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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

過去問なんですが答えを貰っておらず分からないので教えてください よろしくお願いします

9 次の英文を読んで、後の問いに答えなさい。 Naln was an 'exchange student from *Tndonesia at Minami High School. Her class was going to nave class activities about Indonesia Nani was asked to introduce some games to play. She thought, “I have an idea. I will introduce a game like Japanese janken. One day after school, Nani was on her way home. It began to rain. She was lucky because she was carrying her pink umbrella with her. She went to a convenience store to buy some "snacks. She Ctered the store and put her umbrella near the door There were some other umbrellas there. When she was looking for some snacks, she saw a tall girl. The girl went out through the door. Nani bought some "pieces of bread and a *pack of orange juice. She found one pink umbrella near the door, but it wasn't hers. She said to herself, "Someone has taken( ). Nani said to the Clerk, "T can't find my umbrella. I put it here but " The clerk thought "for a while and said, "1 guess my daughter, Kumiko, took yours "by mistake. Our shoD is very small, and our “family members Sometimes use that door. Kumiko hurried to her friend's house to return a book. She will be back SOon. Nani said, "No problem." The clerk looked at her uniform and said, "Oh, you are a Minami High School student. Kumiko was a student there, too." Nani said, "My name is Nani. I'm from Indonesia." A few minutes later Kumiko came back and her mother said to her, "Kumiko, this is Nani. You took her umbrella. Both of yours are pink." Kumiko said, "Oh, I'm sorry." Her mother said, "She is an exchange student from Indonesia at Minami High School." Kumiko said, "I was a student there too. Nice to meet you. When I was a student, I was very interested in foreign countries. I wanted to have a friend like you. Did you tell your classmates about your country? Nani said, "Yes, but I want to teach them more. I'm going to introduce Indonesian janken to my classmates. I hope they will enjoy it." Kumiko smiled and said, "A game? That's interestingl I'm interested in it. I'd like to see it. Would you like to come to my room?" Nani said, They went up to Kumiko's room. Nani said, "Ill teach you a game, Suit, from my country. It's like a Japanese janken. This is how to play it. You are three "fingers, a *thumb, a “forefinger and a *little finger. A thumb means an elephant. A forefinger means a man. A little finger means an ant. An elephant is stronger than a man. A man is stronger than an ant. An ant is stronger than an elephant." Kumiko asked, "Why is an ant stronger than an elephant?" Nani answered, "An ant goes into its ear, and the elephant cannot do anything about it. The elephant feels very bad. Do you 1understand?" Kumiko said "Yes, I do. I think it is not difficult to understand this game." Nani was glad to hear that. They played it together. After the first game, they tried it again. Kumiko won the second game. They tried it many times. They had a good time. Kumiko said to Nani. "Thank you for teaching me such an interesting game. Im sure your classmates will be excited too." Two days later, Nani's class had class activities. When Nani introduced the game to her classmates, they were interested in it. I hey enjoyed playing it many times. They had a great time. (注*) exchange student 交換留学生 Indonesia インドネシア snack 軽食 piece 一切れ pack パック for a while しばらくの間 by mistake 間違って family member 家族 thumb 親指 forefinger 人差し指 little finger 小指 finger 指

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English Junior High

過去問なんですが答えを貰っておらず分からないので教えてください よろしくお願いします

was studying エ will study) last イ is studying When Megumi① (ア studies と near She answered, "I will go to Kyoto ウ about night, Kevin called her. He asked her, "What will you do (② (アduring Do you have any plans?" エ of) your summer vacation? I visiting)my grandparents. How about you?" He ViSit と visited to visit E) we She said, "You can come to Kyoto with ④ (ア answered, "I don't have any plans now." ウ エ ours). It will be fun." He was surprised but very glad to hear that. our us と 7 次の英文は、図書館の職員が昨作年行ったアンケートについて説明しているものです。 これを読んで、後の問いに答えなさい。 Last year, we did *research about our library. We asked 2 questions to 200 visitors. Look at the *table. The first question was, "How often did you visit our library?” The number of Visitors who came more than 5 times a month is much smaller than the number of visitors in the other 2 groups. The second question was, "How long did you stay when you visited our library?" Look at the *graph. The number of visitors who stayed 0.5-1 hour is the largest of all. Those people borrowed books at the library and read them at home. Many people read books in the library and stayed here more than 2 hours. Those visitors who stayed less than 0.5 hours are as many as those 1 - 2 hours. These days, people are very busy and don't have time to come to the library. We hope to meet as many people as possible here. is important ) us books, so please come to our library. How often did you visit our library last year? How long did you stay when you visited our library last year? Answer Number of visitors Less than 0.5 hours (%01) more than 2hours More than 5 times 13 (38%) 0.5~1 hour 3~5 times 78 (42%) Less than 3 times 1~2 hours 60L (%01) (注*) research 調査 table 表 graph 図武

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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

「I|次の文を読んで、あとの問いに答えなさい。( wのついた語は文末に注があります。 ns Sitting in the consultation room of a charming cosmetic surgery clinic in Washmgo. D.C., Hudson Young removed his mask under the satisfied gaze of his doctor. Like a grownns number of Americans, Young decided the right time to undergo plastic surgery was middle of a coronavirus pandemic, He knew he would have time to recover in the privacy ot his own home. The main reason, however, was that Young suddenly found himself face to face with his own image while participating in an increasing number of videophone and web A 「Its something new when you have to stare at your face for a couple of hours a day and there's only so much you can do with good lighting and good angles," Young said. The 52-year-old real estate agent had allready been a fan of cosmetic surgery. He had face lift, eyelid surgery and laser resurfacing for the first time in October. "When you see yourself on Zoom, you are shocked," he explained, as Dr. Michael Somenek examined his w barely visible scars. Young is far from the only one who has found himself disappointed with the reflection he has seen in the screen over the past year. Virtual consultations for cosmetic procedures have risen 64% in the United States since the beginning of the COVID-19 pandemic, according to the American Society of Plastic Surgeons. “We have seen an increase in the number of surgical cosmetic procedures that are directly related to Zoom," said Somenek, who has seen a 50% to 60% increase in customers. “I think the pandemic B has given everyone time to take care of those things that we've been putting off until later," explained Ana Caceres, who was able to work from home after C a plastic surgery operation she had wanted for a long time. She recovered at. her parents' house outside Washington after a December cosmetic surgery that helped her D deal with a source of insecurity she had had since adolescence. "I didn't have to days off, because I was still able to work from my bed with my lap-top," the 25-year-old said. “When life is going on and you have places to be, it's s0 easy to put things off," Caceres said, showing off a dress she says she now has the confidence to wear. And she has scheduled more cosmetic surgery. Her surgeon, Dr. Catherine Hannan, says consultations at her clinic in the IIS comit1 E have nearly doubled since the beginning of the pandemic. "Our patients have more lines because the last vear has been so hard. A face or boay change can have a psychological

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