Cook and Reckhow proved in 1979 that the propositional pigeonhole principle has polynomial size extended Frege proofs. Buss proved in 1987 that it also has polynomial size Frege proofs; these Frege proofs used a completely different proof method based on counting. This paper shows that the original Cook and Reckhow extended Frege proofs can be formulated as quasipolynomial size Frege proofs. Th...

Grain quality currently represents a major problem in high yielding rice production in Iran and many other rice producing areas of the world. Quality assessment of rice involves the function of sensory tests and physicochemical determinations based on the chemical composition, cooking quality, gelatinization temperature and physical properties of cooked rice. These research genetic materials we...

Currently, food waste is a global concern, problem that arises mainly at the consumption level and generates environmental, economic, social impacts. One way to reduce use we already have home. However, this causes another which what cook with certain foods. Sometimes do not know recipes can be made. Knowing ingredients mixed how mix them difficult task for beginner cook, so selecting right rec...

grain quality currently represents a major problem in high yielding rice production in iran and many other rice producing areas of the world. quality assessment of rice involves the function of sensory tests and physicochemical determinations based on the chemical composition, cooking quality, gelatinization temperature and physical properties of cooked rice. these research genetic materials we...