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.... 続きを読む

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

問題としてはこのURLのやつでP.144 exercise2.2.1の問題です。 https://www.researchgate.net/profile/Seyed-Yahya-Moradi/post/Can-anyone-suggest-a-wavele... 続きを読む

長文 訳を教えていただきたいです。文法が怪しいので教えていただけると助かります 回答、よろしくお願いします🙇

29 Laundroid is a new robot that folds laundry. Throw in up to 40 items of clean clothing and it goes to work. It analyzes each item、 figures out its ideal foldin shape, and folds it. The problem is that, in the first-generation Laundrold image analysis of each item takes up to 10 minutes, and folding a mintte

こういった問題を早く解けるようにするにはどうしたら良いでしょうか。 読み方のコツとかあれば教えてください😭

T) Read the following passage, and for each of the numbered spaces 【31】- 【35】, hoose the most suitable word from those given below (1-8). Use each number only one time. [67 皮本日 Retirement is the stage when a husband and wife finally have the chance to spend time together, free from the stresses and strains of working life. But far from being an era of relaxed contentment, retirement can actually be a stressful experience for couples. Academics have (【31】 ) that many wives actually begin to suffer from “retired husband syndrome” once their men give up work. They discovered that nearly half of women complained of ( 【32】 ) levels of stress, depression and sleeplessness after their husbands retired. And to make matters worse, Italian researchers also found that with every extra year the husband spent in retirement, the wife's condition became worse. They said that the problem does not only affect housewives, but can be even worse for women who are still (【33】 ) while their husbands stay at home. “We have found that retirement effects are stronger for employed women, who are already stressed by their job and have( 【34】 ) time to deal with the additional requests by their retired husbands," they said. Part of the cause of greater stress was that women were faced with an increase in housework, the authors wrote. They also had to deal with the added burden of reduced income, an extra concern' for both partners. The research was ( 【35】 ) out by social scientists Dr. Marco Bertoni and Dr. Giorgio Brunello, from the University of Padova, who analysed interviews with 840 Japanese Women between 2008 and 2013. 1. carried 2. increasing 3. less 4. much 5. reducing 6. reported 7. suitable 常 () 8. working 帰 副内王 蓄田

答えがbなのですが、なぜaspectになるのかが分かりません

3 次の各文の下線部に最も近い意味を表す語を、a~dのうちから1つ選びなさ い。 17. Everything in her story is correct down to the smallest detail. b. aspect c.design d. range a. analysis

答えbなのですが、なぜaspectになるのか納得できません あと、correct downは｢修正する｣で合っていますか？

3 次の各文の下線部に最も近い意味を表す語を、a~dのうちから1つ選びなさ い。 17. Everything in her story is correct down to the smallest detail. b.aspect C. design d. range a. analysis

正解しているのですが、どうしてlocatedが入るのでしょうか？ 詳しく説明をお願いします！

問10 Chokai-san, the second highest mountain in the Tohoku region, is an active volcano 10 on the border of Akita and Yamagata prefectures. イ locating ロ 1ocation ハ/located ニ locational ー 20-

この文をthe skill of reasoning and of thinking crtically, habits of analysis and judgement としたときに意味の違いは出てきますか？

「~と関係がある」の意。 1much [a lot] ② something have to do with ③ little ④ nothing 「~と関係が1大いにある ②いくらかある ③ほとんどない 4④全くない」 ■ 3.2 the skills of reasoning and thinking critically, habits of analysis and of judgment 「論理的考察や批判的思考の技術, 分析や判断の習慣」 動 名詞 reasoningは, 「論理(reason) を用いること」 であって, 「推理」と訳すこ ともある。critically は直前の thinking を修飾。「批判的に考察する」とは, 予想 される反論に堪えられるよう自分の考察をより客観的なものに仕上げていくことを いう。 analysis 「分析」は全体を細分化し精査することであるが, judgment 「判 断」は全体について何らかの評価を下すこと。それらを habits「習慣」 という名詞 にまとめているのは、そのような知的行為を日常的に実践

36,37,38の答えが分かりません。 どなたか教えていただけませんか？

asked strange questions so that the answers would sound funny and make them smile. that answer was true or not. Later in the interview, the volunteers were deliberately In the study, the scientists conducted interviews with volunteers. The volunteers recent study by scientists at the University of Portsmouth has shown that people can When people communicate face to face, they do not just communicate by speaking language. There are other factors involved, such as gestures. If the person you are tell if a speaker is smiling or not even without seeing their face but just by listening were asked to answer all questions with “I do in the summer,” regardless of whether talking to frowns, you know that he or she is unhappy. Whena person laughs during a conversation, you can tell that that person thought something was funny. However, a The interviews were videotaped with the purpose of gathering samples of different C 35) Smiling from Ear to Ear to their voice. of smiles. The scientists then analyzed the smiles. types According to the scientists, there are as many as 50 different kinds of smiles. T he researchers then had different group of volunteers listen to the audio portion of the recordings. This group of volunteers could tell what kind of smile the speaker had on his or her face by just hearing their voice. This indicated to the scientists that the voice has characteristics that communicate feelings and that people can interpret them. Another study also suggests that customer satisfaction is closely related to friendliness. As we all know, the best way to show friendliness is to smile. Researchers think that using the smiling voices in products or services effectively, Such as answering systems and computer programs, can contribute to better customer service. This can also be applied to hiring and training staff. Since people can tell ifa smile is real or not by a person's facial expression, and it has been proven that people, for example, customers can tell if a staff member's smile is real or not just by listening, then smiling not only from the bottom of your heart, but with your voice may be a g0od way to improve business.

和訳の確認をしてほしいです！ お願いします🙇‍♂️🙇‍♀️

TR3T Humans usually breathe from sixteen to twenty times each minute. If you analyzed 01 the air you breathe, you would find it is a mixture of different gases. Most of it is *nitrogen about four-fifths. One-fifth is oxygen. There is also a tiny amount of carbon dioxide, a little "water vapor (which gives air its humidity), and some "traces of 05 what are called "rare gases. If you were to put a bag over your nose and mouth to catch the air you breathe out, i図 you would find (1)Some strange changes. There would still be the same amount of nitrogen. There would also be the same traces of rare gases. But there would be much less oxygen and a hundred times more carbon dioxide than in the air you breathe in. 10 There would also be considerably more water vapor. TR33 ,What happens is that each time you breathe, an exchange takes place. You keep Some oxygen; you breathe out much more carbon dioxide and water vapor than you breathed in. 、The reason is that every moment of the day and night your body is using up energy. Your heart uses up energy as it beats. Your muscles use up energy. So 15 does your brain, and so does every other part of you. All this energy is produced by the work of the millions and millions of cells that make up your body. Every one of these cells needs Oxygen in order to do its work. As the cells use up oxygen, they form carbon dioxide, which is a “waste product. So your body carries out these two processes at the same time. You breathe in the m3 20 OXygen that cells need to produce energy. You breathe out the carbon dioxide that is harmful. It sounds so simple. Yet your life depends on these processes happening dav and night without interruption.