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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 高校生

すみませんカッコの中に入る正しい答えが分からないので教えてください🙇‍♀️

James What time do you wake up? Chris I get up 6:30 every school day. James What do you before you come to school1? Chris I and Finally, I James How about weekends? Chris Saturdays I get up 10 AM. the winter months I sleep later, because it's cold. How about you? How late do you sleep? James Well, last night I got 10 hours of great sleep. I slept like Conversation2 Unit 7 Future Tense Yoko Do you have plans for this coming vacation? Runa Yes. I'm going to America. Yoko How exciting! Where you going to go in America? Runa To New York. After that, I'm not sure. Maybe I go to Boston. Or perhaps I travel to LA. How about you? Yoko staying here in Yamagata because of my job. But next summer, my roommate and I visiting Thailand. Runa That's great. But be sure to travel Don't take too much luggage with you! Conversation3 Unit 8 Present Perfect Tense Mike Have you ever Thai food? Pam No, I How about you? Mike Yes, I It was very spicy. Pam Have you ever to a foreign country? Mike No, I have never traveled Have you? Pam been to Korea and Taiwan. I really loved eating the food there. It was delicious. Mike All this talk about food is making me hungry. you eaten yet? Pam I eaten anything. Let's go toa café. Mike Sounds Conversation 4 Unit 9 Auxiliary Verbs Mai Excuse me, Shun. I borrow a pen? Shun Sure. You look tired. What's up? Mai Well, I really finish this report by tomorrow's deadline! By the way, how is your part time job? Shun It's hard work, but I save money for the future. If I don't shop for clothes too much, that is. Mai You try looking for sales. Clothes don't have to cost an if you look for discounts. Shun You're right. I buy my clothes from second hand shops. And there's one other thing. Mai What is it? Shun I borrow ¥2000 for my next shopping spree?

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