Inheritance of cleistogamy in interspecific hybridization of Gossypium barbadense L.

Studies of the inheritance and and variability of chasmo- and cleistogamous types of cotton flower on the base of intraspecies hybridization of Gossypium barbadense L. are an urgent genetical task, whose applications involve plant breeding and seed industry. The purpose of our study was to determine the genetic control of this trait on the base of the regularity of alternative chasmo- and cleistogamous types of flowers in intraspecific hybrids of G. barbadense species. It is of theoretical and practical significance in the development of isogenic forms, lines, and varieties with the fully closed cleistogamous type of flowers, possessing important commercial traits. A pioneering method was elaborated for determining the genetic control of chasmo- and cleistogamous types of flowers in inrtaspecific hybridization of Gossypium barbadense L., which was a continuation of our studies on interspecific cotton hybridization. Two strategies were applied to the genetic analysis of hybrids: (1) paired reciprocal hybrids F1, F2 and (2) backcrossed hybrids Fb. On the grounds of these strategies, we determined the inheritance mode of flower types in reciprocal hybrids F1, which possessed the c1cg1Cg2cg2 genotype with chasmogamous flowers without reciprocal difference. The classes segregated in F2 as follows: 1 (cg1cg1Cg2Cg2) : 2 (cg1cg1Cg2cg2) : 1 (cg1cg1cg2cg2), where cleistogamy was double recessive (This trait shows the complete dominance inheritance pattern.) Segregation into two phenotypic classes occurs in the 3:1 ratio, i.e., three plants with chasmogamous flowers per one cleistogamous. The segregation Fb is 1:1; i.e., 1 chasmogamous : 1 cleistogamous. Thus, cotton chasmogamy is inherited in F2 according to the Mendelian law in a completely dominant manner: 3:1, which is proven by the Fb cross

On the lower bound of spectrum of the Schrödinger’s operator for some multi-particle systems

For N - particle Schrödinger’s operator with Column potential with central charge equal Z, it is well known estimation N < 2Z +1, obtained by Lieb E. In the present paper the estimation obtained in case when there is a different interaction between particles