Factors of sums and alternating sums involving binomial coefficients and powers of integers

We study divisibility properties of certain sums and alternating sums involving binomial coefficients and powers of integers. For example, we prove that for all positive integers $n_1,..., n_m$, $n_{m+1}=n_1$, and any nonnegative integer $r$, there holds {align*} \sum_{k=0}^{n_1}\epsilon^k (2k+1)^{2r+1}\prod_{i=1}^{m} {n_i+n_{i+1}+1\choose n_i-k} \equiv 0 \mod (n_1+n_m+1){n_1+n_m\choose n_1}, {align*} and conjecture that for any nonnegative integer $r$ and positive integer $s$ such that $r+s$ is odd, $$\sum_{k=0}^{n}\epsilon ^k (2k+1)^{r}({2n\choose n-k}-{2n\choose n-k-1})^{s} \equiv 0 \mod{{2n\choose n}},$$ where $\epsilon=\pm 1$.Comment: 14 pages, to appear in Int. J. Number Theor

Multiple cyclical fractional structures in financial time series

This paper analyses multiple cyclical structures in financial time series. In particular, we focus on the monthly structure of the Nasdaq, the Dow Jones and the Standard&Poor stock market indices. The three series are modelled as long-memory processes with poles in the spectrum at multiple frequencies, including the long-run or zero frequency

Some Orthogonal Polynomials Arising from Coherent States

We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known orthogonal polynomials but in many cases we encounter a general class of new orthogonal polynomials for which we establish several qualitative results.Comment: 21 page

Scalar Casimir Effect on a D-dimensional Einstein Static Universe

We compute the renormalised energy momentum tensor of a free scalar field coupled to gravity on an (n+1)-dimensional Einstein Static Universe (ESU), RxS^n, with arbitrary low energy effective operators (up to mass dimension n+1). A generic class of regulators is used, together with the Abel-Plana formula, leading to a manifestly regulator independent result. The general structure of the divergences is analysed to show that all the gravitational couplings (not just the cosmological constant) are renormalised for an arbitrary regulator. Various commonly used methods (damping function, point-splitting, momentum cut-off and zeta function) are shown to, effectively, belong to the given class. The final results depend strongly on the parity of n. A detailed analytical and numerical analysis is performed for the behaviours of the renormalised energy density and a quantity `sigma' which determines if the strong energy condition holds for the `quantum fluid'. We briefly discuss the quantum fluid back-reaction problem, via the higher dimensional Friedmann and Raychaudhuri equations, observe that equilibrium radii exist and unveil the possibility of a `Casimir stabilisation of Einstein Static Universes'.Comment: 37 pages, 15 figures, v2: minor changes in sections 1, 2.5, 3 and 4; version published in CQ

A new class of coherent states with Meixner-Pollaczek polynomials for the Gol'dman-Krivchenkov Hamiltonian

A class of generalized coherent states with a new type of the identity resolution are constructed by replacing the labeling parameter zn/n! of the canonical coherent states by Meixner-Pollaczek polynomials with specific parameters. The constructed coherent states belong to the state Hilbert space of the Gol'dman-Krivchenkov Hamiltonian.Comment: 10 pages, Submitte

Orbitofrontal cortex mediates pain inhibition by monetary reward

Pleasurable stimuli, including reward, inhibit pain, but the level of the neuraxis at which they do so and the cerebral processes involved are unknown. Here, we characterized a brain circuitry mediating pain inhibition by reward. Twenty-four healthy participants underwent functional magnetic resonance imaging while playing a wheel of fortune game with simultaneous thermal pain stimuli and monetary wins or losses. As expected, winning decreased pain perception compared to losing. Inter-individual differences in pain modulation by monetary wins relative to losses correlated with activation in the medial orbitofrontal cortex (mOFC). When pain and reward occured simultaneously, mOFCs functional connectivity changed: the signal time course in the mOFC condition-dependent correlated negatively with the signal time courses in the rostral anterior insula, anterior-dorsal cingulate cortex and primary somatosensory cortex, which might signify momentto-moment down-regulation of these regions by the mOFC. Monetary wins and losses did not change the magnitude of pain-related activation, including in regions that code perceived pain intensity when nociceptive input varies and/or receive direct nociceptive input. Pain inhibition by reward appears to involve brain regions not typically involved in nociceptive intensity coding but likely mediate changes in the significance and/or value of pain

Effective superpotentials for compact D5-brane Calabi-Yau geometries

For compact Calabi-Yau geometries with D5-branes we study N=1 effective superpotentials depending on both open- and closed-string fields. We develop methods to derive the open/closed Picard-Fuchs differential equations, which control D5-brane deformations as well as complex structure deformations of the compact Calabi-Yau space. Their solutions encode the flat open/closed coordinates and the effective superpotential. For two explicit examples of compact D5-brane Calabi-Yau hypersurface geometries we apply our techniques and express the calculated superpotentials in terms of flat open/closed coordinates. By evaluating these superpotentials at their critical points we reproduce the domain wall tensions that have recently appeared in the literature. Finally we extract orbifold disk invariants from the superpotentials, which, up to overall numerical normalizations, correspond to orbifold disk Gromov-Witten invariants in the mirror geometry.Comment: 55 pages; v2: references added, typos correcte

Optimized Planar Penning Traps for Quantum Information Studies

A one-electron qubit would offer a new option for quantum information science, including the possibility of extremely long coherence times. One-quantum cyclotron transitions and spin flips have been observed for a single electron in a cylindrical Penning trap. However, an electron suspended in a planar Penning trap is a more promising building block for the array of coupled qubits needed for quantum information studies. The optimized design configurations identified here promise to make it possible to realize the elusive goal of one trapped electron in a planar Penning trap for the first time - a substantial step toward a one-electron qubit

Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

We continue our study of the global properties of the z=2 Schroedinger space-time. In particular, we provide a codimension 2 isometric embedding which naturally gives rise to the previously introduced global coordinates. Furthermore, we study the causal structure by probing the space-time with point particles as well as with scalar fields. We show that, even though there is no global time function in the technical sense (Schroedinger space-time being non-distinguishing), the time coordinate of the global Schroedinger coordinate system is, in a precise way, the closest one can get to having such a time function. In spite of this and the corresponding strongly Galilean and almost pathological causal structure of this space-time, it is nevertheless possible to define a Hilbert space of normalisable scalar modes with a well-defined time-evolution. We also discuss how the Galilean causal structure is reflected and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page

TRIGA-SPEC: A setup for mass spectrometry and laser spectroscopy at the research reactor TRIGA Mainz

The research reactor TRIGA Mainz is an ideal facility to provide neutron-rich nuclides with production rates sufficiently large for mass spectrometric and laser spectroscopic studies. Within the TRIGA-SPEC project, a Penning trap as well as a beam line for collinear laser spectroscopy are being installed. Several new developments will ensure high sensitivity of the trap setup enabling mass measurements even on a single ion. Besides neutron-rich fission products produced in the reactor, also heavy nuclides such as 235-U or 252-Cf can be investigated for the first time with an off-line ion source. The data provided by the mass measurements will be of interest for astrophysical calculations on the rapid neutron-capture process as well as for tests of mass models in the heavy-mass region. The laser spectroscopic measurements will yield model-independent information on nuclear ground-state properties such as nuclear moments and charge radii of neutron-rich nuclei of refractory elements far from stability. This publication describes the experimental setup as well as its present status.Comment: 20 pages, 17 figure