In order to calculate the energy when 0127 is small, we expand the right-hand side of the BrillouinWigner equation in terms of a coupling constant 03BB. Both hierarchies in 0127 and 03BB are connected. The Padé approximants of the right-hand side converge. Tome 40 N° 2 15 JANVIER 1979 LE JOURNAL DE PHYSIQUE LETTRES

In Fitzpatrick and Flynn (J. Symbolic Comput. 13 (1992) 133), a Gröbner basis technique for multivariable Padé approximation problems was developed under a rather restrictive hypothesis on the shape of the numerator and denominator in relation to the approximation conditions desired. In this article, we show that their hypotheses can be replaced by other less stringent conditions, and we show h...

and Applied Analysis 3 Table 1: The operations for generalized differential transform method. Original function Transformed function f n, t g n, t h n, t F n, k G n, k H n, k f n, t αg n, t F n, k αG n, k f n, t ∂g n, t /∂t F n, k k 1 G n, k 1 f n, t g n, t h n, t F n, k ∑k r 0 G n, r H n, k − r f n, t ∂g n, t /∂t F n, k k m G n, k m f n, t g n s, t F n, k G n s, k To improve the accuracy and c...

1 Plane Curves 2 1.1 Computation of Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Expansion at Simple Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Expansion at Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Newton Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.4 Local...

We present a differential formulation of the recursion formula of the hierarchical model which provides a recursive method of calculation for the high-temperature expansion. We calculate the first 30 coefficients of the high temperature expansion of the magnetic susceptibility of the Ising hierarchical model with 12 significant digits. We study the departure from the approximation which consist...

An important hurdle in multi-exponential analysis is the correct detection of the number of components in a multi-exponential signal and their subsequent identification. This is especially difficult if one or more of these terms are faint and/or covered by noise. We present an approach to tackle this problem and illustrate its usefulness in motor current signature analysis (MCSA), relaxometry (...

We apply Padé approximation techniques to deduce lower bounds for simultaneous rational approximation to one or more algebraic numbers. In particular, we strengthen work of Osgood, Fel’dman and Rickert, proving, for example, that max {∣∣∣√2− p1/q∣∣∣ , ∣∣∣√3− p2/q∣∣∣} > q−1.79155 for q > q0 (where the latter is an effective constant). Some of the Diophantine consequences of such bounds will be d...

After a prolonged and arduous fight with cancer, our beloved Herbert Robert Stahl1 died in his 71st year on April 22, 2013, in Berlin. Herbert was born on August 3, 1942, in Fehl-Ritzhausen, in the German state of RheinlandPfalz. At the age of 16, he started to work as an electrician for Allgemeine ElektricitätsGesellschaft (AEG, General Electricity Company), and by the time of his retirement i...

We calculate accurate eigenvalues of a bounded oscillator by means of the Riccati–Padé method that is based on a rational approximation to a regularized logarithmic derivative of the wavefunction. Sequences of roots of Hankel determinants approach the model eigenvalues from below with remarkable convergence rate.

We show that a simple and straightforward rational approximation to the Thomas– Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Padé approximants are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas–Fermi equation for isolated atoms and for atoms in strong magnetic fields.