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The results obtained here are a generalization of the corresponding results of Guo Dajun (1988, 1992), Pan Xingbin (1988) and Li Fuyi >amp;amp; Liang Zhandong(1994).


A criterion of the nonexistence of periodic solutions for a generalized li énard system and its applications


In this paper, a new criterion of the nonexistence of periodic solutions for a generalized liénard system is given, which generalizes and extends some known results of Sugie et al.


Let Sn be the symmetric group, gi+=(123i), gi=(li32) and Mn+={gi+∶4≤i≤n}, then Mn+ is a minimal generating set of Sn, where n≥5.


Boundary value problem for a generalized Liénard equation

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 This is a continuation of a previous study (Li, L. Y, et al. 1951, Fukien Agr. Jour., 12(3, 4): 107112) on the outdoor culture of straw mushroom in Fukien. The present work includes: (1) investi gations on the analysis of fresh Fukien grown straw mushroom, (2) isolation and culture of Volvaria esculenta and our trials in using pureculture spawns to grow mushroom, and (3) preliminary obser vations made on the environmental requirements of Volvaria esculcnta The results are briefly summarized as follows:... This is a continuation of a previous study (Li, L. Y, et al. 1951, Fukien Agr. Jour., 12(3, 4): 107112) on the outdoor culture of straw mushroom in Fukien. The present work includes: (1) investi gations on the analysis of fresh Fukien grown straw mushroom, (2) isolation and culture of Volvaria esculenta and our trials in using pureculture spawns to grow mushroom, and (3) preliminary obser vations made on the environmental requirements of Volvaria esculcnta The results are briefly summarized as follows: 1. Our analytical work shows that the straw mushroom con tains 92. 39％ water, 206. 275mg. of ascorbic acid in 100g. of fresh mushroom, 2. 6024％ sugar, 2. 6603％ protein, 2. 2406％ oil, and 0. 9118％ ash. 2. Pure cultures of Volvaria esculenta could be readily obtained by innoculation with spores from fresh unopened mushroom. Cultures grow well on potato, corn, rice and ricekernel husk media. 3. By employing pureculture spawns, it takes only ten days for the first appearance of mushroom after spawnning while it takes three weeks usually if mixed cultures are used instead. The total period of mushroom production is likewise prolonged by the use of pureculture spawns. 4. Preliminary observations indicate an atmospheric tempera ture of 70°to 80°F., and a humidity of above 80% are favorable for the growth of straw mushroom. Production of mushroom stops when the atmospheric temperature falls below 70°F. The period of outdoor culture in Fcochow is from the latter part of April till the end of October.  本文旨在介绍草菰的营养价值,纯种培植的方法,及草菰生长状况。经分析结果,草菰的营养价值较一般蔬菜为高,尤以丙种维生素更为丰富。用纯种培植草菰较普通方法培植的不仅可以提早一半时间出菰,且产菰日期延长,菰之产量亦提高一倍。草菰生长速度从菰纽露面至菰伞平张需经过四十八小时,采为食用,以在菰疱破裂后十小时左右采收为佳。  This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with nonprismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the... This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with nonprismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the sum of modified stiffness of all the barends at a joint as the auxiliary frame constant. The basic frame constants at the left of right ends of all the bars are computed by the consecutive applications of a single formula in a chain manner. The auxiliary frame constant at any joint where it is needed is computed from the basic frame constants at the two ends of any bar connected to the joint, so that its value may be easily checked by computing it from two or more bars connected to the same joint.Although the principle of this method was developed by Dr. Klouěek and Prof. Meng, the formulas presented in this paper for computing the basic and auxiliary frame constants, besides being believed to be original and by no means the mere amplification of those presented by the two predecessors, are of much improved form and more convenient to apply.By the author's formula, the basic frame constants in closed frames of comparatively simple form may be computed in a straightforward manner without much difficulties, and this is not the case with any other similar methods except Dr. Klouěek's.The case of sidesway is treated as usual by balancing the shears at the tops of all the columns, but special formulas are deduced for comput ing those column shears directly from joint rotations and sidesway angle without precomputing the moments at the two ends of all the columns.In the method of propagating unbalanced moments proposed by Mr. Koo IYing and improved by the author, the unbalanced moments at all the barends of each joint are first propagated to the barends of all the other joints to obtain the total unbalanced moments at all the barends, and then are distributed at each joint only once to arrive at the balanced moments at all the barends of that joint. Thus the principle of propagating joint rotations with indirect computation of the barend moments is ingeneously applied to propagate unbalanced moments with direct computation of the barend moments, and, at the same time, without the inconvenient use of two different moment distribution factors as necessary in all the onecycle methods of moment distribution. The basic frame constant employed in this method is the same as that in the method of propagating joint rotations, so that its nearest approximate value at any bar end may be computed at once by the formula deduced by the author. Evidently, this method combines all the main advantages of the methods proposed by Profs.T. Y. Lin and Meng ChaoLi and Dr. Klouěek, and is undoubtedly the most superior onecycle method of moment distribution yet proposed as far as the author knows.Typical numerical examples are worked out in details to illustrate the applications of the two methods.  本文為著者前文“剛構常數與剛構分析”之補充,其目的在將角變傳播法及不均衡力矩傳播法加以改善,以便實用。此二法均只需一個公式以計算剛構中所有各桿端之基本剛構常數(即任何二相鄰結點间之角變傳播係數),將此項公式與柯勞塞克之公式相比較,藉以指出前者較後者為便於應用,並亦可用之以直接分析較簡單之閉合式剛構,此外補充說明此法中之剛構常數與定點法之關係,剛構有側移時計算各結點角變所需之各項公式亦行求出。不均衡力矩傳播法係顧翼鹰同志最近研究所得者,既係直接以桿端力矩為計算之對象,而且只須採用不均衡力矩分配比將各結點作用於各桿端不均衡力矩之總和,一次分配,即得所求各桿端分配力矩之總值,實係力矩一次分配法之一大改進,著者將顧氏之法加以推廣与改善,使其原則簡明而計算便捷,著者認為此法係將林、柯、孟三氏法之所有優點熔冶於一爐,實可稱為现下最優之力矩一次分配法。最後列舉算例,以說明此二法在實際工作中之應用。  Many methods of analyzing statically indeterminate structures are now available. The method of redundant forces and that of deformations (i. e. the slopedeflection method), heretofore generally used in the U. S. S. R., both require the solution of a system of simultaneous simple equations. In the case of multistorey and multibay bents, the large number of such equations would greatly complicate the calculation work, it being both timeconsuming and liable to make mistakes. The method of moment distribution... Many methods of analyzing statically indeterminate structures are now available. The method of redundant forces and that of deformations (i. e. the slopedeflection method), heretofore generally used in the U. S. S. R., both require the solution of a system of simultaneous simple equations. In the case of multistorey and multibay bents, the large number of such equations would greatly complicate the calculation work, it being both timeconsuming and liable to make mistakes. The method of moment distribution simplifies calculations to a great extent, as there is no need to solve simultaneous equations, and therefore it has been warmly received bY practical engineers. Many soviet scholars are also devoted to its study. There are, however, defects in this method, namely: (1) Should the moments obtained in the successive cycles of distribution and carryingover prove to converge very slowly, twenty or more such cycles must be done if fairly accurate results are expected.(2) In the case of analyzing structures under various conditions of loading, while it is possible to find the influence moments by applying a unit moment at each joint as proposed by Prof. Hardy Cross, it would bequite laborious in the case of multistorey and multibay bents containing a large number of members, especially when subjected to unsymmetrical loadings.For the remedy of the first defect, such Chinese scholars as Profs. Lin Tung Yen, Chao Tsu Wu, Meng Chao Li and Tsai Fang Yin have made much contribution, and the author of this paper has recently written a discussion on the two papers of the lastmentioned scholar. For the remedy of the second defect, the author is unaware of any except that mentioned below.One of the soviet scholars, Dr. P. P. Shaggin (i.e.) has suggested important improvements with regard to both these defects. For the former, he adopted a method of singlecycle distribution; and for the latter, he invented the method of successive conjugation which greatly reduces the work of calculation in finding the influence moments. The essence of these methods is wellworth studying on the part of our Chinese engineers. After an intensive study, the author of this paper thinks that, while Dr. Shaggin's methods are quite correct in principle, his methods of calculation can still be somewhat improved, as described herein, so as to be made more easily applied in practice.This paper Shaggin based upon the book, (Calculation of Multistorey Frames by the Method of Successive Conjugation) published in 1954 by Dr. P. P. Shaggin in Leningrad, U. S. S. R., shows that, in applying a unit moment at each joint of a given statically indeterminate structure, one can easily find the influence moments at the ends of all the members, and that, after multiplying the unbalanced fixedend moments at each joint calculated in accordance with the given external loads, by the respective influence moments, the sum of such products added to the original fixedend moments will give at once the actual moments at each end of the members in the structure.Three notable improvements are indicated in this paper:(1) Dr. Shaggin's formula (5") on page 11 of his book, has been altered to formulas (3) in this paper. (2) For multistorey bents, Dr. Shaggin's method of finding the conjugate moments (i. e. the influence moments) by formulas is replaced by the usual method of simple momentdistribution.(3) The author of the paper has extended the method to the analysis of multistorey and multibay bents under any system of unsymmetrical loading.Of course, for structures under a single system of loading, influence moments need not be found and, generally speaking, it would be more convenient to apply the original method of momentdistribution; for a multistorey bent, it would be better, even in this case, to modify it by applying the method of successive conjugation.The author is of the opinion that the application of the methods described in this paper, being convenient and timesaving, would be useful to the practical engineers.  本文以蘇聯學者沙金博士最近出版之“用逐次互聯法計算多層排架”一書为依據,叙述在已知超靜定結構中每一結點,施以單位力矩,可以很容易地求得各桿端的影響力矩;然後依照其所受外力荷載,求得各結点處的定端力矩,分別乘以相當的影響力矩,相加之後並加以原有的定端力矩,即得各該桿端的實際力矩。若結構承受多種多样的荷載(不問其為豎向的或平向的、對稱的或不對稱的),用此篇所述之方法以推算各桿端力矩,著者認為最便利、最省時,並且適合實際工作者之需要。   << 更多相关文摘 
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