The force between Giant Magnons

We compute the force and torque between well-separated, slowly-moving Giant Magnons with arbitrary orientations on S⁵$S^5$. We propose an effective Hamiltonian for Giant Magnons in this regime.     

Estimation of speed of sound in dual-layered media using medical ultrasound image deconvolution

The speed of sound in soft tissues is usually assumed to be 1540 m/s in medical pulse-echo ultrasound imaging systems. When the true speed is different, the mismatch can lead to distortions in the acquired images, and so reduce their clinical value. Previously we reported a new method of sound-speed estimation in the context of image deconvolution. Unlike most other sound-speed estimation methods, this enables the use of unmodified ultrasound machines and a normal scanning pattern. Our approach was validated for largely homogeneous media with single sound speeds. In this article, we demonstrate that sound speeds of dual-layered media can also be estimated through image deconvolution. An ultrasound simulator has been developed for layered media assuming that, for moderate speed differences, the reflection at the interface may be neglected. We have applied our dual-layer algorithm to simulations and in vitro phantoms. The speed of the top layer is estimated by our aforesaid method for homogeneous media. Then, when the layer boundary position is known, a series of deconvolutions are carried out with dual-layered point-spread functions having different lower-layer speeds. The best restoration is selected using a correlation metric. The error level (e.g., a mean error of −9 m/s with a standard deviation of 16 m/s) for in vitro phantoms is found to be not as good as that of our single-speed algorithm, but is comparable to other local speed estimation methods where the data acquisition may not be as simple as in our proposed method.     

On the ν1/2 ν2 Resonance in the Complex of Carbon Dioxide with Dimethyl Ether

Infrared and Raman spectra of solutions in liquid argon and krypton containing dimethyl ether or its fully deuterated isotopomer and ¹²CO₂ or ¹³CO₂ are investigated. The spectra lead to new data on the ν₁/2 ν₂ resonances appearing in the complex of CO₂ with the ether. The experimental data, and their interpretation, is supported by MP2/6‐311++G(2d,2p) calculations of the cubic and quartic force constants and of the first and higher order dipole moment derivatives required for the modelling of the Fermi and Darling‐Dennison resonances observed.     

Asymptotic type for sectorial operators and an integral of fractional powers

There is a standard notion of type for a sectorial linear operator acting in a Banach space. We introduce a notion of asymptotic type for a linear operator V, involving estimates on the resolvent ⁻¹(λI+V) as λ→0. We show, for example, that if V is sectorial and of asymptotic type ω then the fractional power Vα is of asymptotic type αω for a suitable range of positive α. Moreover, we establish various properties of the operator ; in particular, this operator is of asymptotic type 0, for a sectorial operator V. This result has an application to the construction of operators satisfying the well-known Ritt resolvent condition.     

Proficiency testing in analytical chemistry,microbiology and laboratory medicine – working group discussions on current status,problems and future directions

Working group (WG) discussions on proficiency testing and external quality assessment held at the Eurachem workshop, Portorož, Slovenia 26–27 Sept 2005 are summarised. The discussions focused on performance criteria (WG 1), different aspects of accreditation (WGs 2–3), the revised international harmonised protocol (WG 4), pre- and post-analytical schemes (WG 5), Internet applications (WG 6), experience from the CoEPT project (WG 7), and future aspects (WG 8). Current status, problems and future directions were identified. The WG contained a mix of participants with different expertise. This was done to promote cross-fertilisation of ideas between sectors. The WG issues reflected the content of the keynote lectures and some issues were covered from different perspectives by more than one WG.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia.     

Displacement of Cu(II) by Ag(I) in solvated metal sulfides. A DFT and AIM computational study

The substitution of Cu2+ by Ag+ in hydrated CuIIS and (CuII)3S3 was modeled computationally by density functional theory quantum theory of atoms in molecules, and solvent field methods. The coordination, first-shell and partly second-shell molecular structures, and thermochemical data for solvated Cu2+, Ag+, CuIIS, (CuII)3S3, AgCu2S3 and their reactions were obtained. The thermochemical data showed that displacement of Cu2+ and Cu+ from CuIIS and (CuII)3S3 by Ag+, while unfavorable in the gas phase, is facilitated in an aqueous environment. Several covalently bonded species were examined as intermediates in the substitution reactions.     

Synthesis, characterization, and DNA-binding studies of nitro(oligopyridine)ruthenium(II) complexes

The complexes of general formulas [RuII(terpy)(4-CO2H-4'-Mebpy)(X)]n+ (X = NO (n = 3) and NO2 (n = 1); 1, 2) and [RuII(terpy)(4-COGHK-4'-Mebpy)(X)] (X = NO (n = 3) and NO2 (n = 1); 3, 4) were synthesized and characterized. The complex [RuII(terpy)(4-CO2-4'-Mebpy)(NO2)]_7.5H2O has also been characterized by X-ray crystallographic studies. It crystallizes in the triclinic system: a = 9.4982(1) A, b = 13.1330(1) A, c = 14.2498(2) A; alpha = 110.5870(6) x bc, beta = 98.4048(5) x bc, gamma = 106.4353(5), P1, Z = 2. The crystal structure reveals an extended hydrogen-bonding network. Two water molecules form strong hydrogen bonds with the nitro and the carboxylic oxygen atoms of two separate units of the complex, resulting in a dimeric unit. The dimers are bridged by a (H2O)15 cluster, consisting of two cyclo-(H2O)6 species, while an exo-H2O(8) connects them. Two more exo-H2O molecules are joined together and connect the cyclo-(H2O)6 units with the H2O(1) of the dimeric unit. It was found that complexes 1 and 3 can be transformed into their nitro derivatives in aqueous media at neutral pH. Photorelease of NO in dry MeCN solutions was observed for complexes 1 and 3. Also, complex 2 partially releases (NO2)- in MeCN upon visible light irradiation. Complex 2 interacts with short fragments (70-300 bp) of calf thymus DNA shortening slightly the apparent polynucleotide length, while the conjugation of the peptide GHK to it (2) affects its DNA-binding mode. The peptide moiety of complex 4 was found to interact with the DNA helix in a synergistic way with the whole complex. Preliminary results of photocleavage of DNA by complex 2 are also reported.     

A Note on Time Regularity for Discrete Time Heat Kernels

We offer a new, simple method of deriving time regularity estimates for discrete time "heat kernels". Our method applies, for example, to suitable Markov chains and to random walks on weighted graphs, and provides Gaussian estimates or L^p off-diagonal estimates for time differences of the iterated kernels.     

Synthesis of aluminium complexes bearing a piperazine-based ligand system

Aluminium complexes bearing the N,N-chelating ligand 1,4-bis(2-hydroxy-3,5-di-tert-butyl)piperazine (1) have been synthesised. Both monometallic and bimetallic aluminium methyl complexes (2 and 3, respectively) were prepared by treatment of 1 with the appropriate amount of AlMe₃. Complex 2 can be converted to 3 by addition of excess AlMe₃. Bimetallic aluminium-ethyl complex 4 was also prepared. Treatment of 1 with AlEt₂Cl afforded the monometallic chloride complex 5. Treatment of this latter complex with potassium alkoxides (KOR, R = Me, Et, ⁱPr, ^tBu) or AgOTf afforded the corresponding aluminium alkoxide complexes (6, R = Et; 7, R = Me; 8, R = ⁱPr; 9, R = ^tBu; 10, R = OTf) in good yields. Aluminium ethoxide complex 6 was also synthesised by treatment of 1 with AlEt₂OEt. All of these complexes were tested as potential catalysts in the ring-opening polymerisation of rac-lactide and caprolactone with limited success.     

IRMPD spectroscopy of metal-ion/tryptophan complexes

Infrared multiple-photon dissociation (IRMPD) spectroscopy is employed to obtain detailed binding information on singly charged silver and alkali metal-ion/tryptophan complexes in the gas phase. For these complexes the presence of the salt bridge (i.e. zwitterionic) tautomer can be virtually excluded, except for perhaps a few percent in the case of Li+. Two low-energy structures having the charge solvation form are shown to be likely, where the metal cation is either in a tridentate N/O/Ring conformation or in a bidentate O/Ring conformation. These two structures can be conveniently discriminated and their relative quantities can be approximated by IR spectroscopy, based principally on diagnostic modes near approximately 1150 (N/O/Ring) and 1400 (O/Ring) cm(-1). Interestingly, the smaller cation complexes (i.e. Ag+ and Li+) display exclusively the N/O/Ring conformation, whereas the O/Ring conformer becomes progressively more abundant with increasing alkali metal size, eventually representing the majority of the ion population for Rb+ and Cs+. These spectroscopic findings are in excellent agreement with thermochemical density functional theory (DFT) calculations, giving support to the utility of high-level quantum-chemical calculations for such systems. Moreover, in contrast to other mass spectrometry-based techniques, IRMPD spectroscopy allows clear differentiation and semi-quantitative approximation of these metal-ligand binding motifs, thereby underlining its importance in thermochemical model benchmarking.