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English Senior High

文章が何を言っているか掴めません。できれば部分的でもいいのでSVなどを振ってくれると嬉しいです

向想 く1 >次の英文を読んで、下の設問に答えよ。 Perhaps the single biggest mistaké we make when we say 'No' is to start from 'No'. , We derive our ‘No' from what we are against- the other's demand or behavior. A positive ‘No' calls on us to do the exact opposite and base our ‘No' on what we are for. Instead of starting from ‘'No', start from ‘Yes'. Root your ‘No' in a deeper 'Yes' -a Yes' to your core interests and to what truly matters. Nowhere didI learn this more clearly than from a relative of mine who suffered from a serious addiction to alcohol that nearly cost him and others their lives in a car accident. He tried many times to give up the habit but always failed. Then at the age of sixty, just when all hope seemed lost, he found in himself the will to say ‘'No' and stop drinking. The secret? “"When my first grandchild was born," he says, “I wanted more than anything to live long enough to see him grow up. It was his birth that motivated me to get treatment and stop drinking. Since then, for over fifteen years now, I have not touched a drop." His 'Yes' to being present for his grandchildren - to be able to play with them and see them grow - motivated his powerful ‘No' to alcohol. His story serves to illustrate an everyday paradoxical truth: the power of your ‘No' comes directly from the power of your 'Yes'. 1our Yes is the underlying purpose for which you are saying 'No', The first step in the method is to uncover the Yes' that lies behind your'No'.(1)The deeper you go into vour core motivation, the more powerful your Yes' will be and thus the more powerful your 'No'. aht ha Tt is ourselves. It is our 1*em ;TL

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Mathematics Undergraduate

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... Read More

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.

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