Necessary and sufficient condition on real quadratic algebraic function fields K is given for theirideal class groups H(K) to contain cyclic subgroups of order n. And eight series of such real quadratic functionfields...Necessary and sufficient condition on real quadratic algebraic function fields K is given for theirideal class groups H(K) to contain cyclic subgroups of order n. And eight series of such real quadratic functionfields K are obtained whose ideal class groups contain cyclic subgroups of order n. In particular, the ideal classnumbers of these function fields are divisible by n.展开更多
In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic...In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic).展开更多
The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the...The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e. g., if D = F 2 + c, then h(D) ≥ degF/degP; if D = (SG)2 + cS, then h(D) ≥ degS/degP; if D = (A m + a)2 + A, then h(D) ≥ degA/degP, where P is an irreducible polynomial splitting in K, c ∈ F q . In addition, three types of quadratic function fields K are found to have ideal class numbers bigger than one.展开更多
The matrix equation AX-XB=C is quite well known and basic. It plays an important role in algebra and applied mathematics. This paper is an extension of the author’s previous work. Using the continued fraction associa...The matrix equation AX-XB=C is quite well known and basic. It plays an important role in algebra and applied mathematics. This paper is an extension of the author’s previous work. Using the continued fraction associated with A and B, one obtains a standard constructive formula of the solution X in an algebraic form. In contrast to other known results, it can simplify the numerical computation of X. When B=-A is asymptotically stable and C is a positive definite Hermitian matrix, the Hermitian form with the coefficient matrix X for a Liapunov function can be immediately decomposed as the sum of some nonnegative definite Hermitian forms by this formula.展开更多
The algebraic independence of e^θ1,…,e^θs is proved, where θ1,… ,θs are certain gap series or power series of algebraic numbers, or certain transcendental continued fractions with algebraic elements.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071041).
文摘Necessary and sufficient condition on real quadratic algebraic function fields K is given for theirideal class groups H(K) to contain cyclic subgroups of order n. And eight series of such real quadratic functionfields K are obtained whose ideal class groups contain cyclic subgroups of order n. In particular, the ideal classnumbers of these function fields are divisible by n.
文摘In the present paper, an efficient algorithm based on the continued fractions theory was established for the universal Y’s functions of space dynamics. The algorithm is valid for any conic motion (elliptic, parabolic or hyperbolic).
文摘The theory of continued fractions of functions is used to give a lower bound for class numbers h(D) of general real quadratic function fields over k = F q (T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e. g., if D = F 2 + c, then h(D) ≥ degF/degP; if D = (SG)2 + cS, then h(D) ≥ degS/degP; if D = (A m + a)2 + A, then h(D) ≥ degA/degP, where P is an irreducible polynomial splitting in K, c ∈ F q . In addition, three types of quadratic function fields K are found to have ideal class numbers bigger than one.
文摘The matrix equation AX-XB=C is quite well known and basic. It plays an important role in algebra and applied mathematics. This paper is an extension of the author’s previous work. Using the continued fraction associated with A and B, one obtains a standard constructive formula of the solution X in an algebraic form. In contrast to other known results, it can simplify the numerical computation of X. When B=-A is asymptotically stable and C is a positive definite Hermitian matrix, the Hermitian form with the coefficient matrix X for a Liapunov function can be immediately decomposed as the sum of some nonnegative definite Hermitian forms by this formula.
文摘The algebraic independence of e^θ1,…,e^θs is proved, where θ1,… ,θs are certain gap series or power series of algebraic numbers, or certain transcendental continued fractions with algebraic elements.
