Ear Decompositions of Matching Covered Graphs

G different from and has at least Δ edge-disjoint removable ears, where Δ is the maximum degree of G. This shows that any matching covered graph G has at least Δ! different ear decompositions, and thus is a generalization of the fundamental theorem of Lovász and Plummer establishing the existence of ear decompositions. We also show that every brick G different from and has Δ− 2 edges, each of which is a removable edge in G, that is, an edge whose deletion from G results in a matching covered graph. This generalizes a well-known theorem of Lovász. We also give a simple proof of another theorem due to Lovász which says that every nonbipartite matching covered graph has a canonical ear decomposition, that is, one in which either the third graph in the sequence is an odd-subdivision of or the fourth graph in the sequence is an odd-subdivision of . Our method in fact shows that every nonbipartite matching covered graph has a canonical ear decomposition which is optimal, that is one which has as few double ears as possible. Most of these results appear in the Ph. D. thesis of the first author [1], written under the supervision of the second author. Received: November 3, 1997     

Does the entropy and volume dependence of the structural α-relaxation originate from the Johari–Goldstein β-relaxation?

Conventional theories of glass transition are focussed on reproducing the thermodynamic and dynamic properties of the structural α-process. However, in the last decade a class of secondary relaxations, called the Johari–Goldstein (JG) β-relaxations, has attracted attention in view of the existence of various correlations and similarities of its properties with the structural α-process. These experimental evidences suggest that the secondary process may play a fundamental role in glass transition, and any theory of glass transition would be incomplete until the inter-relations between the JG β-relaxation and the structural relaxation have been considered. In this paper, some significant experimental results showing several general and nontrivial connections between structural relaxation and JG β-relaxation are reported. In particular, these connections indicate that, like the structural relaxation, the JG β-relaxation is entropy and volume dependent. The experimental facts are consistent with the results of the coupling model.     

Limitations to testing the equivalence principle with satellite laser ranging

We consider the possibility of testing the equivalence principle (EP) in the gravitational field of the Earth from the orbits of LAGEOS and LAGEOS II satellites, which are very accurately tracked from ground by laser ranging. The orbital elements that are affected by an EP violation and can be used to measure the corresponding dimensionless parameter η are semimajor axis and argument of pericenter. We show that the best result is obtained from the semimajor axis, and it is limited—with all available ranging data to LAGEOS and LAGEOS II—to η ≃ 2 × 10⁻⁹, more than 3 orders of magnitude worse than experimental results provided by torsion balances. The experiment is limited because of the non uniformity of the gravitational field of the Earth and the error in the measurement of semimajor axis, precisely in the same way as they limit the measurement of the product GM of the Earth. A better use of the pericenter of LAGEOS II can be made if the data are analyzed searching for a new Yukawa-like interaction with a distance scale of one Earth radius. It is found that the pericenter of LAGEOS II is 3 orders of magnitude more sensitive to a composition dependent new interaction with this particular scale than it is to a composition dependent effect expressed by the η parameter only. Nevertheless, the result is still a factor 500 worse than EP tests with torsion balances in the gravitational field of the Earth (i.e. at comparable distance), though a detailed data analysis has yet to be performed. While EP tests with satellite laser ranging are not competitive, laser ranging to the Moon has been able to provide a test of the EP almost 1 order of magnitude better than torsion balances. We show that this is due to the much greater distance of the test masses (the Earth and the Moon) from the primary body (the Sun) and the correspondingly smaller gradients of its gravity field. We therefore consider a similar new experiment involving the orbit of LAGEOS: testing LAGEOS and the Earth for an EP violation in the gravitational field of the Sun. We show that this test may be of interest, though it is a factor 300 less sensitive than in the case of the Moon due to the fact that LAGEOS is closer to the Earth than the Moon and consequently its orbit is less affected by the Sun. The limitations we have pointed out for laser ranging can be overcome by flying in low Earth orbit a spacecraft carrying concentric test masses of different composition with the capability, already demonstrated in ground laboratories, to accurately sense in situ any differential effects between them. An erratum to this article can be found at     

Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model

Linear models and synchronous response are generally adequate to describe and analyze rotors supported by hydrodynamic bearings. Hence, stiffness and damping coefficients can provide a good model for a wide range of situations. However, in some cases, this approach does not suffice to describe the dynamic behavior of the rotor-bearing system. Moreover, unstable motion occurs due to precessional orbits in the rotor-bearing system. This instability is called “oil whirl” or “oil whip”. The oil whirl phenomenon occurs when the journal bearings are lightly loaded and the shaft is whirling at a frequency close to one-half of rotor angular speed. When the angular speed of the rotor reaches approximately twice the natural frequency (first critical speed), the oil whip phenomenon occurs and remains even if the rotor angular speed increases. Its frequency and vibration mode correspond to the first critical speed. The main purpose of this paper is to validate a complete nonlinear solution to simulate the fluid-induced instability during run-up and run-down. A flexible rotor with a central disk under unbalanced excitation is modeled. A nonlinear hydrodynamic model is considered for short bearing and laminar flow. The effects of unbalance, journal-bearing parameters and rotor arrangement (vertical or horizontal) on the instability threshold are verified. The model simulations are compared with measurements at a real vertical power plant and a horizontal test rig.     

在硅胶表面制备牛血红蛋白分子印迹聚合物

采用表面印迹法, 以乙烯基三甲氧基硅烷修饰的硅胶为载体, 丙烯酰胺为功能单体, N,N-亚甲基双丙烯酰胺为交联剂, 并将改性聚乙烯醇(PVA)作为辅助识别聚合物链(ARPCs)引入聚合体系中, 制备了牛血红蛋白分子印迹聚合物(MIP). 实验使用红外光谱分析了改性PVA的结构特征, 用扫描电镜(SEM)观察MIP的表面形貌, 考察了ARPCs的含量对MIP吸附性能的影响. 吸附动力学实验研究表明, 聚合体系中ARPCs的引入使MIP对模板牛血红蛋白(BHb)的吸附量明显提高|十二烷基磺酸钠-聚丙烯酰胺凝胶电泳(SDS-PAGE)结果显示, MIP对BHb的特异性吸附能力明显提高.     

Emergence of a new feature in the high pressure-high temperature relaxation spectrum of tri-propylene glycol

We investigated dielectric relaxation of a tri-propylene glycol system under high compression. By increasing temperature and pressure we observed that a new relaxation process emerges from the low frequency tail of the structural peak. This new peak starts to be visible at about 0.5 GPa and becomes clearly evident at 1.7 GPa. However, this additional peak merges again with the structural one as the glass transition is approached, since it has a weaker temperature dependence. This finding enriches the relaxation scenario of molecular glass formers confirming that the application of very high hydrostatic pressure can favor the detection of new relaxation or otherwise unresolved processes in supercooled liquid systems.     

TRANSFER MECHANISM OF QUININE DRUG ACROSS THE OIL/WATER (O/W) INTERFACE

The transfer phenomena of quinine drug at the aqueous 1,2- dichloroethane (DCE)interface have been studied by the current- scanning polarography. The relationships be-tween the wave height and pH of aqueous phase, concentration of quinine as well as therate of water drop are discussed. The effect of supporting electrolyte, buffer solution andthe nature of organic solvent on the polarographic wave is studied. The transfer char-acteristics of quinine in aqueous phase and in organic phase are compared, The mono- pro-tonated and diprotonated quinines can both transfer at the interface so as to produce twopolarographic waves. The transfer process of quinine at the interface is simultaneouslycontrolled by diffusion and reestablishment of the disturbed protonated equilibrium ofquinine. A further investigation is made by chronopotentiometry. On the basis of thetheoretical analysis, the formulae of the limiting current are derived and discussed. Thetheoretical results are in agreement with the experimental ones.     

The perfect matching polytope and solid bricks

The perfect matching polytope of a graph G is the convex hull of the set of incidence vectors of perfect matchings of G. Edmonds (J. Res. Nat. Bur. Standards Sect. B 69B 1965 125) showed that a vector x in Q^E belongs to the perfect matching polytope of G if and only if it satisfies the inequalities: (i) x0 (non-negativity), (ii) x(∂(v))=1, for all vV (degree constraints) and (iii) x(∂(S))1, for all odd subsets S of V (odd set constraints). In this paper, we characterize graphs whose perfect matching polytopes are determined by non-negativity and the degree constraints. We also present a proof of a recent theorem of Reed and Wakabayashi.