The concept of weak strictly positive real regions is introduced, and its properties are discussed . By using the complete discrimination system for polynomials, complete characterization of the (weak) strictly positi...The concept of weak strictly positive real regions is introduced, and its properties are discussed . By using the complete discrimination system for polynomials, complete characterization of the (weak) strictly positive real regions for transfer functions in coefficient space is given. A new effective method for robust strictly positive real synthesis is proposed. This method results in necessary and sufficient conditions for low-order stable interval polynomials and segment polynomials, and is also efficient for high-order cases. Numerical examples are provided to illustrate the effectiveness of this method.展开更多
By the complete discrimination system for polynomials, we classify exact traveling wave solutions to the Zhiber-Shabat equation, and compute some new traveling wave solutions.
不等式的机器判定,因其广泛的用途和内在的复杂性,已成为定理自动证明领域的研究热点和难点.针对代数不等式提出了一种分拆降幂的机械化判定方法.首先对待证的n元不等式进行齐次化对称化处理,再通过初等对称式表示和降幂分拆,将其等价...不等式的机器判定,因其广泛的用途和内在的复杂性,已成为定理自动证明领域的研究热点和难点.针对代数不等式提出了一种分拆降幂的机械化判定方法.首先对待证的n元不等式进行齐次化对称化处理,再通过初等对称式表示和降幂分拆,将其等价转化为具有特殊形式的一类多项式不等式,然后对多项式的系数作非负性判定.当转化后的多项式非平凡即系数不是全为非负时,则可以应用经改进的柱形分解程序BOTTEMA和QEPCAD对其作整体判定,或利用多项式完全判别系统,将其转化为一组n-2变元不等式的判定问题再进行判定.最后将此方法编制为Maple通用程序SymProve3,能够快速判定大量次数高至数百、项数数千的多元代数不等式,形成了一个以降低幂次数为主要证题特征的代数不等式判定系统.将其应用于《567 Nice and Hard Inequalities》中列出的209个多元初等不等式的证明,仅用33秒.展开更多
文摘The concept of weak strictly positive real regions is introduced, and its properties are discussed . By using the complete discrimination system for polynomials, complete characterization of the (weak) strictly positive real regions for transfer functions in coefficient space is given. A new effective method for robust strictly positive real synthesis is proposed. This method results in necessary and sufficient conditions for low-order stable interval polynomials and segment polynomials, and is also efficient for high-order cases. Numerical examples are provided to illustrate the effectiveness of this method.
文摘By the complete discrimination system for polynomials, we classify exact traveling wave solutions to the Zhiber-Shabat equation, and compute some new traveling wave solutions.
文摘不等式的机器判定,因其广泛的用途和内在的复杂性,已成为定理自动证明领域的研究热点和难点.针对代数不等式提出了一种分拆降幂的机械化判定方法.首先对待证的n元不等式进行齐次化对称化处理,再通过初等对称式表示和降幂分拆,将其等价转化为具有特殊形式的一类多项式不等式,然后对多项式的系数作非负性判定.当转化后的多项式非平凡即系数不是全为非负时,则可以应用经改进的柱形分解程序BOTTEMA和QEPCAD对其作整体判定,或利用多项式完全判别系统,将其转化为一组n-2变元不等式的判定问题再进行判定.最后将此方法编制为Maple通用程序SymProve3,能够快速判定大量次数高至数百、项数数千的多元代数不等式,形成了一个以降低幂次数为主要证题特征的代数不等式判定系统.将其应用于《567 Nice and Hard Inequalities》中列出的209个多元初等不等式的证明,仅用33秒.
