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 ✅).

どこの大学の何年の問題でしょうか？

〔3〕 xyz 空間において, 東大、一橋 |x|≦1, |y|≦1, z=1 を満たす点(x, y, z) からなる板Tを考える. 点光源 P 円 x2 + y2 = 1, z = 2 上を1周するとき, 光が板Tにさえぎられてzy 平面上にできる影の通過する部分の図を描き, その面積Sを求めよ. (AL

何年の岐阜大の問題でしょうか？

<参考題> [p.105~110] 〔1〕 my 平面上で曲線 C: y=x^(π>0) 上の点P を中心とし, 軸に接する円を考える.Pが C上を動くとき,この円の内部が動く範囲を図示せよ.

名詞にaが付くのはどんな時ですか？単数でも、つくときと付かない時があるし母音がa,i,u,e,oでも付き合ない時があったりしてちゃんと理解できていないです。 簡単に教えていただけると嬉しいです。

Sukkahs generally have three walls, and the roof i made with leaves and has openings so that the stars are visible above. 仮庵は通常、壁が3面で、屋根は... 続きを読む

27と28の解説お願いします！ 答えは27が2で28が1と4です

(27) Strange ( ), I didn't really enjoy the musical. Isaid 2to say (28) Jim ( A ) coffee ( B (A) Dkept drinking (B) ①because he stayed ③say ④saying ) awake, but he still couldn't keep his eyes, open. kept to drink ③was keeping drinking was keeping to drink for staying ③since he stayed to stay (29) Which sentence is grammatically correct?

3問とも正しい答えを教えてください😭

22 vixie b Low-thin 5 7 Choose the best option. (1) Protecting the world's cultural and natural ( main jobs. a. historian b. kingdom (2) In the ( b. invention a. memory (3) The ( a. period (各3点) (22 ) sites is one of UNESCO's d. heritage c. explorer Snormigo gniwollor on ), people cooked food outdoors over an open fire. oblido To bed 916 29 d. past c. modern ) from 1868 to 1912 is called the Meiji Era in Japanese history. b. present c. ancient d. decade

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

英語の文法系の問題なんてすが、明日テストで分からなくて、教えて欲しいです。 お願いします。至急です。

2 下線部のうち, 誤った英語表現を含むものを1つ選びなさい。 (1) My father used to 1 working ② part-time ③ delivering newspapers when he was a student, so he was accustomed to ④ getting up early in the morning. (佛教大) (2) ① Even with current technology, ② we are still difficult ③ to make accurate ④ predictions about the weather. (東海大) an (3) Because news of the scandal ① spreads out ② across the internet, ③ the company finally ④ opened internal investigation. (早稲田大)

至急⚠️ 奇数の問題の答え合わせをしたいです。 なぜその答えになるのかも教えていただきたいです。 よろしくお願いします。

EXERCISE A >> 空所に入れるのに最も適切なものを選びなさい。 of gabilat S 01 It is difficult ( ) the English exam. ①in passing ge2 to passed 3 to pass 4 pass 〈福岡大〉 ni miwa S to talk 2 talking 02 The young woman had no one ( ) with about her future. 3 of talking to have talked (*) 03 Susan opened the box, ( 2 next 1 but ) to find it empty. 3 only 4 soon lig 〈立教大〉 04 His grandfather lived ( ) ninety-two and was the head of the company for many years. 1 being 3 for being 105 2 to be 4 till he would be BE <東海大 > er It was careless (b) him to forget to lock the door. top bolid W 1 for 2 of 3 with on 08 4 to a don <*> 06 My friends were warned ( ) the mountain in such bad weather. 3 of no climbing to climb 〈センター試験〉 Din climbing 2 not to climb 107 Half of the houses on the island are said ( ①having 2 to be being 3 to have ) damaged by the typhoon. 4 to have been() of warts 80 The boy turned on his father's computer, though he had been told ( 〈 青山学院大 〉 ). 08 1 not do it 2 not to 3 to do not 4 to not 09 The textbook is ( 9D ①easy enough ) for a college student to read. 2 so easy as 3 so easy that 4 such easy (***) The 10 Mr. Smith doesn't know ( 1 way to use 3 the way of use ) a computer and is afraid to touch one. 2 how he should to use 4 how to use <東京経済大 〉 11 I can't decide ( I to if ) go to Australia or New Zealand. 2 whether ③3 whether to 4 to whether <福岡大〉 12 To begin ( 1 from ), let's have a look at Chapter 5. 2 by 3 for 4 with 〈九州産業大〉 □13 To ( ) the truth, I still haven't finished my homework. 1 say 2 tell 3 speak 4 mention 〈大阪学院大 〉 05 95 不定詞