Stability: W-transform Method II

Author(s):  
Leonid Berezansky ◽  
Alexander Domoshnitsky ◽  
Roman Koplatadze
Keyword(s):  
Author(s):  
T. Hirayama ◽  
Q. Ru ◽  
T. Tanji ◽  
A. Tonomura

The observation of small magnetic materials is one of the most important applications of electron holography to material science, because interferometry by means of electron holography can directly visualize magnetic flux lines in a very small area. To observe magnetic structures by transmission electron microscopy it is important to control the magnetic field applied to the specimen in order to prevent it from changing its magnetic state. The easiest method is tuming off the objective lens current and focusing with the first intermediate lens. The other method is using a low magnetic-field lens, where the specimen is set above the lens gap.Figure 1 shows an interference micrograph of an isolated particle of barium ferrite on a thin carbon film observed from approximately [111]. A hologram of this particle was recorded by the transmission electron microscope, Hitachi HF-2000, equipped with an electron biprism. The phase distribution of the object electron wave was reconstructed digitally by the Fourier transform method and converted to the interference micrograph Fig 1.


2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 


Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.


2010 ◽  
Vol 59 (4) ◽  
pp. 1462-1472 ◽  
Author(s):  
Zaid M. Odibat ◽  
Cyrille Bertelle ◽  
M.A. Aziz-Alaoui ◽  
Gérard H.E. Duchamp

Author(s):  
D. A. SMITH ◽  
W. Y. TOH

The classical half-line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition $$bq(0,t) + {q_x}(0,t) = 0$$ is replaced with a dynamic Robin condition; $$b = b(t)$$ is allowed to vary in time. Applications include convective heating by a corrosive liquid. We present a solution representation and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential equation for the Dirichlet boundary value. We implement the fractional Frobenius method to solve this equation and justify that the error in the approximate solution of the original problem converges appropriately. We also demonstrate an argument for existence and unicity of solutions to the original dynamic Robin problem for the heat equation. Finally, we extend these results to linear evolution equations of arbitrary spatial order on the half-line, with arbitrary linear dynamic boundary conditions.


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