grown at ?197 °C) of ZnO provide more positive conditions for efficient Al diffusion in comparison with crystalline structure (samples grown at 400 °C). A detailed investigation by SIMS depth profiling confirmed a homogeneous chemical composition of annealed and recrystallized films which exhibited a porous nature and wurtzite crystalline structure.     

Delayed gadolinium-enhanced MRI of the fibrocartilage disc of the temporomandibular joint – a feasibility study

Objective

To 1) test the feasibility of delayed Gadolinium-Enhanced Magnetic Resonance Imaging of Cartilage (dGEMRIC) at 3 T in the temporomandibular joint (TMJ) and 2) to determine the optimal delay for measurements of the TMJ disc after i.v. contrast agent (CA) administration.

Design

MRI of the right and left TMJ of six asymptomatic volunteers was performed at 3 T using a dedicated coil. 2D inversion recovery (2D-IR) sequences were performed at 4 time points covering 120 minutes and 3D gradient-echo (3D GRE) dual flip-angle sequences were performed at 14 time points covering 130 minutes after the administration of 0.2 mmol/kg of Gd-diethylenetriamine pentaacetic acid ion (Gd-DTPA)^2-, i.e., 0.4 mL of Magnevist™ per kg body weight. Pair-wise tests were used to assess differences between pre-and post-contrast T1 values.

Results

2D-IR sequences showed a statistically significant drop (p < 0.001) in T1 values after i.v. CA administration. The T1 drop of 50% was reached 60 minutes after bolus injection in the TMJ disc. The 3D GRE dual flip-angle sequences confirmed these results and show plateau of T1 after 60 minutes.

Conclusions

T1(Gd) maps calculated from dGEMRIC data allow in vivo assessment of the fibrocartilage disc of the TMJ. The recommended measurement time for dGEMRIC in the TMJ after i.v. CA administration is from 60 to 120 minutes.     

Photostability of D–π–A nonlinear optical chromophores containing a benzothiazolium acceptor

For the practical application of second‐order NLO materials, not only a high molecular quadratic hyperpolarizability β but also good thermal, chemical, and photochemical stabilities are required. Most of the state‐of‐the‐art chromophores with high NLO response cannot be put to use because they are photochemically highly unstable. Good thermal and photochemical stabilities with preserved high hyperpolarizabilities can be achieved by replacement of an aromatic ring with easily delocalizable heteroaromatics, e.g., with benzothiazole. Furthermore, desirable modifications of the benzothiazole fragment lead to improvement in β values. Here we report results of a comprehensive investigation of the photochemical stability of seven D–π–A push–pull molecules based on a N‐methylbenzothiazolium acceptor and a N,N‐dimethylaminophenyl donor with a different length of conjugated bridge and different acceptor strength. The quantum yield (Φ) and the kinetic parameters of photoreactions were determined for existing photodegradation pathways on irradiation at 300–850 nm in MeOH. Trans–cis photoisomerization is proposed as a fast but inefficient photobleaching mechanism for these irradiation wavelengths. Self‐sensitized photooxidation by ¹O₂ makes very slow parallel photodegradation pathway and, albeit to small value of Φ, plays a dominant role in the photodegradation of the compounds investigated. Both structural modifications (extension of conjugated bridge and an additional acceptor group bonded to heterocycle) resulting in an increase of NLO response led to a decrease in photostability due to the self‐sensitized ¹O₂ photooxidative attack. Thus a compromise should be found between an increase in NLO response and a decrease in photostability to make a choice of studied compounds for practical applications. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation by NMR Spectroscopy and Molecular Modeling of the Conformations of Some Modified Disaccharide Antigens for Shigella Dysenteriae Type 1

Abstract

The O-polysaccharide of Shigella dysenteriae type 1 is made up of multiple repeats of the linear tetrasaccharide 3)-α-L-Rhap-(1→2)-α-D-Galp-(1→3)-α-D-GlcpNAc-(1→3)-α-L-Rhap-(1→, for which the antigenic determinant for a murine monoclonal IgM antibody is the disaccharide α-L-Rhap-(1→2)-α-D-Galp. This disaccharide and various analogs have been studied by 2D NOESY, ROESY, and TOCSY NMR spectroscopy, in conjunction with proton spin-lattice relaxation rate measurements, restrained molecular mechanics, and restrained molecular dynamics with simulated annealing. It has been found that replacement of any single hydroxyl group in the determinant by a hydrogen atom, or replacement of any single hydroxyl group in the Gal residue by a fluorine atom has little if any influence on the conformation of the resulting derivatives.

     

Ab initio theory of complex electronic ground state of superconductors: I. Nonadiabatic modification of the Born-Oppenheimer approximation

The ARPES of high-T_c cuprates and theoretical results of low-Fermi energy band structure fluctuation for different groups of superconductors indicate that electron coupling to pertinent phonon modes drive system from adiabatic into anti-adiabatic state (ω>E_F). At these circumstances, not only Migdal-Eliashberg approximation is not valid, but basic adiabatic Born-Oppenheimer approximation (BOA) does not hold. At these circumstances, electronic structure has to be studied as explicitly dependent on instantaneous nuclear coordinates Q as well as on instantaneous nuclear momenta P.In the present paper—part I, it has been shown that Q, P-dependent modification of the BOA for ground electronic state can be derived by sequence of canonical transformations of the basis functions. The effect of nuclear coordinates and momenta on electronic structure is presented in the form of corrections to zero-, one- and two-particle terms of clamped nuclear Hamiltonian. In the anti-adiabatic state, correction to electronic ground state energy (zero-particle term correction) is negative and system can be stabilized in the anti-adiabatic state at distorted geometry with respect to adiabatic equilibrium structure and gap in one-particle spectrum of quasi-continuum states at Fermi level can be opened. Stabilization effect is solely the consequence of nuclear dynamics (P) that is crucial in anti-adiabatic state. It has been shown that nuclear dynamics also increases electron correlation until system at nuclear motion remains in a bound state. Corresponding corrections to electronic wave function are also specified.On the other hand, when system remains at vibration motion of nuclei in adiabatic state, the influence of nuclear dynamics (P-dependence) is negligible. In this case, all basic effects are covered through nuclear coordinates (Q-dependence) within the adiabatic BOA and standard results of solid-state (or molecular) physics are recovered.