Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the approximation may not inherit these properties automatically.We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials and rational functions that preserve nonnegativity.(trigonometric) polynomials;rational functions;semidefinite programming;regression;(Chebyshev) approximation

Tracking Growth and the Business Cycle: a Stochastic Common Cycle Model for the Euro Area

This paper proposes a new model-based method to obtain a coincident indicator for the business cycle. A dynamic factor model with trend components and a common cycle component is considered which can be estimated using standard maximum likelihood methods. The multivariate unobserved components model includes a stationary higher order cycle. Also higher order trends can be part of the analysis. These generalisations lead to a business cycle that is similar to a band-pass one. Furthermore, cycle shifts for individual time series are incorporated within the model and estimated simultaneously with the remaining parameters. This feature permits the use of leading, coincident and lagging variables to obtain the business cycle coincident indicator without prior analysis of their lead-lag relationship. Besides the business cycle indicator, the model-based approach also allows to get a growth rate indicator. In the empirical analysis for the Euro area, both indicators are obtained based on nine key economic time series including gross domestic product, industrial production, unemployment, confidence indicators and interest rate spread. This analysis contrasts sharply with earlier multivariate approaches. In particular, our more parsimonious approach leads to a growth rate indicator for the Euro area that is similar to the one of EuroCOIN. The latter is based on a more involved approach by any standard and uses hundreds of time series from individual countries belonging to the Euro area.

Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the approximation may not inherit these properties automatically.We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials and rational functions that preserve nonnegativity.

Gamma-widths, lifetimes and fluctuations in the nuclear quasi-continuum

Statistical $\gamma$-decay from highly excited states is determined by the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma$SF). These average quantities have been measured for several nuclei using the Oslo method. For the first time, we exploit the NLD and $\gamma$SF to evaluate the $\gamma$-width in the energy region below the neutron binding energy, often called the quasi-continuum region. The lifetimes of states in the quasi-continuum are important benchmarks for a theoretical description of nuclear structure and dynamics at high temperature. The lifetimes may also have impact on reaction rates for the rapid neutron-capture process, now demonstrated to take place in neutron star mergers.Comment: CGS16, Shanghai 2017, Proceedings, 5 pages, 3 figure

Extraction of level density and gamma strength function from primary gamma spectra

We present a new iterative procedure to extract the level density and the gamma strength function from primary gamma spectra for energies close up to the neutron binding energy. The procedure is tested on simulated spectra and on data from the Yb-173(He-3,alpha)Yb-172 reaction.Comment: 23 pages including 1 table and 7 figure

Enhanced radiative strength in the quasi-continuum of 117Sn

Radiative strength functions of 117Sn has been measured below the neutron separation energy using the (3He,3He'gamma) reactions. An increase in the slope of the strength functions around E_gamma= 4.5 MeV indicates the onset of a resonance-like structure, giving a significant enhancement of the radiative strength function compared to standard models in the energy region 4.5 <= E_gamma <= 8.0 MeV. For the first time, the functional form of this resonance-like structure has been measured in an odd tin nucleus below neutron threshold in the quasi-continuum region.Comment: 4 pages, 3 figure

Evidence for the pair-breaking process in 116,117Sn

The nuclear level densities of 116,117Sn below the neutron separation energy have been determined experimentally from the (3He,alpha gamma) and (3He,3He gamma') reactions, respectively. The level densities show a characteristic exponential increase and a difference in magnitude due to the odd-even effect of the nuclear systems. In addition, the level densities display pronounced step-like structures that are interpreted as signatures of subsequent breaking of nucleon pairs.Comment: 7 pages, 5 figures, accepted for publication in Phys. Rev. C, 22 December 200