The concepts of an annihilator and a relative annihilator in an autometrized $l$-algebra are introduced. It is shown that every relative annihilator in a normal autometrized $l$-algebra $\mathcal {A}$ is an ideal of $\mathcal {A}$ and every principal ideal of $\mathcal {A}$ is an annihilator of $\mathcal {A}$. The set of all annihilators of $\mathcal {A}$ forms a complete lattice. The concept of an $I$-polar is introduced for every ideal $I$ of $\mathcal {A}$. The set of all $I$-polars is a complete lattice which becomes a two-element chain provided $I$ is prime. The $I$-polars are characterized as pseudocomplements in the lattice of all ideals of $\mathcal {A}$ containing $I$.
The organo-mineral coatings of soil aggregates, cracks, and biopores control sorption and macropore-matrix exchange during preferential flow, in particular in the clay-illuvial Bt-horizon of Luvisols. The soil organic matter (SOM) composition has been hypothesized to explain temporal changes in the hydraulic properties of aggregate surfaces. The objective of this research was to find relations between the temporal change in wettability, in terms of droplet infiltration dynamics, and the SOM composition of coated and uncoated aggregate surfaces. We used 20 to 40 mm sized soil aggregates from the Bt2 horizon of a Haplic Luvisol from loess that were (i) coated, (ii) not coated (both intact), and (iii) aggregates from which coatings were removed (cut). The SOM composition of the aggregate surfaces was characterized by infrared spectroscopy in the diffuse reflection mode (DRIFT). A potential wettability index (PWI) was calculated from the ratio of hydrophobic and hydrophilic functional groups in SOM. The water drop penetration times (WDPT) and contact angles (CA) during droplet infiltration experiments were determined on dry and moist aggregate samples of the three types. The decrease in the CA with time was described using the power function (CA(t) = at–b). For dry aggregates, the WDPT values were larger for coated as compared to uncoated regions on the aggregate surfaces, and increased with increasing PWI value (R2 = 0.75). The a parameter was significantly related to the WDPT (R2 = 0.84) and to the PWI (R2 = 0.64). The relations between the b parameter and the WDPT (R2 = 0.61) and the PWI (R2 = 0.53) were also significant. The WDPT values of wet soil aggregates were higher than those of dry aggregates due to high water contents, which limited the droplet infiltration potential. At the wet aggregate surfaces, the WDPT values increased with the PWI of the SOM (R2 = 0.64). In contrast to dry samples, no significant relationships were found between parameters a or b of CA(t) and WDPT or PWI for wet aggregate surfaces. The results suggest that the effect of the SOM composition of coatings on surface wettability decreases with increasing soil moisture. In addition to the dominant impact of SOM, the wettability of aggregate surfaces could be affected by different mineralogical compositions of clay in coatings and interiors of aggregates. Particularly, wettability of coatings could be decreased by illite which was the dominant clay type in coatings. However, the influence of different clay mineral fractions on surface wettability was not due to small number of measurements (2 and 1 samples from coatings and interiors, respectively) quantified.
The paper deals with the branch of imaging optics based on diffraction, and a special attention is concentrated on diffraction elements, which are not restricted on the paraxial space. The analysis is related first of all to distribution of rings on the element. Discussed are both plane and particularly spherical substrates of elements. The elements can not be designed for the object in infinity and therefore the image at the focusing distance only as it is in the original configuration, but for the axial object and image points in finite distances as well. The most general example of the element on the spherical substrate and design points in finite distances is an extend of the author’s previous paper published in a foreign journal. and Článek se zabývá oborem zobrazovací optiky založené na difrakci, zvláštní pozornost je věnována difrakčním prvkům, které se neomezují na paraxiální prostor. Analýza se týká především rozložení kroužků na prvku. Jsou diskutovány jak rovinné podložky prvků, tak zejména podložky kulové. Tyto prvky nemusejí být navrhovány pouze na předmět v nekonečnu, a tedy obraz v ohniskové rovině, jak je tomu u výchozí konfigurace, ale na osový předmětový i obrazový bod v konečných vzdálenostech. Nejobecnější případ prvku na kulové podložce a návrhových bodů v konečných vzdálenostech je rozšířením autorovy dřívější práce v zahraničním časopisu.