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数学 大学生・専門学校生・社会人

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

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英語 高校生

教えてほしいです!!お願いします!!

問題は【1】~【4】まである。答えは各問題の指示に従って別紙の解答用紙に書きなさい。 【1】次の英文を読んで設問に答えなさい。 Headaches are a big problem. Each year, millions of people suffer from severe headaches that affect their enjoyment of life, (1) not to mention their productivity at work. estimate, headaches cost individuals and businesses more than (2) $50 billion each year! (3) This is one of the reasons research into headaches has become a worldwide effort. Although he did not know much about how headaches work, Hippocrates was the first doctor to find a way to treat them. By 400 BC, Hippocrates had discovered that the *bark from willow trees was useful in treating pain. He made a white powder from the tree's bark and gave it to his patients. Hippocrates did not know it, but he was actually prescribing a natural chemical in willow bark called salicin. Whena person eats salicin, the chemical is changed inside his or her body into (4) salicylic acid. It turns out that salicylic acid is good for stopping pain, including headache pain, but it is bad for a person's stomach. In the 1800s, a chemist in Germany slightly changed easier for people to take. commonly known as aspirin. Aspirin was used throughout most of the 1900s to treat headaches, but doctors had little idea about what really caused headaches. When doctors can *diagnose the cause of a disease, they can find better ways to treat it. Therefore, as medical technology developed, doctors began to use it to learn more about the human brain and about headaches. In fact, according to one m to make it This new form of the chemical was called acetylsalicylic acid, now acid's Now doctors classify headaches ( A ) two general types: primary and secondary. A primary headache is a condition ( B) as only the headache itself. one caused by another physiological condition, such as an *infection or a *tumor. For primary headaches, doctors have determined three possible causes. headache is caused by stress. characteristically felt on both sides of the head as a dull, steady pain. Another kind of primary headache is the *migraine headache. Exactly what causes these headaches is not well understood, but many experts believe it could be abnormal brain activity causing changes in the brain's chemistry and blood flow. For many people, migraines are caused by certain (5) stimuli, such as poor sleep or particular foods or smells. A sufferer usually feels intense pain on one side of the head and becomes sensitive to light and noise. If the migraine is severe, the sufferer may *vomit repeatedly. The third kind of primary headache is known as the cluster headache. Cluster headaches typically occur around the same time each day for weeks or months at a time. The person ( C)from this kind of headache usually feels pain on one side of her or his head, and the pain is centered around one of the eyes. Doctors do not know much (6) at present about cluster headaches, but they seem to be more common among men and could be related to alcohol or other things that affect a person's blood flow. Using computers and more advanced medical equipment, doctors continue to learn more about what happens in the brain before and during headaches. Especially in the case of migraines, some doctors believe they have found the part of the brain that sets off the reaction for severe attacks. With these insights into brain processes, doctors hope new ways will be discovered to stop headaches before they begin. On the other hand, a secondary headache is One kind of primary Doctors usually call these tension headaches, and they are 注: bark 樹皮 diagnose ~を診断する、~を突き止める 感染症·伝染病 migraine (headache) 偏頭痛 infection tumor 腫場 vomit 食べたものを吐く (出典:READING FOR THE REAL WORLD 3rd edition, Compass Publishing より)

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英語 中学生

どこを読んだら答えに導けますか? 答えは1がenjoyed.2がeasy3がstoryです! 長文のコツを教えてください、、

restaurant was on the first floor in the hotel. When we got to the hotel, we tried to find the 次の英文は,中学生の真紀(Maki)が, 夏休みの課題として,イギリス(the UK)を旅行したこと the restaurant was. She said, “The restaurant isn't on this floor. Please *go upstairs, On our first night in London, my family went toa restaurant in a hotel. My father heart ) restaurant on the first floor for a long time, but we could not find it. So I asked a woman We went upstairs and found the restaurant. We enjoyed dinner there, *garden. His family welcomed us and they made us lunch. We had lunch in the garden. It was エ from) Mr. Brown. He said His name is Mr. Brown B[ A[ (2)本 えなさ 4 とに(注)があります。 (56点) (3)本文中 I visited the UK with my family this summer. (4)本文 記々 We visited his family during our stav in the UK. I had a very good ue. about the restaurant ① (ア on イ since ウ for the ア A a but I did not know why the restaurant was on the second floor. The next day we visited Mr. Brown's house. Around his house, B beautiful was a SO nice. After lunch, I told Mr. Brown about the restaurant we C | the first night in London. I asked him about the floors. “Whyis the restaurant on the second floor:" He answered. “On the second floor? "I did not understand what he meant. Then Mr Brown said, "Oh, I see. The first floor in the UK is the second floor in your country. Im sorry ] didn't tell you about that." I was a little surprised to hear this. "As you know, we have many *castles in the UK. A long time ago, each castle ② (ア have イ has ウ had エhaving) its *entrance on the second floor. People went up to the second floor when they wanted to go into the castle. So the second floor is called the first floor. It's one example of *British English," said Mr. Brown. His story was very interesting to me. I said to him," he told me 3(ア another イ other ウ others I many) example of British English. C “Sure," he said. Then We enjoyed talking with each other. Now I understand that people in the UK speak British English. It's a little different from the English I am learning in Japan. I also enjoyed *communicating with people in English during this trip. I want to know more about the UK through English. In the future, I would like to visit the country again. It was a wonderful summer vacation.

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