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The Center and the Fine Focus for a Class of Quartic Polynomial Poincare Equations 被引量:2
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作者 TIANDe-sheng ZENGXian-wu YUChang-chun LIPei-luan 《Wuhan University Journal of Natural Sciences》 CAS 2004年第6期867-870,共4页
We study a class of quartic polynomial Poincare equations by applying a recurrence formula of focal value. We give the necessary and sufficient conditions for the origin to be a center, and prove that the order of fin... We study a class of quartic polynomial Poincare equations by applying a recurrence formula of focal value. We give the necessary and sufficient conditions for the origin to be a center, and prove that the order of fine focus at the origin for this class of equations is at most 6. Key words quartic polynomial Poincare equation - center - fine focus - order CLC number O 175. 12 Foundation item: Supported by the National Natural Science Foundation of China (19531070)Biography: TIAN De-sheng (1966-), male, Ph. D candidate, research direction: qualitative theory of differential equation. 展开更多
关键词 quartic polynomial Poincare equation CENTER fine focus order
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A New General Equation of State 被引量:1
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作者 云志 秦金平 +1 位作者 史美仁 时钧 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 1999年第2期161-165,共5页
A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous ... A new general equation of state is presented, which can be used to express not only common cubic equations of state, but also quartic equations of state and so on. Main advantage of the new equation over the previous general equations is that it is in simple form, and is easy to manipulate mathematically. 展开更多
关键词 equation of state general equation cubic equation quartic equation
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Some Notes on the Positive Definite Problem of a Binary Quartic Form
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作者 CHEN Bao-xing (Department of Mathematics, Zhangzhou Teacher’s College, Zhangzhou 363000, China) 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第1期68-73,共6页
In this paper, we discuss the positive definite problem of a binary quartic form and obtain a necessary and sufficient condition. In addition we give two examples to show that there are some errors in the paper [1].
关键词 positive definite binary quartic form quartic equation
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FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS 被引量:2
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作者 H.Azadi KENARY A.R.ZOHDI M.Eshaghi GORDJI 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期1113-1118,共6页
The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of ... The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability (briefly, HUR-stability) originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. 展开更多
关键词 generalized Hyers-Ulam stability quartic functional equation Banach mod-ule unital Banach algebra generalized metric space fixed point method
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Complete solution of the diophantine equation A^2x^4-By^2=1 and some related problems 被引量:1
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作者 曹珍富 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2001年第2期108-110,共3页
We prove that diophantine equation in title has at most one positive integer solution for any positive integers A>1, B>1. It follows that Lucas problem is very simple to solve and a recent result of Bennett ... We prove that diophantine equation in title has at most one positive integer solution for any positive integers A>1, B>1. It follows that Lucas problem is very simple to solve and a recent result of Bennett is very simple to prove. 展开更多
关键词 quartic diophantine equation COMPUTER C++
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On the Diophantine Equation y^2= px(x^2+ 2)
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作者 WANG Xiao-ying 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期499-503,共5页
For any fixed odd prime p, let N(p) denote the number of positive integer solutions (x, y) of the equation y^2 = px(x^2 + 2). In this paper, using some properties of binary quartic Diophantine equations, we pro... For any fixed odd prime p, let N(p) denote the number of positive integer solutions (x, y) of the equation y^2 = px(x^2 + 2). In this paper, using some properties of binary quartic Diophantine equations, we prove that ifp ≡ 5 or 7(mod 8), then N(p) = 0; ifp ≡ 1(mod 8), then N(p) 〈 1; if p〉 3 andp ≡ 3(rood 8), then N(p) ≤ 2. 展开更多
关键词 cubic and quartic Diophantine equation number of solutions upper bound 2000 MR Subject Classification: 11D25
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