A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.
This paper presents closed form solution for unsteady flow equation corresponding to the transient hydraulic head, flow rate and volumetric exchange of a confined aquifer which is in contact with a constant piezometric head at one end and a stream whose water level is rising at a constant rate at the other end. The aquifer is also subjected to receive constant inflow due to rain infiltration. The unsteady groundwater flow equation is solved using Laplace transform to get analytical expressions for the transient hydraulic head and flow rate at the left and right interfaces and the net volumetric exchange of water at the aquifer-stream interface. The analytical results presented here show the effect of recharge due to rain infiltration on the net volumetric exchange and reveal the conditions for which net inflow in the aquifer could be positive, negative or zero. The results obtained have the capability to determine transient hydraulic head for two extreme scenarios: (i) very slow rise and (ii) very fast rise in the stream water. Analytical result show that the net volumetric exchange could be positive, zero or negative depending on the surface infiltration and stream water rise rate. and Príspevok obsahuje analytické riešenie rovnice neustáleného prúdenia vzhľadom na neustálenú hydraulickú výšku, rýchlosť prúdenia a objemové toky vo zvodnenom kolektore s napätou hladinou, ktorý je v kontakte s konštantnou piezometrickou výškou na jednej strane a s tokom s konštantne sa zvyšujúcou hladinou vody na strane druhej. Zvodnený kolektor je tiež napájaný konštantnou rýchlosťou infiltrovanou vodou zo zrážok. Rovnica neustáleného prúdenia podzemnej vody je riešená s použitím Laplaceovej transformácie, aby sme získali neustálenú tlakovú výšku na ľavej aj pravej strane a objemový prítok vody na rozhraní zvodnený kolektor - tok. Výsledky analytického riešenia, ktoré predkladáme, ukazujú vplyv infiltrácie zrážok na doplňovanie podzemnej vody a odhaľujú podmienky, za ktorých prítok do zvodneného kolektora môže byť kladný, negatívny, alebo nulový. Získané výsledky umožňujú určiť neustálené hydraulické výšky pre dva extrémne scenáre: (i) veľmi pomalé a (ii) veľmi rýchle zvýšenie hladiny vody v toku. Analytické riešenie ukazuje, že objem vody, ktorou je zvodnený kolektor doplňovaný, môže byť kladný, záporný, alebo nulový, v závislosti na intenzite infiltrácie a rýchlosti zvyšovania sa hladiny vody v toku.
Chaotic behaviour in the solar system is very often connected with resonance. Great progresses have been made in the last few years to relate the existence of the Kirkwood gaps with chaos. Uses of mappings have allowed cheap computations over millions of years. Unexpected intermittent increase of orbital eccentricities due to the existence of thin chaotic zone provides a mechanism for planetary close approach. However semi-analytical developments show that at least for the 2/1 resonance the problem remains open. Chaotic rotations of satellites like Hyperion or Miranda and chaotic motion of comets in nearly parabolic orbits are predicted and some physical implications discussed. Both comet Halley and Hyperion appear to be good candidates for real examples of dynamical chaos in the solar system.
For the safe and economical design and operation of freight pipelines it is necessary to know slurry flow behaviour in inclined pipe sections, which often form significant part of pipelines transporting solids. Fine-grained settling slurry was investigated on an experimental pipe loop of inner diameter D = 100 mm with the horizontal and inclined pipe sections for pipe slopes ranging from –45° to +45°. The slurry consisted of water and glass beads with a narrow particle size distribution and mean diameter d50 = 180 μm. The effect of pipe inclination, mean transport volumetric concentration, and slurry velocity on flow behaviour, pressure drops, deposition limit velocity, and concentration distribution was studied. The study revealed a stratified flow pattern of the studied slurry in inclined pipe sections. Frictional pressure drops in the ascending pipe were higher than that in the descending pipe, the difference decreased with increasing velocity and inclination. For inclination less than about 25° the effect of pipe inclinations on deposition limit velocity and local concentration distribution was not significant. For descending pipe section with inclinations over –25° no bed deposit
was observed.
Irrespective of the originál habitat of cassava {Manihot esculenta Crantz) cultivars, net photosynthetic rate (P^) was substantially reduced in leaves developed in a cool climate as compared with warm-climate leaves. Cool-climate leaves paitially recovered their photosynthetic capacity after 7 d acclimation in warm climate. The hot-climate cultivar showed a broad optimum temperature from 30 to 40 "C, while the cool-climate cultivar showed an upward shift in optimum temperature in the acclimated and warm-climate leaves. In field-grown cassava, maximum of upper canopy leaves was greater than 40 pmol(C02) m'^ s'i when measured in high rainfall season and the rates did not show saturation by radiant energy up to 1800 pmol m'2 s'i PAR. The seasonal average of upper canopy leaves was significantly correlated with both root yield and harvestable biomass. The selection for high in parental materials may lead to high yields when combined with other yield determinants.