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Mathematics Undergraduate

問題としてはこのURLのやつでexercise2.2.9の問題です。 2.2.9. Define T : ℓ^2(Zn ) → ℓ^2(Zn ) by (T(z))(n) =z(n + 1) − z(n). Find all eigenvalues of T.... Read More

16:22マ l 全 の Exerc: 164/520 matrices, convolution operators, and Fourier r operators. 2.2.9. Define T:l'(Zn) - → e°(ZN) by ニ Find all eigenvalues of T. 2.2.10. Let T(m):e'(Z4) → '(Z) be the Fourier multipliei (mz)' where m = (1,0, i, -2) defined by T (m)(2) = i. Find be l(Z4) such that T(m) is the convolutior Tb (defined by Th(Z) = b*z). ii. Find the matrix that represents T(m) with resp standard basis. 2.2.11. i. Suppose Ti, T2:l(ZN) → e(ZN) are tra invariant linear transformations. Prove that th sition T, o T, is translation invariant. ii. Suppose A and B are circulant NxN matric directly (i.e., just using the definition of a matrix, not using Theorem 2.19) that AB is Show that this result and Theorem 2.19 imp Hint: Write out the (m + 1,n+1) entry of the definition of matrix multiplication; compare hint to Exercise 2.2.12 (i). iii. Suppose b,, bz e l'(Zn). Prove that the cor Tb, o Tb, of the convolution operators Tb, and convolution operator T, with b = 2 bz * b.. E Exercise 2.2.6. iv. Suppose m,, mz € l"(Z). Prove that the cor T(m2) ° T(m) and T(m) is the Fourier multiplier operator T) m(n) = m2(n)m」(n) for all n. v. Suppose Ti, T2:l"(Zw) → e'(Zn) are linear tra tions. Prove that if Ti is represented bya matri respect to the Fourier basis F (i.e., [T; (z)]F =A Tz is represented by a matrix Az with respect t the composition T20T, is represented by the ma with respect to F. Deduce part i again. Remark:ByTheerem 2.19, we have just proved of the Fourier multiplier operat Aresearchgate.net - 非公開

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English Junior High

これの5の答えはイだったんですけどなんでそうなるのか解説をお願いします。

次の左利き(left-handed)と右利き (right-handed) についての英文を読んで, 1~5の問いに答え なさい。 =~する可能性が高い rate (s) =割合 serious injuries =重傷 (注)life span (s) 3D寿命 feel down = 落ち込む be likely to ~= data = データ allergies = アレルギー advantage = 有利な点 academic success = 学問的な成功 president (s) =大統領 Are you left-handed or right-handed? Do you use your right hand or left hand when you do some activities? In this world, some people usually use their right hand, and others use their left hand. Is there any difference between these people? Some scientists) have discovered an interesting fact, about the life span of left-handed people and right-handed people. They. say that left-handed people have a shorter life span than right-handed people. This idea comes from Da study in 1991 It showed that the population of left-handed people becomes smaller with age. The scientists said that left-handed people live in ② a world for right handed people. Some things, such as a knife, a guitar, a baseball glove, and a keyboardof personal Computers, are made for right-handed people. Left-handed people are more likely to have trouble using those things, and have-accidents and serious injuries.. In 1992, one scientist, that the life spans of left-handed people are about nine years shorter than those of right-handed people. Were left-handed people given a bad hand? If you are a left-handed person, don't feel down. In 2000, a scientist showed that ④ Coren's idea was not. true. Here is the reason: some elderly right-handed people started as left-handed people, but their parents and teachers changed them into right-handed when they were children. That means many of left-handed people died as right-handed. Like this, there are some questions about Coren's data, so we cannot say that left-handed people have a shorter life span. Also, other studies showed that the life spans of right-handed people and left-handed people are not so different. Stanley Coren, said that these make their life spans shorter. He found Still, some people say that there are some bad points in being left-handed. Because they live in a world for right-handed people, left-handed people may have higher rates of some diseases such as mental disease,and allergies. However, we can also find a lot of good points in being left-handed. They have an advantage in sports like_tennis and baseball. Also, they are likely to have more academic success and higher IQs. Five of America's last eleven presidents were left-handed people, though ( 6 11人の5人

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Chemistry Senior High

詳しく解説してください!

化学 MISSION 5 解答||の 解説 問題集 O P8 化学 MISSION 5 実験結果を表にまとめて考える(2) O日標時間4分 次の有機化合物A~Eに対し、以下の確認実験1~5を行った。しかし、これらの実験だけでは、 A-Eの5種類の化合物を判別することはできなかった。さらにどのような実験を行えば、すべ ての有機化合物を判別できるか。最も適当なものを、下のD~5のうちから一つ選べ。 - 問われている内容を確認する。 A:乳酸 B:アラニン C:アニリン D:グルコース E:サリチル酸 実験1 水に溶けるかどうかを調べる。 実験2 アンモニア性硝酸銀水溶進を加え,銀が析出するかどうかを調べる。 実験3 塩化鉄(I)水溶液を加え、赤紫色になるかどうかを調べる。 実験4 酸酸性ニクロム酸カリウム水溶流を加え、黒色物質が生じるかどうかを調べる。 実験5 統酸を触媒にしてメタノールを加え。選炎鎮痛剤のにおいがするかどうかを調べる。 実験結果を表にO×でまとめる。 0 フェーリング液を加え,穏やかに加熱する。 ウ素溶液を加える。 フェノールフタレイン溶流を加える。 の ニンヒドリン溶液を加える。 5 水酸化ナトリウム水洋液を加えた後。少量の確機鋼(I)木審液を加える。

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