Results 251 to 260 of about 7,930,128 (288)

Long-term attraction in higher order neural networks

IEEE Transactions on Neural Networks, 1998
Recent results on the memory storage capacity of higher order neural networks indicate a significant improvement compared to the limited capacity of the Hopfield model. However, such results have so far been obtained under the restriction that only a single iteration is allowed to converge.
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Phases of higher-order terms in the topological expansion

Physical Review D, 1985
We give here the general rules for determining the relative phases of higher-order terms in the topological expansion. We treat separately topological amplitudes and their discontinuities. Phases associated with the various discontinuities of a given topological amplitude are found to be (-1)/sup n/, where n is the total number of quark loops in the ...
, Jones, , Uschersohn
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Derivation of Skyrme Lagrangian and higher-order term

Physical Review D, 1990
The fermion loop of the nonlinear O({ital N}) {sigma} model leads to the Skyrme Lagrangian and a higher-order term without the destabilizing symmetric term.
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The Effects of Higher Order Dispersion Terms

1975
We have already mentioned previously (section 6.2) that Raynes’ treatment of a solvent site factor is, at least formally, equivalent to the inclusion of higher order dispersion terms. It should be realised, however, that even solvent atoms have higher order dispersion terms.
P. Diehl, E. Fluck, R. Kosfeld
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Higher-order annotated terms for proof search

1996
A notion of embedding appropriate to higher-order syntax is described. This provides a representation of annotated formulae in terms of the difference between pairs of formulae. We define substitution and unification for such annotated terms. Using this representation of annotated terms, the proof search guidance technique of rippling can be extended ...
Alan Smaill, Ian Green
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Nonequilibrium statistical mechanics near equilibrium: computing higher-order terms

Nonlinearity, 1998
Summary: Using Sinai-Ruelle-Bowen measures to describe nonequilibrium steady states, one can in principle compute the coefficients of expansions around equilibrium. We discuss how this can be done in practice, and how the results correspond to the zero noise limit when there is a stochastic perturbation. The approach used is formal rather than rigorous.
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Remainder terms in a higher order Sobolev inequality

Archiv der Mathematik, 2010
A remainder term for a higher-order Sobolev embedding is obtained in this paper. More precisely, if \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) with \(\mathbb{C}^m\) boundary (\(m>1\) is an integer), then there exists a constant \(c(\Omega, m)> 0\) such that \(\| u\|^2- S|u|^2_{2^*}\geq C|u|_w\) for any \(u\) in the space \(\{u\in H^m\Omega\mid ...
GAZZOLA, FILIPPO, T. Weth
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Higher order terms in the saddle point approximation

Proceedings of the IEEE, 1967
An integral of the type which commonly occurs in radiation theory is evaluated by the method of steepest descent to optain a well-known asymptotic expansion. The coefficients of the first three terms of this expansion are given in terms of functions and derivatives of functions which appear in the integrand; the coefficient of the third term does not ...
R.H. Schafer, R.G. Kouyoumjian
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Higher Order Terms in the Lamb Shift Calculation

Physical Review Letters, 1960
Following previously described techniques, the atomic energy level displacements of order alpha (Z alpha )/sup 6/ ln/sup 2/ (Z alpha )mc/sup 2/ have been calculated and yield a result in agreement with that of Layzer. An addition is introduced which corresponds to a change of gauge of the virtual photon defining one-photon Lamb shift and serves to ...
H. M. Fried, D. R. Yennie
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Higher order Hardy-Rellich inequalities with boundary remainder terms

2009
We determine boundary remainder terms for some higher order Hardy–Rellich inequalities involving the polyharmonic operator $(−\Delta)^m$. The results are proved by studying suitable auxiliary boundary eigenvalue problems, the optimal constants found may not be the classical Hardy–Rellich ones.
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