Search results for "Remainder"
showing 10 items of 14 documents
Ejection and collision orbits of the spatial restricted three-body problem
1985
We begin by describing the global flow of the spatial two body rotating problem, μ=0. The remainder of the work is devoted to study the ejection and collision orbits when μ>-0. We make use of the ‘blow up’ techniques to show that for any fixed value of the Jacobian constant the set of these orbits is diffeomorphic to S2×R. Also we find some particular collision-ejection orbits.
An analysis of Ralston's quadrature
1987
Ralston's quadrature achieves higher accuracy in composite rules than analogous Newton-Cotes or Gaussian formulas. His rules are analyzed, computable expressions for the weights and knots are given, and a more suitable form of the remainder is derived.
Continuum elastic sphere vibrations as a model for low-lying optical modes in icosahedral quasicrystals
2004
The nearly dispersionless, so-called "optical" vibrational modes observed by inelastic neutron scattering from icosahedral Al-Pd-Mn and Zn-Mg-Y quasicrystals are found to correspond well to modes of a continuum elastic sphere that has the same diameter as the corresponding icosahedral basic units of the quasicrystal. When the sphere is considered as free, most of the experimentally found modes can be accounted for, in both systems. Taking into account the mechanical connection between the clusters and the remainder of the quasicrystal allows a complete assignment of all optical modes in the case of Al-Pd-Mn. This approach provides support to the relevance of clusters in the vibrational prop…
Force probe simulations using a hybrid scheme with virtual sites.
2017
Hybrid simulations, in which a part of the system is treated with atomistic resolution and the remainder is represented on a coarse-grained level, allow for fast sampling while using the accuracy of atomistic force fields. We apply a hybrid scheme to study the mechanical unfolding and refolding of a molecular complex using force probe molecular dynamics (FPMD) simulations. The degrees of freedom of the solvent molecules are treated in a coarse-grained manner while atomistic resolution is retained for the solute. The coupling between the solvent and the solute is provided using virtual sites. We test two different common coarse-graining procedures, the iterative Boltzmann inversion method an…
High order normal form construction near the elliptic orbit of the Sitnikov problem
2011
We consider the Sitnikov problem; from the equations of motion we derive the approximate Hamiltonian flow. Then, we introduce suitable action–angle variables in order to construct a high order normal form of the Hamiltonian. We introduce Birkhoff Cartesian coordinates near the elliptic orbit and we analyze the behavior of the remainder of the normal form. Finally, we derive a kind of local stability estimate in the vicinity of the periodic orbit for exponentially long times using the normal form up to 40th order in Cartesian coordinates.
Motif patterns in 2D
2008
AbstractMotif patterns consisting of sequences of intermixed solid and don’t-care characters have been introduced and studied in connection with pattern discovery problems of computational biology and other domains. In order to alleviate the exponential growth of such motifs, notions of maximal saturation and irredundancy have been formulated, whereby more or less compact subsets of the set of all motifs can be extracted, that are capable of expressing all others by suitable combinations. In this paper, we introduce the notion of maximal irredundant motifs in a two-dimensional array and develop initial properties and a combinatorial argument that poses a linear bound on the total number of …
An efficient Chinese remainder theorem based node capture resilience scheme for Mobile WSNs
2010
Node capture attack is a critical issue in Mobile WSNs where attacker-controlled replicas may act maliciously. In this paper, we present a novel Chinese remainder theorem based node capture resilience scheme that can be utilized to discover and revoke captured nodes. Moreover, our scheme can limit the ability of captured nodes to further compromise forward security, backward security, and launch collusion attacks. Detailed analysis shows that our scheme indeed achieves the expected design goals.
CONSTRUCTION OF METASTABLE STATES IN QUANTUM ELECTRODYNAMICS
2004
In this paper, we construct metastable states of atoms interacting with the quantized radiation field. These states emerge from the excited bound states of the non-interacting system. We prove that these states obey an exponential time-decay law. In detail, we show that their decay is given by an exponential function in time, predicted by Fermi's Golden Rule, plus a small remainder term. The latter is proportional to the (4+β)th power of the coupling constant and decays algebraically in time. As a result, though it is small, it dominates the decay for large times. A central point of the paper is that our remainder term is significantly smaller than the one previously obtained in [1] and as…
Does one need theO(ε)- andO(ε2)-terms of one-loop amplitudes in a next-to-next-to-leading order calculation ?
2011
This article discusses the occurrence of one-loop amplitudes within a next-to-next-to-leading-order calculation. In a next-to-next-to-leading-order calculation, the one-loop amplitude enters squared and one would therefore naively expect that the $\mathcal{O}(\ensuremath{\epsilon})$- and $\mathcal{O}({\ensuremath{\epsilon}}^{2})$-terms of the one-loop amplitudes are required. I show that the calculation of these terms can be avoided if a method is known, which computes the $\mathcal{O}({\ensuremath{\epsilon}}^{0})$-terms of the finite remainder function of the two-loop amplitude.
Complementary mobile-phase optimisation for resolution enhancement in high-performance liquid chromatography.
2000
An optimisation methodology in high-performance liquid chromatography (HPLC) is presented for the selection of two or more mobile phases having an optimal complementary resolution. The complementary mobile phases (CMPs) are selected in such a way that each one resolves optimally only some compounds in the mixture, while the remainder, resolved by the other mobile phase(s), can overlap among them. The methodology is based on the computation of a peak purity measurement for each solute, using an asymmetrical peak model for peak simulation. Two global resolution criteria (product of elementary resolutions and worst elementary resolution) and two methods for solving the problem (a systematic ex…