Sampling the Flow of a Bandlimited Function

We analyze the problem of reconstruction of a bandlimited function f from the space–time samples of its states $$f_t=\phi _t*f$$ f t = ϕ t ∗ f resulting from the convolution with a kernel $$\phi _t$$ ϕ t . It is well-known that, in natural phenomena, uniform space–time samples of f are not sufficient to reconstruct f in a stable way. To enable stable reconstruction, a space–time sampling with periodic nonuniformly spaced samples must be used as was shown by Lu and Vetterli. We show that the stability of reconstruction, as measured by a condition number, controls the maximal gap between the spacial samples. We provide a quantitative statement of this result. In addition, instead of irregular space–time samples, we show that uniform dynamical samples at sub-Nyquist spatial rate allow one to stably reconstruct the function $$\widehat{f}$$ f ^ away from certain, explicitly described blind spots. We also consider several classes of finite dimensional subsets of bandlimited functions in which the stable reconstruction is possible, even inside the blind spots. We obtain quantitative estimates for it using Remez-Turán type inequalities. En route, we obtain Remez-Turán inequality for prolate spheroidal wave functions. To illustrate our results, we present some numerics and explicit estimates for the heat flow problem.

Experimental and Numerical Investigation of the Surface Layer Conditions after Carbonitriding of Powder Metallurgical Steels. Part 1: Diffusion in Components of Graded Porosity

Case hardening processes such as carbonitriding can be used to improve the performance of powder metallurgical structural components. Due to the amount of carbon and nitrogen introduced, it is possible to adjust the hardness and residual stress of the surface layer. Due to their porosity, powder metallurgical components show a significantly increased diffusivity and therefore increased demands on the process control. In order to be able to make a quantitative statement about the effects of diffusivity as a function of porosity, common densities of 6.9 g/cm3, 7.2 g/cm3and 7.35 g/cm3for PM-steel are examined in a total of ten process sequences. By means of simulative approaches, the resulting element depth profiles can be calculated and the surface layer condition can be predicted by a subsequent heat treatment simulation. In a two-part work, the mass transport during carbonitriding is investigated in the first part and the resulting surface layer conditions after heat treatment in the second part. By considering different process combinations and porosities, model approaches of volume and pore diffusion can be formulated and quantitative element depth profiles can be predicted and validated depending on the process parameters. ◼

Efficacy of Canadian health warning statements on caffeinated energy drinks: an experimental study among young Canadians

The current study examined the efficacy of health warnings on caffeinated energy drinks (CEDs). Participants aged 12–24 years (n = 2040) completed an online survey where they were asked to recall any existing warning statements on CED products and were randomized to one of 29 experimental warning conditions. Regression models were fitted to examine differences between conditions in product appeal, perceived safety and message recall. Overall, fewer than 30% of participants were able to accurately describe an existing CED product warning. Experimental findings indicated that exposure to CEDs with warning labels resulted in greater recall. Warnings on the back of CED cans featuring large font, a border, and a ‘caution’ heading resulted in significantly greater recall (P < 0.05 for all). Front-of-package ‘High source of caffeine’ labels resulted in greater recall than a quantitative description (P < 0.001); caffeine labels generally elicited lower product appeal (P < 0.001) and perceived safety (P = 0.002) ratings vs. no caffeine labels, and the qualitative caffeine statement elicited lower perceived safety ratings than the quantitative statement (P = 0.02). Existing warning statements in Canada have low levels of awareness. Warnings on CEDs could be enhanced to increase the salience of messages, with greater impact from clear, descriptive, front-of-package ‘High source of caffeine’ labels.

Sign Changes of Kloosterman Sums with Almost Prime Moduli. II: Corrigendum

We give a corrigendum to the previous paper [ 8] and recover the same quantitative statement: the Kloosterman sum changes sign infinitely often as the modulus runs over squarefree numbers with at most seven prime factors.

Analysis of Subdaily Meteorological Measurements by Louis Morin in the Late Maunder Minimum 1665 – 1713 in Paris

<p>Based on copies of the original data (source: Oeschger Center for Climate Change Research) we perform climate reconstructions for Paris. The focus lies on the following meteorological variables: temperature, cloudiness, moving direction of clouds and precipitation. We assess the early instrumental temperature dataset with state of the art statistical methods to get further knowledge of inhomogeneities. There are already several studies showing monthly and yearly means of the temperature, but a detailed statistical analysis based on the original measurements has not been done yet. Due to the lack of metadata, we do a qualitative analysis. With rare contemporary time series, like the CET (Central England Temperature), and proxydata, like grape harvest dates, we attempt to make a quantitative statement. We analyse and discuss the documentary datasets of the cloudiness and the moving direction of the clouds relating to the cooling in the Late Maunder Minimum. Because of the subjective character of documentary records, we compare these results with available data from former publications. Precipitation is given in terms of intensity and duration. We calculate indices like rainfall frequency and average rainfall per year/season/month.</p>

Verification of Redox Flow Batteries’ Functionality by Electrochemical Impedance Spectroscopy Tests

The state-of-the-art functionality test of classic redox-flow-stacks measures the current–voltage characteristic with the technical electrolyte. This research paper aims to simplify the validation of redox flow batteries’ functionality by conducting electrochemical impedance spectroscopy (EIS) on redox flow stacks. Since the electrolyte used in the batteries is usually toxic and aggressive, it would be a significant simplification to verify the functionality with an alternative, non-toxic fluid. EIS measurements on batteries with larger sized electrodes, multiple cells, and different fluids were performed. It was demonstrated that all impedances are repeatable, thereby validating this procedure as a qualification method for full-size and complex batteries with an alternative fluid. EIS measurements were able to detect deliberately manipulated cells. This research uses three different analysis methods for the acquired data to identify errors. The respective approaches are, firstly, (1) a comparison of the Nyquist plots; secondly, (2) a comparison of the Bode plots; and thirdly, (3) a comparison of the calculated characteristic values of the equivalent circuits. The analysis found that all methods are suitable to detect errors in the batteries. Nevertheless, the bode-plot comparison method proves to be especially advantageous, because it enables a quantitative statement.

The Koreans in Second World War Philippines: Rumour and history

‘Mas malupit ang mga Koreano kaysa mga Hapon’ is a rumour about Koreans in Second World War Philippines that has persisted to this day. A comparative, quantitative statement, it is roughly translated as ‘The Koreans committed more atrocities than the Japanese in Second World War Philippines’. This is a half-true memory: true, there were Koreans in the Philippines; false, they could not have committed more atrocities than the Japanese because there were very few of them, as archival evidence discussed in this article proves. If only the Koreans and their role in the war were properly discussed in Philippine textbooks, this rumour would not have persisted to this day.