On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions

Excitation of the Earth's Chandler wobble by southern oscillation/El Nino, 1900-1979

The southern oscillation/El Nino (ENSO) is the single most prominent interannual signal in global atmospheric/oceanic fluctuations. The following question is addressed: how important is the angular momentum carried by ENSO in exciting the Earth's Chandler wobble? The question is attacked through a statistical analysis of the coherence spectra (correlation as a function of frequency) between two data sets spanning 1900 to 1979-the southern oscillation index (SOI) time series and the excitation function psi (with x-component psi sub x and y-component psi sub y) of the Chandler wobble derived from the homogeneous ILS (International Latitude Service) polar motion data. The coherence power and phase in the Chandler frequency band (approx. 0.79 to 0.89 cpy) are studied. It is found that, during 1900 to 1979 the coherence between SOI and psi sub x is significant well over the 95% confidence threshold whereas that between SOI and psi sub y is practically nil. Quantitatively, the coherence study shows that ENSO provides some 20% of the observed Chandler wobble excitation power. Since earlier investigations have shown that the total atmospheric/oceanic variation can account for the Chandler wobble excitation at about 20% level, the implication is that ENSO maybe an important (interannual) part of the atmospheric/oceanic variation that is responsible for the Chandler wobble excitation during 1900 to 1979

Predictability of the Earth's polar motion

A comprehensive, experimental study of the predictability of the polar motion using a homogeneous BIH (Bureau International de l'Heure) data set is presented. Based on knowledge of the physics of the annual and the Chandler wobbles, the numerical model for the polar motion is constructed by allowing the wobble periods to vary. Using an optimum base length of 6 years for prediction, this floating-period model, equipped with a non-linear least-squares estimator, is found to yield polar motion predictions accurate from 0.012 to 0.024 inches depending on the prediction length up to one year, corresponding to a predictability of 91-83%. This represents a considerable improvement over the conventional fixed-period predictor, which does not respond to variations in the apparent wobble periods. The superiority of the floating-period predictor to other predictors based on critically different numerical models is also demonstrated

On excitation of Earth's free wobble and reference frames

The excitation of the Earth's polar motion in connection with problems that are associated with the diversity of reference frames involved in observations and theoretical computations is studied. Following the dynamics of the Earth's polar motion, the kinematics that relates observations from different reference frames is developed. The conventional procedures of studying the seismic excitation of polar motion are re-examined, subject to the question: relative to what reference frame? It is concluded that an inconsistency in reference frames has prevailed in the literature. While this inconsistency is indeed far from trivial, the resultant discrepancy, however, is small for all practical purposes

Bosonic Super Liouville System: Lax Pair and Solution

We study the bosonic super Liouville system which is a statistical transmutation of super Liouville system. Lax pair for the bosonic super Liouville system is constructed using prolongation method, ensuring the Lax integrability, and the solution to the equations of motion is also considered via Leznov-Saveliev analysis.Comment: LaTeX, no figures, 11 page

Two ultracold atoms in a completely anisotropic trap

As a limiting case of ultracold atoms trapped in deep optical lattices, we consider two interacting atoms trapped in a general anisotropic harmonic oscillator potential, and obtain exact solutions of the Schrodinger equation for this system. The energy spectra for different geometries of the trapping potential are compared.Comment: 4 pages, 2 figure

Change of sea level trend in the Mediterranean and Black seas

Sea level anomaly (SLA) data in the Mediterranean and Black seas obtained by ocean radar altimetry missions (TOPEX/Poseidon, Jason, ERS-1/2 and ENVISAT) are studied in conjunction with corresponding sea-surface temperature (SST) data. The studied time span is 11 years long, 1993-2003. Besides confirming previously published results, we report a significant, but enigmatic, abrupt change in the SLA trend that took place in mid-1999 which has been corroborated by independent tide gauge data. Results obtained from an Empirical Orthogonal Function (EOF) analysis show that the change in 1999 is not uniform in the Mediterranean Sea, which can thus be divided into 6 sub-regions. This 1999 kink in the rate-of-change happened in four of these sub-regions as well as in the Black Sea. Upon splitting the time series at mid-1999, we see a good spatial correlation for the first period between SLA and SST trend maps in both the Mediterranean Sea and the Black Sea, while for the second period such correlation virtually disappeared in the Mediterranean and is greatly reduced in the Black Sea. It implies that prior to 1999 the steric effect was a major factor in interannual variability of sea level in the Mediterranean and Black seas, but after the time the SLA inverted its trend in mid-1999, this steric effects became less important as a forcing factor. It is premature to draw conclusions about the physical processes involved based on the data sets we study, but it appears that the Mediterranean Sea might be seeing a restoration of Adriatic as the main source of deep water in the eastern basin, while the Black Sea level has been largely controlled by an interannual or interdecadal steric effect

Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk models in the literature. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. In the case of unrestricted payment scheme, by solving the associated integro-differential quasi-variational inequality, we obtain the value function as well as an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we provide easily verifiable conditions under which the threshold and barrier strategies are optimal restricted and unrestricted dividend payment policies, respectively. The main results are illustrated with several examples, including a new example concerning regressive growth rates.Comment: Key Words: Piecewise-deterministic compound Poisson model, optimal stochastic control, HJB equation, quasi-variational inequality, threshold strategy, barrier strateg

First measurements of the flux integral with the NIST-4 watt balance

In early 2014, construction of a new watt balance, named NIST-4, has started at the National Institute of Standards and Technology (NIST). In a watt balance, the gravitational force of an unknown mass is compensated by an electromagnetic force produced by a coil in a magnet system. The electromagnetic force depends on the current in the coil and the magnetic flux integral. Most watt balances feature an additional calibration mode, referred to as velocity mode, which allows one to measure the magnetic flux integral to high precision. In this article we describe first measurements of the flux integral in the new watt balance. We introduce measurement and data analysis techniques to assess the quality of the measurements and the adverse effects of vibrations on the instrument.Comment: 7 pages, 8 figures, accepted for publication in IEEE Trans. Instrum. Meas. This Journal can be found online at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=1

Decays of the Meson BcB_c to a PP-Wave Charmonium State χc\chi_c or hch_c

The semileptonic decays, $B_{c}{\longrightarrow}{\chi_c}(h_c)+{\ell}+{{\nu}}_{\ell}$, and the two-body nonleptonic decays, $B_{c}{\longrightarrow}{\chi_c}(h_c)+h$, (here $\chi_c$ and $h_c$ denote $(c\bar c[^3P_J])$ and $(c\bar c[^1P_1])$ respectively, and $h$ indicates a meson) were computed. All of the form factors appearing in the relevant weak-current matrix elements with $B_c$ as its initial state and a $P$-wave charmonium state as its final state for the decays were precisely formulated in terms of two independent overlapping-integrations of the wave-functions of $B_c$ and the $P$-wave charmonium and with proper kinematics factors being `accompanied'. We found that the decays are quite sizable, so they may be accessible in Run-II at Tevatron and in the foreseen future at LHC, particularly, when BTeV and LHCB, the special detectors for B-physics, are borne in mind. In addition, we also pointed out that the decays $B_c\to h_c+...$ may potentially be used as a fresh window to look for the $h_c$ charmonium state, and the cascade decays, $B_c\to \chi_c[^3P_{1,2}]+l+\nu_l$ ($B_c\to \chi_c[^3P_{1,2}]+h$) with one of the radiative decays $\chi_c[^3P_{1,2}] \to J/\psi+\gamma$ being followed accordingly, may affect the observations of $B_c$ meson through the decays $B_{c}\to {J/\psi}+{l}+\nu_{l}$ ($B_c\to J/\psi+h$) substantially.Comment: 24 pages, 3 figures, the replacement for improving the presentation and adding reference