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In order to deal with large problems, a pair of trust region subproblems in horizontal and vertical subspaces is used to replace the general full trust region subproblem.
      
The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint.
      
That is, the plot with the fitted response ? on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function.
      
Results showed that topographic characteristics and disturbance pattern have much more impacts on the distribution of landscape elements than do horizontal geographical position in the study area.
      
With respect to horizontal distribution, roots (d>amp;lt;10 mm) under SDI were distributed mainly near the subsurface emitters and the amount of roots in 3 m in a row under SDI were 50% less than under CK.
      
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Upper air visibility and vertical visibility are different from horizontal far distance visibility. They have special signifigance in aviation.In this paper the atmospheric extinction coefficieat, the upper air visibility and vertical visibility are calculated by observing the polit balloons and radiosonde balloons.The principle of visibility instrument is used that is making use of optical wedge, photoelectric cell etc, to carry out the measurement. Foitzik 1947, Duntley 1948, and some other scientists...

Upper air visibility and vertical visibility are different from horizontal far distance visibility. They have special signifigance in aviation.In this paper the atmospheric extinction coefficieat, the upper air visibility and vertical visibility are calculated by observing the polit balloons and radiosonde balloons.The principle of visibility instrument is used that is making use of optical wedge, photoelectric cell etc, to carry out the measurement. Foitzik 1947, Duntley 1948, and some other scientists have disscnsed the problem of vertical visibility. Their method is to carry out the calculation with given atmospheric extinction coefficient, while in practical application this calculation is the second step, what we need to find out first is the atmospheric extinction coefficient. In Duntley's paper, he assumes that within the limit of discussion, the intensity of sky light is constant. But this can only be true within a very thin layer of atmosphere, as to the atmosphere which is kilometres thick, it has to consider the attenuation of light by the atmosphere. Furthermore he assumes that the anisotropy of atmosphere's scattering function is invariant with height and then it is considered as a molecular atmosphere. But this has been proved by several authors in theory and in experiment to be not true, especially in the lower atmosphere. Certainly, Duntley's calculation is not accurate and is limited in application.A correction has been given to the above mentioned assumptions in this paper. Finally, the problem of light of source visibility in night and some other materials on observation are being discussed.

高空能见度,垂直能见度是和地平远程能见度不相同的。在航空方向,高空能见度与垂直能见度具有着特殊的意义。 本文藉助于测风气球及雷送气球的观测,计算大气削弱系数,从而计算高空能见度与垂直能见度。 我们利用莎罗诺夫能见度仪器的原理:利用光楔,光电池等进行测量。

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...

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跨变影響之兩项原理。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“跨变横梁”,故桁架刚構亦与拱式及山墙式剛構相同,係一種“跨变剛構”。若根據此兩项原理,分别计算柱与桁架兩端的撓曲常数,再用分析跨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跨变刚構一類型,分析後者之任何方法均可用以分析前者,本文无須贅述。但取一兩跨之桁架刚構為例,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...

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跨变影響之兩项原理。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“跨变横梁”,故桁架刚構亦与拱式及山墙式剛構相同,係一種“跨变剛構”。若根據此兩项原理,分别计算柱与桁架兩端的撓曲常数,再用分析跨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跨变刚構一類型,分析後者之任何方法均可用以分析前者,本文无須贅述。但取一兩跨之桁架刚構為例,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。

Since the year 1886, the Dupuit-Forchheimer theory and formulas for gravityflows toward wells and galleries have been broadly used in all nations of theworld. In these formulas, assumptions are made for underground flows fromfarther distances in horizontal directions at a constant rate toward wells andgalleries. According to the author's analysis, these assumptions are not consistentwith the actual conditions of flow, hence the formulas obtained therefrom are notrational, and the employment of these formulas...

Since the year 1886, the Dupuit-Forchheimer theory and formulas for gravityflows toward wells and galleries have been broadly used in all nations of theworld. In these formulas, assumptions are made for underground flows fromfarther distances in horizontal directions at a constant rate toward wells andgalleries. According to the author's analysis, these assumptions are not consistentwith the actual conditions of flow, hence the formulas obtained therefrom are notrational, and the employment of these formulas to investigate the general effectof surface drop or well diametre upon yield is devoid of rational foundations. According to the author's analysis, the flows toward wells or galleries areactually supplied vertically by draining the stored water above the free surface inthe course of its descending and enlarging. As the drainage of gravity water fromthe pores of soil particles in order to reduce the water content to that of filmshells takes one to two days, as the capillary water columns are interconnectedand mutually supplied sidewise, this vertical supply of water may maintain quite along time, yet the flow may not be absolutely steady. As regards vertical supply of water with unsteady regimen, equations of freesurface for flow pattern near galleries are deduced, corresponding to the Boussinesqpartial differential equation. Besides, the author has derived simplified equationsfor computing flows into wells and galleries. The latter, in comparison with theDupuit-Forchheimer formulas, gives a higher yield, while the free surface curve isreasonably tangent to the horizontal water table at a point which moves fartheraway as time goes on. J. Kozeny first pointed out the phenomenon that the water depth in the groundon the wall will not be further lowered when it reaches one half of the depthbefore pumping. The author hereby proposes a theoretical proof of it on the basisof theorem of least work. Based upon these theories, formulas are proposed for maximum possible yieldof wells and galleries dug to horizontal impervious strata, to be used in prelimi-nary estimations for hydro-geological workers.

1886年以来,杜布义-福熙罕默(Dupuit-Forchheimer)的井流及沟流的理论与计算用公式被世界各国广泛地应用着。公式假设地下水从远处沿着水平方向以定率流向井内或沟内,按作者分析这种假设并不符合实际情况,因之所得公式也不合理,用这些公式来推论水位降落或井径对於出水率的影响也没有合理的凭据。作者推论,井流或沟流的水实际上是从水面线以上,在其降落并扩大的过程中,排除了存积的水,沿着直垂方向所供应着的。因为从土壤颗粒的空隙间排除重力水,使减为薄膜水,每需时一两天,而水面上的毛细管水又是横向贯通并互相接济着,所以垂直供水可以维持很久,而潜流也决不会绝对稳定。根据这垂直供水的不定汉条件引出了沟流的水面线公式,结果符合蒲薪奈斯克的偏微分方程式。另外,作者又拟具了简化的井流及沟流计算用公式。这些公式和杜氏-福氏公式比较,所得出水率较大,而水面线则合理地切於静水线,切点随着时程向远处移动。柯臣尼(J.Kozeny)最早指出井边地内水深不会低於静水深一半的现象,本文中作者根据最小工作定律试拟了理论的证明以支持之。根据这些理论,引出了从静水中抽水时井流、沟流最大可能出水率的公式,以供水文地质工作者初步估算之用。

 
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