On the spectra of the quantized action-variables of the compactified Ruijsenaars-Schneider system

A simple derivation of the spectra of the action-variables of the quantized compactified Ruijsenaars-Schneider system is presented. The spectra are obtained by combining Kahler quantization with the identification of the classical action-variables as a standard toric moment map on the complex projective space. The result is consistent with the Schrodinger quantization of the system worked out previously by van Diejen and Vinet.Comment: Based on talk at the workshop CQIS-2011 (Protvino, Russia, January 2011), 12 page

Hamiltonian reductions of free particles under polar actions of compact Lie groups

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifolds meeting all orbits orthogonally in the configuration space. Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of spin Calogero-Sutherland type.Comment: 15 pages, minor correction and updated references in v

Zoological collectings in Albania between 2004 and 2010 by the Hungarian Natural History Museum and the Hungarian Academy of Sciences

The Albanian locality data of zoological collectings carried out by the Hungarian Natural History Museum and theHungarian Academy of Sciences during 30 tours to the Balkans between 2004 and 2010 are enumerated. The localities andmethods of collecting are enumerated in chronological order. Sites are marked on the map of Albania

Normkonvergenz von Fourierreihen in rearrangement invarianten Banachräumen

AbstractThis paper studies rearrangement invariant Banach spaces of 2π-periodic functions with respect to norm convergence of Fourier series. The main result is that norm convergence takes place if and only if the space is an interpolation space of (Lp′(T), Lp(T)), 1 < p < 2, 1p′ + 1p = 1, and Lp′(T) is dense in it (compare Satz 2.8). Since norm convergence and continuity of the conjugation operator are closely connected (compare Satz 2.2), this is achieved by a careful examination of this operator similar to that of D. W. Boyd for the Hilbert transform on the whole real axis. Finally, there are applications to Orlicz and Lorentz spaces

Network Changes during tACS Induced Oscillations

Oscillatory neural activity is considered a basis of signal transmission in brain networks. However, the causal role of neural oscillations in regulating cortico-cortical signal transmission has so far not been directly demonstrated. To date, due to methodological limitations, studies on the online modulatory mechanisms of transcranial alternating current stimulation (tACS)-induced neural oscillations are confined to the primary motor cortex. To address the causal role of oscillatory activity in modulating cortico-cortical signal transmission, we have established a new method using concurrent tACS, transcranial magnetic stimulation (TMS) and electroencephalography (EEG). Through tACS, we introduced 6-Hz (theta) oscillatory activity in the human dorsolateral prefrontal cortex (DLPFC). During tACS, we applied single-pulse TMS over the DLPFC at different phases of tACS and assessed propagation of TMS-induced neural activity with EEG. We show that tACS-induced theta oscillations modulate the propagation of TMS-induced activity in a phase-dependent manner and that phase-dependent modulation is not simply explained by the instantaneous amplitude of tACS. The results demonstrate a phase-dependent modulatory mechanism of tACS at a cortical network level, which is consistent with a causal role of neural oscillations in regulating the efficacy of signal transmission in the brain

A note on the Gauss decomposition of the elliptic Cauchy matrix

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.Comment: 5 page

Brain stimulation techniques as novel treatment options for insomnia: A systematic review.

Despite the success of cognitive behavioural therapy for insomnia and recent advances in pharmacotherapy, many patients with insomnia do not sufficiently respond to available treatments. This systematic review aims to present the state of science regarding the use of brain stimulation approaches in treating insomnia. To this end, we searched MEDLINE, Embase and PsycINFO from inception to 24 March 2023. We evaluated studies that compared conditions of active stimulation with a control condition or group. Outcome measures included standardized insomnia questionnaires and/or polysomnography in adults with a clinical diagnosis of insomnia. Our search identified 17 controlled trials that met inclusion criteria, and assessed a total of 967 participants using repetitive transcranial magnetic stimulation, transcranial electric stimulation, transcutaneous auricular vagus nerve stimulation or forehead cooling. No trials using other techniques such as deep brain stimulation, vestibular stimulation or auditory stimulation met the inclusion criteria. While several studies report improvements of subjective and objective sleep parameters for different repetitive transcranial magnetic stimulation and transcranial electric stimulation protocols, important methodological limitations and risk of bias limit their interpretability. A forehead cooling study found no significant group differences in the primary endpoints, but better sleep initiation in the active condition. Two transcutaneous auricular vagus nerve stimulation trials found no superiority of active stimulation for most outcome measures. Although modulating sleep through brain stimulation appears feasible, gaps in the prevailing models of sleep physiology and insomnia pathophysiology remain to be filled. Optimized stimulation protocols and proof of superiority over reliable sham conditions are indispensable before brain stimulation becomes a viable treatment option for insomnia

Mass transport from the envelope to the disk of V346 Nor: a case study for the luminosity problem in an FUor-type young eruptive star

A long-standing open issue of the paradigm of low-mass star formation is the luminosity problem: most protostars are less luminous than theoretically predicted. One possible solution is that the accretion process is episodic. FU Ori-type stars (FUors) are thought to be the visible examples for objects in the high accretion state. FUors are often surrounded by massive envelopes, which replenish the disk material and enable the disk to produce accretion outbursts. However, we have insufficient information on the envelope dynamics in FUors, about where and how mass transfer from the envelope to the disk happens. Here we present ALMA observations of the FUor-type star V346 Nor at 1.3 mm continuum and in different CO rotational lines. We mapped the density and velocity structure of its envelope and analyze the results using channel maps, position-velocity diagrams, and spectro-astrometric methods. We found that V346 Nor is surrounded by gaseous material on 10000 au scale in which a prominent outflow cavity is carved. Within the central $\sim$700 au, the circumstellar matter forms a flattened pseudo-disk where material is infalling with conserved angular momentum. Within $\sim$350 au, the velocity profile is more consistent with a disk in Keplerian rotation around a central star of 0.1 $M_{\odot}$. We determined an infall rate from the envelope onto the disk of 6$\times$10$^{-6}\,M_{\odot}$yr$^{-1}$, a factor of few higher than the quiescent accretion rate from the disk onto the star, hinting for a mismatch between the infall and accretion rates as the cause of the eruption.Comment: 16 pages, 8 figures, published in Ap

A class of Calogero type reductions of free motion on a simple Lie group

The reductions of the free geodesic motion on a non-compact simple Lie group G based on the $G_+ \times G_+$ symmetry given by left- and right multiplications for a maximal compact subgroup $G_+ \subset G$ are investigated. At generic values of the momentum map this leads to (new) spin Calogero type models. At some special values the `spin' degrees of freedom are absent and we obtain the standard $BC_n$ Sutherland model with three independent coupling constants from SU(n+1,n) and from SU(n,n). This generalization of the Olshanetsky-Perelomov derivation of the $BC_n$ model with two independent coupling constants from the geodesics on $G/G_+$ with G=SU(n+1,n) relies on fixing the right-handed momentum to a non-zero character of $G_+$. The reductions considered permit further generalizations and work at the quantized level, too, for non-compact as well as for compact G.Comment: shortened to 13 pages in v2 on request of Lett. Math. Phys. and corrected some spelling error

Spin-stretching modes in anisotropic magnets: spin-wave excitations in the multiferroic Ba2CoGe2O7

We studied spin excitations of the multiferroic Ba2CoGe2O7 in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multi-boson spin-wave theory can capture these unconventional modes, that include spin-stretching modes associated with an oscillating magnetic dipole (or only quadrupole) moment. The lack of the inversion symmetry allows these modes to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or non-centrosymmetric lattice structure.Comment: 5+4 pages, 3 figures, supplement added, manuscript revise