Singular Indefinite Sturm-Liouville Operators with a Spectral Gap

Singular Sturm-Liouville operators with the indefinite weight sgn(·) and a symmetric potential which has a positive limit at ∞ have a gap in the essential spectrum. Under an additional condition it is shown that in this gap are no eigenvalues. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a class of Sturm-Liouville operators which are connected to PT symmetric problems

A prominent class of -symmetric Hamiltonians is for some nonnegative number N. The associated eigenvalue problem is defined on a contour Γ in a specific area in the complex plane (Stokes wedges), see [3, 5]. In this short note we consider the case N = 2 only. Here we elaborate the relationship between Stokes lines and Stokes wedges and well-known limit point/limit circle criteria from [6,10,11]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gas-phase toluene LIF temperature imaging near surfaces at 10 kHz

Information on transient temperature distributions is important for the study of heat transfer and reacting flows, including combustion. Laser diagnostic methods have been developed for temperature imaging purposes but so far have largely been constrained to low temporal resolution measurements. Diode-pumped solid-state lasers and high frame rate CMOS cameras have enabled the development of a gas-phase temperature imaging method based on laser-induced fluorescence of toluene. Excitation of toluene at 266 nm results in temperature-dependent fluorescence emissions that were detected in two spectral regions, yielding a temperature-dependent signal ratio that was calibrated for the range of 100 to 600°C. Experiments were performed in a well-stabilized heated nitrogen jet, seeded with toluene. The precision of the diagnostics increases with decreasing temperature due to an overall increase in signal strength. The application of this technique to measure the transient temperature field at 10 kHz frame rates in the boundary layer of a hot gas jet impinging on a cooled metal plate is demonstrated.     

VACUUM ULTRAVIOLET CIRCULAR DICHROISM OF DOUBLE STRANDED NUCLEIC ACIDS

The vacuum ultraviolet (VUV) circular dichroism (CD) of double stranded DNA and RNA is greater in amplitude than the CD of these molecules for wavelengths longer than 200 nm. The amplitude of the VUV-CD depends on the base composition of DNA, with guanine-cytosine base pairs contributing more intensity than adenine-thymine base pairs. The shape and amplitude of the VUV-CO are better indicators of nucleic acid conformation (A, B or Z) than are those of the longer wavelength CD. We illustrate the unique features of VUV-CD with specific examples. In the presence of Cs⁺ and ethanol, VUV-CD reveals that poly(dA-dC)poly(dG-dT) forms a right handed double helix despite the inversion of the longer wavelength CD, which usually is used as a benchmark for the left-handed form. The greater magnitude of the VUV-CD of DNA and RNA compared to longer wavelengths means that the VUV-CD is less susceptible to distortion by the induced CD of UV-absorbing ligands like mitomycin C and N-2-acetylaminofluorene.     

Direct growth of crystalline triazine-based graphdiyne using surface-assisted deprotection–polymerisation

Graphdiyne polymers have interesting electronic properties due to their π-conjugated structure and modular composition. Most of the known synthetic pathways for graphdiyne polymers yield amorphous solids because the irreversible formation of carbon–carbon bonds proceeds under kinetic control and because of defects introduced by the inherent chemical lability of terminal alkyne bonds in the monomers. Here, we present a one-pot surface-assisted deprotection/polymerisation protocol for the synthesis of crystalline graphdiynes over a copper surface starting with stable trimethylsilylated alkyne monomers. In comparison to conventional polymerisation protocols, our method yields large-area crystalline thin graphdiyne films and, at the same time, minimises detrimental effects on the monomers like oxidation or cyclotrimerisation side reactions typically associated with terminal alkynes. A detailed study of the reaction mechanism reveals that the deprotection and polymerisation of the monomer is promoted by Cu(ii) oxide/hydroxide species on the as-received copper surface. These findings pave the way for the scalable synthesis of crystalline graphdiyne-based materials as cohesive thin films.

We present a one-pot deprotection/polymerisation protocol for the synthesis of crystalline graphdiynes on top of a copper surface starting with stable trimethylsilylated alkyne monomers.      

Bounds on the non-real spectrum of differential operators with indefinite weights

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and $\infty $ are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non-real spectrum is contained in a compact set and with definite type real spectrum outside this set. The main results are quantitative estimates for this set, which are applied to Sturm–Liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains.     

Frequency compensation for a class of DAE's arising in electrical circuits

Structured perturbations of regular pencils of the form , are considered which model the addition of a capacitance c in an electrical circuit in order to improve the frequency response. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Compact and Finite Rank Perturbations of Closed Linear Operators and Relations in Hilbert Spaces

For closed linear operators or relations A and B acting between Hilbert spaces and the concepts of compact and finite rank perturbations are defined with the help of the orthogonal projections P _A and P _B in onto the graphs of A and B. Various equivalent characterizations for such perturbations are proved and it is shown that these notions are a natural generalization of the usual concepts of compact and finite rank perturbations. Sadly, our colleague and friend Peter Jonas passed away on July, 18th 2007.     

Bounds on the Non-real Spectrum of a Singular Indefinite Sturm-Liouville Operator on ℝ

A simple explicit bound on the absolute values of the non-real eigenvalues of a singular indefinite Sturm-Liouville operator on the real line with the weight function sgn(·) and an integrable, continuous potential q is obtained. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)