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数学 大学生・専門学校生・社会人

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 ✅).

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英語 中学生

(1)の答えがD、(3)の答えがウ、(6)の答えがイ なんですけど、なんでそれになるかと、5⃣で3~5程の段落で分けるとしたらどこになるのか、またその段落はそれぞれどんな題名になるのかを教えて欲しいですm(_ _)m

学院) E J 5 次の英文を読んで、あとの問いに答えなさい。 < 星野改〉 High schools in Minnesota have a problem Many students are late to school. They are often tired. Some students fall asleep in class. They often get sick, too. The local governments take that as a problem. They make a small change.) It helps a school day a little later/ A lot! What do they do? They start the D- This small change makes a big difference. Why? Most teens are very tired early in the morning. They usually don't go to bed until after midnight In the morning, they wake up between 6:00 and 6:30 for school. So they don't get enough sleep! They are still tired early in the morning. But after the change/ teens are more awake and later start time is better for a teen's body clock I be ready/class/to/in). A be in ready class Everyone has a body clock. An adult's body clock works like this: most adults get tired between 9:00 and 11:00 at night. They usually go to bed before midnight. Adults can get up early in the morning. It's not a problem. But a teen's body clock is different. Teens don't get tired at midnight. They usually stay up later. But early in the morning, they need more sleep. B FO C The schools in Minnesota pay attention to the teen's body clock. They change the start of the school day from 7:20 a.m. to 8:40 a.m., 80 minutes later. Other schools in the United States change their start times too. Some schools change the time by only 30 minutes, but they still get good results. ( 2 ), the results are amazing! ③(Many) students are on time. Morning classes are easier to teach. Students are getting ①(good) grades. Students have fewer illnesses, so they are ⑤(little) absent. In Minnesota, there is another important effect: fewer students drop out of school or change schools. D Today, more and more high schools are starting later. Most schools can't start two hours later. But they can change the start time a little. A small change can make a very big difference! Just ask the students. Minnesota ミネソタ (アメリカ合衆国中央北部の州) (1) 次の英文を入れるのに最も適する位置を, 本文中のA~Dから1つ選びなさい。 Now the students are happier, and also the parents and teachers too. D(A) (2)下線部①の ( )内の語を並べかえて正しい英文を作るとき, 3番目にくるものをア~エから1つ選びなさい。 ア be イ ready ウ class I to (3) 20)( )に適するものを, ア~エから1つ選びなさい。 7 On the other hand (4) 3~50)( 1 However ウ In fact I Even so )内の語をそれぞれ比較級にかえなさい。 (3) much (5)本文の内容にあうものを,ア~エから1つ選びなさい。 more (T!) better ⑤⑤ fewer Less High school students in Minnesota are always taking classes seriously. Most teens usually go to bed as early as possible. Most adults don't stay up late because of their body clocks. I Some schools changed the school time but their students did not have good grades. 本文のタイトルとして最も適するものを,ア~エから1つ選びなさい。 7 Fewer Illnesses 1 Late Start Body Clock I Good Sleep イ (土)

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生物 高校生

①〜⑳を教えてくださいお願いします

問8. 細胞分裂に関して表にまとめた。 図1は、ある生物の体細胞分裂の各時期を模式的に示したもので ある。これについて、以下の問に答えよ。 【表1 細胞分裂に関して】 【図1】 分裂の順序 分裂期の名称 分裂の様子 a (6)期 染色体は散在しており、 ( 12 ) の準備が整えられる。 (13)の凝縮が始まる。 (1) (7)期 核膜や核小体が消失する。 (14)がのびてきて、( 15 )に付着する。 (2) (8)期 (13)が( 16 )にならぶ。 (3) (9)期 各 (13) が2本に分離し、 両極に引かれ移動する。 もとの状態に戻りだす。 (4) (10)期 動物細胞は外側から( 17 ) るように、 植物細胞は( 18 )ができる。 2つの(19)ができる。 (5)... (11) 期 母細胞と(20)の染色体を含む。 PP e (1) 表の空欄部分をうめよ。 (1)~(5)に関しては、図より選んで (b)~ (f)の記号で答えよ。 (6)~(20) には適切な言葉を語群より選んで記号で答えよ。 何回使ってもよい。 【語群】 (オ)異数(カ) 植物 (キ) くびれ (ス) 赤道面 核 (ナ)細胞壁 (二) 中心体 (7)紡錘糸 (ア)前)染色体 (ウ) ちぎれる ( ) 娘細胞 (ク) 葉緑体 (ケ)減数分裂 (コ) 線上 (サ)同数 (シ)後 (タ) 動原体 (チ)細胞板(ツ) 細胞質 テ) 中(ト) 動物 (ネ)間(ノ)分裂 (ハ) 紡錘体 (ヒ) 星状体 (ヌ) 細胞膜

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