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数学 大学生・専門学校生・社会人

この問題の問題13-1(3)(4)、問題13-2の解答を作ってください! お願いします!

2021年 物理学演習2 第13回 デルタ関数 関数f(x)がどのような関数であっても次のような関係を満たす8(x) をデルタ関数という。 「r86) = f0) JO (x * 0) l0(x = 0) 8(x) = このデルタ関数は物理学者の P.A. Dirac によって発明された。名前に関数とついているが、正確 には関数ではなく汎関数の一種の超関数で、線型性と連続性などを満たした汎関数である。 関数: 数 → 数 例えば x → y=f(x) 汎関数:関数 → 数例えば f(x) → f(0) = Sf(x)6(x)dx デルタ関数は関数では無いが、実際には下記のような関数の極限とみなすことができ、どの表現も 同等である。 8(x) = lim 8,(x), ど→+0 8,(x) = {o (x> £/2) 1 28 8(x) = lim 8,(x), E→+0 6,(x) = 2x?+ 2 1 8(x) = lim 8,(x), ど→+0 6(x) = e VTE 8(x) = lim 8,(x), 1 8,(x) = 「e-ddk Zt J-o 1(x2 0) lo (x < 0) 8(x) = 0'(x), 0(x) = 3次元のデルタ関数は以下のように1次元のデルタ関数の積になる。 8(r) = 6(x)6(y)8(z) (o (x =y=z= 0) lo (x =y=z=0以外の場合) 8(r) = 問題13-1 f(x)はx| → oで0となるなめらかな関数とする。デルタ関数8(x) f(x)6(x - a)dx= f(a) について次の性質を証明しなさい。 (1) x6(x) = 0 (2) 6(ax) = )(a>0) (3) 6(x) = 0°(x) so (x< 0) l1 (x> 0) 0(x)は階段関数(ヘビサイド関数)であり、e(x) = である。 {8(x - a) + 6(x + a)}(a> 0) 問題13-2 正規分布を表す次式 = (x)9 がa→ +0 のときにデルタ関数となることを証明しなさい。 1 -exp V2To 2g2

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TOEIC・英語 大学生・専門学校生・社会人

これ読んだんですけど、自分は世界史を理解してなかったので分からなくて翻訳アプリ使ったんですけどそれでも分からなかったので分かる方できれば解読お願いします┏●

Denmark in World War II お んれ By Hannah Arendt Hannab Arendt (1906-1975) was a political scientist! and pbilosopber born in Hanover, Germany. Wben Hitler came to power, sbe was forced to leave Germany and came to the United States in 1940. Sbe continued ber academic career by lecturing and teacbing at arious colleges, including The New Scbool for Social Researcb in New York City. Among the many books sbe urote were Eichmann in Jerusalem, On Revolution, and The Origins of Totalitarianism. Editor's Insert During the Second World War. the Germans invaded Denmark in April, 1940. In the beginning of her essay, Hannah Arendt explains that of the four countries almost completely immune to anti-Semitism- Denmark, Sweden, Italy, and Bulgaria Denmark challenged its German masters directly. As soon as the German authorities talked about forcing Jews to wear the yellow badge,' the Danes replied that all Danish citizens, including the King, would be wearing it the next day if the policy were carried out. In addition, all Danish government officials threatened 舌は the German authorities with their immediate resignation if the Germans started to implement any anti-Jewish actions. The following excerpt from Eicbmann in Jerusatem shows how the Danes sabotaged the German plan to carry out the mass extermination of the Jews. only 2タカ人の What happened then was truly amazing; compared with what took place in other European countries, everything went topsy-turvey. In August, ー after the German offensive in Russia had failed, the Afrika Korns 1943 had surrendered in Tunisia, and the Allies had invaded Italy すgovernment canceled its 1940 agreement with Germany which had permitted German troops the right to pass through the country. Thereupon. the Danish workers decided that they could help a bit in hurrying things そのうえに up: riots broke out in Danish shipyards, where the dock workers refused to repair German ships and then went on strike. The German militarv commander proclaimed a state of emergency and imposed martial la and Himmler thought this was the right moment to tackle the Te the Swedish す。 (continued on next page) themselves as Jews secret police), and overseer of the concentration camps

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