A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chvátal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces where each nonzero distance equals $1$ or $2$.
The responses to root oxygen deficiency conceming the photosynthesis, saccharide contents and minerál uptake háve been investigated in Carex species, which were different in their anoxia-tolerance. The net rate of photosynthesis (Fn) anoxia- sensitive C. extensa was not affected by root anaerobiosis. Despite short-term effects of root anaerobiosis on values in the anoxia-tolerant species C. remota and C. pseudocyperus, root oxygen supply did not influence P^, when the plants were allowed to acclimate. The saccharide contents of the anoxia-tolerant species were almost not affected by prolonged anaerobiosis. 40 days of root oxygen deficiency led to significant changes in the shoot saccharide composition of C. extensa: contents of glucose and fructose were increased 4-fold and sucrose content was significantly decreased. In the roots no sucrose could be detected, but the starch content was increased, and the glucose and fructose contents did not change when compared with aerobic conditions. Under anaerobic conditions, minerál uptake of the anoxia- sensitive species decreased by 50 %, while the minerál uptake of the anoxia-tolerant species was significantly increased or did not change at all, in comparison with the aerobic conditions. The growth reduction of C. extensa under anaerobic conditions was therefore primarily due to inability to také up an adequate amount of nutrients.
Simultaneous measurements of net photosynthetic rate {P^ and fluorescence were taken on flag leaves of fíeld-grown wheat {Triíicum aestivum L., Thlicum durum L.) from anthesis to senescence. By using leaf discs inaintained in saturating CO2 in tlie O2 electrode we found that the electron transport measured by fluorescence, and that calculated from O2 evolution rate were similar througliout the experimental period, which indicated that fluorescence might be ušed to measure the linear electron transport rate. In field measurements on intact attached leaves, the electron transport rate declined less than during leaf senescence, Measurements taken in the aftemoon indicated that the electron transport remained constant during the day while slightly decreased. Thus, in fíeld-grown wheat leaves photoinhibition was not a relevant phenomenon. When the alternativě electron routes were negligible, the increasing discrepancy between Pn and the electron transport during leaf senescence could be explained by an increment in photorespiration rate (Pp), The change of oxygenation to carboxylation ratio (Vq/Vj,) might be caused by increasing resistances to CO2 diffusion in the leaf CO2 lost through photorespiration was about half of that fixed with Pn in the sun-exposed leaves. Yet Pp was lower in the basal part of leaves which mostly grew in shade. Fluorescence coupled with gas exchange proved to be a useful method for evaluation of the photorespiratory losses in field conditions.
A possible optimal way of measurement and computer evaluation of the locally-shift invariant modulation transfer function of a given digital video-camera in its photographical regime is described in this article. Such a way is based on exploitation of the power spectral density of a static two-dimensional reflection random chart, incoherently illuminated by the white light, and its digital electro-optical image. This chart simulates the white-noise distribution. For its production and for evaluation of the imagedata, the specially developed computer programs were exploited under framework of the computer tool MATLAB 6.5. The chosen evaluational procedure follows from the presented spectral transfer equations containing the squared modulation transfer function which was then smoothed needfully in addition. Some obtained results are presented graphically under the pixel scale of relative spatial frequencies and also evaluated in view of the utilized different camera pixel resolutions and image gathering quality levels. They demonstrate the possibility of the exploited evaluational way to compare the image quality of the digital video-camera under chosen imaging conditions already mentioned. and Článek pojednává o možném optimálním způsobu měření a počítačového vyhodnocování lokálně invariantní funkce přenosu modulace dané digitální videokamery ve fotografickém režimu pomocí spektrální hustoty výkonu bílým světlem nekoherentně osvětleného statického dvourozměrného reflexního náhodného testu a jeho digitálního elektrooptického obrazu. Tento test simuluje bílý šum a k jeho výrobě a k vyhodnocování obrazových dat bylo využito speciálně vyvinutých programů v rámci počítačového prostředí MATLAB 6.5. Zvolený vyhodnocovací postup vyplývá z prezentovaných spektrálních přenosových rovnic obsahujících kvadrát zjišťované funkce přenosu modulace, který byl potom navíc požadovaně vyhlazen. Některé získané výsledky jsou prezentovány graficky v pixelové škále relativních prostorových frekvencí a zhodnoceny se zřetelem k využitým rozdílným efektivním kamerovým pixelovým rozlišením a kvalitám obrazového snímání. Potvrzují, že využitý vyhodnocovací způsob umožňuje srovnávat zobrazovací kvalitu digitální videokamery při zmíněných volbách zobrazovacích podmínek.