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A recognition problem in converting linear programming to network flow models


A routing in a network assigns to each ordered pair of nodes a fixed path.


When either a node or a link in a faulttolerant network fails, the communication from one node to another using this faulty element must be sent via one or more intermediate nodes along a sequence of paths determined by this routing.


An important and practical problem is how to choose a routing in the network such that intermediate nodes to ensure communication are small for any faultset.


The result shows that most inverse network optimization problems with l∞ objective function can be solved in the polynomial time.

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 Properties of the electric network determinants are throughly investigated. The new rules for obtaining the denominator and the numerators of the electric network determinants due to K. T. Wang are generalized. Both the generalized rules and the rules given by Kirchhoff are proved from the properties of the determinants studied. A new inductive method for obtaining the denominator and the numerators is offered.  本文所述为对于电网络行列式各种性质之彻底探讨。从探讨所得,可将最近王季同氏所发明分解电网络之新方法,加以普遍化。此经过普遍化之新方法,以及Kirchhoff氏原有求此类行列式分母分子之规则,皆可从行列式之性质,求得严格的证明。最后著者并供献一更觉简便的分解电网络之推演方法。  Formulas are derived for the solution of the transient currents of resistanceterminated dissipative πtype lowpass, T and πtype highpass electric wave filters. Oseillograms taken by cathode ray oscillograph for dc. and ac. cases are found to agree with the results calculated from these formulas. From these calculations, the following conclusions are derived: (1) When the terminating resistance is gradually increased from 0, the damping constants of the damped sine terms begin to differ greatly from each... Formulas are derived for the solution of the transient currents of resistanceterminated dissipative πtype lowpass, T and πtype highpass electric wave filters. Oseillograms taken by cathode ray oscillograph for dc. and ac. cases are found to agree with the results calculated from these formulas. From these calculations, the following conclusions are derived: (1) When the terminating resistance is gradually increased from 0, the damping constants of the damped sine terms begin to differ greatly from each other, ranging in decreasing magnitudes from the first damped sine term to the last term of cutoff frequency. Hence the transient is ultimately of the cutoff frequency. At the cutoff frequency, this constant is greater than the corresponding constant (R/2L) when the termination is absent. (2) For each increase of one section, there is introduced an additional damped sine term with smaller damping constants. Therefore transients die out faster in filters of small no. of sections. (3) With the same network constants, the damping constants of πtype filters are greater than the corresponding values of Ttype filters. As a result, transients die out faster in πtype filters. (4) The amplitudes of the transient terms in the attenuation and transmission ranges are of the same order of magnitude, and the filtering property only exists in the steady states. (5) The cutoff frequency of the πtype filters varies with the no. of sections used. When only two sections of low, or, highpass filter are used, the variation amounts to nearly 26 per cent from the theoretical value.  此篇先推求收端加电阻时,低频与高频滤波器瞬流之公式依此公式算出之图与用阴极光示波器映出之曲线相符合。自推算之结果,可得下列结论: (一)在滤波器收端电阻渐加时,瞬流各项之挫率渐渐互异其数量,由第一挫波项至最後隔阻频项,顺序渐减;其最小数仍比收端无电阻时之挫率(约等于R/2L)为大。故瞬流终必变为隔阻频之电流,而较收端无电阻时易于消灭。 (二)当滤波器增加一段时,瞬流之项数亦加一,所加项之挫率皆比前有者为小,故少段滤波器之瞬流易于消灭。 (三)在π式滤波器中,其瞬流各项之挫率恒较同一电恒数T式滤波器中之相当项之挫率为大故在π式滤波器中,瞬流消灭较易。 (四)在隔阻频后瞬流之数量与在其前者相彷,恒较隔阻频后之安定数量大数十倍,故滤波器之特性仅能见之于安定状态之下。 (五)π式滤波器之隔阻电频随所用之段数而变化在二段之滤波器中,此变化数为最高,其数与理想之数相差百分之二十六。  Formulas are derived for the solution of the transient currents of resistanceterminated dissipative T& πtype bandpass electric wave filters of the constant X type. Oscillagrams taken hy cathode ray oscillograph for dc. & ac. cases are found to agree with the calculated results. From these calculations, the following conclusions are derived: (1) No matter what the impressed frequencies are, the transient is ultimately of the lower cutoff frequency. (2) The receivingend indicial admittance consists of... Formulas are derived for the solution of the transient currents of resistanceterminated dissipative T& πtype bandpass electric wave filters of the constant X type. Oscillagrams taken hy cathode ray oscillograph for dc. & ac. cases are found to agree with the calculated results. From these calculations, the following conclusions are derived: (1) No matter what the impressed frequencies are, the transient is ultimately of the lower cutoff frequency. (2) The receivingend indicial admittance consists of transient terms symmetrical with respect to the midfrequency term. (3) The transients die out faster in the filters of smaller number of sections. (4) With the same network constants, the transients die out faster in the ttype filters. (5) Filtering property only exists in the steady state. (6) The band width increases with the number of sections. This increase is greater in πtype filters, but the band width is greater in Ttype filters.  此篇先推求收端加电阻时,频带滤波器瞬流之公式依此公式算出之图与用阴极光示波器映出之曲线相符合自推算之秸果可得下列结论: (一)在滤波器收端加电阻时,瞬流终必变为低隔阻频之电流,而较收端无电阻时易于消滅。 (二)收端直瞬流之各项均对称於中频项。 (三)在段数较少之滤波器中瞬流易于消滅。 (四)在π式滤波器中,瞬流消滅较在T式中为易。 (五)滤波器之特性仅能见於安定状态之下。 (六)滤波器之带宽随所用之段数而增加。   << 更多相关文摘 
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