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 ✅).

下の式の解説をお願いします🙇‍♀️

dax 例 5.1.13.a >1に対して I = a loga である. dx 証明: a™ =(eloga)x=ezlogaなので,u=ælogaとおけば da = dx 例 5.1.14. 次の関数 f(x) を deu du du dx =e" log a = a log a.

教えてほしいです (画像横になっているかもしれません)

・次の文を分詞構文に書きかえなさい。 また, 英文全体を日本語に直しなさい。 (1) As I had never eaten that fish, I didn't want to eat it. ( (2) He doesn't know how to play the game, so he won't join us. ( (3) She has never been to Europe. Therefore she really wants to visit there. (4) Because nobody came to our house, we had a lot of free time. ike tomor (5) As we haven't done the work yet, we can't go skiing. )

答え教えてください🙇🏻‍♀️🙇🏻‍♀️

2. 家を持たずにインターネットカフェで寝泊まりする人たちがいます。 There are people and obse Jeunem ahezu

三平方の定理の点線で示した対角線の長さを求める問題です。 3辺はどこの長さを通っているんですか? 教えてください🙏

(5)BP:PF=1:3, DQ:QH=2:1 (6)M は DE の中点 - B P A 12 E C D F 6 G 100 8 8 B 15v2 S P Q D F M H E 0.011167 152 3

iii)の所が分かりません。 解説をお願いします🙇 答えは②です。

問8 0.10mol/Lの塩酸 10mL に 0.10mol/Lの水酸化バリウム Ba (OH)2 水溶液を滴 下していった。このとき, Ba (OH)2 水溶液の滴下量 (mL) と水溶液中の水酸化物 イオンOHの物質量(mol) の関係を表したグラフとして最も適当なものを, 次 ①~④のうちから一つ選べ。 8 ① 2.5 OHの物質量(×10-3mol) OH-の物質量(×10mol 2.0 ②S 2.5 2.0 20 だし、 1.5 10 1. 108[H +00 1.0 1.0 0.5 0.5 2.5 2.0 1.5 1.0 0.5 0 5 10 15 20 25 Ba (OH)2 水溶液の滴下量(mL) 5 10 15 20 25 Ba (OH)2 水溶液の滴下量(mL) 5 10 15 20 25 Ba (OH)2 水溶液の滴下量(mL) OH-の物質量 (×10-3mol) 2.5 2.0 225 1.5 1.0 0.5 0 5 10 15 20 25 Ba (OH)2 水溶液の滴下量(mL)

化学　分子式 なぜ硫酸ナトリウムはNa2SO4って2とか4が付くのですか？NaSOではないんですか?

上のやつの文構造が取れないです🙏🏻教えてください🙇‍♀️

H 少女を主人公とする次の英文を読んで, あとの問いに答えよ。 ンド (Osmund)はリーヴァの近所に住む少年, ハリー (Har 図書館で働く青年である。(配点 43) ☆☆ Aが~と思い当たる もちろん ydgerbo adger books book under her bed it struck her that of course if we anout/and for the same reason She had. He'd probably hidde 00. /S bo She and Osmund had walked the same path. nd Boy awake and scratching at the *cupboard floor again.) 1 n I? Well then, you'll have to come with me today. Wait here. eave Leeva left for the basement get some *twine She knew she'd was her job to bundle upy the old Nutsmore Weeklys and store allowed the subscription because there were e/so manythings he subscription because th ア for things that otherwise might have to be purchased thingsの もし…でなければい everything in the housy ofthem firmly refused would be made of newspaper Leeva's toilet paper bei she alloweuris とした態度を取る ゆるすの逆 強制!! se he burned the issues for heat. In summer, he made Leeva fold 暖をとるためにも新聞けしたのために ndow shades. Except for his recliner, all the furniture on his made of newspapers, clefy folded and taped by Leeva. 00 - - her coverlet, her slippers, her stool 座面 side all newspaper. She'd we Your Vocabulary" pages for the stool's seat, and it brought her a -h upon precious words, but the rest of the th s were a くすくする 壊れやすい frail とい

(2)で解説とやり方が違うんですけど、答えが合わなくて、どこが間違っていますか？

- - 12 - WA 302- (a-4) 0:4 ot A 2 こ "\ 1+3F+1 n +323.35- 3(3-1) 1+3 + 3. 3-1 3.3 (31) +(3-1) 2 2/2 (123n+2_9) 1/12(3h+28) n 3K Meu

英文の読み方の流れを教えて欲しいです！

Tehrani, an anthropologist at LAGIO relationship to Little Red Riding Hood. He argues that folktales evolve just like) biological organisms, as they adapt to different local cultures. He also shares an important finding about the 同時に H> origins of this particular tale. Made famous through its inclusion in the famous book of Grimm's Fairy Tales, Little Red Riding Hood is generally) considered a traditional European story. However, some researchers had claimed that the story was originally inspired from Lon Po Po. They thought that Lon Po Po made its way from Asia to Europe to become Little Red Riding Hood. Tehrani's research challenges this assumption. He claims that the opposite process is more likely. His theory