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When coupled with the Poisson Summation formula, these results become applicable to the theory of WeylHeisenberg systems, in the form of lattice sum


This inequality is not applicable here and it is noticeable that the Cotlar's inequality maybe fails under Hormander's condition.


The Adomian decomposition method is straightforward, applicable for broader problems and avoids the difficulties in applying integral transforms.


It is pointed out that this graphic approach is also applicable even when the link function is not monotonic.


This makes a controller designed without considering delays still applicable in NCS.

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 It is pointed out in this paper that the following apparent discrepancies exist in Coulomb's Theory: (1) In any problem in mechanics, a force to be definite must have all the three factors involved under consideration. In Coulomb's Theory, however, the point of application of the soil reaction on the plane of sliding is somehow neglected, thus enabling the arbitrary designation of the obliquity of the earth pressure on the wall to be equal to the friction angle between the wall surface and soil. As a matter... It is pointed out in this paper that the following apparent discrepancies exist in Coulomb's Theory: (1) In any problem in mechanics, a force to be definite must have all the three factors involved under consideration. In Coulomb's Theory, however, the point of application of the soil reaction on the plane of sliding is somehow neglected, thus enabling the arbitrary designation of the obliquity of the earth pressure on the wall to be equal to the friction angle between the wall surface and soil. As a matter of principle, the point of application should never be slighted while the obliquity of the earth pressure could only have a value that is compatible with the conditions for equilibrium. (2) If the point of application of the soil reaction is taken into account in the problem, the sliding wedge would only tend to slide either on the plane of sliding or on the surface of wall but not on both at the same time, thus frustrating the very conceptidn of sliding wedge upon which Coulomb's Theory is founded. (3) The above discrepancies arise from the fact that the shape of the surface of sliding should be curvilinear in order to make the wedge tend to slide as desired, while Coulomb, however, adopted a plane surface instead. (4) Coulomb, in finding the plane of sliding, made use of the maximum earth pressure on the wall (for active pressure), which refers to the different magnitudes of pressure corresponding to different assumed inclinations of the plane of sliding. But from the relation between the yield of wall and amount of pressure, this maximum value is really the minimum pressure on the wall, which it is the purpose of the theory to find. In engineering books, however, this terminology of maximum pressure has caused considerable confusion, with the result that what is really the minimum pressure is carelessly taken as the maximum design load for the wall. How can a minimum load be used in a design?This paper also attempts to clarify some contended points in Rankine's Theory: (1) It is claimed by Prof. Terzaghi that Rankine's Theory is only a fallacy because of the yield of wall and that of the soil mass on its bed. This charge is unjust as it can be compared with Coulomb's Theory in the same respect. (2) Some books declare that Rankine's Theory is good only for walls with vertical back, but it is proved in this paper that this is not so. (3) It is also generally believed that Rankine's Theory is applicable only to wall surfaces with no friction. This is likewise taken by this paper as unfounded and illustration is given whereby, in this regard, Rankine's Theory is even better than Coulomb's, because it contains no contradiction, as does Coulomb's.  本文從力學觀點對庫隆理論提出下列問題:(1)在解算力學問題時,每個力有三個因素都該同時考慮,但庫隆對土楔滑動面上土反力的施力點竟置之不理,因而才能對擋土墙上土壓力的傾斜角作一硬性假定,使它等於墙和土間的摩阻角,然而施力點是不能不管的,因而土壓力的傾斜角是不能離開平衡條件而被隨意指定的。(2)如果考慮了土反力的施力點,則土楔祇能在滑動面上,或在墙面上,有滑動的趨勢,而不能同時在兩個面上都有滑動的趨勢,因而庫隆的基本概念“滑動土楔”就站不住了。(3)問題關鍵在滑動面的形狀;如要使土楔在滑動面和墙面上同時有滑動趨勢,則滑動面必須是曲形面,然而庫隆採用了平直形的滑動面。(4)庫隆的土楔滑動面是從墙上最大的土壓力求出的(指主動壓力),這裏所謂“最大”是指適應各個滑動面的各個土壓力而言,但對適應墙在側傾時土壓力應有的變化來說,這個最大土壓力却正是墙上極限壓力的最小值。一般工程書籍,以為這土壓力既名為最大,就拿它來用作設計擋土墙的荷載,荷載如何能用最小的極限值呢?本文對朗金理論中的下列問題作了一些解釋:(1)朗金理論在擋土墙的位移問題上所受的限制,是和庫隆理論一樣的,竇薩基教授曾就此問題認為朗金理論是幻想,似乎是無根據的。... 本文從力學觀點對庫隆理論提出下列問題:(1)在解算力學問題時,每個力有三個因素都該同時考慮,但庫隆對土楔滑動面上土反力的施力點竟置之不理,因而才能對擋土墙上土壓力的傾斜角作一硬性假定,使它等於墙和土間的摩阻角,然而施力點是不能不管的,因而土壓力的傾斜角是不能離開平衡條件而被隨意指定的。(2)如果考慮了土反力的施力點,則土楔祇能在滑動面上,或在墙面上,有滑動的趨勢,而不能同時在兩個面上都有滑動的趨勢,因而庫隆的基本概念“滑動土楔”就站不住了。(3)問題關鍵在滑動面的形狀;如要使土楔在滑動面和墙面上同時有滑動趨勢,則滑動面必須是曲形面,然而庫隆採用了平直形的滑動面。(4)庫隆的土楔滑動面是從墙上最大的土壓力求出的(指主動壓力),這裏所謂“最大”是指適應各個滑動面的各個土壓力而言,但對適應墙在側傾時土壓力應有的變化來說,這個最大土壓力却正是墙上極限壓力的最小值。一般工程書籍,以為這土壓力既名為最大,就拿它來用作設計擋土墙的荷載,荷載如何能用最小的極限值呢?本文對朗金理論中的下列問題作了一些解釋:(1)朗金理論在擋土墙的位移問題上所受的限制,是和庫隆理論一樣的,竇薩基教授曾就此問題認為朗金理論是幻想,似乎是無根據的。(2)有些工程書中認為朗金理論是專為垂直的墙?  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... 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。  Fineness modulus (F. M.) has served as an index of fineness of aggregates since it was first introduced by Prof. Duff A. Abrams in 1918. In the concrete mix design, the F. M. of sand governs the sand content and hence the proportions of other ingredients. But there are undesirable features in F. M.: it does not represent the grading of sand and manifests no significant physical concept.Prof. suggested an "average diameter" (d_(cp)) in 1943 as a measure of fineness of sand. In 1944, d_(cp) was adopted in 278144... Fineness modulus (F. M.) has served as an index of fineness of aggregates since it was first introduced by Prof. Duff A. Abrams in 1918. In the concrete mix design, the F. M. of sand governs the sand content and hence the proportions of other ingredients. But there are undesirable features in F. M.: it does not represent the grading of sand and manifests no significant physical concept.Prof. suggested an "average diameter" (d_(cp)) in 1943 as a measure of fineness of sand. In 1944, d_(cp) was adopted in 278144 as national standard to specify the fine aggregate for concrete in USSR. It was introduced to China in 1952 and soon becomes popular in all technical literatures concerning concrete aggregates and materials of construction.After careful and thorough investigation from ordinary and special gradings of sand, the equation of d_(cp) appears to be not so sound in principle and the value of d_(cp) computed from this equation is not applicable to engineering practice. The assumption that the initial average diameter (ν) of sand grains between consecutive seives is the arithmetical mean of the openings is not in best logic. The value of an average diameter computed from the total number of grains irrespective of their sizes will depend solely on the fines, because the fines are much more in number than the coarses. Grains in the two coarser grades (larger than 1.2 mm or retained on No. 16 seive) comprising about 2/5 of the whole lot are not duly represented and become null and void in d_(cp) equation. This is why the initiator neglected the last two terms of the equation in his own computation. Furthermore, the value of d_(cp) varies irregularly and even inversely while the sands are progressing from fine to coarse (see Fig. 4).As F. M. is still the only practical and yet the simplest index in controlling fineness of sand, this paper attempts to interpret it with a sound physical concept. By analyzing the F. M. equation (2a) in the form of Table 9, it is discovered that the coefficients (1, 2…6) of the separate fractions (the percentages retained between consecutive seives, a1, a2…a6) are not "size factors" as called by Prof. H. T. Gilkey (see p. 93, reference 4), but are "coarseness coefficients" which indicate the number of seives that each separate fraction can retain on them. The more seives the fraction can retain, the coarser is the fraction. So, it is logical to call it a "coarseness coefficient". The product of separate fraction by its corresponding coarseness coefficient will be the "separate coarseness modulus". The sum of all the separate coarseness moduli is the total "coarseness modulus" (M_c).Similarly, if we compute the total modulus from the coefficients based on number of seives that any fraction can pass instead of retain, we shall arrive at the true "fineness modulus" (M_f).By assuming the initial mean diameter (ν') of sand grains between consecutive seives to be the geometrical mean of the openings instead of the arithmetical mean, a "modular diameter" (d_m), measured in mm (or in micron) is derived as a function of M_c (or F. M.) and can be expressed by a rational formula in a very generalized form (see equation 12). This equation is very instructive and can be stated as a definition of mqdular diameter as following:"The modular diameter (d_m) is the product of the geometrical mean ((d_0×d_(1))~(1/2) next below the finest seive of the series and the seive ratio (R_s) in power of modulus (M_c)." If we convert the exponential equation into a logarithmic equation with inch as unit, we get equation (11) which coincides with the equation for F. M. suggested by Prof. Abrams in 1918.Modular diameter can be solved graphically in the following way: (1) Draw an "equivalent modular curve" of two grades based on M_c (or F. M.) (see Fig. 6). (2) Along the ordinate between the two grades, find its intersecting point with the modular curve. (3) Read the log scale on the ordinate, thus get the value of the required d_m corresponding to M_c (see Fig. 5).As the modular diameter has a linear dimension with a defin  細度模數用為砂的粗細程度的指標,已有三十餘年的歷史;尤其是在混凝土的配合上,砂的細度模數如有變化,含砂率和加水量也要加以相應的調整,才能維持混凝土的稠度(以陷度代表)不變。但是細度模數有兩大缺點,一個是模數的物理意義不明,另一個是模數不能表示出砂的級配來。蘇聯斯克拉姆塔耶夫教授於1943年提出砂的平均粒徑(d_(cp))來,以為砂的細度指標;雖然平均粒徑仍不包含級配的意義,但是有了比較明確的物理意義,並且可以用毫米來度量,這是一種新的發展。不過砂的細度問題還不能由平均粒徑而得到解决,且平均粒徑計算式中的五項,僅首三項有效,1.2和2.5毫米以上的兩級粗砂在計算式中不生作用,以致影響了它的實用效果。本文對於平均粒徑計算式的創立方法加以追尋和推演,發現其基本假設及物理意義,又設例演算,以考察其變化的規律性;認為細度模數還有其一定的實用價值,不能為平均粒徑所代替。至於補救細度模數缺點的方法,本文試由模數本身中去尋找;將模數的計算式加以理論上的補充後,不但能分析出模數的物理意義,並且還發現模數有細度和粗度之別。根據累計篩餘計算出來的F.M.應稱為“粗度模數”,根據通過量計算出來的才是“細度模數”。假定兩隣篩间的顆粒是... 細度模數用為砂的粗細程度的指標,已有三十餘年的歷史;尤其是在混凝土的配合上,砂的細度模數如有變化,含砂率和加水量也要加以相應的調整,才能維持混凝土的稠度(以陷度代表)不變。但是細度模數有兩大缺點,一個是模數的物理意義不明,另一個是模數不能表示出砂的級配來。蘇聯斯克拉姆塔耶夫教授於1943年提出砂的平均粒徑(d_(cp))來,以為砂的細度指標;雖然平均粒徑仍不包含級配的意義,但是有了比較明確的物理意義,並且可以用毫米來度量,這是一種新的發展。不過砂的細度問題還不能由平均粒徑而得到解决,且平均粒徑計算式中的五項,僅首三項有效,1.2和2.5毫米以上的兩級粗砂在計算式中不生作用,以致影響了它的實用效果。本文對於平均粒徑計算式的創立方法加以追尋和推演,發現其基本假設及物理意義,又設例演算,以考察其變化的規律性;認為細度模數還有其一定的實用價值,不能為平均粒徑所代替。至於補救細度模數缺點的方法,本文試由模數本身中去尋找;將模數的計算式加以理論上的補充後,不但能分析出模數的物理意義,並且還發現模數有細度和粗度之別。根據累計篩餘計算出來的F.M.應稱為“粗度模數”,根據通過量計算出來的才是“細度模數”。假定兩隣篩间的顆粒是兩篩篩孔的幾何平均值,以代替數學平均值(即斯氏平均?   << 更多相关文摘 
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