Risk-Smoothing Across Time and the Demand for Inventories: A Mean-Variance Approach

The standard production smoothing model of inventory demand cannot represent the added incentives for smoothing risks or explain the impact of market shocks that independently affect expectations and uncertainty. Those limitations are overcome by modeling inventory demand as a problem in deterministic optimal control, with the risk-averse firm maximizing utility that is a separable function of the mean and variance of returns and the firm controlling on two decision variables, production and inventory investment. Support for the mean-variance approach comes from regressions using Survey of Professional Forecasters data to show how changes in the mean forecasts of the GDP price deflator and changes in the disagreement among deflator forecasts can explain changes in aggregate inventory investment over time. Further support comes from the ability of the model to explain the excess volatility of industry output over sales—a fact at odds with the production smoothing theory.

Uniform asymptotics of the coefficients of unitary moment polynomials

Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in explicit form. Numerical data to support these calculations are presented. Some apparent connections between random matrix theory and the Riemann zeta function are discussed.Comment: 31 pages, 1 figure, 2 tables. A few minor misprints fixe

A polynomial approach to cocycles over elementary abelian groups

We derive bivariate polynomial formulae for cocycles and coboundaries in Z2(xs2124pn,xs2124pn), and a basis for the (pn-1-n)-dimensional GF(pn)-space of coboundaries. When p=2 we determine a basis for the $(2^n + {n\choose 2} -1)$-dimensional GF(2n)-space of cocycles and show that each cocycle has a unique decomposition as a direct sum of a coboundary and a multiplicative cocycle of restricted form

Ultrasound enhancement of microfiltration performance for natural organic matter removal

Sonication of water at 1500 W power prior to microfiltration showed that short sonication times (60 s) gave a reduced flux decline. It is suggested that a less potent, smaller molecular form of the natural organic matter (NOM) was produced by sonication. Longer sonication times diminished this beneficial effect. This may be due to the formation of aggregates or compounds that are more readily adsorbed on the membrane. Where the sonication was preceded by an alum treatment, the flux loss showed a regular decrease with longer sonication times. It is suggested that the effects of sonication on the alum flocs and on the flocs; NOM interactions may play a critical role in regulating the flux. Where sand was present on sonication at 800 and 1400 W, the cavitational energy was focussed on adsorbed organic material, resulting in more efficient destruction and the formation of compounds that counteracted the flux enhancement

Autocorrelation of Random Matrix Polynomials

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions

Crystallization of random trigonometric polynomials

We give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing. This can be viewed as a toy model of crystallization in one dimension. In particular we determine the asymptotics of the distribution of the roots around the crystalline configuration and find that the distribution is not Gaussian.Comment: 10 pages, 3 figure

Adding value and meaning to coheating tests

Purpose: The coheating test is the standard method of measuring the heat loss coefficient of a building, but to be useful the test requires careful and thoughtful execution. Testing should take place in the context of additional investigations in order to achieve a good understanding of the building and a qualitative and (if possible) quantitative understanding of the reasons for any performance shortfall. The paper aims to discuss these issues. Design/methodology/approach: Leeds Metropolitan University has more than 20 years of experience in coheating testing. This experience is drawn upon to discuss practical factors which can affect the outcome, together with supporting tests and investigations which are often necessary in order to fully understand the results. Findings: If testing is approached using coheating as part of a suite of investigations, a much deeper understanding of the test building results. In some cases it is possible to identify and quantify the contributions of different factors which result in an overall performance shortfall. Practical implications: Although it is not practicable to use a fully investigative approach for large scale routine quality assurance, it is extremely useful for purposes such as validating other testing procedures, in-depth study of prototypes or detailed investigations where problems are known to exist. Social implications: Successful building performance testing is a vital tool to achieve energy saving targets. Originality/value: The approach discussed clarifies some of the technical pitfalls which may be encountered in the execution of coheating tests and points to ways in which the maximum value can be extracted from the test period, leading to a meaningful analysis of the building's overall thermal performance