The maximum modulus of a trigonometric trinomial

Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda

Optimal actuator design based on shape calculus

An approach to optimal actuator design based on shape and topology optimisation techniques is presented. For linear diffusion equations, two scenarios are considered. For the first one, best actuators are determined depending on a given initial condition. In the second scenario, optimal actuators are determined based on all initial conditions not exceeding a chosen norm. Shape and topological sensitivities of these cost functionals are determined. A numerical algorithm for optimal actuator design based on the sensitivities and a level-set method is presented. Numerical results support the proposed methodology.Comment: 41 pages, several figure

Isomorphie

Bezeichnung für die 1:1-Beziehung zwischen Ausdruck und Bedeutung

The health impact of urban poor housing and environmental conditions

If health were considered a product, medical care would simply be one input used in producing it. Unfortunately, the economics literature generally ignores this. Research just focuses on medical care, medical insurance, and the workings of its markets. But as Arrow (1963) himself admits, "particularly at low levels of income, other commodities such as nutrition, shelter, clothing, and sanitation may be much more significant" than medical care as causal factors in health

Democracy, Globalization and Private Investment in Ghana

The article examines the effects of democracy and globalization on private investment in Ghana for the period 1980–2012, using the autoregressive distributed lag (ARDL) bounds test for cointegration and the error correction model (ECM). Two models are used. In Model 1, democracy is proxy by an index for institutional quality (Polity 2), while Model 2 uses an index for civil liberties as proxy for democracy. The results for Model 1 show globalization and public investment increase private investment, while exchange rate volatility and trade openness decrease private investment in both the long and short run. In addition, national income and interest rate reduce private investment in the short run. In the case of Model 2, credit to the private sector and public investment increase private investment, while exchange rate volatility and trade openness decrease private investment in both the long and short run. Finally, national income and interest rate reduce private investment in the short run. The findings and policy recommendations of the article provide vital information for policy implementation in Ghana

Energy cycle associated with inter-member variability in a large ensemble of simulations with the Canadian RCM (CRCM5)

In an ensemble of Regional Climate Model\ud (RCM) simulations where different members are initialised\ud at different times but driven by identical lateral\ud boundary conditions, the individual members provide\ud different, but equally acceptable, weather sequences.\ud In others words, RCM simulations exhibit the phenomenon\ud of Internal Variability (or inter-member variability—\ud IV), defined as the spread between members in an\ud ensemble of simulations. Our recent studies reveal that\ud RCM’s IV is associated with energy conversions similar\ud to those taking place in weather systems. By analogy\ud with the classical work on global energetics of weather\ud systems, a formulation of an energy cycle for IV has been\ud developed that is applicable over limited-area domains.\ud Prognostic equations for ensemble-mean kinetic energy\ud and available enthalpy are decomposed into contributions\ud due to ensemble-mean variables and those due to\ud deviations from the ensemble mean (IV). Together these\ud equations constitute an energy cycle for IV in ensemble\ud simulations of an RCM. A 50-member ensemble of\ud 1-year simulations that differ only in their initial conditions\ud was performed with the fifth-generation Canadian\ud RCM (CRCM5) over an eastern North America domain.\ud The various energy reservoirs of IV and exchange terms\ud between reservoirs were evaluated; the results show a\ud remarkably close parallel between the energy conversions\ud associated with IV in ensemble simulations of RCM and the energy conversions taking place in weather systems\ud in the real atmosphere