Characterization and computation of canonical tight windows for Gabor frames

Let $(g_{nm})_{n,m\in Z}$ be a Gabor frame for $L_2(R)$ for given window $g$. We show that the window $h^0=S^{-1/2} g$ that generates the canonically associated tight Gabor frame minimizes $\|g-h\|$ among all windows $h$ generating a normalized tight Gabor frame. We present and prove versions of this result in the time domain, the frequency domain, the time-frequency domain, and the Zak transform domain, where in each domain the canonical $h^0$ is expressed using functional calculus for Gabor frame operators. Furthermore, we derive a Wiener-Levy type theorem for rationally oversampled Gabor frames. Finally, a Newton-type method for a fast numerical calculation of \ho is presented. We analyze the convergence behavior of this method and demonstrate the efficiency of the proposed algorithm by some numerical examples

Dutch listeners' use of suprasegmental cues to English stress

Dutch listeners outperform native listeners in identifying syllable stress in English. This is because lexical stress is more useful in recognition of spoken words of Dutch than of English, so that Dutch listeners pay greater attention to stress in general. We examined Dutch listeners’ use of the acoustic correlates of English stress. Primary- and secondary-stressed syllables differ significantly on acoustic measures, and some differences, in F0 especially, correlate with data of earlier listening experiments. The correlations found in the Dutch responses were not paralleled in data from native listeners. Thus the acoustic cues which distinguish English primary versus secondary stress are better exploited by Dutch than by native listeners

On Lerch's transcendent and the Gaussian random walk

Let $X_1,X_2,...$ be independent variables, each having a normal distribution with negative mean $-\beta<0$ and variance 1. We consider the partial sums $S_n=X_1+...+X_n$, with $S_0=0$, and refer to the process $\{S_n:n\geq0\}$ as the Gaussian random walk. We present explicit expressions for the mean and variance of the maximum $M=\max\{S_n:n\geq0\}.$ These expressions are in terms of Taylor series about $\beta=0$ with coefficients that involve the Riemann zeta function. Our results extend Kingman's first-order approximation [Proc. Symp. on Congestion Theory (1965) 137--169] of the mean for $\beta\downarrow0$. We build upon the work of Chang and Peres [Ann. Probab. 25 (1997) 787--802], and use Bateman's formulas on Lerch's transcendent and Euler--Maclaurin summation as key ingredients.Comment: Published at http://dx.doi.org/10.1214/105051606000000781 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

High voltage solid-state relay

Hybrid microelectronics relay has characteristics significantly superior to conventional solid state relays. Relay provides 2500 Vdc input to output isolation and operates from high threshold logic signal to switch load of 400 Vdc at 2 mA. Technology should be of interest to manufacturers of discrete components

Heat buffers improve capacity and exploitation degree of geothermal energy sources

This research focuses on the role of heat buffers to support optimal use of combinations of traditional and renewable heat sources like geothermal heat for greenhouse heating. The objective was to determine the contribution of heat buffers to effective new combinations of resources that satisfy greenhouse heat, carbon dioxide and electricity demand at minimum cost. Tank buffers, basement buffers and aquifers were considered as short and long term buffers. Simulations were carried out for a 10ha sweet pepper and a 30ha tomato greenhouse (15ha intensively lighted). Standard heating systems based on central boiler and co-generation were used as a reference and compared with combinations of boilers, co-generators, geothermal heat and heat buffer strategies. Crop production and greenhouse climate were simulated and resource demand determined for normal greenhouse operation. A linear programming algorithm was used to apply resources and equipment available to the model at minimum cost. Results show that heat buffers help to reduce the required capacity of a geothermal heat source, and increase both the utilisation degree of the source and the cover percentage of greenhouse heat demand. The technically most feasible solution for long term buffering was the basement buffer which allows high buffer volumes without loss of useful space and heat loss contributes to greenhouse heating, however this solution was economically not feasible. Also the deep aquifer was a good option, however exploitation risks and manageability are potential problems. Integration of geothermal heat with other sources resulted in the best solutions that were both technically and economically feasible. Simulation showed at gas price level 30¿ct.m-3, that geothermal heat was cheaper than central boiler and even co-generation heat when hours of operation exceed 1000h.y-1. Instead of using large buffers, peak loads can also be covered by central boilers. Simulated solutions reduced gas consumption with 60 to 95%