An examination of the IFS corporation tax forecasting record

This paper examines the corporation tax forecasting techniques used by the Institute for Fiscal Studies. For current year forecasts a judgemental forecast is found to have performed better than relying solely on a simple model or information on the receipts available so far in the current financial year. For longer time horizons the judgemental forecast has performed slightly less well than the modelled forecast. While forecasts made later in the financial year have led to more accurate estimates of receipts in the current year no evidence is found that this has improved the accuracy of longer run forecasts. In the short term inaccuracies in the modelling process are found to be more important than errors in forecasting growth in corporate profits. However the latter is still an important component of errors and one that grows substantially in relative importance as the forecast horizon increases

Super Rogers-Szeg\"o polynomials associated with BCNBC_N type of Polychronakos spin chains

As is well known, multivariate Rogers-Szeg\"o polynomials are closely connected with the partition functions of the $A_{N-1}$ type of Polychronakos spin chains having long-range interactions. Applying the `freezing trick', here we derive the partition functions for a class of $BC_N$ type of Polychronakos spin chains containing supersymmetric analogues of polarized spin reversal operators and subsequently use those partition functions to obtain novel multivariate super Rogers-Szeg\"o (SRS) polynomials depending on four types of variables. We construct the generating functions for such SRS polynomials and show that these polynomials can be written as some bilinear combinations of the $A_{N-1}$ type of SRS polynomials. We also use the above mentioned generating functions to derive a set of recursion relations for the partition functions of the $BC_N$ type of Polychronakos spin chains involving different numbers of lattice sites and internal degrees of freedom.Comment: 33 pages, minor typos corrected, journal reference give

Software for cut-generating functions in the Gomory--Johnson model and beyond

We present software for investigations with cut generating functions in the Gomory-Johnson model and extensions, implemented in the computer algebra system SageMath.Comment: 8 pages, 3 figures; to appear in Proc. International Congress on Mathematical Software 201

On the Power-Law Tail in the Mass Function of Protostellar Condensations and Stars

We explore the idea that the power-law tail in the mass function of protostellar condensations and stars arises from the accretion of ambient cloud material on to a condensation, coupled with a nonuniform (exponential) distribution of accretion lifetimes. This model allows for the generation of power-law distributions in all star-forming regions, even if condensations start with a lognormal mass distribution, as may be expected from the central limit theorem, and supported by some recent numerical simulations of turbulent molecular clouds. For a condensation mass $m$ with growth rate $dm/dt \propto m$, an analytic three-parameter probability density function is derived; it resembles a lognormal at low mass and has a pure power-law high-mass tail. An approximate power-law tail is also expected for other growth laws, and we calculate the distribution for the plausible case $dm/dt \propto m^{2/3}$. Furthermore, any single time snapshot of the masses of condensations that are still accreting (and are of varying ages) also yields a distribution with a power-law tail similar to that of the IMF.Comment: 5 pages, 4 figures, to appear in MNRAS (Letters section

Comparison of High-degree Solar Acoustic Frequencies and Asymmetry between Velocity and Intensity Data

Using the local helioseismic technique of ring diagram we analyze the frequencies of high--degree f- and p-modes derived from both velocity and continuum intensity data observed by MDI. Fitting the spectra with asymmetric peak profiles, we find that the asymmetry associated with velocity line profiles is negative for all frequency ranges agreeing with previous observations while the asymmetry of the intensity profiles shows a complex and frequency dependent behavior. We also observe systematic frequency differences between intensity and velocity spectra at the high end of the frequency range, mostly above 4 mHz. We infer that this difference arises from the fitting of the intensity rather than the velocity spectra. We also show that the frequency differences between intensity and velocity do not vary significantly from the disk center to the limb when the spectra are fitted with the asymmetric profile and conclude that only a part of the background is correlated with the intensity oscillations.Comment: Accepted for publication in Astrophysical Journa

A Mass Formula from Light to Hypernuclei

Simultaneous description of ordinary and hypernuclei masses by a single mass formula has been a great challenge in nuclear physics. Hyperon-separation energies of about forty Lambda($\Lambda$), three Lambda-Lambda($\Lambda\Lambda$), one Sigma($\Sigma$) and seven Cascade($\Xi$) hypernuclei have been experimentally found. Many of these nuclei are of light masses. We prescribe a new mass formula, called BWMH, which describes the normal and hypernuclei on the same footing. It is based on the modified-Bethe-Weizs\"acker mass formula (BWM). BWM is basically an extension of the Bethe-Weizs\"acker mass formula (BW) for light nuclei. The parameters of BWM were optimized by fitting about 3000 normal nuclei available recently. The original Bethe-Weizs\"acker mass formula (BW) was designed for medium and heavy mass nuclei and it fails for light nuclei. Two earlier works on hypernuclei based on this BW show some limitations. The BWMH gives improved agreement with the experimental data for the line of stability, one-neutron separation energy versus neutron number spectra of normal nuclei, and the hyperon-separation energies from hypernuclei. The drip lines are modified for addition of a $\Lambda$ hyperon in a normal nucleus.Comment: Presented at the "XXIX Mazurian Lakes Conference on Physics: Nuclear Physics and the Fundamental Processes, Piaski, Poland, August 30 - September 6, 2005." (7 pages, 1 Table, 1 Figure

Isobaric incompressibility of the isospin asymmetric nuclear matter

The isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibility $K_\infty (X) = K_\infty + K_\tau X^2 + O(X^4)$ at saturation density is systematically studied using density dependent M3Y interaction. The $K_\tau$ characterizes the isospin dependence of the incompressibility at saturation density $\rho_0$. The approximate expression $K_{asy} \approx K_{sym}-6L$ is often used for $K_\tau$ where $L$ and $K_{sym}$ represent, respectively, the slope and curvature parameters of the symmetry energy at $\rho_0$. It can be expressed accurately as $K_\tau=K_{sym}-6L-\frac{Q_0}{K_\infty}L$ where $Q_0$ is the third-order derivative parameter of symmetric nuclear matter at $\rho_0$. The results of this addendum to Phys. Rev. C 80, 011305(R) (2009) indicate that the $Q_0$ contribution to $K_\tau$ is not insignificant.Comment: 4 pages including 1 table and 1 figur