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Dual Integrable Representations of Hypergroups
Seyyed Mohammad, Tabatabaie,Soheila, Jokar Department of Mathematics 2022 Kyungpook mathematical journal Vol.62 No.4
In this paper, we study dual integrable representations of locally compact commutative hypergroups and give a sufficient and necessary condition for a dual integrable representation to have an admissible vector.
Maryam Pezhmanmehr,Mohammad Esmail Hassani,Mohammad Fakhre Tabatabaie,Javad Hadian 한국원예학회 2009 Horticulture, Environment, and Biotechnology Vol.50 No.2
In this study, genetic diversities of 24 populations were evaluated and of 6 selected populations of Black cummin (Bunium persicum (Boiss.) B. Fedtsch.) were studied using randomly amplified polymorphic DNA (RAPD) markers. Among the 24 populations, 15 selected random primers produced 228 scorable bands of which 196 (86%) bands were polymorphic. Estimation of genetic similarity based on the polymorphic bands ranged from 0.19 to 0.75. A dendrogram was constructed based on Jaccard’s similarity data by applying the UPGMA method. Maximum and minimum similarity were detected between Circh and Jiroft-Darin and between Bam and Sistan-Baluchestan, respectively. In addition, 6 populations of Black cummin from the main growing areas in Iran were selected to study genetic diversity within populations. Application of 15 RAPD primers produced 229 bands with an average of 14.4 bands per primer of which 216 (94%) bands were polymorphic. Genetic diversity within populations was studied with the average of Nei’s gene diversity analysis and Shannon's information index. Based on RAPD data, maximum and minimum genetic diversity were observed within populations of Ghazvin and Esfahan provinces, respectively. Regarding the ratio of effective number of alleles to observed number of alleles within each population, all populations showed equilibrant allelic distribution according to Hardy-Wienberg equilibrium. High Fst index derived by this study showed that investigated populations were completely different with independent evolution. The results generally showed a high level of genetic diversity among and within evaluated Black cummin populations. This research indicated that RAPD technique is an efficient tool for assessing genetic diversity in Black cummin populations. Understanding genetic variability in this valuable species provides information related to domestication and conservation efforts.