Hopef bifurcation of Fitzhugh's nerve conduction equation is dealt with dx/dy= α+x+y-1/3x~3, dy/dx= ρ(A-x-By) whereα, A∈ ( -∞, +∞), ρ, B∈ (0, 1)are real parameters. The proposition of Hopf bifurcation of this equation for every parameter is obtained.
A branch-and-price algorithm for solving the cutting strips problem
After giving a suitable model for the cutting strips problem, we present a branch-and-price algorithm for it by combining the column generation technique and the branch-and-bound method with LP relaxations.
The double points may be the double points of either branch, or the intersection points of the two branches.
When the thickness is d >amp;gt; 2 Rg (radius of gyration), the polymer can crystallize into spherulites; when Rg >amp;lt; d >amp;lt; 2 Rg, a dense-branch morphology and dendrites could be found; when d >amp;lt; Rg, an "islands" structure could be obtained.
In addition, considering the non-convex and non-concave nature of the sub-problem of combinational optimization, the branch-and-bound technique was adopted to obtain or approximate a global optimal solution.
The result generalizes and implies the classical "branching rules" that describe the restriction of an irreducible representation of the symmetric groupSn toSn-1.
The proposed superaugmented eccentric connectivity indices exhibited high sensitivity towards branching, exceptionally high discriminating power, and extremely low degeneracy.
Some theoretical issues and implementation details about the algorithm are discussed, including the solution of the pricing subproblem, the quality of LP relaxations, the branching scheme as well as the column management.
Spectral radiuses of the galton-watson branching processes
The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated.