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Among them were new generating functions, transforms, and asymptotic expansions.
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This expansion follows directly from the asymptotic expansion for the exponential integral.
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Analysis of the mathematical model is done with the help of asymptotic expansion.
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Voronovskaya Type Asymptotic Expansions for Error Function Based Quasi-Interpolation Neural Network Operators
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The advantage of the Edgeworth series is that the error is controlled, so that it is a true asymptotic expansion.
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The key was to modify the doubly asymptotic expansion based on a detailed analysis of the scalar wave equation formulated in spherical coordinates.
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Building on previous research, a doubly asymptotic expansion of the SBFE dynamic stiffness was employed to address the mathematical challenge of accurately modelling radiation damping.
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Often, the resulting inaccuracy (i.e., the partial sum of the omitted terms) can be described by an equation involving Big O notation (see also asymptotic expansion).
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Similarly, asymptotic expansions in powers of 1/R have been obtained to high order by Cizek et al. for the lowest ten discrete states of the hydrogen molecular ion (clamped nuclei case).
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Based on fractional calculus theory we derive a fractional Voronovskaya type asymptotic expansion for the error of approximation of these operators to the unit operator, as we are studying the univariate case.
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Briefly, the positive mass conjecture says that if a three-dimensional manifold has positive scalar curvature and is asymptotically flat, then a constant that appears in the asymptotic expansion of the metric is positive.
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Siegel (1932) and Edwards (1974) derive the Riemann–Siegel formula from this by applying the method of steepest descent to this integral to give an asymptotic expansion for the error term R(s) as a series of negative powers of Im(s).
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This integral transform is closely connected to the theory of Dirichlet series, and is often used in number theory, mathematical statistics, and the theory of asymptotic expansions; it is closely related to the Laplace transform and the Fourier transform, and the theory of the gamma function and allied special functions.
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The expansion might slow to almost nothing, asymptotically approaching zero, but it would never stop.
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Compact families of holomorphic functions with asymptotic expansion in an open convex subset of Cn.
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To prove the pointwise asymptotic expansion of the spectral shift function, we establish a limiting absorption Theorem for P(h).
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Note that although the generalized Lambert W function eigenvalue solutions supersede these asymptotic expansions, in practice, they are most useful near the bond length.
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... the relations between convergent series and asymptotic expansions, the zeros and the addition theorem of the Bessel functions, various Bessel integrals, spherical harmonics and Fourier series.
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Based on fractional calculus theory we derive fractional Voronovskaya type asymptotic expansions for the error of approximation of these Full-Text comments powered by Disqus. comments powered by Disqus
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Moreover, after properly taking care of (hidden) local UV singularities, we perform a straightforward asymptotic expansion of the unintegrated amplitude, without having to split the integration domain into several regions.
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Absent dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero.
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The Big Freeze is a scenario under which continued expansion results in a universe that asymptotically approaches absolute zero temperature.
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Although a limit value for lnk of -6 is proposed in the literature (lower values are non-reactive aggregates and higher values are deleterious aggregate), from the analysis of the experimental data it was observed that low values of this parameter could be associated with not asymptotic growth of expansion and, therefore, the aggregates presents a deleterious behavior.
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He is well known for his original results in the spectral theory of differential equations, including the discovery of new methods for the study of the asymptotic behaviour of spectral functions and the convergence expansions in terms of eigenfunctions .
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4) The flow velocity energy after passing through the slits is fully restored to a constant temperature in the expansion chamber due to isobaric control, so the velocity before each slit is asymptotically 0, that is, no air permeability occurs.
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27 sinne gevind in 11 ms. Hulle kom uit baie bronne en word nie nagegaan nie.