The present situation of the mathematics teaching in higher vocational colleges is not optimistic. In the new education system, it is an urgent problem for the mathematics teachers in higher vocational colleges to bri...The present situation of the mathematics teaching in higher vocational colleges is not optimistic. In the new education system, it is an urgent problem for the mathematics teachers in higher vocational colleges to bring forth new ideas for the teaching methods, improve the students＇ interest in learning, and train the application-oriented talented personnel needed by the society. MATLAB software package can help set up a bridge and link for the mathematics teaching and the practical application. Its powerful numerical calculation ability can quickly solve all kinds of calculation problems, so that the basic thinking methods are more closely focused in mathematics teaching and also more conditions are created for mathematics teaching to combine the actual major conditions and life conditions. In this paper, the related problems in the implementation of mathematical modeling software MATLAB and model in higher vocational colleges are discussed.展开更多
Simultaneous contractifications, simultaneous proper contractifications and semigroup(countable family or finite family) of commuting operators and of non-commuting operatorsare first given. Characterizations are give...Simultaneous contractifications, simultaneous proper contractifications and semigroup(countable family or finite family) of commuting operators and of non-commuting operatorsare first given. Characterizations are given for a single bounded linear operator being a topo-logical proper contraction. By using complexification of a real Banach space and by applying afixed point theorem of Edelstein, it is shown that every compact topological strict contractionon a Banach space is a topological proper contraction. Finally, results on simultaneous propercontractification are applied to study the stability of a common fixed point of maps which areFrechet differentiable at that point.展开更多
文摘The present situation of the mathematics teaching in higher vocational colleges is not optimistic. In the new education system, it is an urgent problem for the mathematics teachers in higher vocational colleges to bring forth new ideas for the teaching methods, improve the students＇ interest in learning, and train the application-oriented talented personnel needed by the society. MATLAB software package can help set up a bridge and link for the mathematics teaching and the practical application. Its powerful numerical calculation ability can quickly solve all kinds of calculation problems, so that the basic thinking methods are more closely focused in mathematics teaching and also more conditions are created for mathematics teaching to combine the actual major conditions and life conditions. In this paper, the related problems in the implementation of mathematical modeling software MATLAB and model in higher vocational colleges are discussed.
文摘Simultaneous contractifications, simultaneous proper contractifications and semigroup(countable family or finite family) of commuting operators and of non-commuting operatorsare first given. Characterizations are given for a single bounded linear operator being a topo-logical proper contraction. By using complexification of a real Banach space and by applying afixed point theorem of Edelstein, it is shown that every compact topological strict contractionon a Banach space is a topological proper contraction. Finally, results on simultaneous propercontractification are applied to study the stability of a common fixed point of maps which areFrechet differentiable at that point.
