Working with 2s and 3s
نویسنده
چکیده
We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.
منابع مشابه
Efficient (3S)-Acetoin and (2S,3S)-2,3-Butanediol Production from meso-2,3-Butanediol Using Whole-Cell Biocatalysis.
(3S)-Acetoin and (2S,3S)-2,3-butanediol are important platform chemicals widely applied in the asymmetric synthesis of valuable chiral chemicals. However, their production by fermentative methods is difficult to perform. This study aimed to develop a whole-cell biocatalysis strategy for the production of (3S)-acetoin and (2S,3S)-2,3-butanediol from meso-2,3-butanediol. First, E. coli co-express...
متن کاملEngineering of cofactor regeneration enhances (2S,3S)-2,3-butanediol production from diacetyl
(2S,3S)-2,3-Butanediol ((2S,3S)-2,3-BD) is a potentially valuable liquid fuel and an excellent building block in asymmetric synthesis. In this study, cofactor engineering was applied to improve the efficiency of (2S,3S)-2,3-BD production and simplify the product purification. Two NADH regeneration enzymes, glucose dehydrogenase and formate dehydrogenase (FDH), were introduced into Escherichia c...
متن کاملمحاسبه سطح مقطع کل تهییج در برخورد یون برهنه+Aq با اتم هیدروژن در گذار از حالت پایه به حالتهای 2s و 3s در تقریب بورن- فادیف
In this work, total excitation cross section of atomic hydrogen in the collision of bare ion was calculated employing a three body Faddeev formalism. In the present calculation, initially the first order electronic amplitude was calculated using the interaction potential which led to inelastic form factor. Secondly, the first order nuclear amplitude was calculated and added to the first order ...
متن کاملPREPARATION OF 2S,3S-N-ISOBUTYL-N-(2- HYDROXY-3-AMINO-4-PHENYLBUTYL)-P- NITROBENZENESULFONYLAMIDE HYDROCHLORIDE AND OTHER DERIVATIVES OF 2-HYDROXY-l,3- DIAMINES
The present invention provides a new process for the preparation of 2S,3S-N-isobutyl-N-(2-hydroxy-3-amino-4phenylbutyl)-p-nitrobenzenesulfonylamide hydrochloride, wherein this compound is prepared directly from the chloromethylalcohol. Importantly, the process of the present invention results in higher yields of 2S,3S-N-isobutyl-N-(2hydroxy -3 -amino -4-phenylbu tyl) -pnitrobenzenesulfonylamide...
متن کاملMetabolic engineering of Escherichia coli for production of (2S,3S)-butane-2,3-diol from glucose
BACKGROUND Butane-2,3-diol (2,3-BD) is a fuel and platform biochemical with various industrial applications. 2,3-BD exists in three stereoisomeric forms: (2R,3R)-2,3-BD, meso-2,3-BD and (2S,3S)-2,3-BD. Microbial fermentative processes have been reported for (2R,3R)-2,3-BD and meso-2,3-BD production. RESULTS The production of (2S,3S)-2,3-BD from glucose was acquired by whole cells of recombina...
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