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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choosing、(2)の答えがウ、(5)の答えがアで、それぞれなんでその答えになるのかと、 5⃣の本文を上から4行、4行、5行、4行、3行、2行で分けた時それぞれに題名を付けるとしたらどうなりますか? 教えて欲しいですm(_ _)m

5 次の英文を読んで, あとの問いに答えなさい。 <川越東改> Origami is the Japanese art of folding paper. To do origami, the artist starts with a square piece of paper. Some people like to use special origami paper that is two colors. The front of the paper is one color, and the back of the paper is another color. Other people like to use origami paper that has patterns on it. After ①(choose) your paper, you can find many instructions for folding the paper into different things. Many people enjoy (make) origami flowers, animals, or things ( 3 ). For all of these things, there are a few kinds of folds that you need to use. For example, sometimes you need to fold the paper in half. Sometimes, the paper must be folded from corner to corner. If you follow the directions carefully, you can create a beautiful paper flower or animal. However, origami is more than folding paper. First, origami is an important part of Japanese life. For example, nature is important in Japan. In Japan, people care about the seasons, weather, water, or other things in nature. Origami is also a part of nature. That is why the most popular origami shapes are things like animals. Birds, fish, flowers, and stars are all popular shapes. It is a quiet activity, and can calm the mind and body. People who do origami like the activity as much as the art. They like it because origami demands a lot of attention. When people think hard about creating something, they forget about their problems. This allows them ④ to calm down. ⑤ Origami is also good for teaching children. They also learn to work carefully. Also, origami has squares and triangles. These shapes are important in all kinds of learning. Origami helps children to learn about these shapes. Maybe you can try to do origami yourself. You only need some paper and a book of instructions. You can find instructions for many origami shapes on the Internet. instruction direction (1)①,②の( )内の語を適する形にかえなさい。 (2) 30( に適するものを, ア~エから1つ選びなさい。 (3) (4) 7 to paint with 1 to talk with 1 (2) making. to play with I to help with (イ) ④に適するものを,ア~エから1つ選びなさい。 Origami is also easy to learn. 1 Origami is also good for your imagination. Origami is also difficult to learn. I Origami is also good for your mind. ⑤にはA~Cの文が入ります。 自然な流れの文章になる配列を, ア~エから1つ選びなさい。 A Children must follow these steps exactly. B First, origami has many steps. C This way, children can learn to follow instructions. ア A-B-C イ A-C-B B-A-C I B-C-A (5)本文の内容にあうものを, ア~エから1つ選びなさい。 If you follow some instructions for paper folds, you can enjoy many different origami shapes. Learning origami gives us a good chance to help animals on the earth. You may feel tired if you try hard to do origami carefully. I The most important thing for children's education is origami. (土)

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英語 高校生

何個もすみません…… 論表のワークです! 10時までにお願いできる方いませんか!!

a E Read the following passage and answer the questions below. I'm 15. I love esports. I hope to become a good esports player. (1) It's my future dream. But (2)my parents (become / don't/me/to/ want) an esports player. They say playing computer games is only a waste of time. Am I wrong? Answer I live in South Korea. I'm working hard to become a professional esports player. You have the same dream, too, right? Then, learn the following things. 1. Be strong and healthy physically and (3). 2. Improve your (4) skills especially English skills. 3. (5) Cultivate your spirit of fair play. I know these are not easy. But if you work hard, your parents will understand you. 1. 下線部(1)は何を指していますか。 英語で答えなさい。 【内容についての思考力・判断力・表現力】(2点) 2. 下線部(2) が 「私の両親は私にeスポーツ選手になってほしくないと思っている」 という意味 になるように, )内の語を適切に並べかえなさい。 【表現と文法の知識】 (3点) 3. 空所 (3),(4)に入る最も適当な語を選びなさい。 【語彙の知識, 内容についての思考力・判断力・表現力】 (各2点) (3) ア. friendly イ. mentally ウ.nationally I. seriously (4) ア.computer イ. driving ウ. language I. sports 4. 下線部 (5) を日本語にしなさい。 【語彙と表現の知識】 (3点) 5. 次の問いに英語で答えなさい。 【内容についての思考力・判断力・表現力】 (各4点) (1) What do the boy's parents say about playing computer games? (2) What does the South Korean girl want to become?

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英語 高校生

論表のワークです!お願いします🙏🏻 ̖́-

Lesson 4 Esports' Time Has apniwellot er /50 A Translate the English into Japanese and the Japanese into English. 【語彙の知識】(各1点) 1. various 形 B1 [ ] 2. 名 B1 戦闘, 対戦 3. respond B1 ] 4. strategy 名 A2 [ 5. 名 A2 社会, 世間 6. 名 A2 基本, 原理 ] B Choose the word whose underlined part is pronounced differently from the other three 【発音の知識】 (2点) 1. 7. basic イ. battle ウ. practice I. strategy 2. ア. another イ. gold 7. over I. program 3. ア. electronic 1. popular ウ. respond I. society C Complete the following English sentences to match the Japanese. 【表現と文法の知識】 1. そのテニスの試合は4月30日に開催されます。 The tennis tournament will ( 2. 私は美術や音楽のような芸術系の教科が好きです。 I like artistic subjects ( ) ( 3. 近頃, ますます多くの人が東京を訪れている。 ) and ( ) ( ) on April 30. ) art and music. (各3点) 1) people are visiting Tokyo these days. D Arrange the words in the proper order to match the Japanese. 【表現と文法の知識・技能】 Arranga. 1. プロ野球選手になるのは有名な歌手になるのと同じくらい難しい。 (各3点) Becoming a professional baseball player (as/as/becoming / difficult / is a famous singer. 2. 私にこの機械の使い方を教えてください。 Please (teach/use/to/me/how) this machine. 3. 私の試験の結果は彼女ほどはよくなかった。 My exam results (as/as/good/hers / weren't).

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英語 高校生

この答えを教えて頂けると嬉しいです。 手間だと思うのですがよろしくお願いします🙇

be 使わ EXERCISES 助動詞② (must / should) さ A 1 日本語に合うように,( )に適語を入れなさい。 (1) 私は読書感想文を書かないといけない。st air diiw vqqnd od Jeum rodiond yM O I ( )( )( )abook report. of smod ad bluode fesug w (2) 私たちはお互いを理解しなければならない。 We()() each other. (3) 私は昨日, 消しゴムを買わなければならなかった I (a) (4) (+) an eraser yesterday. of svad of ever! (4) 私は今度の土曜日, 会議に出なければならないだろう。wensingh sub od of and eid I ( ) ( ) ( )) attend the meeting next Saturday. (5) あなたは自分の楽器を持ってくる必要はない。 You don't()( 100 your own instrument. 2 ( )内から適切な語句を選びなさい。 B (1) If you feel sick, you (should/ ought ) go to the nurse's room. (2) Jack (ought to not/ ought not to) smoke. 「いない」 [10-10 85-1 (3) You (had better not / had not better) miss that class. (4) We (ought / should) to tell the truth to everyone. 3 与えられた状況に合うように( )内の語句を並べかえ, 全文を書きなさい。 ただし, 不要な語 句が1つずつ含まれています。 B 909-seat owens of ald は (1)状況 仕事に忙殺され, 体調を崩した私。 お見舞いに来た同僚が言った。 You (take / until / it / feeling / easy / should/ you're / had) better. buda) (2)状況 大事な試合でチームが負けてしまった。 するとコーチがあなたたちを呼びだしてこう言いました。 (blamed / not / you/be/should/ ought to) + sver bluorle\fzum S81-021.09 (3)状況 今日は, 家族旅行の予定でしたが, 台風が接近中。次第に風雨が強まってきたので・・・。 We (not/ought to / had better / out/in/go) this storm.pl avsd jeum H (4)状況 友人の言うことに何でも従っているリョウタにあなたはこう言いました。こ (everything/follow/to/ had / not/you/ought) he says. Dworal leum 11 14 [ ]内の語を参考にして ~, に自由に語句を入れ, オリジナルの英文をつくりなさい。 solybe uoy neat sved of duo ISAB (1)~(人)は明日・・・する必要はない。 [tomorrow] than on go yabinoda), (2)〜(人) は・・・しないといけない。 [ better] [n ton triguojy'nbluode uoys 35

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