The minimal free resolution of a Borel ideal

We consider the Eliahou–Kervaire minimal free resolution of a 0-Borel ideal and its applications.     

Structural and Optical Properties of Pure and Sulfur-Doped Silicate–Phosphate Glass

A series of silicate–phosphate glass materials from the SiO₂-P₂O₅-K₂O-MgO system (pure and doped with sulfur ions) were synthesized by melting raw material mixtures that contained activated carbon as a reducer. The bulk composition of glass was confirmed with X-ray fluorescence spectroscopy. The homogeneity of the glass was confirmed through elemental mapping at the microstructural level with scanning electron microscopy combined with an analysis of the microregions with energy-dispersive X-ray spectroscopy. The structural and optical properties of the glass were studied by using spectroscopic techniques. The infrared spectroscopy studies that were conducted showed that the addition of sulfur caused changes in the silicate–phosphate networks, as they became more polymerized, which was likely related to the accumulation of potassium near the sulfur ions. By using irradiation with an optical parametric oscillator (OPO) nanosecond laser system operating at the second harmonic wavelength, the glass samples emitted a wide spectrum of luminescence, peaking at about 700 nm when excited by UV light (210–280 nm). The influence of the glass composition and the laser-processing parameters on the emission characteristics is presented and discussed. This work also referred to the density, molar volume, and theoretical optical basicity of pure and sulfur-doped glass.     

Infrared spectra of lanthanide complexes with eriochrome cyanine r

An infrared spectroscopic study of the composition of these complexes in the solid state is described. Evaluation of the spectra made it possible to distinguish changes in the character of the lanthanide—ligand bonds in the series La — Lu, and to study the “double-double” effect.     

Well-posedness and sharp uniform decay rates at the L 2(Ω)-Level of the Schrödinger equation with nonlinear boundary dissipation

We prove that the Schr?dinger equation defined on a bounded open domain of and subject to a certain attractive, nonlinear, dissipative boundary feedback is (semigroup) well-posed on L₂(Ω) for any n = 1, 2, 3, ..., and, moreover, stable on L₂(Ω) for n = 2, 3, with sharp (optimal) uniform rates of decay. Uniformity is with respect to all initial conditions contained in a given L₂(Ω)-ball. This result generalizes the corresponding linear case which was proved recently in [L-T-Z.2]. Both results critically rely—at the outset—on a far general result of interest in its own right: an energy estimate at the L₂(Ω)-level for a fully general Schr?dinger equation with gradient and potential terms. The latter requires a heavy use of pseudo-differential/micro-local machinery [L-T-Z.2, Section 10], to shift down the more natural H¹(Ω)-level energy estimate to the L₂(Ω)-level. In the present nonlinear boundary dissipation case, the resulting energy estimate is then shown to fit into the general uniform stabilization strategy, first proposed in [La-Ta.1] in the case of wave equations with nonlinear (interior and) boundary dissipation.     

Subcritical scattering from buried elastic shells

Buried objects have been largely undetectable by traditional high-frequency sonars due to their insignificant bottom penetration. Further, even a high grazing angle sonar approach is vastly limited by the coverage rate dictated by the finite water depth, making the detection and classification of buried objects using low frequency, subcritical sonar an interesting alternative. On the other hand, such a concept would require classification clues different from the traditional high-resolution imaging and shadows to maintain low false alarm rates. A potential alternative, even for buried targets, is classification based on the acoustic signatures of man-made elastic targets. However, the elastic responses of buried and proud targets are significantly different. The objective of this work is to identify, analyze, and explain some of the effects of the sediment and the proximity of the seabed interface on the scattering of sound from completely and partially buried elastic shells. The analysis was performed using focused array processing of data from the GOATS98 experiment carried out jointly by MIT and SACLANTCEN, and a new hybrid modeling capability combining a virtual source-or wave-field superposition-approach with an exact spectral integral representation of the Green's functions for a stratified ocean waveguide, incorporating all multiple scattering between the object and the seabed. Among the principal results is the demonstration of the significant role of structural circumferential waves in converting incident, evanescent waves into backscattered body waves, emanating to the receivers at supercritical grazing angles, in effect making the target appear closer to the sonar than predicted by traditional ray theory.     

Molecular weight dependent charge carrier mobility in poly(3,3' '-dioctyl-2,2':5',2' '-terthiophene)

Poly(3,3' '-dioctyl-2,2':5',2' '-terthiophene), a polymer recently used for the fabrication of organic field effect transistors, has been fractionated into five fractions distinctly differing in their molecular weights (Mn), with the goal of determining the influence of the degree of polymerization (DPn) on its principal physicochemical parameters. It has been demonstrated that within the Mn range studied (from 1.5 kDa to 10.5 kDa by SEC), corresponding to DPn from 10 to 38, the polymer band gap steadily decreases with growing molecular weight, which is clearly manifested by an increasing bathochromic shift of the band originating from the pi-pi* transition. The same trend is observed for the HOMO level, determined from the onset of the p-doping in cyclic voltammetry, which shifts from -5.10 eV to -4.90 eV for the lowest and the highest molecular weight fractions, respectively. The most pronounced influence of DPn has been found for the charge carriers' mobility-one of the most important parameters of field effect transistors (FETs) fabricated from this polymer. A fourfold increase in DPn results in an increase of the carriers' mobility by more than 3 orders of magnitude. Comparison of these results with those obtained for fractionated regioregular poly(3-hexylthiophene) shows a strikingly similar behavior of both polymers with respect to the molecular weight.     

Acid-base equilibria in 5,10,15,20-tetrakis(4-sulfonatophenyl)chlorin: Role of conformational flexibility

The acid-base equilibria in 5,10,15,20-tetrakis(4-sulfonatophenyl)chlorin were studied in aqueous solution and compared with the respective data for the corresponding porphyrin. The reduction of the pyrrole ring in the tetrapyrrolic macrocycle noticeably influences both free base/monoprotonated and mono-/diprotonated species equilibria. In strong acidic solutions protonation of 4-sulfonatophenyl groups takes place in addition to protonation of the macrocycle core. The photophysical properties of all ionic forms are influenced by an enhanced rate of internal S1 --> S0 conversion, leading to about 50% and 90% deactivation through this channel for the free base and diprotonated species, respectively. The enhancement of the rate of the radiationless transitions is explained by an increased conformational flexibility of the chlorin macrocycle with respect to that of a porphyrin. Structural volume change measurements with laser-induced optoacoustic spectroscopy support this explanation. The contraction upon triplet state formation of the free base is about one-half of that measured for the corresponding porphyrin. This contraction should be due to intramolecular structural rearrangements of the macrocycle to adopt a minimum energy conformation in case of the chlorin. On the contrary, for the more rigid porphyrin macrocycle the interactions of the molecule with the solvent environment play a more important role. The diprotonated forms of both porphyrin and chlorin show a high radiationless S1 --> S0 conversion rate and seem to have a similar conformational flexibility. In agreement with previous calculations, the conformational flexibility of the diprotonated forms appears to be higher than that of the free base molecule.     

Surface structure of Langmuir-Blodgett films of lipophilic guanosine derivatives

We studied surface organization of lipophilic guanosine derivatives with one, two and three alkanoyl tails in thin films on water surface and in Langmuir-Blodgett (LB) films transferred onto freshly cleaved mica substrate. The derivative with one alkanoyl group exhibits irreversible pressure-area isotherms and ribbon-like LB film structures. The derivatives with two and three side groups show reversible isotherms with similar critical surface pressures, while their LB film structures are quite different. The derivative with two tails forms films with flat terraces of micrometer size, while the derivative with three tails exhibits irregular thread-shaped assemblies. These observations demonstrate that molecular assembly of LB films of guanosine derivatives can be effectively manipulated by altering the number of attached lipophilic groups.     

High pressure spectroscopy of chromium doped LiTaO3 crystals

Abstract

The effect of pressure on the luminescence spectrum of the weak field system Cr³⁺ : LiTaO₃ is presented. By using pressure to induce a low to high crystal field strength transition, we demonstrate the ability of pressure to identify distinct dopant bonding environments in luminescent materials.