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A wheat (Triticum aestivum L.) line 4844 with superior numbers of florets and grains per spike was derived from the cross between Fukohokomugi wheat and Agropyron cristatum (L.) Gaertn. In order to determine the genetic control of floret and kernel number per spike in this line, chromosome addition and substitution lines that were derived from line 4844… (More)
A pair of Wolfe type non-differentiable second order symmetric primal and dual problems in mathematical programming is formulated. The weak and strong duality theorems are then established under second order F-convexity assumptions. Symmetric minimax mixed integer primal and dual problems are also investigated.
Some new results which generalize the Hahn-Banach theorem from scalar or vector-valued case to set-valued case are obtained. The existence of the Borwein-strong subgradient and Yang-weak subgradient for set-valued maps are also proven. we present a new Lagrange multiplier theorem and a new Sandwich theorem for set-valued maps.