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.     

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.     

On the existence of more positive solutions of periodic bvps with singularity

We consider Periodic boundary value problems for ordinary second order differential equations of the form u′′=f(t,u,u′), Where f satisfies the (local) Carathéodory conditions and can have a singularity in the second variable.Writing our problem in an operator can be computed on. These sets are not convex, in general. Using the degree theory we get at least one fixed point of the operator at each such set which leads to the existence and localization of more solutions of the related Periodic boundary value problem. Our results are based on the generalized lower and upper functions method from Rach?nková and Tvrdý[15].     

Antioxidant Activities of Some New Chromonyl-2,4-Thiazolidinediones and Chromonyl-2,4-Imidazolidinediones Having Chromone Cores

The antioxidant properties of 11 new synthesized chromonyl-2,4-thiazolidinediones and chromonyl-2,4-imidazolidinediones (CBs) were investigated. The antioxidant activities and mechanisms of the CBs interaction with reactive oxygen species (ROS) were clarified using various in vitro antioxidant assay methods including superoxide anion radical ( $ \mathrm{O}\overline{{}_2^{\bullet }} $ ), hydroxyl radical (HO^?), 1,1-diphenyl-2-picryl-hydrazyl free radical (DPPH^?) scavenging activity and the iron (II)-ferrozine complex formation. The potassium superoxide/18-crown-6 ether dissolved in dimethylsulfoxide (DMSO) was applied as a source of superoxide anion radical. Hydroxyl radicals were produced in the Fenton-like reaction Fe(II)+H₂O₂. Chemiluminescence, spectrophotometry, and electron paramagnetic resonance (EPR) spectroscopy using 5,5-dimethyl-1-pyrroline-1-oxide (DMPO) as spin trap were applied as the measurement techniques. The CBs examined that exhibited good free radical scavenging activity also showed strong total antioxidant power capacity. Possible mechanisms of antioxidation are proposed to explain the differences in the experimental results between the chromone derivatives with imidazolidine-2,4-dione ring and those with thiazolidine-2,4-dione ring. In conclusion, some of the new CBs are promising to be applied as inhibitors of free radicals.     

Antiferroelectric phase transitions in single crystals PbZrO3:Sn revisited

This paper is a review of earlier results which have been completed with recent investigations on the nature and sequence of phase transitions evolving in the antiferroelectric PbZr_1–xSn_xO₃ single crystals (0 < x < 0.35). It was found that these crystals undergo several first-order phase transitions. To investigate these transitions, five experimental methods were used to characterize the crystal properties: birefringence, Raman light scattering, dielectric, thermodynamic and electromechanical methods, and the atomic force microscopy-piezoresponse force microscopy (AFM-PFM) method to focus also on nanoscale properties. Temperature dependencies have been tentatively measured in a wide range, including a region above T_C, where precursor dynamics is observed in the form of non-centrosymmetric regions existing locally in crystal lattices.

New experimental data (Raman light scattering and PFM) are presented mainly to revise the phase diagram and, at the same time, to complement other studies on the problem of pre-transitional effects. The phase transition mechanism in PbZr_1–xSn_xO₃ is discussed taking into account the incommensurability of crystal lattices, ferroelastic behavior of multicell cubic phases, electric field influence on antiferroelectric to ferroelectric transformation, and flexoelectric effect.     

Nonlinear Optical Switching in Regioregular Porphyrin Covalent Organic Frameworks

Covalent organic frameworks (COFs) have garnered immense scientific interest among porous materials because of their structural tunability and diverse properties. However, the response of such materials toward laser‐induced nonlinear optical (NLO) applications is hardly understood and demands prompt attention. Three novel regioregular porphyrin (Por)‐based porous COFs—Por‐COF‐HH and its dual metalated congeners Por‐COF‐ZnCu and Por‐COF‐ZnNi—have been prepared and present excellent NLO properties. Notably, intensity‐dependent NLO switching behavior was observed for these Por‐COFs, which is highly desirable for optical switching and optical limiting devices. Moreover, the efficient π‐conjugation and charge‐transfer transition in ZnCu‐Por‐COF enabled a high nonlinear absorption coefficient (β=4470 cm/GW) and figure of merit (FOM=σ₁/σ_o, 3565) value compared to other state‐of‐the‐art materials, including molecular porphyrins (β≈100–400 cm/GW), metal–organic frameworks (MOFs; β≈0.3–0.5 cm/GW), and graphene (β=900 cm/GW).     

Application of different thermal analysis techniques for the evaluation of petroleum source rocks

In the paper, various laboratory pyrolytic methods were used to evaluate selected petroleum source rocks. The methods used are: Rock–Eval pyrolysis, Py–GC pyrolytic technique and TG/DTG/DSC. The experiments of the last method were performed according to three different procedures. Each of them provided different, specific data. The selected rock sample material was diversified in terms of stratigraphical position, structural unit and place of collection (outcrop or borehole). Based on the Rock–Eval analysis results, kerogen in samples can be classified as type II. Additional information on the quality of pyrolysis products was obtained from the Py–GC analysis. Thanks to the combination of the all three implemented pyrolytic techniques, the quality of the generation potential of the source rocks can be evaluated in details. In some samples, the oxidation and pyrolysis of organic matter occur in two stages, what is the evidence of the complex nature of the organic substance. The maximum of pyrolysis reaction is detected by TG/DTG measurement in the range of temperature from 450 to 580 °C, depending on the maturity of organic matter. The maturity level increases with the rock stratigraphic position. The proportions of loss in mass observed in respective stages of pyrolysis in course of TG/DTG experiment are in correspondence with the observations of the released fractions in the Py–GC analysis. The Carpathian Menilite shales could be classified as source rocks with high oil generation potential. Also, the Lower Silurian and Ordovician shales are characterized by high oil-producing potential with a lower content of mineral matter. Cambrian rocks show a different character and gas-prone generation potential.