Furlable antenna

An improved furlable antenna particularly suited for use in a celestial space environment is described. The antenna is characterized by an actuator comprising an elastomeric member of an annular configuration, an annular array of uniformly spaced antenna ribs rigidly affixed at the base ends to an actuator which enables it to be supported for pivotal displacement from a deployed configuration. The ribs are radially extended from the actuator to a furled configuration. The ribs are extended parallel to the axis of the actuator with flexible reflecting web affixed to the ribs, with angularly spaced bearing blocks

Corrigendum to "The holomorphic flow of the Riemann Zeta function"

Theorem 4.5 of [2], describing the topological type of the zeros of the flow s˙ = ζ(s) at reflected points off the critical line, claiming they were the same, contains an error. We gratefully acknowledge Professor Cevat Gokcek for pointing out the error to us

Linear law for the logarithms of the Riemann periods at simple critical zeta zeros

Each simple zero 1/2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow s˙ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn →∞, log Tn ≥ π/4 γn + O(log γn). Numerical evaluation leads to the conjecture that this inequality can be replaced by an equality. Assuming the Riemann Hypothesis and a zeta zero separation conjecture γn+1 − γn≥ γn-θ for some exponent θ > 0, we obtain the upper bound log Tn ≤ γn2 + θ Assuming a weakened form of a conjecture of Gonek, giving a bound for the reciprocal of the derivative of zeta at each zero, we obtain the expected upper bound for the periods so, conditionally, log Tn = π/ 4 γn +O(log γn). Indeed, this linear relationship is equivalent to the given weakened conjecture, which implies the zero separation conjecture, provided the exponent is sufficiently large. The frequencies corresponding to the periods relate to natural eigenvalues for the Hilbert–Polya conjecture. They may provide a goal for those seeking a self-adjoint operator related to the Riemann hypothesis

Consumer Demand and Labor Supply (scanned out-of-print 1981 Elsevier book)

The following highly-cited research monograph, although widely available in libraries, is now out of print: William A. Barnett, Consumer Demand and Labor Supply, North Holland, Amsterdam, 1981. In case you do not have access to the printed book, I have scanned it and put it online below. Since scanners are not perfect at scanning mathematics, you should prefer the printed book, if you can borrow it from a library. Otherwise, you are free to read any of its chapters online. The chapters in this Table of Contents are hyperlinked to the online chapters.consumer demand, labor supply, systemwide models, systems of equations, aggregation theory, index number theory, Divisia, household production, simultaneous estimation

Supply of Money

This short paper is the encyclopedia entry on Supply of Money to appear in the second edition of the International Encyclopedia of the Social Sciences. The encyclopedia is edited by William A. Darity and forthcoming from Macmillan Reference USA (Thomson Gale).monetary aggregation; index number theory; Divisia index; encyclopedia entry; aggregation theory; supply of money

Is Macroeconomics a Science?

This paper was written as the first draft of the invited Foreword for the book, Money and the Economy, by Apostolos Serletis. The paper provides a critical view of those areas in which methodology in economics deviates from that in the physical sciences, provides examples and illustrations of those deviations, and emphasizes those areas of and approaches to economic research that most closely correspond with the nature of research in the physical sciences.science; social science; politics; Federal Reserve; monetary policy

The holomorphic flow of the Riemann zeta function

The flow of the Riemann zeta function, ś = ς(s), is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases the zero is a sink. To produce these portraits, the zeta function was evaluated numerically to 12 decimal places, in the region of interest, using the Chebyshev method and using Mathematica. The phase diagrams suggest new analytic properties of zeta, of which some are proved and others are given in the form of conjectures

Population need and geographical access to general practitioners in rural New Zealand

To use a geographical information system (GIS) approach to demonstrate the extent to which different areas in New Zealand vary in their geographical access to GPs, and to analyse the extent to which spatial access varies in relation to different population groups. Methods Three methods; population/GP ratios, least cost path analysis (LCPA), and an allocation method (which considered the capacity constraint of GPs) were used to demonstrate differences in geographic accessibility to GPs. Travel time, and distance to the closest GP, was calculated for every census enumeration district in New Zealand (n=38336)—thus enabling population-based accessibility statistics to be calculated and aggregated to the territorial local authority level. These calculations include the average travel time if everybody visited a GP once and the population more than 30 minutes from a GP. The composition of this population is analysed according to three criteria of need: the level of deprivation (NZDep2001), ethnicity (%Maori), and age (% <5 years, and %65 years and over). Results There are significant regional variations in geographical accessibility in New Zealand, and these differences are dependent upon the method to calculate accessibility. Ratio measures give a different picture of GP access than the other two indicators, reflecting the fact that TAs with similar ratios often have wide variations in travel times as well as the size and proportion of the population living more than 30 minutes from the closest GP. TAs with larger numbers and a higher proportion of their populations living in such areas tend to be more deprived and have a higher proportion of Maori, especially in the North Island. There appears to be no significant trend by age. Conclusion Given the health and service consequences of poor access, the results suggest that more attention needs to be paid to extending the spatial information base in primary care, in order to achieve more effective planning of services for disadvantaged populations

Rotterdam vs Almost Ideal Models: Will the Best Demand Specification Please Stand Up?

Among the many demand specifications in the literature, the Rotterdam model and the Almost Ideal Demand System (AIDS) have particularly long histories, have been highly developed, and are often applied in consumer demand systems modeling. Using Monte Carlo techniques, we seek to determine which model performs better in terms of its ability to recover the true elasticities of demand. We derive the correct formulae for the AIDS models elasticities, when the Törnqvist or two modified versions of the Stone index are used to linearize the model. The resulting linearized AIDS are compared to the full AIDS

Boundary quasi-orthogonality and sharp inclusion bounds for large Dirichlet eigenvalues

We study eigenfunctions and eigenvalues of the Dirichlet Laplacian on a bounded domain \Omega\subset\RR^n with piecewise smooth boundary. We bound the distance between an arbitrary parameter $E > 0$ and the spectrum $\{E_j \}$ in terms of the boundary $L^2$-norm of a normalized trial solution $u$ of the Helmholtz equation $(\Delta + E)u = 0$. We also bound the $L^2$-norm of the error of this trial solution from an eigenfunction. Both of these results are sharp up to constants, hold for all $E$ greater than a small constant, and improve upon the best-known bounds of Moler--Payne by a factor of the wavenumber $\sqrt{E}$. One application is to the solution of eigenvalue problems at high frequency, via, for example, the method of particular solutions. In the case of planar, strictly star-shaped domains we give an inclusion bound where the constant is also sharp. We give explicit constants in the theorems, and show a numerical example where an eigenvalue around the 2500th is computed to 14 digits of relative accuracy. The proof makes use of a new quasi-orthogonality property of the boundary normal derivatives of the eigenmodes, of interest in its own right.Comment: 18 pages, 3 figure