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61.
Lusternik–Schnirelmann category of a manifold gives a lower bound of the number of critical points of a differentiable map
on it. The purpose of this paper is to show how to construct cone-decompositions of manifolds by using functions of class
C
1 and their gradient flows, where cone-decompositions are used to give an upper bound for the Lusternik–Schnirelmann category
which is a homotopy invariant of a topological space. In particular, the Morse–Bott functions on the Stiefel manifolds considered
by Frankel (1965) are effectively used to construct the conedecompositions of Stiefel manifolds and symmetric Riemannian spaces to determine
their Lusternik–Schnirelmann categories. 相似文献
62.
63.
The purpose of this article is to study an existence of p-bases and mainly to give some regularity criteria for semilocal rings essentially of finite type over fields. 相似文献
64.
o-Ethynylbenzyl phenyl selenides regioselectively reacted with trifluoromethanesulfonic acid to afford the (Z)-1-methylidene-2-phenyl-1,3-dihydro-1H-benzo[c]selenophenium salts as the major products during the 5-exo-dig mode cyclization in good yields together with minor E isomers. The structure of the major (Z)-selenophenium salt was established by the single crystal X-ray crystallographic analysis using a tert-butyl derivative. 相似文献
65.
66.
Under pathological conditions, morphological changes of the cells and tissues may differ from those of normal conditions, which can be reflected by changes in light scattering (LS). Consequently, LS has been recognized as a potential non-invasive tool for optical diagnosis of living tissue. This paper aimed to identify the basic properties of LS of isolated brain mitochondria in vitro under normoxic and anoxic conditions in the presence and absence of Mg2+. An increase in LS was observed during anoxia in both the presence and absence of Mg2+. In both cases, the changes in LS initiated by anoxia and reoxygenation started concomitantly with the reduction of heme aa3. The rates of LS changes were slower than those of heme aa3, particularly in the presence of Mg2+. Mg2+ inhibited the morphological responses of mitochondria caused by the addition of ADP and ATP, and significantly reduced the oxygen consumption rate in state 4. These results are due to modulation of the K+/H+ antiporter affected by Mg2+. In addition, the mitochondria were well coupled, although the basal level of LS fell after addition of Mg2+. Therefore, the observed responses of mitochondria at anoxia were physiological and independent of the presence or absence of Mg2+. The relationship between LS and redox state of cytochrome c oxidase, an anoxic indicator, provides a basis to assess the tissue conditions in vivo. 相似文献
67.
Takashi Ishida Mamoru Shoji Yoshiyuki Miyabata Yasumasa Shibata Eiji Ohno Shunji Ohaira 《Optical Review》1994,1(2):183-187
A high density mark edge recording method on a phase change rewritable disk is reported. A carrier-to-noise ratio of 55 dB for a mark length of 0.55,μm is obtained by using a 680 nm, NA 0.6 head and a phase change rewritable disk. In mark edge recording, it is necessary to record each mark in correct length. A new laser power modulation pattern is proposed. This pattern consists of a first-pulse, a multi-pulse chain and a last-pulse. Both positions of the first-ptilse and the last-pulse are movable. By adjusting these positions, a jitter, σ/Tw (Tw is window margin), is improved to 6.5% in high density EFM (Eight to Fourteen Modulation) recording of 0.4 μm/bit. 相似文献
68.
Jin Akiyama Hiroshi Era Severino V. Gervacio Mamoru Watanabe 《Journal of Graph Theory》1989,13(5):571-573
Let the finite, simple, undirected graph G = (V(G), E(G)) be vertex-colored. Denote the distinct colors by 1,2,…,c. Let Vi be the set of all vertices colored j and let <Vi be the subgraph of G induced by Vi. The k-path chromatic number of G, denoted by χ(G; Pk), is the least number c of distinct colors with which V(G) can be colored such that each connected component of Vi is a path of order at most k, 1 ? i ? c. We obtain upper bounds for χ(G; Pk) and χ(G; P∞) for regular, planar, and outerplanar graphs. 相似文献
69.
70.
The effects of the homogeneity of precursor non-crystalline Pb---Ti---O gels on their transformation to crystalline PbTiO3 were studied. Hydrous gels were prepared via two different routes, i.e., (i) mixing two unitary sols (MS), and (ii) co-precipitation (CP). Mechanical pretreatment was also carried out, primarily for the purpose of homogenization. The local homogeneity was evaluated by elementary microanalysis using a transmission electron microscope. The process of ball-milling the MS gel for 3 h improved its homogeneity only slightly. However, the homogeneity of the ball-milled MS gel suddenly increased to that of the CP gel on subsequent heating to a temperature as low as 483 K. This type of thermal homogenization was not observed for the unground MS gel. The evaporation of lead monoxide on further heating to 1023 K was also suppressed by preliminary ball-milling. All these results suggest that the ionic migration and the formation of Pb---O---Ti bonds in the gels take place during the mechanical activation with the aid of OH groups. 相似文献