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Algebraic monoids with affine unit group are affine


In this short paper we prove that any irreducible algebraic monoid whose unit group is an affine algebraic group is affine.


One outcome is a simple proof that for $g_{m \alpha , n \beta}$ to span $L^2,$ the lattice $(m \alpha , n \beta )$ must have at least unit density.


This is done by proving that a wellknown method, the construction of a Perron Tree, can be applied to a larger collection of subsets of the unit circle than was earlier known.


In the special case of Ω=Id, the ddimensional unit cube, we prove this conjecture, with Ω'=Id, for d≤3, describing all the tilings by Id, and for all d when Λ is a discrete periodic set.

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 In this paper the logical structure of contactless telemechanical system for distributed objects is discussed. A simple method of variable system structure for transmitting and receiving telemechanical information is adopted. The idea is that the information occurred in every controlled point (station) and the information of some of those objects,which frequently change their states, are transmitted continually and cyclically, while for other objects their information is transmitted only after any change in... In this paper the logical structure of contactless telemechanical system for distributed objects is discussed. A simple method of variable system structure for transmitting and receiving telemechanical information is adopted. The idea is that the information occurred in every controlled point (station) and the information of some of those objects,which frequently change their states, are transmitted continually and cyclically, while for other objects their information is transmitted only after any change in their states. Thus,the speed of operation will be increased, and also the error probability of system synchronization will be decreased. For the realization of the variable logical system structure, several blocks are used repetitively. For example, two commutators and one simple logical unit are used to construct a simple automatic sequential encoder, and at the same time, the two commutators are used also to operate as a matrix commutator for receiving telesignalling information etc. Therefore the system is comparatively simplified and attains a higher degree of "minimization".  本文研究了无触点集中分散目标远动系统的逻辑结构.文中提出了采用简单的系统变结构来发送和接收信息的逻辑结构方式.对被控制点及一部分比较重要或变化比较频繁的被控制目标的信息,保留了循环传送,而对大部分变化比较慢的被控制目标则采用目标有变化时才传送信号的方式,这样就提高了系统的平均动作速度,同时也减小系统的失步概率.文中采用环节的复合利用及简化的逻辑单元线路来实现这种系统的逻辑结构.例如用两个分配器和一个简单的逻辑单元“和”线路组成了很简化的选点自动程序编码器,同时这两个分配器又复合利用兼组成目标信号接收矩阵式分配器等,因而可以使得这种系统同时又具有较高的极简化度.  A right hallow circular cylinder of quartz having its generator parallel to the principal axis liberates electricity when subjected to torsion about its axis. Charges of opposite signs appear on the inner and outer surfaces. When torsion is applied in the same sense as that of the optical rotation, positive electricity is developed on the outer surface, and vice versa. The quantity of electricity produced by the action of a couple of moment C on a hollow quartz cylinder of external diameter d0, internal diameter... A right hallow circular cylinder of quartz having its generator parallel to the principal axis liberates electricity when subjected to torsion about its axis. Charges of opposite signs appear on the inner and outer surfaces. When torsion is applied in the same sense as that of the optical rotation, positive electricity is developed on the outer surface, and vice versa. The quantity of electricity produced by the action of a couple of moment C on a hollow quartz cylinder of external diameter d0, internal diameter di and length l is klC/do dodi), where k is equal to 9.2x108 in absolute C. G. S. electrostatic units.  割水晶成一圆柱,圆柱之轴即为晶体之光轴,在圆柱之中心穿一孔道,使成一空心圆柱壳,以金属箔敷於圆柱壳内外侧面成两电极。当圆柱之一端固定,一端被扭,则两电极发生异号而等量之电荷,扭转之方向既易,内外两极电荷之号亦互易。若扭力偶矩左旋,则左旋水晶柱之外极得正电;若扭力偶矩右旋则右旋水晶柱之外极得正电。 吾人曾由实验测定水晶圆柱之长短l,内外直径d_i及d_0之大小,与由扭偶矩C所生电量q之关系式如次: q=k(l/(d_0(d_0d_i)))C式中K为一常数,在C.G.S.绝对静电单位制中等於9.2×10~(8)。  The difference of two unit functions is used to represent a pulse voltage of abrupt rise and abrupt fall. By the principle of superposition, the currents produced by such a voltage on fifteen different circuits, covering twenty cases and thirtysix types are analyzed. Many interesting graphs are included. The main characteristics of the pulse currents are given by formulas with a system of notations.  代表过渡现象之算式,有一式可名曰单变函数,本 文用二单变函数之较,以表骤上骤下之脉压;而按重叠原理;以研究此种电压在各电路上所发之脉流。茲所研究者,有十五不同之电路,计刮二十类三十六种。其间插有许多有趣之图示,所得各脉流之特性,以一有秩序之方法,皆用算式表出之。   << 更多相关文摘 
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