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The Balian-Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(t-na)\}_{m,n \in \mbox{\bf Z}}$
      
The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number of Minimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA.
      
This phenomena is related to the invariant cycles under the transformation We also give a characterization of all low-pass filters for MSF wavelets.
      
The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA.
      
We also give a characterization of all low-pass filters for MSF wavelets.
      
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The problem of investigating the vibration properties of continuous girders on elastic piers frequently occurs in practical design work. An approximate method of attack is to replace the elastic pier by a spring support. This method simplifies greatly the analysis and is generally adopted in practice. In the first part of this paper, this approximate method is investigated in detail and complete solutions including the effect of initial conditions are given. The computations are made more systematic and simple...

The problem of investigating the vibration properties of continuous girders on elastic piers frequently occurs in practical design work. An approximate method of attack is to replace the elastic pier by a spring support. This method simplifies greatly the analysis and is generally adopted in practice. In the first part of this paper, this approximate method is investigated in detail and complete solutions including the effect of initial conditions are given. The computations are made more systematic and simple by the adoption of a system of constants defined as the dynamic shape constants and load constants of the structure. In the second part of this paper, the more accurate method of analysis is investigated. The exact frequency equations of the system are obtained by writing down the dynamic equations of the girders and the piers simultaneously and the boundary conditions are taken into consideration. It is shown that by taking only the fist one or two terms of the series expansions, the exact frequency equation reduces to the approximate one. It is concluded that the approximate method will give adequate solutions in the case when the piers are rigid and when only the lower frequencies of the natural mode need be considered. Particular solutions of structures under transverse vibrations are worked out and is found more involved than that given by the approximate method.

本文所謂架空結構是指搁置在較高的支墩上的連續梁結構,例如高架橋梁或水電站的架空輸水管道等。這類結構在承受震動荷載(例如地震)時,常會引起較大的變形和应力。如支墩較粗矮,則在計算較的頻率時,其作用可近似的以一彈簧支座代替之,而忽略支墩本身的結構震動影響。這是一個常用的假定,可以使計算工作充分簡化。本文首先對這一情况作了詳盡討論,給出较完整的解答,包括起始條件影響在内,並提出用“載常數”及“形常數”的觀念來進行計算。然后本文給出考虑支墩的震動影響時的精確解答,分別就縱横方向的震動進行討論,並指出近似計算公式和精確公式间的關係,近似公式只能在支墩較剛固和計算较階的頻率時才適用。文中列出了結構作横向諧和震動時的特別解答,可見其計算工作量將比近似法增加不少。

~~

本工作的主要目的是利用华北、中南和西南部分地区各地质年代岩石的天然剩余磁性资料来研究古地极位置,从而提供解决中苏太平洋区域成矿带地质构造问题的一些古地磁资料.我们用无定向磁力仪测定了175块岩石标本的天然剩余磁化强度.这些标本分别属于泥盆纪、石炭纪、二迭纪、三迭纪和侏罗纪五个地质年代.测定的结果是:泥盆纪的地极位置在北大西洋;石炭纪的地极位置比较散乱,这可能跟标本的天然剩余磁性较弱和测量仪器精密度较有关;二迭纪和三迭纪的地极位置都在北太平洋;侏罗纪的地极位置在印度洋.这些结果跟其他学者分别按照欧美地区岩石天然剩余磁性所获得的结果并不一致.原因何在?目前还不能确定,有待进一步的研究.但若把中国地质矿藏情况进行检查,在这些年代里的古气候都更接近于赤道这一现象,使我们相信本工作的结果更与实际相符合.

Starting from the frequently adopted formula h=△_i/(10~((I_0-I_i)/S)—1)~(1、2),where h is the focal depth, Ai is the mean radius of the ith isoseismal, I_0 is the epicentral intensity and s is a parameter and taking the common logarithm, we have log h=log△_i—1/2log (10~(I_0-I_i)/S)—1),A graticule can be constructed on the basis of this formula with s as a variable parameter. By use of this graticule, the values of s and h for 19 Chinese earthquakes were determined and it was found that the s-values for Eastern...

Starting from the frequently adopted formula h=△_i/(10~((I_0-I_i)/S)—1)~(1、2),where h is the focal depth, Ai is the mean radius of the ith isoseismal, I_0 is the epicentral intensity and s is a parameter and taking the common logarithm, we have log h=log△_i—1/2log (10~(I_0-I_i)/S)—1),A graticule can be constructed on the basis of this formula with s as a variable parameter. By use of this graticule, the values of s and h for 19 Chinese earthquakes were determined and it was found that the s-values for Eastern China are lower than those for Western China. According to the material for 61 earthquakes, it was found that the value of s increases with the focal depth; however, its relation with the low-velocity layer is not evident.

根据常用公式 h=Δ_i/10~((I_0-I_i)/s)-1~(1/2), 式中h为震源深度,Δ_i为烈度为I_i的等震綫半径,I_0为震中烈度,S为一系数;取(1)式的对数得 logh=logΔ_i-1/2log[10~((I_0-I_i)/s)-1], 按(2)式可以作成一量版,以同时測定h和s。利用这个量版測定了19个中国地震的s和h,結合文献[4]的資料,指出中国东部的s系数比西部的偏;且当深度加大时,s系数加大。采用文献[1,5]的資料測定了61个地震的s系数,結果表明s的数值随深度的增加而加大,占与速层的关系并不明显。

 
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