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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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TOEIC・英語 大学生・専門学校生・社会人

答えを教えてください! よかったら,根拠も教えてください

la vitbl Questions 4-7 refer to the following letter. January 10 Ms. Erin Murphy Customer Service Department Westcoast Airlines Major Miles Program 345 Brook Street Dallas, TX 75218 Dear Ms. Murphy, As per your request during our telephone conversation on January 8, I am sending you Los Angeles International Airport last December. Please note that my ticket was upgraded itinerary and ticket number for my recent roundtrip flight from JFK International Airport business class with a Major Miles Gold Class voucher and should therefore be eligible f full business class mileage credit. 62 Section Il over 15 years. I must confess that I find the new restrictions to your flight voucher pla I am a Gold member in the Major Miles program and have been a Westcoast customer 1 genuinely confusing. I fail to understand why the burden of proof for my mileage cred rests with me. Shouldn't this information be on your ticketing computer? This was my itinerary. MD My ticket number was #YB42565697. Departed JFK, December 22 at 10:20 for LAX Returned to JFK from LAX on December 29 at 16:40 My seat number was 14B. 7B My Major Miles number is # 04356721 (Gold Card). I sincerely hope that this issue will be resolved quickly as I am counting on my miles eame during this trip to upgrade my hotel room next May. Thank you very much for your attention in this matter. Sincerely Yours, Jarrod Watkins Jarrod Watkins 4. 5. 6. What does Ms. Murphy do? (A) She makes airline reservations. (B) She deals with unhappy customers. (C) She issues new tickets. (D) She upgrades people to business class. What is the purpose of this letter? (A) To upgrade his ticket to business class (B) To buy a flight upgrade coupon (C) To complain about his seat reservation (D) To receive more mileage credits How does Mr. Watkins feel about the new frequent flier program rules? (A) He would like them to be simpler. (B) He believes they are unfair. (C) He finds them to be convenient. (D) He hopes that they will benefit hold Card members more. Which of the following is NOT mentioned in the letter? (A) His ticket number (B) His frequent flier level (C) His credit card number (D) His flight information inq M:8 big en enthovenot cold w lar hud,mq 01X in jord is di Hal Unit 2: Letters, E-mails, & Text message chains 63

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TOEIC・英語 大学生・専門学校生・社会人

自分の回答と照らし合わせて確認したいので、答えがなにになるかどなたか教えてください。 解説もあると助かります。

5 A Matter of Taste Reading Passage 042 At the age of just 22, Jamie Oliver became well known across the UK as "The Naked Chef." He called himself this not because he cooked wearing no clothes, but because he wanted to simplify food preparation so that everybody could follow his recipes. He wanted to "strip down" the idea of cooking. Since then he has had numerous TV shows, published 50 many books, and has become a household name in the UK. Today, one of the activities Jamie Oliver is best known for is his great effort to improve the school dinners that children eat every day. One day, he visited the kitchen of a typical London secondary school, and he was shocked to see how much processed junk food the kids were given to eat each day. Fat and sugar levels were extremely high, and nutritional values very 10 low. The "turkey twizzler" became the symbol of these unhealthy meals: processed meat containing 21.2% fat and only 34% actual turkey. Oliver ran the school kitchen for one year and tried to show that it was possible to serve healthy meals on a limited budget—and that kids actually enjoyed eating them. His mission was to radically change the eating habits of children in that school, and across the country. 150 200 15 20 25 CULTIES 250 His project (the "Feed Me Better" campaign) has had some influence on school dinners in the UK. After watching the documentary Jamie's School Dinners, 271,677 people signed a petition calling for healthier school meals. This led the Prime Minister to agree to spend 280 million pounds (about 37 billion yen) on school dinners, to ban some junk food from school menus, and to create a School Food Trust to provide support and advice for people preparing school meals. Research, by the way, shows that children who stop eating sugary, fatty food and instead eat Oliver's school dinners are better behaved in class, and they get higher test 300 scores, too. 350 Of course, the project has had some problems. At first, many students (and even parents) resisted the removal of the junk food they were so used to. In one famous instance, some parents were passing local takeaway food to their children through the school fence. Also, schools that followed the plan for a while were often found to gradually drift back into bad habits. After all, it is easier and cheaper to just give the kids junk food. However, Oliver's efforts represent a positive start, and with obesity becoming such a huge problem (see Unit 4), 400 it's a very necessary start.

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TOEIC・英語 大学生・専門学校生・社会人

【至急】この穴埋め問題の答えを教えて欲しいです。

Progress test (Part 1) Drag the words into the correct spaces. some of few 1/2 some a few enough neither lots of both little every each no information about attractions in the city. There are Coming to London for a weekend? Here's interesting places to visit - you won't have time to see them all. Firstly, visit to London would be complete without seeing Big Ben. The clock at the Houses of Parliament has become a symbol of London, but few✔ tourists know that Big Ben is actually the name of the bell, not day, so arrive early. the clock or the clock tower. On the opposite side of the river is the London Eye, the world's biggest observation wheel. holding 25 people, but there are still queues nearly There are 32 sections, If you'd like somewhere scientific, you could go to the Natural History Museum or the Science Museum. Entry to of these appeal to you, you may prefer Madame Tussaud's, the museum where is free. Or, if you can meet the world's most famous people made of wax. You could meet the Queen of England there, or you could hope to see her at Buckingham Palace, her London home, just the most valuable jewels in the world. stops away on the London Underground 'Tube' train. If you want to see more royal palaces, try the Tower of London, where you can see the Crown Jewels, If that isn't for one trip, why not go to Shakespeare's Globe Theatre, a reconstruction of the 1599 theatre extra money, you can even see a play there. where his plays were performed. If you have a

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TOEIC・英語 大学生・専門学校生・社会人

英文法の穴埋め問題をどなたか教えていただきたいです。1〜8までの正解と解説をお願いします。

10 abc X₂ X² Aa A AⓇ フォント # V 1.4 2 ← 2 E 2. The shepherd has a habit of counting his sheep every night to make sure that all there. (A) ite (B) it's (C) their (D) they're E for her best-selling nature photography books, Naomi Ward opens a photography school next month. (A) Know (B) Knowing (C) Known (D) To know 3.4 2 2 段落 e beginning and advanced courses in cellular biology include lecture and laboratory time. (A) Both (B) Each 4. An all-staff meeting on November 6th will focus on ------ each department is doing to prepare for our annual inspection. (A) howe (B) whate (C) Either (D) Every アクセシビリティ: 検討が必要です 2 2 f E 5. John Berg went to his office to talk with his boss he returned from his overseas business trip. (A) as far as E 2 2 6. Bill Cain had never heard of the company; he could not say anything when his A S 8. E ------ ← 標準 I (B) once + ■行間詰め (C) so that (D) whereas 7. This fall, Plasma Tech Inc. is offering a new line of digital metering products that are compact, ---, and reasonably priced.< (A) consistente (B) conveniente (C) insistent (D) present 見出し1 boss asked him about it. (A) however (B) meanwhile (C) nonetheless- (D) therefore On Saturday, October 19, Headlands Sports Club is holding Day. (A) it (B) its 見出し 2 annual Open スタイル E 表題

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