How to collect balls moving in the Euclidean plane

In this paper, we study how to collect n balls moving with a fixed constant velocity in the Euclidean plane by k robots moving on straight track-lines through the origin. Since all the balls might not be caught by robots, differently from Moving-target TSP, we consider the following 3 problems in various situations: (i) deciding if k robots can collect all n balls; (ii) maximizing the number of the balls collected by k robots; (iii) minimizing the number of the robots to collect all n balls. The situations considered in this paper contain the cases in which track-lines are given (or not), and track-lines are identical (or not). For all problems and situations, we provide polynomial time algorithms or proofs of intractability, which clarify the tractability-intractability frontier in the ball collecting problems in the Euclidean plane.     

Trinuclear coordinatively labile Cu(II) complex of 4,6-O-ethylidene-beta-D-glucopyranosylamine derived Schiff base ligand and its reactivity towards primary alcohols and amines

A novel neutral trinuclear Cu(II) complex of a Schiff base ligand derived from D-glucose has been synthesised and structurally characterised, which exhibits excellent alcohol binding affinity and activates the C-Cl bond of chloroform in the presence of primary amine.     

Algebraic description of spin 3/2 dynamics in NMR experiments

The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.     

Triple-quantum-filtered imaging of sodium in presence of B(0) inhomogeneities

Triple quantum filtered sodium MRI techniques have been recently demonstrated in vivo. These techniques have been previously advocated as a means to separate the sodium NMR signal from different physiological compartments based on the differences between their relaxation rates. Among the different triple quantum coherence transfer filters, the three-pulse coherence transfer filter has been demonstrated to be better suited for human imaging than the traditional four-pulse implementation. While the three-pulse structure has distinct advantages in terms of RF efficiency, the lack of a refocusing pulse in the filter introduces an increased dependence on the main magnetic field inhomogeneities, which can sometimes lead to significant signal loss. In this paper, we characterize these dependencies and introduce a method for their compensation through the acquisition of a B(0) map and the use of a modified phase cycling scheme.     

Laponite: aging and shear rejuvenation of a colloidal glass

We study the nonlinear rheological behavior and the microscopic particle dynamics for a colloidal glass, to see whether recently developed models for driven glassy systems can be applied to predict the rheology. Qualitatively, all the findings predicted by the models can be retrieved in our system. Notably, the viscosity decreases strongly with the shear rate. Since it is difficult to predict non-Newtonian viscosities of colloidal systems due to long-ranged hydrodynamic interactions, this shows the promise of this approach for predicting flow behavior. In addition, the measurements allow us to relate the microscopic diffusion dynamics to the macroscopic viscosity of the system.     

A “ladder” Morphology in an ABC Triblock Copolymer

ABC triblock copolymers are known to exhibit a wide variety of unique types of morphologies compared to AB diblock copolymers. In the present study, poly(styrene-block-(ethylene-alt-propylene)-block-(methyl methacrylate)) (SEPM) triblock copolymers were synthesized and their morphologies were extensively studied by transmission electron microtomography (TEMT). In the SEPM triblock copolymer, two kinds of morphologies coexist: One was the well-known knitting morphology, and the other was a novel morphology called the “ladder morphology”. The ladder morphology was a major morphology in the SEPM copolymer, the stability of which was discussed in terms of the interfacial area and the solubility parameters between the three components.     

Constraint isomorphism and correction algorithms for violations

When a problem can be characterized by different parameter sets, constraints imposed on one parameter set must be consistent with, or isomorphic to, constraints imposed on other parameter sets. When mapping among the parameter sets is not so visibly obvious, one might overlook consistency violations, which have occurred in the past. This paper examines such violations and possible correction algorithms. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of Chiral MOF-74 Frameworks by Post-Synthetic Modification by Using an Amino Acid

The synthesis of chiral metal–organic frameworks (MOFs) is highly relevant for asymmetric heterogenous catalysis, yet very challenging. Chiral MOFs with MOF-74 topology were synthesised by using post-synthetic modification with proline. Vibrational circular dichroism studies demonstrate that proline is the source of chirality. The solvents used in the synthesis play a key role in tuning the loading of proline and its interaction with the MOF-74 framework. In N,N′-dimethylformamide, proline coordinates monodentate to the Zn²⁺ ions within the MOF-74 framework, whereas it is only weakly bound to the framework when using methanol as solvent. Introducing chirality within the MOF-74 framework also leads to the formation of defects, with both the organic linker and metal ions missing from the framework. The formation of defects combined with the coordination of DMF and proline within the framework leads to a pore blocking effect. This is confirmed by adsorption studies and testing of the chiral MOFs in the asymmetric aldol reaction between acetone and para-nitrobenzaldehyde.