Rapid LC-MS detection of cyanobacterial hepatotoxins microcystins and nodularins—Comparison of columns

Eight reversed-phase columns intended for rapid HPLC were assessed for the separation of thirteen microcystins and nodularins, cyclic peptidic hepatotoxins. The instrumentation consisted of an Agilent Technologies 1200 Rapid Resolution high performance liquid chromatography system coupled to a mass spectrometer, Bruker Daltonics Ultra Performance High Capacity Ion Trap MS (HCT Ultra) with electrospray ionisation (RRLC-ESI-IT-MS). The columns tested were 2-2.1 mm × 50 mm in diameter and length, and contained small particles (1.8-2.7 μm), or monolithic silica supports for fast performance. The shortest total run time achieved was 3 min 15 s including equilibration and injection. Critical microcystin pairs were still resolved. Several columns showed excellent performance.     

On finite rank perturbations of definitizable operators

It was shown by P. Jonas and H. Langer that a selfadjoint definitizable operator A in a Krein space remains definitizable after a finite rank perturbation in resolvent sense if the perturbed operator B is selfadjoint and the resolvent set ρ(B) is nonempty. It is the aim of this note to prove a more general variant of this perturbation result where the assumption on ρ(B) is dropped. As an application a class of singular ordinary differential operators with indefinite weight functions is studied.     

Electronic spectroscopy of I(2)-Xe complexes in solid Krypton

In the present work, we have studied ion-pair states of matrix-isolated I(2) with vacuum-UV absorption and UV-vis-NIR emission, where the matrix environment is systematically changed by mixing Kr with Xe, from pure Kr to a more polarizable Xe host. Particular emphasis is put on low doping levels of Xe that yield a binary complex I(2)-Xe, as verified by coherent anti-Stokes Raman scattering (CARS) measurements. Associated with interaction of I(2) with Xe we can observe strong new absorption in vacuum-UV, redshifted 2400 cm(-1) from the X → D transition of I(2). Observed redshift can be explained by symmetry breaking of ion-pair states within the I(2)-Xe complex. Systematic Xe doping of Kr matrices shows that at low doping levels, positions of I(2) ion-pair emissions are not significantly affected by complexation with Xe, but simultaneous increase of emissions from doubly spin-excited states indicates non-radiative relaxation to valence states. At intermediate doping levels ion-pair emissions shift systematically to red due to change in the average polarizability of the environment. We have conducted spectrally resolved ultrafast pump-probe ion-pair emission studies with pure and Xe doped Kr matrices, in order to reveal the influence of Xe to I(2) dynamics in solid Kr. Strikingly, relaxed emission from the ion-pair states shows no indication of complex presence. It further indicates that the complex escapes detection due to a non-radiative relaxation.     

Selfadjoint Schrödinger operators on the half-space with compactly supported Robin boundary conditions

Schrödinger differential operators on a half-space with compactly supported Robin boundary conditions are studied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary triples and quasi boundary triples for elliptic operators

The abstract concepts of boundary triples and their recent generalizations are useful tools to parametrize the self-adjoint and maximal dissipative/maximal accumulative extensions of formally symmetric elliptic differential expressions with the help of explicit boundary conditions. In the present note the parametrizations induced by the “natural” quasi boundary triple with the Dirichlet and Neumann trace as boundary maps are compared with the parametrizations induced by a “classical” ordinary boundary triple, where a regularized Neumann trace is used for one of the boundary maps. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz.     

A note on the Pauli problem in light of approximate joint measurements

We show that there exist informationally incomplete phase space observables such that the Cartesian margins are informationally equivalent with position and momentum. This shows that it is possible to reconstruct the position and momentum distributions of a quantum system from the statistics of a single observable, and thus a single measurement, even though the state of the system is not uniquely determined by the statistics.     

On the negative squares of indefinite Sturm-Liouville operators

The number of negative squares of all self-adjoint extensions of a simple symmetric operator of defect one with finitely many negative squares in a Krein space is characterized in terms of the behaviour of an abstract Titchmarsh-Weyl function near 0 and ∞. These results are applied to a large class of symmetric and self-adjoint indefinite Sturm-Liouville operators with indefinite weight functions.     

Quasihyperbolic geodesics in convex domains

We show that quasihyperbolic geodesics exist in convex domains in reflexive Banach spaces and that quasihyperbolic geodesies are quasiconvex in the norm metric in convex domains in all normed spaces.     

Algorithms for manipulation of level sets of nonparametric density estimates

Summary  We present algorithms for finding the level set tree of a multivariate density estimate. That is, we find the separated components of level sets of the estimate for a series of levels, gather information on the separated components, such as volume and barycenter, and present the information together with the tree structure of the separated components. The algorithm proceeds by first building a binary tree which partitions the support of the density estimate, followed by bottom-up travels of this tree during which we join those parts of the level sets which touch each other. As a byproduct we present an algorithm for evaluating a kernel estimate on a large multidimensional grid. Since we find the barycenters of the separated components of the level sets also for high levels, our method finds the locations of local extremes of the estimate. Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/8-1.