Characterizations of some properties of generalized R0 and R1 topological spaces by using closure operator defined on a generalized topological space will be given. It is also shown that
many results done in this area in some previous papers can be considered as special cases of our results.
In acid soil, Al is solubilised into a phytotoxic form, Al(H2O)63+ which is known as Al3+. Al toxicity is the primary growth-limiting factor for plants in acid soils. Breeding of rice for Al tolerance are important approach for increasing grain yield in acid soils. In the present endeavour, rice genotypes were screened at seedling stage based on vigour index, root tolerance index and hematoxylin staining in stressed nutrient solutions to select the tolerant genotype(s) against Al toxicity. It was observed that use of different screening indices for Al toxicity tolerant genotypes of rice have given different results. Thus, screening of tolerant genotypes using one index may lead to inappropriate conclusion. Comparing all the selection indices it was found that Radhunipagal and UBKVR-16 were the common genotypes which fallen into tolerant class for every index. Finally genotypes were grouped into different clusters using D2 statistic to find out whether the tolerant genotypes fall into one cluster. Those two Al toxicity tolerance genotypes were grouped into one cluster, which strengthens our findings.
A new kind of sets called generalized μ-closed (briefly g μ-closed) sets are introduced and studied in a topological space by using the concept of generalized open sets introduced by Á. Császár. The class of all g μ-closed sets is strictly larger than the class of all μ-closed sets. Furthermore, g-closed sets (in the sense of N. Levine ) is a special type of g μ-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of μg-regular and μg-normal spaces have been given.
The kinetics of strontium tungstate crystallization from sodium tungstate melts in platinum crucibles were studied by differential thermal analysis at crystallization temperaturesT0=800, 900 and 1000° by continuous cooling at ratesRT=40, 120 and 200° per hour. Heterogeneous nuclei that first formed on the metal platinate particles in the solution during the induction periods (t) grew to small crystallites (¯l). The main crystal growth started after the development of some excess solute concentration (Δ¯C) at the end of the induction temperatures (¯T). For the first 80% crystallization, the average crystal lengths (lτ) varied with the growth time (τ) according to the relation
is the diffusion rate constant at temperatures nearT, andM is the metal salt molecular weight. The initial growth rates and the ratioslτ2/τ depended onΔ¯C instead ofRT The last 20% growth was controlled only by the rate of development of the excess solute concentration.