关键词：
Positive solution;Existence;Neutral differential equation;Fixed point
摘要：
Necessary and sufficient conditions for the existence and classification of positive solutions of the higher order neutral differential equations were obtained. Some lemmas were introduced which were useful in the proofs of the results. The results show that the higher order neutral differential equation has an eventually positive solution which converges to a positive constant.
摘要：
A new necessary and sufficient condition for the existence of eventually positive solutions was obtained for a class of odd-order neutral differential equations. Some lemmas were also introduced that were useful in the proof of main results. The obtained results indicate that neutral differential equation has no eventually positive solution.
作者机构：
[Pan, LQ] Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China.;Univ Rovira & Virgili, Res Grp Math Linguist, E-43005 Tarragona, Spain.;Nanhua Univ, Dept Math & Phys Sci, Hengyang 421001, Peoples R China.
通讯机构：
[Pan, LQ] H;Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China.
关键词：
DNA computing;NP-complete problem;coloring problem
摘要：
DNA computing has the potential to tackle computationally difficult problems that have real-world implications. The parallel search capabilities of DNA make it a valuable tool for approaching intractable computational problems, for which conventional computers have limited potentials. Up to now, many accomplishments have been achieved to improve its performance and increase its reliability. In this paper, the coloring problem has been solved by means of molecular biology techniques. The coloring problem is a well-known NP-complete problem. This work represents further evidence for the ability of DNA computing to solve NP-complete problems.
作者机构：
Nanhua Univ, Dept Math & Phys, Henyang 421001, Peoples R China.;E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China.;[Li, XY] Department of Mathematics and Physics, Nanhua University, Hengyang 421001, China, Department of Mathematics, East China Normal University, Shanghai 200062, China;[Zhu, DM] Department of Mathematics, East China Normal University, Shanghai 200062, China
通讯机构：
[Li, X.] D;Department of Mathematics and Physics, Nanhua University, China
关键词：
Convergence;Oscillation;Permanence;Population model
摘要：
In this paper, the qualitative behavior of solutions of the bobwhite quail population model x(n+1) = ax(n) + bx(n)/(1 x(n-k)(p))(c), n = 0, 1, ..., where 0 < a < 1 < a + b, p, c is an element of (0, infinity) and k is a nonnegative integer, is investigated. Some necessary and sufficient as well as sufficient conditions for all solutions of the model to oscillate and some sufficient conditions for all positive solutions of the model to be nonoscillatory and the convergence of nonoscillatory solutions axe derived. Furthermore, the permanence of every positive solution of the model is also showed. Many known results axe improved and extended and some new results are obtained for G. Ladas' open problems.
摘要：
Oscillation properties of the solutions of a class of odd order neutral delay parabolic differential equations were investigated via the method of differential inequalities. Necessary and sufficient conditions for oscillation of odd order neutral delay parabolic differential equations were studied. Numerical method were used for the investigation .
期刊：
Journal of Difference Equations and Applications,2003年9(9):833-839 ISSN：1023-6198
通讯作者：
Li, XY
作者机构：
[Li, XY] Nanhua Univ, Dept Math & Phys, Hengyang 421001, Peoples R China.;E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China.
通讯机构：
[Li, XY] N;Nanhua Univ, Dept Math & Phys, Hengyang 421001, Peoples R China.
关键词：
rational difference equation;global asymptotic stability;semicycle;equilibrium point
摘要：
In this paper, a sufficient condition is obtained for the global asymptotic stability of the following rational difference equation x(n+1) = x(n)x(n-1)+a/x(n)+x(n-1), n = 0, 1, 2,..., where a is an element of [0, infinity) and the initial values x(-1), x(0) is an element of (0, infinity).
作者机构：
[Li, XY] School of Mathematics and Physics, Nanhua University, Hengyang 421001, China;[Li, XY; Zhu, DM] Department of Mathematics, East China Normal University, Shanghai 200062, China
通讯机构：
[Li, XY ] ;E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China.
作者机构：
Nanhua Univ, Dept Math & Phys, Henyang 421001, Peoples R China.;E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China.;[Ruan Hang; Zhang Lei; Long Teng] Beijing Institute of Technology
通讯机构：
Department of Mathematics and Physics, Nanhua University, China
关键词：
Population model;oscillation;convergence;permanence
摘要：
In this paper, the qualitative behavior of solutions of the bobwhite quail population model x(n+1) = ax(n) + bx(n)/(1 x(n-k)(p))(c), n = 0, 1, ..., where 0 < a < 1 < a + b, p, c is an element of (0, infinity) and k is a nonnegative integer, is investigated. Some necessary and sufficient as well as sufficient conditions for all solutions of the model to oscillate and some sufficient conditions for all positive solutions of the model to be nonoscillatory and the convergence of nonoscillatory solutions axe derived. Furthermore, the permanence of every positive solution of the model is also showed. Many known results axe improved and extended and some new results are obtained for G. Ladas' open problems.
作者机构：
[Pan, LQ] Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China.;Nanhua Univ, Inst Engn & Technol, Dept Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Pan, LQ] H;Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China.
关键词：
DNA computing;NP-complete problem;minimal vertex cover problem
摘要：
DNA computing was proposed for solving a class of intractable computational problems, of which the computing time will grow exponentially with the problem size. Up to now, many achievements have been made to improve its performance and increase its reliability. It has been shown many times that the surface-based DNA computing technique has very low error rate, but the technique has not been widely used in the DNA computing algorithms design. In this paper, a surface-based DNA computing algorithm for minimal vertex cover problem, a problem well-known for its exponential difficulty, is introduced. This work provides further evidence for the ability of surface-based DNA computing in solving NP-complete problems.
摘要：
Several comparison theorems for oscillation and nonoscillation of neutral difference equations with continuous arguments are established. Some known results are included and improved. All results obtained in this paper are new.
作者机构：
[Pan, LQ] Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China.;Nahua Univ, Inst Engn & Technol, Dept Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Pan, LQ] H;Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China.
关键词：
DNA computing;Maximal clique problem;NP-complete problem
摘要：
The maximal clique problem is an NP (nondeterministic polynomial time)-complete problem. We present an algorithm that solves maximal clique problem within the framework of a surface-based model of computation. The time complexity of our algorithm is O(n2), and the number of kinds of short oligonucleotides needed to encode maximal clique problem is n + 3, where n is the size of the graph. In our algorithm, immobilizing DNA (deoxyribonucleic acid) strands to a solid surface reduces the possibility of error resulting from the loss of DNA strands in solution. A solution-based algorithm solving maximal clique problem has previously been proposed by Qi Ouyang et al.. In their algorithm, the number of enzyme is equal to the number of vertices of the graph, which causes the difficulty of encoding and scaling up, because the DNA sequences of restriction enzyme sites should not be present in otherwhere. Using surface-based model, we designed an algorithm for maximal clique problem, which needs only one enzyme.
期刊：
Journal of Chemical Information and Modeling,2002年42(3):524-528 ISSN：1549-9596
通讯作者：
Liu, YC
作者机构：
[Liu, YC] Nanhua Univ Hengyang, Dept Math & Phys Sci, Hunan 421001, Peoples R China.;Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Peoples R China.
通讯机构：
[Liu, YC] N;Nanhua Univ Hengyang, Dept Math & Phys Sci, Hunan 421001, Peoples R China.
摘要：
The graph-theoretic parameter that bas probably received the most attention over the years is the chromatic number. As is well-Known, the coloring problem is an NP-Complete problem. In this paper, it has been solved by means of molecular biology techniques. The algorithm is highly parallel and has satisfactory fidelity. This work shows further evidence for the ability of DNA computing to solve NP-Complete problems.
摘要：
In this paper we consider a kind of nonlinear neutral difference equations with continuous arguments. First, we obtain some sufficient conditions for the oscillation. When the coefficients in the equations are constants, these conditions are also necessary. Secondly, we derive a necessary and sufficient condition for the nonoscillation. Finally, we give a sufficient condition for the asymptotic behavior of the nonoscillatory solutions.
摘要：
The oscillation and nonoscillation of the advanced differential equations x′(t)−p(t)x(t+τ)=0, t⩾t0(∗) and x′(t)−∑i=1npi(t)x(t+τi)=0, t⩾t0(∗∗) are investigated, where p(t),pi(t)∈C([t0,∞),[0,∞)), τ and τi are positive constants. At first, a sharp sufficient condition for the oscillation of Eq. (∗) is obtained, then the result is generalized to Eq. (∗∗). These results improve the corresponding conclusions derived by Ladas and Stavroulakis (J. Differential Equations 44 (1982) 134–152). Next, two examples are given to illustrate the advantages of our results. Finally, the sufficient conditions for these two equations to be nonoscillatory are also obtained.
