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... Read More

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 ✅).

これの答えは naturalなのですが normalにしたら❌ですか？ 教えてください🙇🏻‍♀️‪‪🙇🏻‍♀️ 彼女が試験に受かったことは当然のことだ It is (n )that she passed the examination. normal→普通、一般... Read More

(10)の問題で2が答えになるのは意味的な選び方を除いて、文法的か選び方はあるのでしょうか？ 意味で考えたらAlthoughが適切だとは思うのですが、文法事項は考慮に入れなくて大丈夫でしょうか？ よろしくお願いします。

- (10) ( 1 Even Mariko studied hard for the final examination, she could not pass it. 2 Although 3 Since (11) My friends hope you'll come back soon and ( ). ④If

(9)の問題で何故2が答えになるのか、そして何故他の3つの答えが不正解なのかできるだけ詳細に文法事項を含めて教えて欲しいです。

(9)( ) with last year, statistics show a 15% reduction in burglary in this area. ①Comparing 2 Compared 3 Having compared ④Compare (10) ( ) Mariko studied hard for the final examination, she could not pass it.

この問題の解き方と答えを教えてください！！

V2 + 1 V2-1 17 ZA - SAZ (6)

至急、下線部訳を教えて頂きたいです。🙇‍♂️

groups can lead to negative images, and in some extreme cases either discrimination o violence. Stereotypes have existed for many years, with the mass media helping to unfavorably shape and promote hostility towards social groups. For example, there is historical evidence of negative stereotyping towards people of color, such as in Japanese children's books, and in the early days of American television where African Americans

ネクステ101です 答えはWith a little more effort なのですが、With more a little effortではないのはなぜですか？

Point 036 badai 11 101 もう少し努力していれば、彼は試験に受かっていただろうに。 □□(if / more / little / a / effort/with), he would have passed the Poinexamination. (1語不要) 80蹊大)

答えとなぜその答えになるのかを出来たら教えて欲しいです!! よろしくお願いします🙏m(_ _)m

1 ( )内から適切な語句を選びましょう。 1372 1. The entrance examination (begins / is going to begin) at 9 o'clock tomorrow morning. 2. I'm (going to go / going) to a concert with Saki this Friday. I hope she is free. 3. Is Kumi back from Canada? Then I ( will see / am going to see) her tomorrow. 4. We are (going to give / giving) a performance at the school festival tomorrow. 2 日本語に合う英文になるように、空所に適切な語を入れましょう。 1.大きくなったら,プロ野球選手になるつもりです。 When I grow up, I ( 2.休暇はどこへ行くつもりですか。 Where are ( bhe?) ( )( ) a professional baseball player. ) to go for your holidays? 3.その飛行機は午前9時30分に東京に向けて出発します。 The plane ( )( 4. 急いで。 電車は数分で出るわよ。 ) Tokyo at 9:30 a.m. Come on! The train ( ) ( ) in a few minutes.

合ってるか見てください🥲‎

演習 1. My dream is to ( @learn ) how to play the piano. learning ③learned □ 2. ( ) is possible to work online from anywhere in the world. ①That ②t ③What (酪農学園大) have learned (亜細亜大 ) Such 3. ペンギンが飛ぶのは不可能だ。 語順整序 (a penguin / fly/for/is/impossible/it/to). It is impossible for a penguin to fly. 4. 彼女はイギリスのテレビ番組を理解するのは難しいとわかった。 (difficult / she / it / understand / found / to) British TV shows. She found it difficult to understand 5. 何を言ったらいいのかわからなかった。 I didn't (say/to/know / what). Know what to say 6. It was typical ( ①on ②to ) him to get angry about it. ③3 with (名城大) ( 広島修道大 ) (東北芸術工科大) (東洋大) of 7. She wants to come to Japan ( ). ①worked having work to be work to work ( 九州産業大) 8. 彼はその試験に合格するために一生懸命に勉強した。 blue wish (大) (in/the/ worked/ examination / order / he / pass / hard / to). He worked hard in order to pass the examination. 9. We will have to be quiet ( ) wake the baby. (福岡大) ①as so not to ③so as not to 2 as to not so ①not so as to 10. She drove to the airport, ( ) to find that her flight had been cancelled. Donly ⑥in in or in order (3 so blan 11. His story about the painter was interesting to ( ). Obe listened 3 listen ④as (駒澤 (天理 be listened to listen to

写真下部右側She is met withからの文の文末にsucceedsが付いているのですが、これがなぜ動詞の形で文末に来ているのかが分かりません。どなたか教えてくださると嬉しいです。

gotten the case. Insightfully judging that media presence 1732 25 is the best way to get her demands met, she rents three billboards and prints offensive remarks on them, homing 718412-18 in on Willoughby, the widely respected chief of police. She 人の is met with fierce opposition from many, but her plan to 反社 しょう。 get her daughter's case back in the spotlight succeeds. Exc2003. 30 Despite this, in the end, the media changes sides and, watching her daughter's case fade out again, she learns that even fierce determination and resourceful thinking is not enough to get her needs addressed. Must she give Insightfu homing いを定 resou Three Billboards Outside Eb