Availability of an anesthesic ventilator, through Fourier finite series

A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain. The starting point is an exact solution to the Laplace equation given in terms of infinite series expansions from an arbitrary z-level. We replace the infinite series operators by finite series (Boussinesq-type) approximations involving up to fifth-derivative operators. The finite series are manipulated to incorporate Padé approximants providing the highest possible accuracy for a given number of terms. As a result, linear and nonlinear wave characteristics become very accurate up to wavenumbers as high as kh = 40, while the vertical variation of the velocity field becomes applicable for kh up to 12. These results represent a major improvement over existing Boussinesq-type formulations in the literature. A numerical model is developed in a single horizontal dimension and it is used to study phenomena such as solitary waves and their impact on vertical walls, modulational instability in deep water involving recurrence or frequency downshift, and shoaling of regular waves up to breaking in shallow water.

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Fifth-order state-space modeling of class E amplifiers with finite-series inductance and an anti-parallel diode at the switch

IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications ◽

10.1109/81.948444 ◽

2001 ◽

Vol 48 (9) ◽

pp. 1141-1146 ◽

Cited By ~ 4

Author(s):

L.S. Tan ◽

D.G.H. Tan ◽

R.A. McMahon ◽

D.R.H. Carter

Keyword(s):

State Space ◽

Finite Series ◽

Space Modeling ◽

State Space Modeling ◽

Fifth Order ◽

Order State ◽

Class E

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General series involving H-functions

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100044443 ◽

1969 ◽

Vol 65 (2) ◽

pp. 461-465

Author(s):

R. N. Jain

Keyword(s):

Hypergeometric Function ◽

Analytic Functions ◽

General Nature ◽

Complex Numbers ◽

Important Class ◽

Vast Number ◽

Finite Series ◽

General Series ◽

Special Cases ◽

Image Position

MacRobert (4–7) and Ragab(8) have summed many infinite and finite series of E-functions by expressing the E-functions as Barnes integrals and interchanging the order of summation and integration. Verma (9) has given two general expansions involving E-functions from which, in addition to some new results, all the expansions given by MacRobert and Ragab can be deduced. Proceeding similarly, we have studied general summations involving H-functions. The H-function is the most generalized form of the hypergeometric function. It contains a vast number of well-known analytic functions as special cases and also an important class of symmetrical Fourier kernels of a very general nature. The H-function is defined as (2)where 0 ≤ n ≤ p, 1 ≤ m ≤ q, αj, βj are positive numbers and aj, bj may be complex numbers.

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