A Removability Result for Holomorphic Functions of Several Complex Variables
Pages 50-52
Juhani Riihentaus

DOI: http://dx.doi.org/10.6000/1927-5129.2016.12.07

Published: 03 February 2016

Abstract: Suppose that Ω is a domain of Cⁿ, n≥1, E⊂Ω closed in Ω, the Hausdorff measure H^2n-1 (E) = 0 , and ƒ is holomorphic in Ω\E . It is a classical result of Besicovitch that if n=1 and ƒ is bounded, then ƒ has a unique holomorphic extension to Ω. Using an important result of Federer, Shiffman extended Besicovitch’s result to the general case of arbitrary number of several complex variables, that is, for  n≥1 . Now we give a related result, replacing the boundedness condition of ƒ by certain integrability conditions of ƒ and of ∂²ƒ/∂Ζ²_j, j=1,2,K ,n.

Keywords: Holomorphic function, subharmonic function, Hausdorff measure, exceptional sets.

Combining Ability Estimates for Yield and Fiber Quality Parameters in Gossypium Hirsutum L. Hybrids
Pages 53-58
Mah-e-Jabeen Memon,Moula Bux Kumbhar, Muhammad Jurial Rind, Mohammad Ibrahim Keerio and Shabana Memon

DOI: http://dx.doi.org/10.6000/1927-5129.2016.12.08

Published: 03 February 2016

Abstract: General and specific combining ability effects were discriminated in different parents and offspring to isolate the potential of genotypes used in diallel system to attain the genetic inheritance pattern ascertain with the nature of gene action. A six-by-six, hirsutum diallel excluding reciprocals, was analyzed for general and specific combining ability estimates and components of genetic variation to investigate the genetic retrospect and inheritance pattern of eleven quantitative and fiber quality characters. Hirsutum cultivars included CIM-506, BH-160, NIAB-111, CIM-497, NIAB-999 and RH-510. Some of the traits like boll number, boll weight and sympodia plant^-1 did not reveal the highest GCA scoring parent for seed cotton yield. The ranking order for GCAs of the parents was not maintained from F₁ to F₂ diallel set and the ranking order of the hybrids with respect to their SCA values was also not maintainable from F₁ to F₂ diallel set. Thus the hybrids could not maintain their superiority (or inferiority) of their SCA values.

Keywords: Cotton, Diallel analysis, Fiber, GCA and SCA, quality, yield.