We consider magnetic Schrödinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the corresponding combinatorial graph and a certain Hill equation. This may be viewed as a generalization of the classical spectral analysis for the Hill operator to such structures. Using this correspondence we show that ...

1. The B.W.K. Method. The B.W.K. procedure1 was discovered in connection with problems of wave mechanics, where Planck's constant h was treated as a very small quantity, and functions could be expanded in series of powers of h. The first terms of the expansion correspond to classical mechanics (completed with some quantum conditions) and higher terms represent typical wave-mechanical effects. O...

A chain of connected genes with activation-repression links is analysed. It is shown that for various promoter activity functions (parametrised by Hill coefficient) the equations describing the concentrations of transcription factors are perturbed completely integrable differential-difference of KdV-type. In the case of large Hill coefficient the proteomic signal along the gene network is given...

Kawamoto had reported that eel hemoglobin has a hyperbolic oxygen equilibrium function, with n in the Hill equation equal to 1. On the basis of Kawamoto's data and with new measurements, it is shown that the equilibrium function is in fact S-shaped, as in most other vertebrates, and n in Hill's equation equals 1.8.

We consider a system of nonlinear differential equations describing the antiferromagnetism victor in ferrite film. The contains two parameters and admits family exact solutions with plane phase trajectories. Perturbation such leads to Hill equation periodic coefficient. study stability equilibrium state equation.

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

A practical real-time auto-focus algorithm for digital camera ispresented. and it improves the reliability and speed of auto-focus process, especially suitable for mega-pixel high definition camera. The proposed algorithm adopts threshold gradient and edge point count technique besides focus value function, instead of traditional two-stage climbing search algorithm that uses focus value functio...