In this paper, approximate analytical solution of SIRC model associated with the evolution of influenza A disease in human population is acquired by the modified differential transform method (MDTM). The differential transform method (DTM) is mentioned in summary. MDTM can be obtained from DTM applied to Laplace, inverse Laplace transform and padé approximant. The MDTM is used to increase the accuracy and accelerate the convergence rate of truncated series solution getting by the DTM. The analytical-numerical technique can be used in order to produce simulations with different initial conditions, parameter values for different values of the basic reproduction number.
Explicit formulas for the magnetic field and divergence of multisolenoid Aharonov-Bohm potential are obtained; the mathematical essence of this potential is explained. It is shown that the magnetic field and divergence of this potential are very singular generalized functions concentrated at a finite number of thin solenoids. Deficiency index is found for the minimal operator generated by the Aharonov-Bohm differential expression.
ABSTRACT.The purpose of this paper is to establish the expansion theorem for a regular right-definite eigenvalue problem for the Laplace operator in Rn, (n > 2) with an eigenvalue parameter % contained in the equation and the Robin boundary conditions on two "parts" of a smooth boundary of a simply connected bounded domain.
The object of this paper is to establish an expansion theorem for a regular rightdefinite eigenvalue problem with an eigenvalue parameter )~ which is contained in the Schr6dinger partial differentia}, equation and in a general type of boundary conditions on the boundary of an arbitrary multiply connected bounded domain in R~(n >_ 2). We associate with this problem an essentially self-adjoint operator in a suitably defined Hilbert space and then we develop an associated eigenfunction expansion theorem.
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