A tutorial on the use of graph coloring for some problems in robotics

We study the problem where a robot has to pick up items of different sizes which are stored along a corridor. A natural requirement is that the items have to be collected in decreasing order of their sizes. We deal with various systems according to the location of the Entry/Exit station where the robot unloads the collected items after each trip along the corridor. The links of these systems with generalized coloring problems and other applications such that train shunting and pallet loading problems are discussed and related results are obtained. We conclude with several open questions on the topic.     

Novel ruthenium(II) complexes with substituted 1,10-phenanthroline or 4,5-diazafluorene linked to a fullerene as highly active second order NLO chromophores

Various Ru(II) complexes with substituted 1,10-phenanthroline or 4,5-diazafluorene are characterized by a good to very large second order NLO response, as determined by EFISH. Among these complexes, [Ru(9-fulleriden-4,5-diazafluorene)(PPh(3))(2)Cl(2)] is particularly appealing due to its huge second-order NLO response and its transparency to the second harmonic generation. The structure of cis-Cl,trans-PPh(3)-[Ru(5-NO(2)-1,10-phen)(PPh(3))(2)Cl(2))] was determined by single-crystal X-ray diffraction.     

Photochromism of spiropyran nanocrystals embedded in sol-gel matrices

Spectroscopic and kinetic properties of a new photochromic medium, consisting of nanocrystals of spyropyran molecules (1,3-dihydro-1,3,3,5',6',pentamethyl-spiro[2H-indole-2,2'-[2H]pyrano [3,2-b]pyridinium] iodide) embedded in an organo-silicate sol-gel film, are presented and compared to microcrystals obtained by slow evaporation of a solvent. High photoconversion efficiencies for both kinds of crystals have been observed. In microcrystals, the photomerocyanine form absorbs at 570 nm with a fading rate of 5 h, in nanocrystals the photomerocyanine form absorbs at 535 nm with a fading rate of 41 h. Therefore, the crystalline structure of nanocrystals is different from the microcrystal one.     

A step size control algorithm for the weak approximation of stochastic differential equations

A vriable step size control algorithm for the weak approximation of stochastic differential equations is introduced. The algorithm is based on embedded Runge–Kutta methods which yield two approximations of different orders with a negligible additional computational effort. The difference of these two approximations is used as an estimator for the local error of the less precise approximation. Some numerical results are presented to illustrate the effectiveness of the introduced step size control method.      

Photocatalytic degradation of ammonia and butyric acid in plug-flow reactor: Degradation kinetic modeling with contribution of mass transfer

Photocatalytic treatment of polluted air by odorous contaminants – ammonia and butyric acid – is investigated in a plug-flow reactor covered by non-woven fiber textile coated with TiO₂. For the first time, the single-component degradation pathway of ammonia by photocatalysis at ambient condition is highlighted. It appears fundamentally different compared to the butyric acid degradation pathway. The ammonia degradation pathway highlights a possible auto-accelerated behavior of the reaction. The chemical degradation kinetics follows the Langmuir–Hinshelwood model, though observed oxidation rates depend upon flow conditions in the reactor. Thus, interpretation of degradation results through a model considering the Langmuir–Hinshelwood approach and mass transfer phenomenon is presented. This model succeeds with a pair of determined kinetic constants and mass transfer coefficients to describe experimental results for different flow rates and for both pollutants, though they present wide dissimilarities in their degradation pathways.     

On a class of asymptotically stationary harmonizable processes

We prove that every harmonizable process with σ-finite bimeasure is asymptotically stationary and we give its associated spectral measure.     

Cyclodextrin-based thiacavitands as building blocks for the construction of metallo-nanotubes

Two new cyclodextrin-based ligands with dual exo/endo binding domains were synthesised in high yields by reacting dimesylated or tetramesylated α-CD derivatives with sodium sulfide in either dimethylsulfoxyde or acetone/18-crown-6. The capping of adjacent glucose units was shown to be strongly favoured in both cases. Depending on the nature of the metal precursor being used, one of the synthesised thiacavitands forms either rigid nanotubular dimers or chelate complexes having receptor properties upon metal complexation.     

The probe profile and lateral resolution of scanning transmission electron microscopy of thick specimens

Lateral profiles of the electron probe of scanning transmission electron microscopy (STEM) were simulated at different vertical positions in a micrometers-thick carbon sample. The simulations were carried out using the Monte Carlo method in CASINO software. A model was developed to fit the probe profiles. The model consisted of the sum of a Gaussian function describing the central peak of the profile and two exponential decay functions describing the tail of the profile. Calculations were performed to investigate the fraction of unscattered electrons as a function of the vertical position of the probe in the sample. Line scans were also simulated over gold nanoparticles at the bottom of a carbon film to calculate the achievable resolution as a function of the sample thickness and the number of electrons. The resolution was shown to be noise limited for film thicknesses less than 1 μm. Probe broadening limited the resolution for thicker films. The validity of the simulation method was verified by comparing simulated data with experimental data. The simulation method can be used as quantitative method to predict STEM performance or to interpret STEM images of thick specimens.