In this paper, the nonexistence, existence and the number of limit cycles for a class of differential systems with positive definite polynomial are considered, and the results obtained generalize and supplement those ...In this paper, the nonexistence, existence and the number of limit cycles for a class of differential systems with positive definite polynomial are considered, and the results obtained generalize and supplement those of [1].展开更多
In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilb...In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference[1]. Moreover, some results on the weak Hilbert property are established. In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference [1]. Moreover, some results on the weak Hilbert property are established.展开更多
文摘In this paper, the nonexistence, existence and the number of limit cycles for a class of differential systems with positive definite polynomial are considered, and the results obtained generalize and supplement those of [1].
基金Project supported by National Natural Science Foundation of China
文摘In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference[1]. Moreover, some results on the weak Hilbert property are established. In this paper, we prove the main result: Let both (K, S) and (K*, S*) be preordered fields, and let (K*, S*) be a finitely generated extension of (K, S). If K* is transcendental over K, then (K*, S*) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference [1]. Moreover, some results on the weak Hilbert property are established.
