If f is a Henstock-Kurzweil integrable function on the real line, the Alexiewicz norm of f is || f || = sup I | f I f| where the supremum is taken over all intervals I ⊂ . Define the translation τx by τxf(y) = f(y − x). Then ||τxf − f || tends to 0 as x tends to 0, i.e., f is continuous in the Alexiewicz norm. For particular functions, ||τxf − f || can tend to 0 arbitrarily slowly. In general, ||τxf − f || ≥ osc f|x| as x → 0, where osc f is the oscillation of f. It is shown that if F is a primitive of f then ||τxF − F || || ≤ ||f || |x|. An example shows that the function y → τxF(y) − F(y) need not be in L 1 . However, if f ∈ L 1 then || τxF − Fk1 || ≤ || f ||1|x|. For a positive weight function w on the real line, necessary and sufficient conditions on w are given so that ||(τxf − f)w || → 0 as x → 0 whenever fw is Henstock-Kurzweil integrable. Applications are made to the Poisson integral on the disc and half-plane. All of the results also hold with the distributional Denjoy integral, which arises from the completion of the space of Henstock-Kurzweil integrable functions as a subspace of Schwartz distributions.
The possibility of simultaneously ušed chlorophyll (Chl) synthesis precursor (glutamic acid) and metal chelator (2,2'-dipyridyl) as a photodynamic inhibitor of the chlorophyll synthesis was studied. Wheat {Triticum aestivum L.) and vegetable marrow {Cucurbita moschata Duch.) leaves were treated with 2,2'-dipyridyl (2,2'- DP), and 2,2'-DP along with glutamic acid which increased the protochlorophyllide (Pchlide) content in the vegetable marrow plants to a higher extent. An irradiation of the treated leaves caused an inhibition of Pchlide reduction which was more notable in those of the dicotyledonous vegetable marrow plant.
The Amur Grape (Vitis amurensis Rupr.) cultivars ’shuangFeng’ and ‘ZuoShanyi’ were grown in shelter greenhouse under natural sunlight and subjected to drought. Sap flow rate, net photosynthetic rate (PN), and chlorophyll (Chl) fluorescence were measured on Amur Grape leaves subjected to different drought treatments. Significant decreases in P N were associated with increasing intercellular CO2 concentration (Ci), suggesting that the reduction in PN was caused by nonstomatal limitation. Analysis of OJIP transients according to the JIP-test protocol revealed that specific (per PSII reaction center) energy fluxes for light absorption, excitation energy trapping and electron transport have significantly changed. The appearance of a pronounced K-step and J-step in polyphasic rise of fluorescence transient suggested the oxygen-evolving complex and electron transport were inhibited. Drought stress has relatively little effect on the parameter maximal quantum yield of PSII photochemistry (Fv/Fm), but the performance index (PIABS) is more sensitive in different drought treatment. There are cultivar differences in the response of PSII activity to drought, the photosynthetic apparatus of ‘ZuoShanyi’ cultivar is more resistant to drought than that of ‘ShuangFeng’, and JIP-test could be a useful indicator for evaluation and selection to drought tolerance., Z. X. Wang ... [et al.]., and Obsahuje bibliografii