449 research outputs found
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 , , and any
nonnegative integer , 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 and positive integer such that is odd, where .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
Single Ion Mass Spectrometry at 100 ppt and Beyond
Abstract. Using a Penning trap single ion mass spectrometer, our group has measured the atomic masses of 14 isotopes with a fractional accuracy of about 10 −10 . The masses were extracted from 28 cyclotron frequency ratios of two ions altenately confined in our trap. The precision on these measurements was limited by the temporal fluctuations of our magnetic field during the 5-10 minutes required to switch from one ion to the other. By trapping two different ions in the same Penning trap at the same time, we can now simultaneously measure their two cyclotron frequencies and extract the ratio with a precision of about 10 −11 in only a few hours. We have developed novel techniques to measure and control the motion of the two ions in the trap and we are currently using these tools to carefully investigate the important question of systematic errors in those measurements. Overview Accuracy in mass spectrometry has been advanced over two orders of magnitude by the use of resonance techniques to compare the cyclotron frequencies of single trapped ions. This paper provides an overview of the MIT Penning trap apparatus, techniques and measurements. We begin by describing the various interesting applications of our mass measurements and the wide-ranging impact they have on both fundamental physics and metrology. In the same section, we also describe further scientific applications that an improved accuracy would open. This serves as a motivation for our most current work (described in Sect. 4) to increase our precision by about an order of magnitude. Before describing the latest results, we give in Sect. 3 an overview of our apparatus and methods, with special emphasis on the techniques which we have developed for making measurements with accuracy around 10 −10 . In those measurements, we alternately trapped two different ions (one at the time) and compared their cyclotron frequencies to obtain their mass ratio. The main limitation of this method was the fact that our stable magnetic field would typically fluctuate by several parts in 10 10 during the 5-10 minutes required to switch from one ion to the other. In order to eliminate this problem, we now confine both ions simultaneously in our Penning trap. In Sect. 4, we describe the various techniques that have allowed us to load a pair in the trap and demonstrate a significant gain in precision from simultaneously measuring both their cyclotron frequencies. New tools to measure and control the motion of the ions are also presented. Those tools are invaluable in our current investigation of the important questio
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
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
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
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for
with arbitrary functions and and integer , where and
are boson annihilation and creation operators, satisfying
. This consequently provides the solution for the exponential
generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics
"Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005),
Myczkowce, Poland. 13 pages, 31 reference
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
A Methodology for Successful University Graduate CubeSat Programs
The University of Colorado Smead Department of Aerospace Engineering has over a decade of success in designing, building, and operating student led CubeSat missions. The experience and lessons learned from building and operating the CSSWE, MinXSS-1, MinXSS-2, and QB50-Challenger missions have helped grow a knowledge base on the most effective and efficient ways to manage some of the “tall poles” when it comes to student run CubeSat missions. Among these “tall poles” we have seen student turnover, software, and documentation become some of the hardest to knock-down and we present our strategies for doing so. We use the MAXWELL mission (expected to launch in 2021) as a road-map to detail the methodology we have built over the last decade to ensure the greatest chance of mission success
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
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