Small deviations in p-variation for stable processes

Let $\{Z_t, t\geq 0\}$ be a strictly stable process on $\R$ with index $\alpha\in (0,2]$. We prove that for every $p > \alpha$, there exists $\gamma = \gamma (\alpha, p)$ and \k = \k (\alpha, p)\in (0, +\infty) such that \lim_{\ee\downarrow 0}\ee^{\gamma}\log\pb\lcr ||Z||_{p}\leq \ee \rcr = - \k, where $||Z||_{p}$ stands for the strong $p$-variation of $Z$ on $[0,1]$. The critical exponent $\gamma (\alpha, p)$ takes a different shape according as $|Z|$ is a subordinator and $p >1$, or not. The small ball constant \k (\alpha, p) is explicitly computed when $p \leq 1$, and a lower bound on \k (\alpha, p) is easily obtained in the general case. In the symmetric case and when $p > 2$, we can also give an upper bound on \k (\alpha, p) in terms of the Brownian small ball constant under the $(1/p)$-H\"older semi-norm. Along the way, we remark that the positive random variable $||Z||^p_{p}$ is not necessarily stable when $p > 1$, which gives a negative answer to an old question of P.~E.~Greenwood.Comment: 16 pages. Submitte

Cultural identity and academic achievement among Māori undergraduate university students

Cultural identity and academic achievement were investigated among a nonrandom sample of 72 undergraduate Māori university students studying at Massey University. Student problems were examined to identify the types of difficulties most prevalent among this population. The degree to which cultural identity moderates the relationship between student problems and academic achievement was then examined. Major findings were that (a) there is a consistent negative relationship between student problems and academic achievement; and (b) cultural identity moderates the effect of student problems on academic achievement, in that: a high degree of problems were associated with decreases in grade point average among respondents with low cultural identity; while among respondents with high cultural identity, high levels of student problems had little negative effect on grade point average. Despite the study having limitations, the findings have important implications for Māori students, deliverers of tertiary education, tertiary education providers, and those involved in the development and implementation of tertiary education policy

The High Chromospheres of the Late A Stars

We report the detection of N V 1239 A transition region emission in HST/GHRS spectra of the A7 V stars, Alpha Aql and Alpha Cep. Our observations provide the first direct evidence of 1-3 x 10^5 K material in the atmospheres of normal A-type stars. For both stars, and for the mid-A--type star Tau3 Eri, we also report the detection of chromospheric emission in the Si III 1206 A line. At a B-V color of 0.16 and an effective temperature of 8200 K, Tau3 Eri becomes the hottest main sequence star known to have a chromosphere and thus an outer convection zone. We see no firm evidence that the Si III line surface fluxes of the A stars are any lower than those of moderately active, solar-type, G and K stars. This contrasts sharply with their coronal X-ray emission, which is >100 times weaker than that of the later-type stars. Given the strength of the N V emission observed here, it now appears unlikely that the X-ray faintness of the A stars is due to their forming very cool, <= 1 MK coronae. An alternative explanation in terms of mass loss in coronal winds remains a possibility, though we conclude from moderate resolution spectra of the Si III lines that such winds, if they exist, do not penetrate into the chromospheric Si III--forming layers of the star, since the profiles of these lines are *not* blueshifted, and may well be redshifted with respect to the star.Comment: LaTex, 12 pages, 3 Postscript figures, uses aaspp4, accepted by Ap

Liquidity forecasting

When central banks enter into transactions to implement their monetary policy, they necessarily make use of their own balance sheets. Whether they are undertaking open market operations (OMO) to inject or drain funds from the banking system, or allowing the banks to use standing facilities to borrow or deposit funds, the central bank’s balance sheet will be impacted: the funds in question are commercial bank balances held at the central bank. Ideally, operations undertaken to implement policy should have a predictable impact on the economy, via the banking system. This means that the central bank needs to know the context in which it is operating: what is the current availability of commercial bank balances compared with the level of demand, and how is this expected to change in the near term? An accurate current picture and good forecast of the central bank’s likely future balance sheet is required. The same information on the central bank’s balance sheet is also needed if the central bank wishes to manage liquidity pro-actively. Most central banks do, whether it is to avoid a shortage of liquidity impacting on the payment system, or an excess impacting short-term yields and/or the exchange rate. This Handbook examines the issues involved in forecasting the central bank’s balance sheet. This is normally referred to as ‘liquidity forecasting’ since the item on the balance sheet which central banks typically try to manage is commercial banks balances, a subset of high-powered liquidity.Liquidity forecasting

Central bank management of surplus liquidity

Following a CCBS seminar in London, in February 2006, on the subject of central bank management of surplus liquidity, participants were invited to contribute to a collection of papers - case-studies of how a range of central banks around the world have tackled or are tackling the issues which arise from excess liquidity in the banking system. One of the aims was to produce something quite quickly. Much more remains to be said about the management of excess liquidity than is covered in this volume; but we hope that it will prove useful material to others who are addressing the same issues. Interested readers are also referred to the CCBS Lecture Series no. 3: “Surplus Liquidity: Implications for Central Banks”, by Joe Ganley.Central Bank,Management, Surplus, Liquidity

The modeling of diffuse boundaries in the 2-D digital waveguide mesh

The digital waveguide mesh can be used to simulate the propagation of sound waves in an acoustic system. The accurate simulation of the acoustic characteristics of boundaries within such a system is an important part of the model. One significant property of an acoustic boundary is its diffusivity. Previous approaches to simulating diffuse boundaries in a digital waveguide mesh are effective but exhibit limitations and have not been analyzed in detail. An improved technique is presented here that simulates diffusion at boundaries and offers a high degree of control and consistency. This technique works by rotating wavefronts as they pass through a special diffusing layer adjacent to the boundary. The waves are rotated randomly according to a chosen probability function and the model is lossless. This diffusion model is analyzed in detail, and its diffusivity is quantified in the form of frequency dependent diffusion coefficients. The approach used to measuring boundary diffusion is described here in detail for the 2-D digital waveguide mesh and can readily be extended for the 3-D case

Manifestly gauge independent formulations of the Z2 invariants

We use a "monodromy" argument to derive new expressions for the ${\bm Z}_2$ invariants of topological insulators with time-reversal symmetry in 2 and 3 dimensions. The derivations and the final expressions do not require any gauge choice and the calculation of the invariants is based entirely on the projectors onto the occupied states. Explicit numerical tests for tight-binding models with strongly broken inversion symmetry are presented in 2 and 3-dimensions