Reeb foliation in the optimal control problem with phase constraints

An optimal control problem with two phase constraints and a two-dimensional control is considered. We prove that its optimal trajectories have a countable number of points of contact with the phase constraint bound on a finite time interval. The optimal synthesis of the problem after applying the quotient mapping by the action of the scale group has a complicated topological structure and, in some neighborhood of singular extremals, it is the Reeb foliation.     

Glasses and glass-ceramics in the oxyfluoride ternary system Pb(PO3)2-WO3-PbF2

Glasses were prepared by the melt-quenching method in the ternary system Pb(PO₃)₂-WO₃-PbF₂ and doped with Er³⁺ in order to prepare luminescent transparent glass-ceramics. This work focused on thermal and structural characterization of tungsten lead-phosphate glasses and crystallization study for preparing transparent glass-ceramics. Thermal properties such as thermal stability and crystallization behavior upon heating were investigated by DSC in function of PbF₂ content. For low PbF₂ concentrations, only one crystallization peak due to Pb₃(PO₄)₂ is observed whereas samples containing more than 15% of PbF₂ present another exothermic event at lower temperatures related with precipitation of PbF₂, Pb₂P₂O₇ and Pb₂OF₂. Structural investigations by Raman spectroscopy suggest that PbF₂ modifies the tungsten-phosphate network through the formation of P―F and P―O―Pb bonds but the average network connectivity remains almost constant. A crystallization study has been performed by DSC to investigate the dominant crystallization mechanisms in these glasses and it has been established that Pb₃(PO₄)₂ is nucleated on the surface whereas PbF₂, Pb₂P₂O₇ and Pb₂OF₂ crystallize dominantly from the glassy bulk. Transparent glass-ceramics containing nanosized PbF₂ crystallites were also prepared by suitable heat-treatment on the glass sample containing 20% of PbF₂ and Raman microscopy of these glass-ceramics supports the crystallization mechanisms determined by DSC.     

Correlative atomic scale characterisation of secondary carbides in M50 bearing steel

Correlative atom probe tomography (APT) and transmission electron microscopy (TEM) are used to characterise the microstructure and chemistry of carbide precipitation in M50 bearing steel. This is a prerequisite in establishing relationships between the microstructure and hydrogen embrittlement (HE) resistance. Secondary carbides are the focus of this study, as they play a major role in improving HE-resistance. Secondary carbides are observed in APT, with compositions close to M₄C_3, M₂C and M₃C. Correlative TEM measured orientation relationships between the martensite matrix and carbides, enabling the confirmation of M₃C cementite precipitates in the corresponding APT reconstruction. Additionally, other precipitates observed in TEM were correlated to the M₂C carbides in APT data. The M₄C₃ carbides are found to have a significantly lower volume fraction than the M₂C carbides.     

New Fluorinated Rhodamines for Optical Microscopy and Nanoscopy

New photostable rhodamine dyes represented by the compounds 1 a – r and 3 – 5 are proposed as efficient fluorescent markers with unique combination of structural features. Unlike rhodamines with monoalkylated nitrogen atoms, N′,N‐bis(2,2,2‐trifluoroethyl) derivatives 1 e , 1 i , 1 j , 3 ‐H and 5 were found to undergo sulfonation of the xanthene fragment at the positions 4′ and 5′. Two fluorine atoms were introduced into the positions 2′ and 7′ of the 3′,6′‐diaminoxanthene fragment in compounds 1 a – d , 1 i – l and 1 m – r . The new rhodamine dyes may be excited with λ=488 or 514 nm light; most of them emit light at λ=512–554 nm (compounds 1 q and 1r at λ=576 and 589 nm in methanol, respectively) and have high fluorescence quantum yields in solution (up to 98 %), relatively long excited‐state lifetimes (>3 ns) and are resistant against photobleaching, especially at high laser intensities, as is usually applied in confocal microscopy. Sulfonation of the xanthene fragment with 30 % SO₃ in H₂SO₄ is compatible with the secondary amide bond (rhodamine‐CON(Me)CH₂CH₂COOH) formed with MeNHCH₂CH₂COOCH₃ to providing the sterically unhindered carboxylic group required for further (bio)conjugation reactions. After creating the amino reactive sites, the modified derivatives may be used as fluorescent markers and labels for (bio)molecules in optical microscopy and nanoscopy with very‐high light intensities. Further, the new rhodamine dyes are able to pass the plasma membrane of living cells, introducing them as potential labels for recent live‐cell‐tag approaches. We exemplify the excellent performance of the fluorinated rhodamines in optical microscopy by fluorescence correlation spectroscopy (FCS) and stimulated emission depletion (STED) nanoscopy experiments.     

X-ray diffraction of the crystallinity of glycolysates derived from PET

Glycolysates coming from the chemical recycling of PET scraps are most often very crystalline compounds making them difficult to perform in further reactions like step growth polyaddition with diisocyanates to obtain polyurethanes. The glycolysis of PET was investigated using unusual reagents: polyesters based oligomers, bisphenol A, cycloaliphatic alcohol and aliphatic diols. The thermal properties of the glycolysates obtained were compared in terms of crystallinity with that of coming from the glycolysis with DEG. The crystallinity extents were calculated using X-ray diffraction. Surprisingly, the crystalline or non-crystalline nature of the reactants do not predict the morphology of the final glycolysates.     

Interchromophore interactions and energy transfer in covalently bound porphyrin-chlorine heterodimer

Energetis of interchromophore interactions in a covalently bound prophyrin-chlorine heterodimer (Por-O-Chl) is investigated at temperatures from 77 to 293 K in solvents with differing polarity (toluene, tetrahydrofurane, and diethyl ether: petroleum ester: isopropanole=5∶5∶2 mixture). We substantiate the conclusion that the strong quenching of fluoresence and phosphorescence of the porphyrin fragments in both stable isomers of the Por-O-Chl heterodimer is induced not by the photoinduced charge transfer but rather by efficient processes of singlet-singlet (probability F^SS=1.3·10¹¹ to 6.8°10¹⁰ sec⁻¹) and triplet-triplet (probability F^TT≥10⁸ sec⁻¹) radiationless electronic excitation transfer. It is shown that the S−S transfer takes place without quantum losses from the thermodynamically equilibrated S₁ state of the donor, and its dynamics and main regularities at temperatures from 77 to 293 K are described by the inductive resonance theory without any additional asssumptions. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 1, pp. 75–82, January–February, 1998.     

Spectral-polarization properties and quantum-chemical calculation of a porphyrin-chlorine heterodimer with a covalent ester bond

The porphyrin-chlorine heterodimer P-O-Chl, in which porphyrin and chlorine fragments are single esterbonded in a covalent manner, is investigated experimentally and theoretically. From absorption and polarized-fluorescence spectra of two stable P-O-Chl isomers it follows that the porphyrin and chlorine fragments preserve their individuality, and their weak interaction does not change the basic photophysical parameters of the chlorine fragment in a temperature interval of 77–293 K. Based on calculations by the method of molecular mechanics with standard parameterization of the force field and the CNDO/S method and comparison of their results with the data on polarized fluorescence, the structure of one of the two isomers is substantiated. From CNDO/S calculations, the authors estimated the energy of the states with charge transfer in the P-O-Chl system, whose lower levels are above the levels of local excited Q-states of the interacting porphyrin and chlorine fragments. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 766–775, November–December, 1997.     

Accumulation of tangent points with the boundary and Lagrangian manifolds in problems with phase constraints

The phenomenon of the existence of optimal trajectories having an infinite number of tangent points with the boundary of the phase constraint is studied. The optimal synthesis and the structure of the corresponding Lagrangian manifolds are obtained. The main tool is the blowing up procedure for the resolution of the singularities of the Poincaré mapping of the constraint boundary on itself. A singularity appears at the point of accumulation of the tangent points with the boundary.