Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

The transverse-momentum spectrum of Higgs bosons near threshold at NNLO

We give next-to-next-to-leading order (NNLO) predictions for the Higgs production cross section at large transverse momentum in the threshold limit. Near the partonic threshold, all radiation is either soft or collinear to the final state jet which recoils against the Higgs boson. We find that the real emission corrections are of moderate size, but that the virtual corrections are large. We discuss the origin of these corrections and give numerical predictions for the transverse-momentum spectrum. The threshold result is matched to the known NLO result and implemented in the public code PeTeR.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Structural Studies of Transition Metal Complexes with 4,5-Bis(2-pyridylmethylsulfanyl)-4‘,5‘-ethylenedithiotetrathiafulvalene: Probing Their Potential for the Construction of Multifunctional Molecular Assemblies

Three divalent transition metal complexes of 4,5-bis(2-pyridylmethylsulfanyl)-4‘,5‘-ethylenedithiotetrathiafulvalene have been prepared and crystallographically characterized. The isostructural Co(II) and the Ni(II) complexes show octahedral geometries around the metal ions with the coordination sites occupied by the pyridyl nitrogen atoms and the thioether sulfur atoms of the ligand and cis coordination of the halide ions. Cyclic voltammetry reveals that the complexation leads to a small anodic shift in the first oxidation potential of the TTF system.

Suprasellar chordoid neoplasm with expression of thyroid transcription factor 1: evidence that chordoid glioma of the third ventricle and pituicytoma may form part of a spectrum of lineage-related tumors of the basal forebrain.

Chordoid glioma of the third ventricle is a rare neuroepithelial tumor characterized by a unique histomorphology and exclusive association with the suprasellar/third ventricular compartment. Variously interpreted as either astrocytic- or ependymal-like, and speculatively ascribed to the lamina terminalis/subcommissural organ, its histogenesis remains, nevertheless, unsettled. Here, we report on a suprasellar chordoid glioma occurring in a 52-year-old man. Although displaying otherwise typical morphological features, the tumor was notable for expression of thyroid transcription factor 1, a marker of tumors of pituicytic origin in the context of the sellar region. We furthermore found overlapping immunoprofiles of this example of chordoid glioma and pituicytic tumors (pituicytoma and spindle cell oncocytoma), respectively. Specifically, phosphorylated ribosomal protein S6, a marker of mTOR pathway activation, was expressed in both groups. Based on these findings, we suggest that chordoid glioma and pituicytic tumors may form part of a spectrum of lineage-related neoplasms of the basal forebrain.

The spectrum of the non-rapid eye movement sleep electroencephalogram following total sleep deprivation is trait-like

The sleep electroencephalogram (EEG) spectrum is unique to an individual and stable across multiple baseline recordings. The aim of this study was to examine whether the sleep EEG spectrum exhibits the same stable characteristics after acute total sleep deprivation. Polysomnography (PSG) was recorded in 20 healthy adults across consecutive sleep periods. Three nights of baseline sleep [12 h time in bed (TIB)] following 12 h of wakefulness were interleaved with three nights of recovery sleep (12 h TIB) following 36 h of sustained wakefulness. Spectral analysis of the non-rapid eye movement (NREM) sleep EEG (C3LM derivation) was used to calculate power in 0.25 Hz frequency bins between 0.75 and 16.0 Hz. Intraclass correlation coefficients (ICCs) were calculated to assess stable individual differences for baseline and recovery night spectra separately and combined. ICCs were high across all frequencies for baseline and recovery and for baseline and recovery combined. These results show that the spectrum of the NREM sleep EEG is substantially different among individuals, highly stable within individuals and robust to an experimental challenge (i.e. sleep deprivation) known to have considerable impact on the NREM sleep EEG. These findings indicate that the NREM sleep EEG represents a trait.