Bifurcation phenomenon of the nonlinear equation f(x,λ)=(x 1x 2 2+λx 2+λ 4,-x 2 1-x 2) T=0 near the origin is studied by using LS reduction and Newton′s diagram,three branches bifur cating equilibrium point is obtained.
A sufficient condition that guarantees every solution of the population model with delay was given N′(t)=r(t)N(t)1-N(t-τ)1-λN(t-τ),t≥0, to converge to the equilibrium N *=1 as t→∞. The results in related reference are improved.
This paper gives a direct criterion theorem to the equilibrium (0,0) of the mathematic model of a class of biological infection dx/dt=ax+by+P (x,y), dy/dt=Q(x,y)(ab≠0). The theorem is simpler than the present one.
In this paper, we consider difference equation xu+1 = αxn/, n = 0, 1, 2,…. where α∈(1, ∞), βi ∈[0, ∞) and β= ∑βi > 0, k ∈{0, l, 2,…}. We obtain sufficient i=1 conditions for the positive equilibrium (α- l)/βof this equation to be global attractor.
The potential function quantitatively describes the critical characters of CO 2 equilibrium state, and the potential energy surface correctly describes the characters of pathway in O( 1D)+CO(X 1Σ +)→CO 2→C( 3P)+O 2(X 3 Σ - g) reaction.
The solubilities of saturated solution of ternary system RECl3(RE=Dy, Yb)-HOAc-H2O(30℃)have been investigated and the corresponding equilibrium diagrams were constructed.
The denaturation data are analyzed based on the effective Gibbs free energy (ΔG°eff) approach and the chemical denaturation parameters including ΔG°eff, m value and equilibrium unfolding constant (KU) were obtained.
Two new classes of life distributions, namely the class of new better than its equilibrium life in convex ordering (NBELC), and its dual class, the class of new worse than its equilibrium life in convex ordering (NWELC), are introduced.