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Rational Interpolation: Analytical Solution
Siberian Mathematical Journal, 2001Summary: The classical problem of interpolation by rational functions is well known to be reduced to a system of linear algebraic equations, but the resultant system is usually complicated for qualitative analysis and numerical implementation. We propose a new approach which generalizes the polynomial interpolation to the rational interpolation both in
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2013
This chapter focuses on analytical solutions for the powersplit control problem defined in the previous chapter. Two well known solution concepts will be considered: the method of Lagrange multipliers and Pontryagin’s Minimum Principle. Both concepts have in common that they obtain the necessary conditions for an optimal solution by evaluating where ...
Bram de Jager +2 more
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This chapter focuses on analytical solutions for the powersplit control problem defined in the previous chapter. Two well known solution concepts will be considered: the method of Lagrange multipliers and Pontryagin’s Minimum Principle. Both concepts have in common that they obtain the necessary conditions for an optimal solution by evaluating where ...
Bram de Jager +2 more
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Poroelastic-plastic consolidation — analytical solution
International Journal for Numerical and Analytical Methods in Geomechanics, 1999Consolidation of a poroelastic material that yields according to Drucker-Prager or Mohr-Coulomb criterion leads to a Stefan problem for time-dependent pore fluid pressure. The solution to the Stefan problem for a column of infinite depth is known and is here adapted to poroelastic/plastic consolidation of a weightless material under a uniform surface ...
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Analytical Methods Of Solution
1969The theory developed in the previous chapters shows that the study of the linearized Boltzmann equation is a worthwhile undertaking and that many of the features of its solutions can be retained by using model equations. We can say more, that practically all the features are retained by a properly chosen model.
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Classical Analytical Solutions
2011Reversible binding to one site can be calculated with analytical solutions. On the basis of these formulas, data can be transformed to appear linear. Straight lines of equilibrium-binding studies in double reciprocal plots or of enzyme kinetics in Lineweaver-Burk plots or of dissociation kinetics in half logarithmic plots indicate simple mechanisms ...
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2014
Integral, or integro-differential equations representing electroanalytical models can rarely be solved analytically. However, in cases when analytical solutions are possible, they usually prove useful. Known analytical solution methods involve: solutions in the form of integrals, power series expansions, exponential series expansions, successive ...
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Integral, or integro-differential equations representing electroanalytical models can rarely be solved analytically. However, in cases when analytical solutions are possible, they usually prove useful. Known analytical solution methods involve: solutions in the form of integrals, power series expansions, exponential series expansions, successive ...
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ANNALI DELL UNIVERSITA DI FERRARA, 1999
This paper presents the proof of two results essentially due to Cattabriga and de Giorgi in 1971 about the solvability of partial differential equations with constant coefficients in the space of real analytic functions. The first theorem states that the operator \(\partial_{x_1}+ i\partial_{y_1}\) is not surjective on the space \(A(\mathbb{R}^3)\) of ...
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This paper presents the proof of two results essentially due to Cattabriga and de Giorgi in 1971 about the solvability of partial differential equations with constant coefficients in the space of real analytic functions. The first theorem states that the operator \(\partial_{x_1}+ i\partial_{y_1}\) is not surjective on the space \(A(\mathbb{R}^3)\) of ...
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Blockchain-Empowered Space-Air-Ground Integrated Networks: Opportunities, Challenges, and Solutions
IEEE Communications Surveys and Tutorials, 2022Yuntao Wang, Zhou, Jianbing Ni
exaly