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 ✅).

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

合っているか教えて欲しいです

Question ( )に入る適切な語を選びましょう。 at (9) The (part/weight /ratio) of salt to the soup is 1 to 100. (10) (A number / The number) of online shopping has been increasing. (11) The (number/ amount) of housework decreased compared to the past. Try it out 1 (→p.53) 1. We can get a great (number /deal) of news on the internet. 2. There were only a (fewy little) people who wanted to work with robots. 3. Almost ((members / all members) on our team agree to introduce the new machines. 4. Robots can do a lot of (work/works) that humans cannot do.

量比の求め方と組成の見方が分かりません！教えて欲しいです！

問題:下のDi-An系の1気圧での相平衡図において, Mの組成のマグマの温度低下に伴う 結晶化の順序を箇条書きにして答えなさい(空欄を埋めよ)。 説明に必要な記号や補 助線等は図中に書き込むこと. 温度(℃) 1600 1400 1200 Di-An系の相平衡図 (Phase Diagram for Di-An system) M 1000 Di+液 Di (CaMgSi206) AAnない 20 An 40 bi60 E 液 共 Di+An 答欄 温度T>T1, 存在する相【液のみ】, 結晶 40 Banbe bi40 60 重量% An+液 80 An 80. Di20 bitu 液組成=M(=Ang(), 結晶組成= 結晶なし, 量比→液100% T=T1, 【液+結晶(fn) ←結晶名】, 液組成 = Ano, 結晶組成=An, 量比→液:結晶 = : An (CaAl2Si Og) T=T2, 存在する相【Ant液 1, 液組成=___(=An6o), 結晶組成=Anto, 量比→液:結晶= : 1553 T1 T2 T=1270℃, 存在する相【 Di + An 1 液組成=(=An40), 結晶組成=An,量比→液:結晶=40: 20 1270 T <1270℃, 存在する相 【結晶2種類 (Di+An)】, 液組成 =液なし, 結晶組成 Di= An, An=An,量比→Di:An= :

この量比ってどうやって求めるんでしょうか？液組成と結晶組成の判別の仕方も教えて欲しいです。

問題: 下のDi-An系の1気圧での相平衡図において, Mの組成のマグマの温度低下に伴う 結晶化の順序を箇条書きにして答えなさい(空欄を埋めよ). 説明に必要な記号や補 助線等は図中に書き込むこと. 温度(℃) 解答欄 1600 1400 1200 1000 Di-An系の相平衡図 (Phase Diagram for Di-An system) M Di+液 Di (CaMgSi206) Anない 20 液 An 40 bi60 E 共 Di+An 結晶 40 温度T> T1, 存在する相【液のみ】, Banbe biyo | An+液 60 重量% An 80. Di20 80 bitau 1553 T1 T2 液組成=M(=Ang(), 結晶組成=結晶なし, 量比→液100% T=Ty, 【 液結晶 (fn) ←結晶名】, 液組成 = Ano, 結晶組成= An, 量比→液:結晶= : 1270 An (CaAl2Si20g) T=T2, 存在する相【Ant液 1. 液組成=___(=An60), 結晶組成 = An60, 量比→液:結晶 = : T=1270℃, 存在する相【Di+An 1 液組成 = (=An40), 結晶組成= An量比→液:結晶=40: 20 T<1270℃, 存在する相【結晶2種類 (Di+An)】, 液組成=液なし, 結晶組成Di= An, An=An,量比→Di:An= :

なぜこの文章はSV…がなく、to不定詞だけなんでしょうか 訳し方がわかりません

1 SPACE JUNK It is hard to believe that space itself can be polluted by human efforts), but 助(皮)Vi it is true even the outer limits can face damage. We have trashed the orbits our 副 助 Vt O spacecraft travel through. So much so that, before every launch of a space shuttle, NASA's high-speed computers run for a full 24 hours on just one element of the M... flight to choose a safe orbit, so that the shuttle will not be destroyed (by colliding) (Vi) M with some other man-made orbiting body) M 形 F!! 71% 形 ace is in fact

2つ質問があります。 一つ目のマーカーのところの「to be」、これはSVOCを振るとすればO(目的語)でしょうか。 二つ目のマーカーの分構造はどうなっているのでしょうか。where以下で動詞が見つけられず、意味がとれません。

Type 8 意図問題 Exercise 19 The author mentions "a cellphone call" in order to ni ed nsp pniwaliofanit toallanitý A compare how different ways of receiving information affects memory emsp erit vert A ® emphasize the importance of repetition to absorb information on ob on ob veriT (8 O demonstrate ways to counteract retroactive inhibition work so ton ob O show how new information can hinder the retention of previously learned TO information € it vit vedT 0. vedtok れ れ to that can changed copia Tvo There are a number of events that can cause humans to forget information they have already learned and stored in their memory. One cause is believed to be a type of interference phenomenon known as retroactive inhibition, where a sudden influx of new information blocks the retention of older learned material. A driver might hear a phone number on the radio that he wants to call, so he repeats it out loud until he can recite it from memory. Then, the driver receives a cellphone call from his manager. In the time it takes the driver to absorb the information from his manager, he has forgotten the number he repeated just a few seconds before. Vildo L

vsコードを使ってJava言語の勉強をしてたんですけど初心者すぎて何が原因で上手くコードの実行ができてないのかわかりません… 勉強の資料として使ってるのは京都大学のJavaによるプログラミング入門 です。

17:43 7月27日 (木) 1.7 使用するサンプルプログラム (TankCalculator.java) 1: public class Tank Calculator { 2: public static void main (String args[]){ final double FLOW_RATE = 1.0; final double TANK_AREA = 20.0; final double INITIAL_LEVEL = 10.0; double time; //s double tankLevel; //m ... ocw.kyoto-u.ac.jp 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: time = 30; 14: tankLevel = INITIAL_LEVEL + FLOW_RATE*time/TANK_AREA; 15: System.out.println("Tank Level at time "+ time + "s = " + tankLevel + "m"); 16: 17: 18: 19: } 20:} 11 System.out.println("Flow Rate = + FLOW_RATE + "m** 3/s"); System.out.println("Tank Area=" + TANK_AREA + "m**2"); System.out.println("Initial Level = " + INITIAL_LEVEL + "m"); time = 60; tankLevel = INITIAL_LEVEL + FLOW_RATE*time/TANK_AREA; System.out.println("Tank Level at time "+ time + "s=" + tankLevel + "m"); 【補足】 // の後ろは,プログラムを後で読解しやすくするための注釈です. Flow Rate = 1.0m**3/s Tank Area = 20.0mm**2 Initial Level = 10.0m 8 Tank Level time 30.0s = 11.5m Tank Level at time 60.0s = 13.0m 1.7.1 サンプルプログラムの入力と実行 先ほどと同じように, 秀丸エディタを開き, 20行のプログラムを書き込んで, Tank Calculator.java と名付け, 保存して, コンパイル, 実行してください. 成功すれば,以下の実行結果が示されます。(失敗してもめげないで, 2.5.1 節を参 考に、原因を考え,再トライしてください) ちなみに, 実行結果をファイルに書き出すにはコマンドプロンプトの「リダイレク ト」 という機能を使います 11. java TankCalculator > result.txt これにより result.txt というファイルが出来ているはずです。 中身は数値や文字列 だけのテキストファイルですのでエディタなどで内容を確認できます。 @91% 11javaプログラムの中で明示的にフ ァイルに出力することもできるので すがここでは安直な方法を取ります

画像の4.2の問題の解き方を教えてください。

106 K M X(T) M. F sin (NT) (1)X 100 -100 ( XImax 80 0 0 4 Dimensional Scaling Analysis + KX = F sin (2T), X(0) = Xo, 1 n 2 10 T 3 Fig. 4.1 The elementary problem of a mass on spring with an applied force: (Left) dimensional parameters, (Right) solutions X(T) for various parameters and (Inset) the amplitude in relation to the forcing frequency ada 4.2 The governing equation for the linear mass-spring system shown in Fig. 4.1 is d²X dT² dX dT\T=0 20 = Vo, where X(T) [m] is the position of the mass as a function of time with mass M [kg], and spring coefficient K [N/m], magnitude of the applied force, F [N], forcing frequency, 2 [s], as well as general initial conditions, Nondimensionalize and select length- and time-scales L, T to normalise the coef- ficients of the terms on the left side of the ODE and the initial condition for position. Write and solve the scaled problem, and identify the dimensionless parameter for the ratio of the forcing frequency to resonant frequency, where the solution's amplitude grows without bound, as shown for 22 in Fig. 4.1. 4.3 Consider the initial value problem for a damped driven nonlinear oscillator:

画像の問題を教えてください！

106 K M X(T) M. F sin (NT) (1)X 100 -100 ( XImax 80 0 0 4 Dimensional Scaling Analysis + KX = F sin (2T), X(0) = Xo, 1 n 2 10 T 3 Fig. 4.1 The elementary problem of a mass on spring with an applied force: (Left) dimensional parameters, (Right) solutions X(T) for various parameters and (Inset) the amplitude in relation to the forcing frequency ada 4.2 The governing equation for the linear mass-spring system shown in Fig. 4.1 is d²X dT² dX dT\T=0 20 = Vo, where X(T) [m] is the position of the mass as a function of time with mass M [kg], and spring coefficient K [N/m], magnitude of the applied force, F [N], forcing frequency, 2 [s], as well as general initial conditions, Nondimensionalize and select length- and time-scales L, T to normalise the coef- ficients of the terms on the left side of the ODE and the initial condition for position. Write and solve the scaled problem, and identify the dimensionless parameter for the ratio of the forcing frequency to resonant frequency, where the solution's amplitude grows without bound, as shown for 22 in Fig. 4.1. 4.3 Consider the initial value problem for a damped driven nonlinear oscillator: