‎‎The equivalence relation isoclinism partitions the class of all pairs of groups‎ ‎into families‎. ‎In this paper‎, ‎a complete classification of the set of all pairs $(G,G')$ is established‏‎,‎ whenever‎ $G$ is a $p$-group of order at most $p^5‎‏$‎ and ‎$p$ is a prime number greater than 3. Moreover‎, ‎the classification of pairs $(H,H')$ for extra special $p$-groups $H$ is also given.

Cotton (Gossypium herbaceum L.) fiber development consists of a fiber elongation stage (up to 20 d post-anthesis) and a subsequent cell wall thickening stage. Cell wall analysis revealed that the extractable matrix (pectic and hemicellulosic) polysaccharides accounted for 30-50% of total sugar content in the fiber elongation stage but less than 3% in the cell wall thickening stage. By contrast,...

Understanding the composition, evolution, and function of the Gossypium hirsutum (cotton) genome is complicated by the joint presence of two genomes in its nucleus (AT and DT genomes). These two genomes were derived from progenitor A-genome and D-genome diploids involved in ancestral allopolyploidization. To better understand the allopolyploid genome, we re-sequenced the genomes of extant diplo...

Colchicine has been used to induce chromosome doubling in plant species. Diploid cotton species have inherited desirable genes that are resistant to biotic and abiotic stresses and also possesses useful fiber quality traits, such as higher fiber length and strength. To transfer these desirable traits to the most extensively cultivated tetraploid cotton species through hybridization, it is a pre...

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...