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  patterns
There are two well known combinatorial tools in the representation theory ofSLn, the semi-standard Young tableaux and the Gelfand-Tsetlin patterns.
      
Using the path model and the theory of crystals, we generalize the concept of patterns to arbitrary complex semi-simple algebraic groups.
      
Lower bounds for Kazhdan-Lusztig polynomials from patterns
      
We give a lower bound for the values Px,w(1) in terms of "patterns".
      
This generalizes the classical definition of patterns in symmetric groups.
      
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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...

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 sub-types 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。

An interference pattern of two systems of fringes has been obtained by vising two radiations in a Hilger prism interferometer A system of white bands with equal spacing which are always parallel to the refracting, edge of the prisin is the result of the intersection of the two systems of fringes. The white bauds travel as one of the reflecting mirror in the interferometer makes a parallel displacement. Let d be the displacement of mirror when the white bauds travel one spacing,Two yellow doublets in sodium...

An interference pattern of two systems of fringes has been obtained by vising two radiations in a Hilger prism interferometer A system of white bands with equal spacing which are always parallel to the refracting, edge of the prisin is the result of the intersection of the two systems of fringes. The white bauds travel as one of the reflecting mirror in the interferometer makes a parallel displacement. Let d be the displacement of mirror when the white bauds travel one spacing,Two yellow doublets in sodium and mercury lamps were used. The values found forA comparison of this method with the visibility corve by Michelson interfero-ineter has been discussed.

在Hilger棱镜干涉仪中,用两辐射线,则在一干涉图形中可得两组不同方向之干涉纹;因两组不同方向之干涉纹之相交,而得一组平行之白色条纹。此种条纹恒与棱镜折射边相平行,而条纹间之间隔为相等。当干涉仪之一反射镜作前後平行移动时,白色条纹则向左或右移动。令白色条纹移过一间隔时,反射镜移动之距离为d.则得 1/(λ_2)-1/(λ_1)=1/2d. 钠光及汞光灯中之黄色双线普用于此实验中。1/(λ_2)-1/(λ_1)之值各求得为17.22厘米~(-1)及63.29厘米~(-1)。此实验与麦凯尔逊干涉仪之明视曲线互见短长,本文曾讨论及之。

A method based upon simple diffraction theory is described for the calculation of modified paraboloid reflectors to produce from a point source a shaped beam of arbitrary shape in one plane and uniformly narrow in the perpendicular planes. A specific application of the shaped beam antennas is in connection with radar antennas designed for height finding. In this case the antenna must have a sharp elevation beam for obtaining precise elevation information and a rapid elevation scan. The beam must be relatively...

A method based upon simple diffraction theory is described for the calculation of modified paraboloid reflectors to produce from a point source a shaped beam of arbitrary shape in one plane and uniformly narrow in the perpendicular planes. A specific application of the shaped beam antennas is in connection with radar antennas designed for height finding. In this case the antenna must have a sharp elevation beam for obtaining precise elevation information and a rapid elevation scan. The beam must be relatively broad in azimuth in order that the target will be held in the beam long enough to obtain height information. If a fixed minimum of illumination is to be achieved at a given linear distance on both sides of the center line of the azimuth beam, the amplitude pattern must have the so-called "double cosecant" or "beavertail" shape.

本论文讨论如何利用简单衍射理论,计算改良抛物面反射器天线幅射之图型。此反射器可将一无方向性辐射源之能量聚集于任何形状之波束中。此原理可以应用在地面上或船面上寻求飞机高度雷达天线之设计。在此类雷达中,天线之方位图型必须为“双馀割平方”式;其特性为自波束对称轴线起,至其两端,辐射一次路程之功率,与方位角之馀割平方成正比。得此图型之最简易方法为置一狭窄之铅垂金属条于一截形抛物面反射器之中心,金属条之宽度,可改变波束之方向性;其支距,即金属条与反射器之距离,可影响两反射波之位相。故改变金属条之宽度及其支距,可得欲得之图型。 利用衍射及干涉理论,计算金属条及截形抛物面所生之总图型为:在方位面内,幅射强度J_H与水平角θ之关系为: J_H =AA[sin~2(15πsinθ)/(15πsinθ)~2-2(1-cosπ/4)sin(2πsinθ)/2πsinθ(sin(2πsinθ)/2πsinθ-sin(15πsinθ)/15πsinθ)]A为辐射波振幅,A为A之复共轭数。计算之结果与实验之结果,颇为一致。

 
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