SPECIAL QUADRATURE ERROR ESTIMATES AND THEIR APPLICATION IN THE HARDY-LITTLEWOOD MAJORANT PROBLEM
The Hardy-Littlewood majorant problem has a positive answer only for exponents p which are even integers, while there are counterexam- ples for all p = 2 2N. Montgomery conjectured that there exist counterex- amples even among idempotent polynomials. This was proved recently by Mockenhaupt and Schlag with some four-term idempotents. However, Mockenhaupt conjectured that even the classical 1 + e 2ix e 2i (k+2)x three-term character sums, should work for all 2k < p < 2k + 2 and for all k 2 N. In two previous papers we proved this conjecture for k = 0;1;2;3;4, i.e. in the range 0 < p < 10, p = 2 2N. Here we demonstrate that even the k = 5 case holds true. Renements in the technical features of our approach include use of total variation and integral mean estimates in error bounds for a certain fourth order quadrature. Our estimates make good use of the special forms of functions we encounter: linear combinations of powers and powers of log- arithms of absolute value squares of trigonometric polynomials of given degree. Thus the quadrature error estimates are less general, but we can nd better constants which are of practical use for us.
Concentration of the Integral Norm of Idempotents
This chapter is a companion of a recent paper, entitled Integral concentration of idempotent trigonometric polynomials with gaps. New results of the present work concern L 1 concentration, while the above-mentioned paper deals with L p concentration. Our aim here is twofold. First we try to explain methods and results, and give further straightforward corollaries. On the other hand, we also push forward the methods to obtain a better constant for the possible concentration (in the L 1 norm) of an idempotent on an arbitrary symmetric measurable set of positive measure. We prove a rather high level γ1 > 0. 96, which contradicts strongly the conjecture of Anderson et al. that there is no positive concentration in the L 1 norm. The same problem is considered on the group \(\mathbb{Z}/q\mathbb{Z}\), with q, say, a prime number. There, the property of absolute integral concentration of idempotent polynomials fails, which is in a way a positive answer to the conjecture mentioned above. Our proof uses recent results of B. Green and S. Konyagin on the Littlewood problem.
Full-scale measurements of SO2 gas phase concentrations and slurry compositions in a wet flue gas desulphurisation spray absorber
Abstract Two measurement campaigns were carried out at ENERGI E2's Asnaes Power plant, unit 5. The unit has a capacity of 620 MW e and is equipped with a wet flue gas desulphurisation (FGD) plant employing a counter-current spray absorber with five spray levels. In the first campaign, the power plant was firing Orimulsion ® with 2.85 wt% S resulting in a flue gas concentration of SO 2 exceeding 2000 ppmv. In the second campaign, the fuel applied was a low-S blended coal and the SO 2 concentration in the raw gas was around 400 ppmv. A novel probe for in situ sampling of gas phase concentrations in wet FGD spray absorbers was developed and applied for measuring axial profiles of the SO 2 gas phase concentrations in the absorber. The expected decrease in SO 2 concentrations along the height of the absorber was found in the spray section (from height 26.5 to 36.2 m) whereas the SO 2 concentration above the holding tank and below the gas inlet was quite low probably due to long local residence times in the region. Horizontal variations, due to somewhat different flow conditions near the column wall were investigated and the SO 2 concentrations were found to be higher near the wall. Measurements at different gross loads showed that the SO 2 gas phase concentration at a given position inside the absorber was roughly linearly related to the L/G ratio in the measuring interval. Turning off one of the lower spray levels, while burning coal with low S content, did not lower the overall removal efficiency of the absorber. However, the SO 2 gas phase concentration inside the lower part of the absorber was increased by a factor of 2–3. Measurements of slurry pH at different positions showed a decrease of approximately 0.5 units from the upper to the lower part of the absorber. The full-scale measurements provide a detailed set of experimental data for validation of mathematical models of a wet FGD spray absorber.