Rigidity of commutators and elementary operators on Calkin algebras

LetA=(A ₁,...,A _n ),B=(B ₁,...,B _n )εL(ℓ ^p ) ⁿ be arbitraryn-tuples of bounded linear operators on (ℓ ^p ), with 1<p<∞. The paper establishes strong rigidity properties of the corresponding elementary operators ε _a,b on the Calkin algebraC(ℓ ^p )≡L(ℓ ^p )/K(ℓ ^p ); , where quotient elements are denoted bys=S+K(ℓ ^p ) forSεL(ℓ ^p ). It is shown among other results that the kernel Ker(ε _a,b ) is a non-separable subspace ofC(ℓ ^p ) whenever ε _a,b fails to be one-one, while the quotient is non-separable whenever ε _a,b fails to be onto. These results extend earlier ones in several directions: neither of the subsets {A ₁,...,A _n }, {B ₁,...,B _n } needs to consist of commuting operators, and the results apply to other spaces apart from Hilbert spaces. Supported by the Academy of Finland, Project 32837.     

Emission studies of InGaN layers and LEDs grown by plasma-assisted MBE

We prepared InGaN layers on GaN/sapphire substrates using rf-MBE. Photoluminescence (PL) from these layers, grown at different temperatures T_S, shows that there is a strong tendency of GaN to form a separate phase as T_S is increased from 600°C to 650°C. Concomitant with the phase separation, the PL from the InGaN phase broadens, which indicates that indium composition in this phase becomes increasingly non-uniform. Indium compositions measured by Rutherford backscattering (RBS) are consistent with these results. We also observed an increase in PL intensity for InGaN layers grown at higher temperatures. In this paper, we also report on preparing a top-contact InGaN/GaN light emitting diode. The device was operated at 447 nm and had the emission line width of 37 nm with no observable impurity related features. The turn-on voltage was 3.0 V. The output power was 20 μW at 60 mA drive current.     

Compact and inessential perturbations of operators with closed range

The size of the perturbation class {SL(E)S has closed range}+I(E) is studied, whereE is a Banach space andI(E) stands for various classical operator ideals. For instance, it is shown for the ideal consisting of the inessential operators that the resulting perturbation class does not exhaust the class of bounded linear operators under natural structural conditions onE. It is known from a recent result of Gowers and Maurey that some conditions are needed.Partially supported by the Academy of Finland     

Triplet harvesting in poly(9‐vinylcarbazole) and poly(9‐(2,3‐epoxypropyl)carbazole) doped with CdSe/ZnS quantum dots encapsulated with 16‐(N‐carbazolyl) hexadecanoic acid ligands

Semiconductor quantum dots (QDs) can be used as alternative for transition metal complexes to harvest the nonemissive triplet excitons in organic light‐emitting diodes (OLEDs). In search for a QD‐based OLED material generating blue emission, poly(9‐vinylcarbazole) (PVK) and poly(9‐(2,3‐epoxypropyl) carbazole) (PEPK) are chosen as host for blue‐emitting CdSe/ZnS core/shell QDs. The QDs are encapsulated with 16‐(N‐carbazolyl) hexadecanoic acid (C16), a ligand terminated by a carbazole moiety. As alternative for PVK, PEPK, where the lower molecular weight and less extensive excimer formation could promise a better film formation and more extensive exciton hopping, is explored. The efficiencies of singlet ( ) and triplet ( ) energy transfer to the C16 capped QDs are estimated by combining stationary photoluminescence spectra and fluorescence decays of pristine polymer films with those of polymer films doped with the QDs. At a loading of 30 wt % of the QDs, increases from 12 ± 1% in PVK to 41 ± 2% in PEPK while increases from 37 ± 22% in PVK to 72 ± 48% in PEPK. The investigation of the film morphology by atomic force microscopy confirms that the main factor limiting the triplet transfer efficiency in the PVK matrix is the clustering of the C16 capped QDs. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 539–551     

Study of Thin Oxide Films by Electron, Ion and Synchrotron Radiation Beams

 Titanium oxide and zirconium oxide thin films deposited on silicon substrates were characterised using electron probe microanalysis (EPMA), Rutherford backscattering spectroscopy (RBS), time-of-flight elastic recoil detection analysis (TOF-ERDA) and scanning photoelectron microscopy (SPEM). The composition and mass thickness of the films were determined and the results of different methods compared. It was revealed that the synchrotron radiation used for SPEM studies caused considerable modification of zirconia films grown at low temperatures.     

1H NMR spectral analysis and conformational behavior of n‐alkanes in different chemical environments

Alkyl chains are common structural units, for example in lipids, and their ¹H NMR spectral parameters offer valuable information about their conformational behavior in solvent environment. Even the spectra of short n‐alkanes are complex, which is obviously a reason why their accurate spectral analyses have not been reported before. The present study reports the quantum mechanical analysis of ¹H NMR spectra of n‐butane, n‐pentane, n‐hexane, and n‐heptane. The spectral parameters were used to characterize the conformational behavior of n‐alkanes. The temperature dependence analysis of coupling constants suggests that the enthalpy difference between the gauche (g) and trans (t) conformations (ΔH_g) of n‐butane in chloroform is 2.55–2.85 kJ mol^?1. The difference between the trans–gauche (tg) and all‐trans (tt) conformers of n‐pentane (ΔH_tg) seems to be 0.1–0.2 kJ mol^?1 higher. The coupling constant information shows that the t_n conformations become more favored with longer chains, although not only for energetic reasons but also partly because the g⁺g^‐ arrangements become sterically unfavorable, which decreases the number of favorable g_n‐type conformations. The analysis of the ¹H NMR spectra of n‐pentane and n‐hexane in solvents representing different chemical environments indicates that polar and spherical dimethyl sulfoxide favors clearly the g conformations, whereas n‐hexane‐d₁₄ favors slightly the extended t_n conformation. In addition to the intrinsic scientific importance for NMR spectral parameter prediction and molecular modeling in solution, the results provide some insights to behavior of hydrocarbon chains and their spectra in different chemical environments. Copyright © 2012 John Wiley & Sons, Ltd.     

On the Gorenstein property of the associated graded ring of a power of an ideal

It has been proved by Herrmann, Ribbe and Schenzel that in a local ring the Gorensteiness of the associated graded ring of a power of an ideal implies the Gorensteiness of the associated graded ring of the ideal provided it is Cohen-Macaulay and the height of the ideal is at least two. We give a new proof to this theorem which covers also the height one case and so answer to a question of Herrmann, Ribbe and Schenzel whether their result holds for ideals of height one.     

Rotational coherence imaging and control for CN molecules through time-frequency resolved coherent anti-Stokes Raman scattering

Numerical wave packet simulations are performed for studying coherent anti-Stokes Raman scattering (CARS) for CN radicals. Electronic coherence is created by femtosecond laser pulses between the X(2)Σ and B(2)Σ states. Due to the large energy separation of vibrational states, the wave packets are superpositions of rotational states only. This allows for a specially detailed inspection of the second- and third-order coherences by a two-dimensional imaging approach. We present the time-frequency domain images to illustrate the intra- and intermolecular interferences, and discuss the procedure to rationally control and experimentally detect the interferograms in solid Xe environment.     

Thermal Degradation of Cellulose Nanocrystals Deposited on Different Surfaces

Thermal degradation of cellulose nanocrystals deposited on flat solid surfaces was monitored by AFM coupled with analysis of obtained images using image processor. The nanocrystals deposited on TiO₂ substrate showed different degradation patterns compared to those deposited on the nanosized layer of amorphous cellulose. The degradation was complete within 20 minutes at 300 °C. The nanocrystal deposited on amorphous cellulose resisted the heat treatment up to 120 minutes. Visual comparison and analysis of the AFM images clearly demonstrated the impact of temperature on the degradation rate of the nanocrystals deposited on TiO₂ substrate.