in order to study the mode of genetic control and heritability of morphological characteristics important for the improvement of root weight, sugar yield and white sugar yield in tropical beet, griffing's diallel cross method along with the biplot display of diallel data were applied. nine sugar beet lines including 7112-36, 7173, 474, 452, 261, 436-104, sb-firoz, rr607 and 436 were crosse...

A a profession, we in medicine find ourselves in exciting times. Breakthroughs in the scientific basis of our knowledge continue to expand in a wealth of literature and journals. As the “art” of medicine becomes more scientific, more measureable, the practicing clinician finds himself buffeted by peer reviews, utilization committees, relicensure movements, hospital admission review programs, an...

Definition 1.1 (Direct Products). Let {Gα}α∈I be a collection of groups indexed by an index set I. We may form the Cartesian product ∏ α∈I Gα. The elements of this Cartesian product can be denoted by tuples (aα)α∈I . We refer to the entry aα as the αth component of this tuple. We define a multiplication on this Cartesian product componentwise, i.e., (aα) ⋆ (bα) = (aα ⋆α bα) where ⋆α is the grou...

i∈N R = {(a0, a1, a2, . . . )|aj ∈ R} is a countable direct product of (R,+) with itself. Thus the elements of R[[x]] are arbitrary sequences with entries in R where addition is componentwise. We define a multiplication ⋆ via (a0, a1, . . . ) ⋆ (b0, b1, . . . ) = (c0, c1, . . . ) where cn = ∑n k=0 akbn−k for all n ∈ N. It is easy to check that the sequence (1, 0, 0, . . . ) is a two-sided ident...

ENWEndNote BIBJabRef, Mendeley RISPapers, Reference Manager, RefWorks, Zotero AMA Islam M, Dey Barna S. Survival analysis of timing early marriage among women in Bangladesh: evidence from the 2014 Bangladesh demographic and health survey. Family Medicine & Primary Care Review. 2021;23(4):429-436. doi:10.5114/fmpcr.2021.110356. APA Islam, M., Barna, (2021). Review, 23(4), 429-436. https://doi.or...

We have previously discussed the basic concepts and fundamental theorems on unique factorization in PIDs. We will provide a few examples of how unique factorization is used in applications to number theory. One cannot stress how important the concept of unique factorization is in many mathematical applications and definately in algebraic number theory. We unfortunately will only have the time t...