This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equati...This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equations which involving arbitrary function.First,Lie algorithm is used to give the determining equations of symmetry for the given equations,which involving arbitrary functions.Next,differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets,which are easy to be solved relatively.Each branch of the decomposition yields a class of symmetries and associated parameters.The algorithm makes the classification become direct and systematic.Yuri Dimitrov Bozhkov,and Pammela Ramos da Conceição have used the Lie algorithm to give the symmetry classifications of the equations talked in this paper in 2020.From this paper,we can find that the differential form Wu’s method for symmetry classification of ODEs with arbitrary function(parameter)is effective,and is an alternative method.展开更多
Rhodobacter sphaeroides is a purple non-sulfur bacterium that belongs to the α-3 subdivision of Proteobacteria. R. sphaeroides is a model bacterial species because of its complex genome structure and expanded metabol...Rhodobacter sphaeroides is a purple non-sulfur bacterium that belongs to the α-3 subdivision of Proteobacteria. R. sphaeroides is a model bacterial species because of its complex genome structure and expanded metabolic capabilities. The genome of R. sphaeroides consists of two circular chromosomes and five endogenous plasmids. It has the ability to grow under a wide variety of environmental conditions. It grows aerobically (~20% O2), semi-aerobically (~2% O2), and photosynthetically (under anaerobic condition plus light). It has been previously shown that many bacterial species utilize a number of alternate carbon sources for their optimal growth under a variety of growth conditions. We hypothesize that different or an additional carbon source in the minimal medium differentially affects the bacterial growth under dark-aerobic conditions. The bacterial growth kinetics and the number of cells in the bacterial culture were analyzed by measuring the optical density (OD at 600 nm) and the colony forming units (CFUs) at regular intervals of bacterial cultures. Results reveal that sodium succinate is the preferred sole carbon source for the optimal growth of R. sphaeroides. The results of growth kinetics and CFUs together concluded that from the tested carbon sources, sodium succinate is the best single carbon source in the minimal media for the optimal growth of R. sphaeroides. Interestingly, cell culture grown in SIS supplemented with sodium acetate exhibits a prolonged lag phase with the lowest ODs and CFUs that later switches to the growth-burst phase support previously discovered similar phenomenon of the growth-rate switch in the presence of acetate metabolism. Future work will utilize the aerobically grown R. sphaeroides’ cells as a biocatalyst to deplete the oxygen levels from natural gas streams and industrial gas pipelines.展开更多
文摘This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equations which involving arbitrary function.First,Lie algorithm is used to give the determining equations of symmetry for the given equations,which involving arbitrary functions.Next,differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets,which are easy to be solved relatively.Each branch of the decomposition yields a class of symmetries and associated parameters.The algorithm makes the classification become direct and systematic.Yuri Dimitrov Bozhkov,and Pammela Ramos da Conceição have used the Lie algorithm to give the symmetry classifications of the equations talked in this paper in 2020.From this paper,we can find that the differential form Wu’s method for symmetry classification of ODEs with arbitrary function(parameter)is effective,and is an alternative method.
文摘Rhodobacter sphaeroides is a purple non-sulfur bacterium that belongs to the α-3 subdivision of Proteobacteria. R. sphaeroides is a model bacterial species because of its complex genome structure and expanded metabolic capabilities. The genome of R. sphaeroides consists of two circular chromosomes and five endogenous plasmids. It has the ability to grow under a wide variety of environmental conditions. It grows aerobically (~20% O2), semi-aerobically (~2% O2), and photosynthetically (under anaerobic condition plus light). It has been previously shown that many bacterial species utilize a number of alternate carbon sources for their optimal growth under a variety of growth conditions. We hypothesize that different or an additional carbon source in the minimal medium differentially affects the bacterial growth under dark-aerobic conditions. The bacterial growth kinetics and the number of cells in the bacterial culture were analyzed by measuring the optical density (OD at 600 nm) and the colony forming units (CFUs) at regular intervals of bacterial cultures. Results reveal that sodium succinate is the preferred sole carbon source for the optimal growth of R. sphaeroides. The results of growth kinetics and CFUs together concluded that from the tested carbon sources, sodium succinate is the best single carbon source in the minimal media for the optimal growth of R. sphaeroides. Interestingly, cell culture grown in SIS supplemented with sodium acetate exhibits a prolonged lag phase with the lowest ODs and CFUs that later switches to the growth-burst phase support previously discovered similar phenomenon of the growth-rate switch in the presence of acetate metabolism. Future work will utilize the aerobically grown R. sphaeroides’ cells as a biocatalyst to deplete the oxygen levels from natural gas streams and industrial gas pipelines.
