Apollonius coordinates,theN-body problem,and continuation of periodic solutions

This paper treats theN-body problem and its relation to various restricted problems. For each solution of the Kepler problem a generalization of the pulsating coordinates used to express the Hamiltonian of the elliptic restricted three-body problem is given. These coordinates are called Apollonius coordinates. The method of symplectic scaling is used to give a precise derivation of the elliptic restricted problem showing the precise asymptotic relationship between the restricted problem and the full three-body problem. This derivation obviates the proof of the fact that a nondegenerate periodic solution of the elliptic restricted three-body problem can be continued into the full three-body problem under mild nonresonance assumptions. Also, the method of symplectic scaling is used to give a precise derivation of the elliptic Hill lunar equation showing the precise relationship between the elliptic Hill lunar equation and the full three-body problem. A similar continuation theorem is established.     

On the equivalence of the BLUEs under a general linear model and its restricted and stochastically restricted models

Necessary and sufficient conditions are derived for the equalities of the best linear unbiased estimators (BLUEs) of parametric functions under a general linear model and its restricted and stochastically restricted models to hold.     

SUBJECT INDEX TO VOLUME 57(2014)

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Analysis of orthogonal multi-matching pursuit under restricted isometry property

Orthogonal multi-matching pursuit(OMMP)is a natural extension of orthogonal matching pursuit(OMP)in the sense that N(N≥1)indices are selected per iteration instead of 1.In this paper,the theoretical performance of OMMP under the restricted isometry property(RIP)is presented.We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y=φx,provided that the sampling matrixφsatisfiesδKN-N+1+(K/N)~(1/2)θKN-N+1,N1.Moreover,the performance of OMMP for support recovery from noisy observations is also discussed.It is shown that,for l_2 bounded and l_∞bounded noisy cases,OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrixφand the minimum magnitude of the nonzero components of the signal.     

Comparison of three methods for fractionation and enrichment of low molecular weight proteins for SELDI-TOF-MS differential analysis

In most diseases, the clinical need for serum/plasma markers has never been so crucial, not only for diagnosis, but also for the selection of the most efficient therapies, as well as exclusion of ineffective or toxic treatment. Due to the high sample complexity, prefractionation is essential for exploring the deep proteome and finding specific markers.In this study, three different sample preparation methods (i.e., highly abundant protein precipitation, restricted access materials (RAM) combined with IMAC chromatography and peptide ligand affinity beads) were investigated in order to select the best fractionation step for further differential proteomic experiments focusing on the LMW proteome (MW inferior to 40,000 Da). Indeed, the aim was not to cover the entire plasma/serum proteome, but to enrich potentially interesting tissue leakage proteins. These three methods were evaluated on their reproducibility, on the SELDI-TOF-MS peptide/protein peaks generated after fractionation and on the information supplied.The studied methods appeared to give complementary information and presented good reproducibility (below 20%). Peptide ligand affinity beads were found to provide efficient depletion of HMW proteins and peak enrichment in protein/peptide profiles.     

On restricted domination in graphs

The k-restricted domination number of a graph G is the minimum number d _k such that for any subset U of k vertices of G, there is a dominating set in G including U and having at most d _k vertices. Some new upper bounds in terms of order and degrees for this number are found.      

Incidence of apparent restricted diffusion in three different models of cerebral infarction

High speed magnetic resonance imaging (MRI) and short diffusion times are used to investigate the appearance of restricted diffusion in three different models of cerebral infarction. The models are: the middle cerebral artery occlusion (MCAO) model in the rat, the carotid occlusion model in the gerbil, and the Rose Bengal microvascular occlusion model in the rat. All three were investigated for 16 b-values equally spaced between 10 and 1510 s/mm² using two distinct experiments. In the ct (constant time) experiment, the diffusion time was held constant at 11.7 ms while the b-value was varied with the gradient strength. In the cg (constant gradient) experiment, the gradient strength was held constant and the b-value increased by varying the diffusion time from 4.4 to 11.7 ms. A monoexponential decay of the signal intensity with b-value in the ct experiment accompanied by nonmonoexponential (NME) decay in the cg experiment is indicative of restricted diffusion. As this phenomenon is detectable only at short diffusion times, it cannot be due to restriction by impermeable membranes, and we have thus termed this apparent restriction. For the MCAO model and the carotid occlusion model, apparent restriction was found both inside the infarct territory and in some regions outside it. No definite evidence for restriction was found for the Rose Bengal model, which was, however, only studied from 24 h post-insult.     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

具有三角分解李代数的积分元和中心扩张

本文将应用广义限制李代数的概念来研究具有三角分解李代数的积分元和中心扩张的关系.对于给定的广义限制普遍包络代数,我们确定了它的积分元并且提供了一种计算dim H2(L,F)的方法.     

限制Hom-李超代数的环面和Cartan-分解

把限制Hom-李代数的性质推广到限制Hom李超代数, 给出限制Hom-李超代数的半单元与环面元的定义和性质及其Hom-李Cartan-子超代数的定义和性质. 确定限制Hom-李超代数的Hom-李Cartan-子超代数可用其极大环面刻画的充要条件, 并给出限制Hom-李超代数极大环面的性质.