This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
To explore the differences of carbohydrate metabolism in two tomato species and discuss the possible regulation of 14-3-3 proteins on the sucrose phosphate synthase （SPS） activity, we determined the contents of solu...To explore the differences of carbohydrate metabolism in two tomato species and discuss the possible regulation of 14-3-3 proteins on the sucrose phosphate synthase （SPS） activity, we determined the contents of soluble sugar and starch through high performance liquid chromatography （HPLC）. The activities of sugar-metabolizing enzymes were assayed in desalted extract, and the relative expression levels of related genes in sugar metabolism were determined though real-time RT-PCR. The results indicated that glucose and fructose were mainly accumulated during the maturation of the fruit because of the high acid invertase （AI） and neutral invertase （NI） in Micro-Tom （Solanum lycopersicum） fruit, while in Solanum chmielewskii fruit, SPS which went along with the change of sucrose content led to the rapid sucrose increase during the fruit ripening. TFT1 and TFT10, belonging to 14-3-3 protein in tomato, were likely to down-regulated SPS activity during young and intumescence period.展开更多
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
基金supported by the Key Technologies R&D Program of China during the 12th Five-Year Plan period(2011BAD12B03)
文摘To explore the differences of carbohydrate metabolism in two tomato species and discuss the possible regulation of 14-3-3 proteins on the sucrose phosphate synthase （SPS） activity, we determined the contents of soluble sugar and starch through high performance liquid chromatography （HPLC）. The activities of sugar-metabolizing enzymes were assayed in desalted extract, and the relative expression levels of related genes in sugar metabolism were determined though real-time RT-PCR. The results indicated that glucose and fructose were mainly accumulated during the maturation of the fruit because of the high acid invertase （AI） and neutral invertase （NI） in Micro-Tom （Solanum lycopersicum） fruit, while in Solanum chmielewskii fruit, SPS which went along with the change of sucrose content led to the rapid sucrose increase during the fruit ripening. TFT1 and TFT10, belonging to 14-3-3 protein in tomato, were likely to down-regulated SPS activity during young and intumescence period.
