多様体を構成するために、位相空間に完全アトラスを導入するところで質問です。 完全アトラスを導入するメリットとして、この文章の下線部を「異なる座標系を用いたのに同じ計算ができてしまうという問題が解消される」解釈したのですが、そこがよくわかりません。座標系を変えて計算する... 続きを読む

1 Two n-dimensional coordinate systems & and ŋ in S overlap smoothly provided the functions on¯¹ and ŋo §¯¹ are both smooth. Explicitly, if : U → R" and ŋ: R", then ŋ 1 is defined on the open set ε (ur) → ° (UV) V and carries it to n(u)—while its inverse function § 4-1 runs in the opposite direction (see Figure 1). These functions are then required to be smooth in the usual Euclidean sense defined above. This condition is con- sidered to hold trivially if u and do not meet. Č (UV) R" Ĕ(U) n(UV) R" S n(v) Figure 1. 1. Definition. An atlas A of dimension n on a space S is a collection of n-dimensional coordinate systems in S such that (A1) each point of S is contained in the domain of some coordinate system in, and (A2) any two coordinate systems in ✅ overlap smoothly. An atlas on S makes it possible to do calculus consistently on all of S. But different atlases may produce the same calculus, a technical difficulty eliminated as follows. Call an atlas Con S complete if C contains each co- ordinate system in S that overlaps smoothly with every coordinate system in C. 2. Lemma. Each atlas ✅ on S is contained in a unique complete atlas. Proof. If has dimension n, let A' be the set of all n-dimensional coordinate systems in S that overlap smoothly with every one contained in A. (a) A' is an atlas (of the same dimension as ✅).

解答と出来れば解説をお願いしたいです

3 次の設問 A、Bに答えなさい。 A 次の会話が成り立つように、( )内の語 () を適切に並べ替えなさい。 ただし、文頭に 来る語も小文字にしてある。 1. A: Guess what? I met John yesterday for the first time in ten years. Never (dream / seeing / I / of / at / did / him) Imari station. B: Is that so? Good for youl 2. A: Welcome back, Kathy. Take off your coat, first. coffee? Would you like some snack and B: Well, I would(if / could / appreciate / help/you/it/me) with some baggage downstairs. 3. A: How was the project you were talking about the other day? B:(gave / advice / to / the / thanks / you / me), that was so successful. 4.A:How much (your computer / have / it / to / repaired / cost / did)? B: It cost 20,000 yen. I regret spilling coffee on the keyboard. 5.A:If (had / your / not / help / it / been / for), I wouldn't have succeeded in the presentation. B: It's my pleasure. B 次の会話文の下線部(1)、(2)を英語に直しなさい。 A: 学校で授業がなかった間、君はオンライン授業を受けたそうだね。 How was it? B: Well, it worked better than I had expected, but my eyes were so tiring. (2) 私はやっぱり友達や先生たちと直接コミュニケーションを取った方がいいな。 A: I know what you mean.

至急お願いします。 英語の穴埋め問題なのですが教えていただきたいです

Part 5: Incomplete Sentences A word or phrase is missing in each sentence. Select the best answer to complete the sentence. 51. Mr. Egan has offered New York. (A) making 52. (C) made the restaurant reservations for the annual meeting in (B) to make (D) being made A B C D low gasoline and diesel prices, the oil company plans to keep on expanding its domestic distribution operations. (A) Between (C) Except 53. Contrary to trip. (A) where (C) what (B) Despite (D) Unlike A B C D he actually had in mind, Lester spent all of his savings on his (B) which (D) that A B C D 54. In today's digital business world, IT networks must respond to progress in technology. (A) quickly (C) quickness (B) quick (D) quicken A B C D 55. We guarantee that delivery will be made 10 days after you place an order on the Web. (A) within (B) for (C) by (D) onto A B C D 56. The president team. the manager to hire three new employees for the accounting (A) intended (C) offered (B) provided (D) permitted A B C D 57. It is admirable that Ms. Arroyo wishes to handle all the transactions by (A) one (C) hers (B) her (D) herself 12 A B C D

お願いです助けてください

ba.jp Before you do the Grammar Activities below, I recommend reading this Grammar Reference: Making requests Agreeing Refusing Would you mind opening the window? Of course not. Sorry, but I'm cold. Could you take off your shoes? Yes, of course. I'd rather not. Can you clean up your room? Sure. No problem. I'm afraid I'm busy. Asking for permission Giving permission Refusing Permission Do you mind if I play my guitar? Is it OK if I turn off the radio? No, not at all. Go ahead. Sure. No problem. I'd rather you didn't. Sorry, but I'm listening. To agree to a request with mind, use the negative: Would you mind opening the door? Not at all. Do you mind if I close the window? Of course not. Notice the different positions for please: Please can you help me? Can you help me, please? Can you please help me? (stronger) ACTIVITY ONE: Put these words in the correct order to make questions. Example: please/you/me/help/could 6月 9 tv JA

この文を急速に訳して欲しいです。 お願いします。

li] You are reading a blog about new English words. 使ってると 意識しないで You are readinged words 過去分詞 41502 2. せる it] There are many blended words in English. [You may be Hords in using them without knowing it. A blended word is created ~なしに 5 動名詞 by combining two different words. Let's look at some examples. What would you call a meal that you have at around 11:00 a.m.? It's too late for breakfast s and too early for lunch. Yes, you call it "brunch." "Brunch" is a blend of breakfast and lunch. "Brexit" is a more recent example. The word concisely explains that Great Britain exited from the EU. Lastly, can you guess the meaning of the word "snaccident"? Let's say you have a snack, such as a pack of cookies, and decide to eat just one cookie. However, you can't stop eating and finish the whole pack by accident. That's a "snaccident"! Blended words show how flexibly people use English.

🚨至急お願いいたします🚨 写真の問題の答えがあっているかどうかの確認を お願いします。 もし、間違っていれば正しい答えと 解説等をお願いします。

Check! II (確認問題) CD 29 DL 29 ( )内の指示に従って、次の1~4の英文の下線部分を書き換えたあと、その英文を日本語にしなさい。 1. My father cuts his nails now. (現在進行形に) 《英語》 My father.is. cutting.his.nails.naw 《日本語》父は今爪を切っている。 2. Rumors flew about their marriage. (過去進行形に) 《英語》Rumers were flying about their marriase. 《日本語》彼らの結婚についてのうわさが飛び交っていた。 3. The building will near completion. (未来進行形に) 《英語》 The building will be nearing completion. 《日本語》この建物も完成に近づいています。 4. Fred practices acupuncture' since 2014. (現在完了進行形に) 《英語》 Fred has been practicing acupuncture since 2014. 《日本語》フレッドは2014年から鍼灸業を営んでいます。 はりきゅう Notes 1. practice acupuncture 「鍼灸業を営む」 をつける。

選択したものは合っていますか？教えてください🙇🏻‍♀️

Part 5 短文穴埋問題 Phase 1 Choose the better word or phrase that suits the blank. 1. I study am studying) English for three hours every Saturday. 2. When (have you / did you) arrive in Japan?---About a week ago. 3. The manager (works / will work) on the project until tomorrow morning.

（　）内に入る単語がわかりません。教えてください🙇🏻‍♀️

Part 4 説明文問題 Phase 1 Fill in the blank with the most appropriate word. (a) Thank you ( (b) The annual conference will be held ( (c) I got an urgent e-mail just ( (d) It is ( ) what we should do but how we should do it that counts. ) e-mailing me about your current situation. ) March 24 next year. ) few minutes ago. 5

分からないので教えて欲しいです🙇‍♀️

Entrance Exam 否定表現 1. almost 2. I( 1()に入れる最も適切な語句を1~4から選びなさい。 1. I don't think David would make a good leader because he can ( difficult circumstances and tends to give up too quickly. 2. extremely 3. hardly ) go to karaoke, I go only once or twice a year. ) be expected to act honorably in 4. neither (明治大) (芝浦工業大 4. never 1. often 3. Unfortunately, ( seldom ) of the 1. a few 2. few 3. ever passengers escaped injury. 3. many (大阪学院大 推) 4. much 4. ( ) children are born with musical talent. (日本大) 1. none of 2. not all. 3. not every 4. no one 5. ( 2. No 1. as far as 2. far from ) of the workers accepted the director's proposal to cut bonuses. 1. Not 6. The future of English society looked ( 7. I didn't like the food at that restaurant. It was (. (東海大 3. Never ) promising in the 1840s. None (立命館大) 3. for far 4. too far ) delicious. (福岡大) 1. anything but 2. nothing but 3. without 4. out of 8. He was so drunk that he could ( ) walk. (大阪学院大) 9. 1. all 1. able 2. unable This train doesn't stop at ( a few 3. hard 4. hardly ) station. 大阪商業大推) 2. 3. little 4. every 2. few 12. " Can 10. The latest model of this mobile phone is ( 1. not seldom 3. all not 11. Before I watched the documentary, I knew ( 1. little à you come to the party tonight?" "( 1. Yes, I can ) easy to use. (獨協大) 2. not necessarily 4. ever not 3. seldom ) about life under the sea. 4. hardly (東京工科大) ). I have a lot of homework." (拓殖大) 2. Yes, I do 3. No, I'm afraid not 13. Japan has ( 1. a little 2. few 4. No, I hope not ) oil and therefore is almost entirely dependent on imports. (センター) 3. little 4. small

この文章で答えってなんですか？ 教えて頂きたいです。

A: I heard the turnout for the House of Representatives election last week in Japan was about 54%. T: The turnout in France is below 50%. On the other hand, that in Australia is above 90%. A: Really? The turnout in Australia is about twice as high as that in France. T: A survey says that many Japanese people don't think they have a great influence on the government even if they vote in an election. A: That's too bad. T: I hope the younger generation gets interested in politics.