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We prove that these determinantal semi-invariants span the space of all semi-invariants for any quiver and any infinite base field.
      
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.
      
In addition, the closed linear span of all translates of any square integrable function on any compact homogeneous space is determined.
      
Functions whose translates span Lp(R) are called Lp-cyclic functions.
      
A W/O microemulsion was prepared with Span80-PS (petroleum sulfonate) as complex emulsifier, isopropanol as cosurfactant and kerosene as oil phase.
      
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The purpose of this paper is to discuss Prof. method of analyzing two-way reinforced concrete slab. This method is based upon the equilibrium of forces under ultimate loading, and consequently the effect of plasticity of the material is included in consideration. If we use this method to design two way reinforced concrete slab, We should not only have much saving of steel, but also a saving of labour in computation. No matter that the slab is continuous over how many spans of unequal lengths, it can be easily...

The purpose of this paper is to discuss Prof. method of analyzing two-way reinforced concrete slab. This method is based upon the equilibrium of forces under ultimate loading, and consequently the effect of plasticity of the material is included in consideration. If we use this method to design two way reinforced concrete slab, We should not only have much saving of steel, but also a saving of labour in computation. No matter that the slab is continuous over how many spans of unequal lengths, it can be easily analyzed, one by one, as a single span slab.

本文的目的是介紹蘇聯格娃斯捷夫教授的計算双向板的公式。這個公式是考慮板在極限平衡狀態,考慮了材料的塑性。用此方法計算雙向板,不但鋼筋經济而計算簡便。無論是多的板或不等的板,都可以视為單板來考虑,本文討論了格娃斯捷夫公式的基本理論,並将此理論应用到不規则形狀板的计算方面。

The so-called "truss rigid frames" are those rigid frames with trusses as their horizontal beams, of which the two ends are rigidly connected to columns. Within the author's knowledge, all the methods available at present for analyzing such rigid frames are based on Certain special assumptions such as (1) that the positions of the points of contra-flexure in all the columns are previously known; (2) that the end rotations of a truss may be reprensented by that of its assumed line of axis as in the case of an...

The so-called "truss rigid frames" are those rigid frames with trusses as their horizontal beams, of which the two ends are rigidly connected to columns. Within the author's knowledge, all the methods available at present for analyzing such rigid frames are based on Certain special assumptions such as (1) that the positions of the points of contra-flexure in all the columns are previously known; (2) that the end rotations of a truss may be reprensented by that of its assumed line of axis as in the case of an ordinary beam; or (3) that the end verticals of trusses may be given certain prescribed deformations. Of course, the adoption of any of such assumptions leads to only approximate results inconsistent with the actual deformations of such rigid frames under any loading. Heretofore, the author did not know any correct method for analyzing such rigid frames. In this paper, the author presents two principles of the correct analysis of truss rigid frames. The first principle is that of "moment action on column" for computing the angle change constants of columns, and the second principle is that of "effect of span-change in truss" for computing the angle and span change constants of trusses.As, for computing the angle change constants of a truss, the dummy unit moment is a couple applied to its end verticals, so, for computing the angle change constants of a column, the dummy unit moment must also be a couple applied to the section of column rigidly connected to the end of a truss, in order to effect a consistent deformation at the joint of the two. This is the first principle.A truss just like a curved or gabled beam of which the effect of span-change can not be neglected, so truss rigid frames belong to the same category of what may be called "span-change" rigid frames such as rigid frames with curved or gabled beams. Therefore the span-change constants of trusses should be included besides their angle-change constants for analyzing truss rigid frames. This is the second principle.With the constants of columns and trusses are all computed in accordance with respectively the first and second principles mentioned above, truss rigid frames may be analyzed by any method including the effect of span-change as in the case of rigid frames with curved or gabled beams, and the results thus obtained will be exactly the same as by the method of least work or deflections without any special assumptions.In this paper, after the two principles are described and the formulas for computing the constants of columns and trusses are derived, the correctness of the two principles are then proved by the methods of least work, deflections and slope-deflection. A two-span truss rigid frame is analyzed under the following three conditions:Ⅰ. Applying both of the two principles to obtain the correct results.Ⅱ. Applying only the first principle to show the discrepancies of neglecting the effect of span-change in trusses as born out by comparing the results of Ⅱ with Ⅰ.Ⅲ. Applying neither of the two principles, and the truss rigid frames being analyzed by the special assumption (2) mentioned above with the line of axis at the bottom chord of truss, in order to show the discrepancies of neglecting the moment action on column as born out by comparing the results of Ⅲ with Ⅱ. For the sake of brevity, only the results are given in Tables 1 to 5 without computations in details.Although the discrepancies of neglecting the moment acticn on column are only slight as shown by comparing the results of Ⅲ with Ⅱ in Tables 2, 4 and 5, there is no reason why special assumptions should not be replaced by the correct principle of moment action on column to obtain correct results. As shown by comparing the results of Ⅱ with Ⅰ in Tables 2, 4 and 5, the discrepancies by neglecting the span change in trusses are generally considerable and, in certain particular part, as large as 3000%. Therefore, for the safe and economical design of truss rigid frames, the effect of span-change in trusses should not be neglected in their analysis.Finally, for analyzing co

所謂“桁架剛構”即以桁架為横梁与柱相剛接之剛構。現下採用分析剛構之任一方法,以分析此項剛構时,均須採用種種特殊之假定而得近似之結果。據著者所知,中外書刊中似尚无此項剛構之正確分析法。於本文中,著者發表关於桁架剛構正確分析之兩項原理,即柱頂力矩作用与桁架变影響之兩项原理。前項原理使柱頂段之角夔与桁架端豎桿相同,以符合柱与桁架剛接处之連续性。後項原理指出桁架与曲梁(即拱)及折梁(即山墙式梁)相同係一種“变横梁”,故桁架刚構亦与拱式及山墙式剛構相同,係一種“变剛構”。若根據此兩项原理,分别计算柱与桁架兩端的撓曲常数,再用分析变刚構之任一分析法以分析此項刚構,則所得之枯果,与不作任何特殊假定用最少功法或变位法所得者完全相同。本文先說明此兩项原理及根據此兩項原理计算柱与桁架撓曲常數之方法。次取一最簡單之桁架刚構为例,證明此丙項原理之正確性。桁架刚構既与拱式及山墙式刚構同属於变刚構一類型,分析後者之任何方法均可用以分析前者,本文无須贅述。但取一兩之桁架刚構為例,列举所得之正確結果,与用近似法所得者相比较,藉以顯出近似法有相當巨大之差誤。關...

所謂“桁架剛構”即以桁架為横梁与柱相剛接之剛構。現下採用分析剛構之任一方法,以分析此項剛構时,均須採用種種特殊之假定而得近似之結果。據著者所知,中外書刊中似尚无此項剛構之正確分析法。於本文中,著者發表关於桁架剛構正確分析之兩項原理,即柱頂力矩作用与桁架变影響之兩项原理。前項原理使柱頂段之角夔与桁架端豎桿相同,以符合柱与桁架剛接处之連续性。後項原理指出桁架与曲梁(即拱)及折梁(即山墙式梁)相同係一種“变横梁”,故桁架刚構亦与拱式及山墙式剛構相同,係一種“变剛構”。若根據此兩项原理,分别计算柱与桁架兩端的撓曲常数,再用分析变刚構之任一分析法以分析此項刚構,則所得之枯果,与不作任何特殊假定用最少功法或变位法所得者完全相同。本文先說明此兩项原理及根據此兩項原理计算柱与桁架撓曲常數之方法。次取一最簡單之桁架刚構为例,證明此丙項原理之正確性。桁架刚構既与拱式及山墙式刚構同属於变刚構一類型,分析後者之任何方法均可用以分析前者,本文无須贅述。但取一兩之桁架刚構為例,列举所得之正確結果,与用近似法所得者相比较,藉以顯出近似法有相當巨大之差誤。關於階形之複式桁架刚構之分析,本文用“代替桁架”之辦法,但只說明其原則,不列出公式及算例。

The analysis of rigid frames with so called "span-change" beams such as curved, gabled, folded or trussed ones is rather difficult. The method of redundant forces or method of slope deflection are too tedious to be used in practical work. In this paper a new method namely the method of propagating unbalanced moments and lateral forces is proposed for analyzing such frames.The principle of this method is some what like that of the one cycle method of moment distribution for analyzing rigid frames with straight...

The analysis of rigid frames with so called "span-change" beams such as curved, gabled, folded or trussed ones is rather difficult. The method of redundant forces or method of slope deflection are too tedious to be used in practical work. In this paper a new method namely the method of propagating unbalanced moments and lateral forces is proposed for analyzing such frames.The principle of this method is some what like that of the one cycle method of moment distribution for analyzing rigid frames with straight beams and its procedure may be briefly described as follows: the unbalanced moments and lateral forces at all joints of the frame are calculated first and propagated successively to all the other joints by means of a set of the so-called constants of deformation-propagation, which are to be computed from the properties of the frame only. Then its original and various propagated unbalanced moments and lateral forces at each joint are summed up and distributed among all the bar-ends at that joint according to special formulas to obtain the distributed moment and lateral force at each bar-end. Finally, the balanced moment and lateral force at each bar-end are obtained simply by summing up the following three components respectively: (1) those at each bar-end assumed fixed, M~F and H~F; (2) those propagated to each bar-end, M~P and H~P; and (3) those distributed to each bar-end, M~D and H~D. That is:M=M~F+M~P+M~D, H=H~F+H~P+H~D.Evidently, the procedure of this method is very simple and direct, and the work of calculations is greatly reduced, especially when any span-change rigid frame is to be analyzed for many loading conditions.Two typical examples are given in this paper to illustrate the application of the method and the author hopes deeply that this method will be found usefull by the structural engineers in designing such rigid frames.

凡具有曲梁、山牆式梁、摺式梁、门式梁、桁架梁或其他“变”横梁之剛構均可称为“变剛構”。变剛構常为高次的超靜定結構,其应力分析至为复杂。採用冗力法、最少功法或角变位移法以分析此类刚構,常嫌过繁,当结構受有多种荷載情形时,更需作多次計算,尤覺繁不堪言,頗不为实际工作者所乐用。著者於本文發表一不均衡力矩及侧力傳播法以分析此类剛構。無論剛構本身以及單个的变横梁是否对称,也不論組成剛構的各个桿件为等截面或为变截面,本法均可适用,因此本法之实用范圍可称广泛。 本法之基本观念可簡單描述如次:首先將作用於各結点的不均衡力矩及側力,傳播至所有其他結点之桿端,求得每一結点的不均衡力矩及侧力的总值,然后經过一次分配則可得出該結点桿端之分配力矩及分配侧力。計算所需之最終桿端力矩及侧力即为a)定端力矩或側力,b)傳播力矩或侧力,以及c)分配力矩或側力三者之和。 本法之性质属于一次分配法之范疇,共精神与我国結構学者蔡方蔭先生所得分析直桿剛構之“不均衡力矩傳播法”甚为相似,如果变横梁变为直桿,則本法所得計算公式即簡化而成蔡氏所得之公式。 文中举二算例,以明本法之应用。 ...

凡具有曲梁、山牆式梁、摺式梁、门式梁、桁架梁或其他“变”横梁之剛構均可称为“变剛構”。变剛構常为高次的超靜定結構,其应力分析至为复杂。採用冗力法、最少功法或角变位移法以分析此类刚構,常嫌过繁,当结構受有多种荷載情形时,更需作多次計算,尤覺繁不堪言,頗不为实际工作者所乐用。著者於本文發表一不均衡力矩及侧力傳播法以分析此类剛構。無論剛構本身以及單个的变横梁是否对称,也不論組成剛構的各个桿件为等截面或为变截面,本法均可适用,因此本法之实用范圍可称广泛。 本法之基本观念可簡單描述如次:首先將作用於各結点的不均衡力矩及側力,傳播至所有其他結点之桿端,求得每一結点的不均衡力矩及侧力的总值,然后經过一次分配則可得出該結点桿端之分配力矩及分配侧力。計算所需之最終桿端力矩及侧力即为a)定端力矩或側力,b)傳播力矩或侧力,以及c)分配力矩或側力三者之和。 本法之性质属于一次分配法之范疇,共精神与我国結構学者蔡方蔭先生所得分析直桿剛構之“不均衡力矩傳播法”甚为相似,如果变横梁变为直桿,則本法所得計算公式即簡化而成蔡氏所得之公式。 文中举二算例,以明本法之应用。 著者認为採用此法以分析变剛构,不仅計算可趋精簡,且当結構承受多种荷載情形时,尤其具有显明?

 
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