On Time-Bounded Incompressibility of Compressible Strings and Sequences

For every total recursive time bound $t$, a constant fraction of all compressible (low Kolmogorov complexity) strings is $t$-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of which every initial segment of length $n$ is compressible to $\log n$ yet $t$-bounded incompressible below ${1/4}n - \log n$; and there are countable infinitely many recursive infinite sequence of which every initial segment is similarly $t$-bounded incompressible. These results are related to, but different from, Barzdins's lemma.Comment: 9 pages, LaTeX, no figures, submitted to Information Processing Letters. Changed and added a Barzdins-like lemma for infinite sequences with different quantification oreder, a fixed constant, and uncountably many sequence

Oxygen supply and consumption in soilless culture: evaluation of an oxygen simulation model for cucumber

A soil oxygen simulation model (OXSI) was tested and evaluated for evaluating growing media with respect to aeration. In the model, local oxygen concentrations are calculated from coefficients of diffusion and consumption (respiration), assuming equilibrium conditions. Apparent oxygen diffusion coefficients (D) were determined under laboratory conditions in 5 cm high samples at different water contents (-3.2, -10 and -20 cm pressure heads). D values were positively related to air-filled porosity (AFP). For fine-graded perlite D ranged from 9.10-7 at AFP of 34 percent to 5.10-9 m2s-1 at AFP of 19 percent. Possibly due to absence of closed pores in rockwool, the AFP vs. D relation was different for rockwool compared to perlite: D for rockwool ranged from 2.10-6 at AFP of 56 percent to 3.10-9 m2s-1 at AFP of 3 percent. A greenhouse experiment with cucumber was carried out to determine respiration and realised oxygen concentrations. The cucumbers were grown in 20 cm high, 3.5 litre containers filled with fine-graded perlite and supplied with high-frequency irrigation. AFP varied between 25 and 45 percent. At three heights and on four occasions during growth, oxygen concentration ( f volume) in the medium varied between 16.6 and 20 n the perlite. Root respiration of the cucumbers as determined by two independent methods (in vivo and in vitro) ranged from 1.4 to 5.4 10-6 ml.ml-1.s-1. Using these respiration rates, OXSI calculated that no oxygen depletion may occur at D > 1 to 5 10-7 m2s-1, corresponding with an AFP of 30 percent for both perlite and rockwool. Anoxic condtions were calculated for D values of 10-8 m2s-1, corresponding with AFP below 10 percent for rockwool and 20 percent for perlite

Characterizing Distance-Regularity of Graphs by the Spectrum

AMS classifications: 05E30; 05B20distance-regular graphs;eigenvalues;cospectral graphs