In this paper, we continues to study the convergent iteration method of order two given by the first author for finding zeros of the derivative. Under one global condition on the function, instead of two, the converge...In this paper, we continues to study the convergent iteration method of order two given by the first author for finding zeros of the derivative. Under one global condition on the function, instead of two, the convergence determinations are established by using quadratic and cubical majorizing functions respectively.展开更多
For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides s...For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.展开更多
A generalization of the usual Green function to a kind of nonlinear elliptic equation of divergence form is discussed. The regularity and comparison principle of Green function in the sense of distribution are shown.
文摘In this paper, we continues to study the convergent iteration method of order two given by the first author for finding zeros of the derivative. Under one global condition on the function, instead of two, the convergence determinations are established by using quadratic and cubical majorizing functions respectively.
文摘For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.
基金Supported by Beijing Jiaotong University Science Research Foundation (2004SM056)
文摘A generalization of the usual Green function to a kind of nonlinear elliptic equation of divergence form is discussed. The regularity and comparison principle of Green function in the sense of distribution are shown.
