多様体の接空間に関する基底定理の証明です。g(q)=∫〜と定義した関数を微積分学の基本定理を用いながら変形してg(q)=g(0)+∑gᵢuⁱと導出するのですが、これがうまくいきません。 自分は、g(q)の式をまず両辺tで微分して、次に両辺uⁱで積分して、最後に両辺tで積分... 続きを読む

12. Theorem.If{ = (x', , x") is a coordinate system in M at p, then its coordinate vectors d, lp, …… 0,l, forma basis for the tangent space T,(M); and D= E(x) 。 i=1 for all ve T(M). Proof. By the preceding remarks we can work solely on the coordinate neighborhood of G. Since u(c) = Othere is no loss of generality in assuming ど(p) = 0eR". Shrinking W if necessary gives E(W) = {qe R":|q| < } for some 8. Ifg is a smooth function on E(W) then for each 1 <isndefine og (tq) dt du g(9) = for all qe {(W). It follows using the fundamental theorem of calculus that g= g(0) + E&,u' on (W). Thus if fe &(M), setting g = f。' yields f= f(P) + Ex on U. Applying d/ax' gives f(p) = (f /0x)(P). Thus applying the tangent vector e to the formula gives (f) = 0+ E(x'(p) + E Ap)u(x) = E(Px). ず ax Since this holds for all f e &(M), the tangent vectors v and Z Ux') d,l, are equal. It remains to show that the coordinate vectors are linearly independent. But if ) a, o.l, = 0, then application to x' yields dxi 0=24 (P) = 2q d」= 4. In particular the (vector space) dimension of T,(M) is the same as the dimension of M.

languageが複数形になるときとならないときの判断の仕方がわかりません。たとえば画像のような問題は複数形でも違和感なく感じます。どなたかよろしくお願いします。

This is something not found among other creatures. It will be one of the basic 組には、おそらく,生活のなかに多少の開の時間を見出した前史時代から This behavior is not seen in any other animal. Like walking upright on two legs かなる動物にも見られないことである。二本足で立って歩くとか,言語を話す raits of humankind such as the erect bipedalism or the use of language. and using language, it may be a fundamental feature of human beings. あたる動物にも見られないことである。二本足で立って歩くとか, 言語を話す D6G1L というのと同じような,基本的な人類の特徴だろう。 199d fon bert 1o bot LECTURE ○「~にも見られない」be not seen in ~ ○「二本足で立って歩く」は walkupright on two legs でよいが, bipedalism 「二足 歩行」という単語を知っていれば簡単に書ける。 ○「基本的特徴」a fundamental feature / a fundamental characteristic/basic trait ANSWER (別解) it

下から2行目のitはなんですが？

I'm always surprised to learn of a company that doesn't edueate its て employees(in the fundamental financial realities of its industry, Employees need to understand the success or failre levels of their industry) so that they know what it is ábout their own job that really couns, ) Qf course, employees have to be willing_students who direct attention to the areas where it makes v the biggest difference) C

5行目のitはなんですか?

I'm always surprised to learn_ef a company that doesn't_edueate its v employees(in the fundamental financial realities of its industryEmployees need to understand the success or failure levels (of their industry) so that they know/what it is ábout their own job that really counts, Of coursé, employees Sv have to be willing_students who direct attention to the areas where it makes v the biggest difference) C and desirable

1つ目の画像の一番下の行のBecauseから、2枚目終わりまでの和訳を教えていただきたいです。よろしくお願いします。(1枚目と2枚目の文章は繋がっています)

1. Introduction In the 1980s, Japanese financial institutions increased their presence in Western financial markets. Japanese financial institutions had close business relationships with large Japanese corporations (interlocking keiretsu business relationships) and suffered few non-performing loans because of the country's steady economic development, making them the soundest financial institutions in the world. Table1 shows the transition in the eredit ratings of major Japanese financial institutions and demonstrates that in 1988, many Japanese financial institutions were given a top credit rating. However, in the 1990s, the financial condition of Japanese financial institutions deteriorated rapidly as a result of an increase in non-performing loans brought on by an economic slump. For example, Figure 1 shows the changes in the balance of non-performing loans that Japanese banks held. At its peak at March 2002 (i.e., the end of FY 2001), this level exceeded ¥40 trillion. Figure 2 clearly indicates the severity of the problem, and Figures 1 and 2 show that, despite disposing of non-performing loans exceeding ¥10 trillion several years in the late 1990s, the balance of non-performing loans stillincreased. In 1997, the financial condition of major banks grew severe, as evidenced by the failure of institutions such as Hokkaido Takushoku Bank, which had a significant standing among major commercial banks, and Yamaichi Securities, one of the four major security corporations. Many financial institutions that survived with government assistance barely escaped bankruptcy. In the past, Japanese banks were subjugated under extremely strict regulations implemented by the Ministry of Finance. In the 1980s, however, financial globalization progressed, increasing the concern that if the regulations did not change, they may promote the hollowing out of domestic markets. Beginning in 1996, the Japanese government advocated Japanese “Big Bang" financial reforms and fundamentally restructured the regulations. These reforms could have becen viewed as a "constructive" approach to financial regulations for a new cconomic environment. On the other hand, the deterioration of the business conditions of financial institutions progressed at a speed and scale greater than what was anticipated. Because the laws that

日本語訳してほしいです。

15 min. 216 words 次の英文を読んで,設問に答えなさい。 An instinctive behavior is inherited: /you're born with it./ In (1 ),a learned behavior is developed from experience. do inherit an instinct to (2a) Although humans and some animals learn, the content of their learning is determined by their 5 experience. Instinctive behavior does not change; it stays the same even when circumstances change. Birds migrate in the winter months even when the weather stays warm. But learned behavior is more( 3). Humans don't *hibernate in winter, and most 10 humans don't change where they live seasonally. Instead, they have learned to dress warmly and heat their houses. Humans are very adaptable. Generally , we don't wait for evolution to change our responses to the environment%; instead, learned behavior enables us to respond quickly to changing circumstances. To learn from an experience, an organism must have a 15 memory to store information to be used later. Memory helps an organism learn through trial and error. In trial-and-error learning, an organism tries to do a task again and again, sometimes (2b) making mistakes, but other times succeeding. Eventually the 20 organism figures out what it did to succeed. A mouse will learn how to get through a maze to find food at the end by trying different routes again and again. The mouse eventually remembers which routes don't lead to food and 'which (2c) do. (注) hibernate: 冬眠する, 冬ごもりする (東北学院大)

人種差別の事について英語で説明する授業があるんですけど、この部分簡単にでも良いので英語に出来る方お願いします😭

全訳お願いします

5 話 Choice js absolutely fundamental to wel-being. Healthy people Want and need to direct their own lives。 On the other hand, the fact that some choice is good doesnt necessarily mean that more choice js better ゥhere Is a cost to having too much choice.。 In our Culture, 4 we have strong, positive feelings about freedom, choice, and variety But holding on to all the choices available to us adds to worry, stress, and unhappiness.

請問各位有有機化學John McMurry,Fundamentals of Organic Chemistry 第七版習題的解答嗎？ 感謝大家

ポレポレです。whichがRegularitiesの関係代名詞となってるのですが、そもそも間にare soughとありかなり離れているのですがこれはアリなのでしょうか？文全体を修飾しているのでしょうか？

ィ7の 原圧 z半 The scientist and the theologian approach the dees QA gionS Of existence( from utterly different starting ww Science is based on careful observation and expenmeu 、enaDbling 3 o be constructed Which connect terent experienCeS Regularities、p MS workings of naturel ave ーーーーでで ゃ| 【 ougjtb which hopefully reveal the fundamental laws Wat 1 作記 gOVern the hGhayi9 8 me a 記 forces, Central to Ra approach js the 人illingnets of the he scientist to abandon s heory evidence iS produced agdinst 人 5 べ大阪府立犬ケーー 生解プロセえ) 6 bontooT | まず, 第1 文,「科学者と神学者は全く違った出発点から深い存在 に取り組む」, 単語は難しいですが構文としては単純で, The scijentist and the theologian approach the-of-Gro