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In our paper [KR] we began a systematic study of representations of the universal central extension[InlineEquation not available: see fulltext.] of the Lie algebra of differential operators on the circle.


Weyl group extension of quantized current algebras


Such central extension gives rise to a goup scheme that leads to a geometric construction of unrestricted representations.


The corresponding monodromyre presentation of the braid group Bg of type g is a deformation of the action of (afinite extension of) W on V.


For the special case of his construction that gives groups of type E6, we connect the two papers by answering the question: Given an Albert algebra A and a separable quadratic field extension K, what is the index of the resulting algebraic group?

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 In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in ndimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the... In this paper the general synthesis problem of optimal control systems with the criterion of transient responses as a positive integral functional (3) is discussed.In the first part it is assumed that the motion of controlled object is described by a system of ordinary differential equations and that the final states of the system form a bounded and closed convex region in ndimentional euclidian phase space. A method is proposed for finding all optimal control functions which lead any starting state into the given final region of states. Some conclusions are obtained from the maximum principle by using transversal conditions of optimal trajectories in terminal points, and the particular properties of the stated problem are pointed out. The case of linear differential equations with integral quadratic functional criterion is investigated in detail.Further, in the second part the fundamental properties of isoloss regions, the relations between the isoloss region and optimal control functions are indicated. As a direct result a partial differential equation determining the optimal lossfunction J (x) is found and the connection between function J (x)and optimal vector control function u (x) is also stated. The methods proposed are practically the extension of the methods used by us for designing time optimal control systems as seen in [5, 6 ,7].Finally, an example is illustrated with optimal trajectories shown in phase plane.The necessary numerical data is calculated by an analog computer with high accuracy.  文中研究了具有公式(3)表示的一般正积分泛函的最优控制系统的综合问题.在第一部分中研究了具有控制参数的一阶微分方程组.控制系统的终点状态为n维相空间内的某一逐段光滑边界的闭性区域Ω.文中指出了根据极大值原理和轨道终点的横截条件寻找引到Ω的所有最优轨迹的方法.这里详细地研究了具有二次泛函和被积函数中不明显含有控制参数的质量指标泛函的线性方程情况.在文中第二部分研究了等损耗区的主要特性.指出了等损耗区与最优控制函数之间的关系.导出了求算最优损耗函数J(x)的偏微分方程,以及这一函数与最优控制函数u(x)的关系.上述方法是我们曾在文献[5,6,7]中用过的最优快速系统的综合方法的推广.文章最后举有例证.  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... 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。  In this paper a method of determining the degree of freedom of motion of framed structures is presented. All the framed structures, plane or space, rigid or hinged, may be analyzed with this method. The principles involved are based on the conception of freedom of motion of structures mentioned in U. S. S. R. literatures. An extension of that conception is made in this paper.From the known U. S. S. R. structural literatures available in China, it seems that the conception of freedom of motion is applied... In this paper a method of determining the degree of freedom of motion of framed structures is presented. All the framed structures, plane or space, rigid or hinged, may be analyzed with this method. The principles involved are based on the conception of freedom of motion of structures mentioned in U. S. S. R. literatures. An extension of that conception is made in this paper.From the known U. S. S. R. structural literatures available in China, it seems that the conception of freedom of motion is applied only to hinged structures, or to bar chains, of which the individual members have no redundants. Therefore it is the purpose of this paper to extend that conception to any structures, hinged or rigid.Two methods, which may be used parallelly, are treated and two illustrations are given, are in this paper.  本文述一檢定結構自由度之方法。所有桿條結構,不論立體平面,鉸接剛接,均可應用本法,所根據之原理,係由蘇聯建築力學中自由度之觀點出發,而加以擴充。文中述及二種方法,可以平行應用。不論平面結構,立體結構,鉸接結點,剛接結點,均巳涉及,並將結構內外部之自由度,視爲一事。文中準對二種方法,舉有二個例題,以為驗算之用。   << 更多相关文摘 
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