CW Type Research Articles

Some Function Spaces of CW Type

J. Milnor’s result on the CW type of certain function spaces ${\operatorname {map}}\left ( {X,Y} \right )$ is extended to allow the case in which $X$ has a finite $k$-skeleton and ${\pi _i}Y = 0$, $i > k$. One conclusion is that the self-equivalence monoid of any Postnikov stage of a finite complex has CW type. Another is that the monoid of pointed self-equivalences of a $K\left ( {\pi ,1} \right )$ manifold has contractible components when $\pi$ is finitely-generated.

Some function spaces of CW type

J. Milnor’s result on the CW type of certain function spaces map ( X , Y ) {\operatorname {map}}\left ( {X,Y} \right ) is extended to allow the case in which X X has a finite k k -skeleton and π i Y = 0 {\pi _i}Y = 0 , i > k i > k . One conclusion is that the self-equivalence monoid of any Postnikov stage of a finite complex has CW type. Another is that the monoid of pointed self-equivalences of a K ( π , 1 ) K\left ( {\pi ,1} \right ) manifold has contractible components when π \pi is finitely-generated.

ベクトル心電図に関する研究

To elucidate the cause of high degree left axis deviation (LAD) revealed in ECG, 86 subjects in total, 60 males and 26 females, whose ECG indicated a QRS-interval less than 0.12 sec and a mean QRS electrical axis in-between -30° to -90°, were selected for analysis of VCG. Lead systems of VCG introduced by Frank and Kimura were employed for this study.As described in preceeding paper, the Kimura lead system is considered to be useful for the analysis of LAD since in experiments of human torso models, this system was demonstrated to have a value in use to detect vertical changes of heart-electromotive-forces. Then, by the analysis of configurations of QRS-loop in the frontal plane of VCG, they were divided as follows; in the Frank lead system: 6 types, F-1 to F-6, in the Kimura lead system: 5 types, CCW(L), CCW(R), CCW(R'), CW(L), CW(R). In the latter, they were furthermore sub-divided into 3 types, a, b, and c, according to the length of the vertical component of QRS-loop. (See the text, Fig. 1 and Fig. 2)Results were as follows: 1) F-4 and F-5 types which are considered to represent the left anterior hemiblock (LAH) in the Frank lead system showed CCW(L) type, left superiorly deviated QRS-loop with elongation, in the Kimura lead system. 2) The SI SII SIII type in the ECG was determined to corespond to F-1, F-2, or F-6 type in the Frank lead system, and to CCW(R), CCW(R'), or CW(R) type in the Kimura lead system in which the right component of QRS-loop was dominant. 3) Several cases classified as F-3 or F-6 type in the Frank lead system which could not be defined as LAH were determined as CCW(L)a type in the Kimura lead system suggesting the LAH. 4) There could not be found correlations between Rosenbaum's diagnostic criteria for LAH and these VCG configurations. Therefore, it was suggested by the present study that the analysis of VCG configurations are useful for the diagnosis of LAH. 5) VCGs of ostium primum atrial septal defect were classified as F-6 and CCW(R') types whose configurations of QRS-loop were different from the one of LAH. 6) Several cases of pulmonary emphysema associating with LAD were disclosed to be classified as F-4 and CCW(L)a types suggesting the LAH.

The Cultural Complexes from the Lagoa Santa Region, Brazil

THE Lagoa Santa region, Minas Gerais, Brazil, has long attracted the attention of the scientific world ever since the Danish naturalist, Peter Wilhelm Lund, announced in the last century the possibility that man in this area was contemporary with extinct Pleistocene animals (Paula Couto 1950). Since then the area has drawn many other investigators, for the sites are numerous and of easy access in the many limestone caves and rock shelters north of Belo Horizonte, the state capital. The majority of reports which have been published on Lagoa Santa, in particular those by the members of the Academy of Science of Minas Gerais, have continued the claim made by Lund that Pleistocene man lived in these caves (Walter n.d.; 1958; Mattos 1946; 1950). Because the conclusions made by these writers have not been accepted universally (Watson 1949; Hrdlicka 1912) a project was initiated in 1956 by the University of South Dakota and the Museu Nacional of Brazil to make further tests in the area1 (Fig. 1). The Lagoa Santa caves and rock shelters are a small part of a large number of caves in prominent limestone masses that in many areas form cliffs in the main valleys and tributaries of the Rio das Velhas and Rio San Francisco in the states of Minas Gerais and Bahia. In the region of Lagoa Santa are many running streams, some of which are partially subterranean, and numerous small lakes and limestone sink holes. The vegetation of the area is mainly of the savannah type of tropical forest, while the climate is of the alternating wet and dry season variety (Koppen's CW type, see Goode 1943:20). Judging by the paintings made in the Lagoa Santa caves the following recent fauna lived in the area: deer, tree sloth, tapir, fox, several varieties of cats, pacas, and marsupials. The limestone masses of Lagoa Santa were deposited during the Paleozoic and hardened into the present-day Bambuhy formation during the Silurian. The geological and climatological history of the Lagoa Santa region has not been investigated or reconstructed in detail by geologists and the interpretation which follows is solely that of the writer's. It is based on personal observation. In addition, the conclusions rest heavily upon comparison with North America, the assumption being that there was a strong correlation in the meteorological cycles in the two continents. (1) During an unknown time in the past when the climate was colder and more humid than at present, perhaps the early Pleistocene, the Lagoa Santa region was covered with extensive lakes. (2) As these lakes rose and subsided wave action and bank erosion cut into the limestone formations, forming sheer cliffs. (3) Caves were cut into the faulted cliffs when the level of the lakes re-