On polyhedra with extremal Euler characteristic

It is the main purpose of this paper to determine the extremal values of the Euler characteristic of unions of at most n polytopes, disregarding the dimension d of the space in which they lie.     

Electrocatalytic cyclization of dithiothreitol on a chemically modified electrode by analogy with protein action

Electrocatalytic oxidative cyclization of dithiothreitol (DTT(SH)2) to a disulfide product was demonstrated on a Nafion/lead-ruthenium oxide pyrochlore chemically modified electrode (NPyCME). The process at the NPyCME with DTT(SH)2 is similar to the behaviour of protein in a disulfide linkage, which can be demonstrated by product analysis using HPLC coupled with UV spectroscopy. A possible electrocatalytic mechanism for DTT(SH)2 oxidation to dihydroxydithiane [i.e. cyclized DTT(S-S)] on the NPyCME was proposed in terms of Py-Ru(IV)/Py-Ru(VI) redox active sites. This physical aspect was further utilized for high precision analytical assays using flow injection analysis (FIA), with a linearity up to 50 microM and a detection limit (S/N = 3) of 28 nM (8.64 pg) in a 20 microL sample loop. This is the most sensitive method ever reported for DTT(SH)2 detection assays. The interference from dissolved oxygen, disulfide and glucose is almost negligible. The present method offers an easy route for extension to redox-related protein studies.     

High energy and short pulses generation by Nd:yttrium aluminum garnet laser mode-locked using frequency-doubling nonlinear mirror

The generation of laser pulses with energies of >40 mJ at 25 Hz and durations variable from 15 ps to 45 ps using an Nd:yttrium aluminum garnet laser mode-locked with a Stankov nonlinear mirror is demonstrated. This laser is used to pump an optical parametric generator-amplifier, which is tunable in the visible spectral range.     

Integration of barotropic vorticity equation over spherical geodesic grid using multilevel adaptive wavelet collocation method

In this paper, we present the multilevel adaptive wavelet collocation method for solving non-divergent barotropic vorticity equation over spherical geodesic grid. This method is based on multi-dimensional second generation wavelet over a spherical geodesic grid. The method is more useful in capturing, identifying, and analyzing local structure [1] than any other traditional methods (i.e. finite difference, spectral method), because those methods are either full or partial miss important phenomena such as trends, breakdown points, discontinuities in higher derivatives of the solution. Wavelet decomposition is used for interpolation and adaptive grid refinement on different levels.     

Multiple parents crossover operators: A new approach removes the overlapping solutions for sequencing problems

Maintaining population diversity throughout generations of Genetic Algorithms (GAs) is key to avoid premature convergence. Redundant solutions is one cause for the decreasing population diversity. To prevent the negative effect of redundant solutions, we propose a framework that is based on the multi-parents crossover (MPX) operator embedded in GAs. Because MPX generates diversified chromosomes with good solution quality, when a pair of redundant solutions is found, we would generate a new offspring by using the MPX to replace the redundant chromosome. Three schemes of MPX will be examined and will be compared against some algorithms in literature when we solve the permutation flowshop scheduling problems, which is a strong NP-Hard sequencing problem. The results indicate that our approach significantly improves the solution quality. This study is useful for researchers who are trying to avoid premature convergence of evolutionary algorithms by solving the sequencing problems.     

Sequencing of T-superfamily conotoxins from <Emphasis Type="Italic">Conus virgo</Emphasis>: Pyroglutamic acid identification and disulfide arrangement by MALDI mass spectrometry

De novo mass spectrometric sequencing of two Conus peptides, Vi1359 and Vi1361, from the vermivorous cone snail Conus virgo, found off the southern Indian coast, is presented. The peptides, whose masses differ only by 2 Da, possess two disulfide bonds and an amidated C-terminus. Simple chemical modifications and enzymatic cleavage coupled with matrix assisted laser desorption ionization (MALDI) mass spectrometric analysis aided in establishing the sequences of Vi1359, ZCCITIPECCRI-NH(2), and Vi1361, ZCCPTMPECCRI-NH(2), which differ only at residues 4 and 6 (Z = pyroglutamic acid). The presence of the pyroglutamyl residue at the N-terminus was unambiguously identified by chemical hydrolysis of the cyclic amide, followed by esterification. The presence of Ile residues in both the peptides was confirmed from high-energy collision induced dissociation (CID) studies, using the observation of w(n)- and d(n)-ions as a diagnostic. Differential cysteine labeling, in conjunction with MALDI-MS/MS, permitted establishment of disulfide connectivity in both peptides as Cys2-Cys9 and Cys3-Cys10. The cysteine pattern clearly reveals that the peptides belong to the class of T-superfamily conotoxins, in particular the T-1 superfamily.     

Dipyrrolylmethane-based macrobicyclic azacryptand: synthesis, X-ray structures, conformational and anion binding properties

A new class of macrobicyclic azacryptand containing dipyrrolylmethane subunits with nitrogen bridgeheads was synthesized by the Mannich reaction of the dipyrrolylmethane in the presence of aqueous ammonia. The azacryptand exhibits a staggered conformation in the solid state, but is in a dynamic equilibrium with the eclipsed conformation in solution studied by the variable-temperature (1)H NMR methods. The azacryptand has a specific size suitable only for fluoride ion; large anions such as NO(3)(-) bind in the clefts of the macrobicycle as shown by the X-ray structures of its fluoride ion inclusion and the nitrate anion complexes. The anion binding studies showed that it has high selectivity and affinity for fluoride ion in acetone over other anions studied, which was supported by (1)H and (19)F NMR methods. The azacryptand has fast fluoride ion-mediated proton-deuterium exchanges with acetone-d(6) studied by the (19)F NMR method.     

Optimal performances of a mode-locking technique: Theoretical and experimental investigations of the frequency-doubling nonlinear mirror

We present a detailed analysis of the mode-locker consisting of a nonlinear crystal and a dichroic mirror, introduced by Stankov and known as the frequency-doubling nonlinear mirror (FDNLM). Our aim is to determine optimal values for two physical parameters: the conversion efficiency η₀ of the nonlinear crystal, and the reflection coefficient R_ω of the output mirror. The optimization is based on a set of three figures of merit: the reflected intensity, the pulse shortening ratio and the Gaussian shape factor, which are combined to yield a final decision factor. Experimental investigations of η₀ and R_ω carried out using a FDNLM mode-locked Nd:YAG laser show good agreement with the theoretical predictions. In addition, a comparative study with other available experimental results is presented. This work demonstrates the capacity of this method to evaluate the best performance of this mode-locking not only for the steady-state pulse domain but also in the transient one.     

Overlimiting current in a microchannel

We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged sidewalls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for overlimiting current in a microchannel: (i)?surface conduction carried by excess counterions, which dominates for very thin channels, (ii)?convection by electro-osmotic flow on the sidewalls, which dominates for thicker channels, and (iii) transitions to electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.     

Tunable wavelength division multiplexing channel isolation filter based on dual chirped long-period fiber gratings

We propose and demonstrate a wavelength tunable wavelength division multiplexing channel isolation filter based on two concatenated chirped long-period fiber gratings (LPGs). An intergrating space (IGS), deliberately introduced between the two gratings, provides an extra phase difference between the core and cladding modes. Changing this phase by heating the IGS without affecting the gratings tunes the channels. A theoretical account of the filter action is also presented and the results are found to be in excellent agreement with the experiments. Unlike the filters based on normal concatenated chirped LPGs without an IGS, the current filter shows a linear tuning over an increased spectral range.