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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 Senior High

答え合わせがしたいので教えてください🙇‍♀️

Come under this heading, and are spending an average of 4 hours each day on care. 60% d of second-year public junior high and 4.1% of second-year public senior high school students |I|次の文を読んで、あとの問いに答えなさい。(~~~~のついた語句は文末に注があります。 |was to create opportunities for the yOung to talk to a school social worker about the domestic issues that were keeping them from attending class without young people who are obliged to help with the care of a family member. It reports that 5.7% has revealed one very different reason for absence, and that is the increase in the number d In its latest study, the Japanese government is making an effort to identify the rees for long-term absence from school. Long-term absence at elementary, junior and senior high levels has various causes, not least of which is the ongoing coronavirus pandemic. The study ow the former, and more than half of the A are looking after a younger brother or siste- though the exact figure is not known. The Asahi Shimbun's article of April 14", 2021 also described the case of one shudee who was looking after a grandparent with dementia because both her parents were working and her absence from school was because she could not get up in the morning. Instead of being treated as a separate reason in itself, like a student's refusal to attend school, or sickness, or economic considerations, family care is put into the category of 'other B to highlight the problem. Despite the recent introduction of reasons'. This does not school social workers, and the understanding that domestic issues are often at the root of school absence, much more needs to be done to provide support to enable these young carers Japanese society still expects the C to have enough time to spend on their studies. family to care for its members. The mental health of these young carers is an important issue, though this problem cannot be solved unless the whole domestic environment in which they are placed Is improved. This has led to the criticism that. although the government study may hdVC nelped to identify some of these young carers, there is not enough actual support bes offered. AS early as 2015, Minami Uonuma City conducted a survey which tried to ldeirers) specific cases in which young children were acting as carers. and then started to p them with real support. D the fear that this might reflect badly on their family.

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English Senior High

なぜ22番の答えが1なのかわかりません わかる方いらっしゃったら解説お願いしますm(_ _)m

2 次の英文A、Bを読み、その文意にそって(21) か ら(26) ま での A その番号を解答用紙の所定欄にマークしなさい。 )に入れるのに最も適切なものを 1,2、3、4の中から一つ選び、 /6 Cycles of Changece The bicycle is an efficient means of transportation. It was invented in the 19th century, and since then, it has been improved many times. Recently; electric bicycles, or "e-bikes," have become widely used. Unlike a regular bicycle, an e-bike has a motor, which allows the rider to go up hills more easily. Sqme cycling fans think that it is "cheating"” to use a bike with a motor. Nevertheless, e-bikes are quickly ( 21 ). In fact, e-bike sales in the United States were eight times greater in 2018 than in 2014 according to one survey. Researchers say this is good news. They claim that e-bikes may have a positive effect on people's health and the environment. One major advantage of e-bikes is that older people and those who do not exercise regularly can cycle. This makes it easier for them to commute to work by bike, which is better for the environment than traveling by car. ( 22 ), e-bikes allow more people to cycle as a hobby. People who could not ride along rough roads or up mountains, for example, can now do so. p Some cycling experts, however, point out problems with the increased use of e-bikes. For one, riders of e-bikes are more likely to be involved in accidents. In response, some people want speed limits to be lowered and other measures to increase safety, such as bike paths. Most importantly, experts say riders of both e-bikes and regular bikes should be careful. It does not matter if a bike has a motor or not. The important thing is to enjoy cycling ( 23 ). 2 causing new problems 4 improving the environment (21) 1 reducing electricity use 3 growing in popularity 3 By contrast, 4 Despite this (22) What is more_ 2 Therefore 2 together with friends 4 while staying safe (23) 1 during the warm months 4 3 in order to keep fit 13の他 21たっク曜師に 4z070も copyright2021 公益財団法人日本英語◆ *ます

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