The Coulomb-Oscillator Relation on n-Dimensional Spheres and Hyperboloids

In this paper we establish a relation between Coulomb and oscillator systems on $n$-dimensional spheres and hyperboloids for $n\geq 2$. We show that, as in Euclidean space, the quasiradial equation for the $n+1$ dimensional Coulomb problem coincides with the $2n$-dimensional quasiradial oscillator equation on spheres and hyperboloids. Using the solution of the Schr\"odinger equation for the oscillator system, we construct the energy spectrum and wave functions for the Coulomb problem.Comment: 15 pages, LaTe

Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere

Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting with a Yang monopole. Then, using a standard trick, we obtain, from the latter system, the pseudospherical and spherical generalizations of the Yang-Coulomb system (the five dimensional analog of MICZ-Kepler system). We present the whole set of its constants of motions, including the hidden symmetry generators given by the analog of Runge-Lenz vector. In the same way, starting from the eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the integrable (pseudo)spherical generalization of the Yang-Coulomb system with the Stark term.Comment: 10 pages, PACS: 03.65.-w, 02.30.Ik, 14.80.H

3D Oscillator and Coulomb Systems reduced from Kahler spaces

We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kahler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid are originated. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is non-Kahler one. Finally, we extend these results to the family of Kahler spaces with conic singularities.Comment: To the memory of Professor Valery Ter-Antonyan, 11 page

Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical generalization of the MICZ-Kepler system with linear and $\cos\theta$ potential terms. We also present the generalization of the parabolic coordinates, in which this system admits the separation of variables. Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page

Large aperture vibrating wire monitor with two mechanically coupled wires for beam halo measurements

Development of a new type of vibrating wire monitor (VWM), which has two mechanically coupled wires (vibrating and target), is presented. The new monitor has a much larger aperture size than the previous model of the VWM, and thus allows us to measure transverse beam halos more effectively. A prototype of such a large aperture VWM with a target wire length of 60 mm was designed, manufactured, and bench-tested. Initial beam measurements have been performed at the Fermilab High Intensity Neutrino Source facility, and key results are presented.open1

Consolidation Potential of the Educational Community

The present paper investigated the possibility of progressive development of a society in the terms of transformation, in particular, by the ability of the educational community to the social cohesion to focus efforts on overcoming challenges of an unstable period of social development. The analysis was performed on the consolidation potential structure of the educational community; and factors of actualization and de-actualization of its potential were identified in order to clarify the conceptual apparatus of definitions "the educational community" and "the consolidation potential of the educational community

Casimir energy in the Fulling--Rindler vacuum

The Casimir energy is evaluated for massless scalar fields under Dirichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on one and two infinite parallel plates moving by uniform proper acceleration through the Fulling--Rindler vacuum in an arbitrary number of spacetime dimension. For the geometry of a single plate the both regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are considered. The zeta function technique is used, in combination with contour integral representations. The Casimir energies for separate RR and RL regions contain pole and finite contributions. For an infinitely thin plate taking RR and RL regions together, in odd spatial dimensions the pole parts cancel and the Casimir energy for the whole Rindler wedge is finite. In $d=3$ spatial dimensions the total Casimir energy for a single plate is negative for Dirichlet scalar and positive for Neumann scalar and the electromagnetic field. The total Casimir energy for two plates geometry is presented in the form of a sum of the Casimir energies for separate plates plus an additional interference term. The latter is negative for all values of the plates separation for both Dirichlet and Neumann scalars, and for the electromagnetic field.Comment: 28 pages, 4 figures, references added, typos corrected, accepted for publication in Phys. Rev.

Quantum oscillator as 1D anyon

It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe

Shortened PQ interval in the differential diagnosis of Anderson-Fabry disease: a case report

In this article, we present a case of a patient with a late diagnosis of Fabry disease caused by a pathogenic variant in the GLA gene (p.1287_1288dup), who repeatedly attempted interventional treatment of Wolff-Parkinson-White Syndrome due to characteristic electrocardiographic pattern of ventricular preexcitation and paroxysmal arrhythmias. The proposed pathognomonic signs of the disease will ensure timely diagnosis and the appointment of specific treatment

Immune complex formation impairs the elimination of solutes from the brain: implications for immunotherapy in Alzheimer's disease

Background: Basement membranes in the walls of cerebral capillaries and arteries form a major lymphatic drainage pathway for fluid and solutes from the brain. Amyloid-β (Aβ) draining from the brain is deposited in such perivascular pathways as cerebral amyloid angiopathy (CAA) in Alzheimer's disease (AD). CAA increases in severity when Aβ is removed from the brain parenchyma by immunotherapy for AD. In this study we investigated the consequences of immune complexes in artery walls upon drainage of solutes similar to soluble Aβ. We tested the hypothesis that, following active immunization with ovalbumin, immune complexes form within the walls of cerebral arteries and impair the perivascular drainage of solutes from the brain. Mice were immunized against ovalbumin and then challenged by intracerebral microinjection of ovalbumin. Perivascular drainage of solutes was quantified following intracerebral microinjection of soluble fluorescent 3kDa dextran into the brain at different time intervals after intracerebral challenge with ovalbumin. Results: Ovalbumin, IgG and complement C3 co-localized in basement membranes of artery walls 24 hrs after challenge with antigen; this was associated with significantly reduced drainage of dextran in immunized mice. Conclusions: Perivascular drainage along artery walls returned to normal by 7 days. These results indicate that immune complexes form in association with basement membranes of cerebral arteries and interfere transiently with perivascular drainage of solutes from the brain. Immune complexes formed during immunotherapy for AD may similarly impair perivascular drainage of soluble Aβ and increase severity of CAA