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As an application we produce complete hyperbolic 5manifolds that are nontrivial plane bundles over closed hyperbolic 3manifolds and conformally flat 4manifolds that are nontrivial circle bundles over closed hyperbolic 3manifolds.


As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.


The proof is an application of a recent result by W.


The application arises because of a very strong homological property enjoyed by certain cell filtrations forqpermutation modules.


We give as an application a family of singular Schubert varieties.

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 1. The conformity of the pattern of Cicindela anchoralis to what has been considered typical of the genus becomes in telligible if the middle band, which is undoubtedly the most variable of the markings of this species, is assumed to have shifted forward and to have developed extensions both cephaled and caudad along the lateral margin and on the disc of the eIytron.2. The variation of the pattern is of the continuous type and proceeds in one principal direction. As expected, some in dividuals depart from... 1. The conformity of the pattern of Cicindela anchoralis to what has been considered typical of the genus becomes in telligible if the middle band, which is undoubtedly the most variable of the markings of this species, is assumed to have shifted forward and to have developed extensions both cephaled and caudad along the lateral margin and on the disc of the eIytron.2. The variation of the pattern is of the continuous type and proceeds in one principal direction. As expected, some in dividuals depart from this main series, in one way or another and ten such subtypes have been recognized in this study. The range of variation is very considerable.3. The male sex is found to have a greater tendency to lose its pigmentation, and this fact is interpreted as indicating its having a more variable middle band.4. Mating between the different types is entirely at random, the frequency of any given combination is apparently a function of the abundance of the individuals in a given class.5. In describing the elytral pattern of this species, Chevrolat (1845) used these words: "vitta anchorali, cum lienola pone humerum (femina amplioribus); cupreis". He evidently had regarded as typical the pattern showing fullest pigmentation. The present study shows, on the other hand, that such a pat tern, while most primitive, is not the most representative. The typical pattern is to be sought in Class Ⅳ, the model class. This last remark certainly has wider application and merits the consideration of taxonomists describing highly variable forms.  斑蝥科甲虫翅鞘色型之差異,在一部份種類中,極为顯著。本篇所論,根據中國种錨紋斑蝥,於廿二年夏採於厦門北岸,計雌雄共九百餘個,內有交配者六十二對,所得結論如下: (一)本種色型,甚为異特。若以美人薛福特氏所立之本屬理想模式色型推解,則其中間淡色横斑,較为移前,其左右則向上下分枝成H形。 (二)此種色型之變異為連續式仝趨一主要方向,但依其變異之分岐,可别为十種副式色型,詳情已於西文中加以討論。 (三)雄虫翅鞘之中間淡色横斑變異較大,其深色紋斑之傾向於縮小亦因之較雌性为甚。 (四)兩性交配,与色型之差異,全無關係。 (五)大部份個數皆呈現中間色型。其趨向於兩極端者(深色或淡色特别發達者)乃屬少数。因此分類學者於記述变異極大之種類時,應发中間色型者為代表。  The main purpose of this paper is, after making some necessary preliminaries on the theory ot linear differential operators in one real variable, to obtain the explicit condition that such an operator of any order be a Hermitean operator, and as application of the result point out various quantummechanical instances.  本文先论一实变数之线形微分演素(operator之若干性质,主旨在寻求Hermite演素之条件,并举出量子力学中之各种例证。  A simple problem in thermodynamics is considered with a view to emphasizing that the application of the adiabatic law pVrconst, for a gas is permissible only when the process is quasistatic.  本文目的在讨论热力学中一个简单问题 以指出不宜随意应用普通气体之绝热方程式pV~γ=c。   << 更多相关文摘 
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