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TOEIC・English Undergraduate

英語の問題です。 この答えが分かる方いらっしゃいますか?

9. Though himself. statesman, James Polk was unusually successful in accomplishing his goals during his term. (A) not yla w op at odw oldiassi oimonoe ai ginimbno JisM al 13. In contrast to popular opinion, measures of intelligence have. teliable predictors of future success. -imaginative U ada t an inola Isoioiso ors 3) never been M. (B) without an (C) he was not (B) not any (C) no TI ni 2stsa2 (D) seldom (D) was not an ntaib gaol 3a uinillida ods daidw. at alolbabus( 14, The name "porpoise" sometimes 10. Blends of spices have been created by spice manufacturers to make the art of scasoning to some members of the dolphin family, (A) it is extended ons Jbodai(A) a quick and casy one ailavon usolnsas (B) is an extension *A (C) extended pollusH (D) is extended (B) casy and quick a one (C) a quick one and easyon Issiufo adh (D) one casy and quick ot 11. During nothe 1950。ch adol bag-baxits5. In old age, the immune system proponents of inguistic relativity believed that - to language or representational functioning. graduaily becomes less resistant to viral fangal, and s od thought- (A) infection by bacteria (A) can reduceitomootains ae 2s oibilids aii (B) bacteria's infection e (B) could be reduced (C) reduces (D) reducing e aoiseniaimbs zot sldienogesn al uo smezqu2 arb 3o soitaui 3oid ad.S 12.- (C) bacterial infection ida lanigho ms a (D) infectious bacteria A that nearly all households will haye broadband internet by the vear baale yiwn olo lo dsso 2015. (A) ExpectingLni s2osh os tiorual atgsimue asar ads gorW.ES (B) Many expecting (C) In expectation nwob" sd oa biea ymaqmoo adt atenoyitisamos (D) It is expected A h o obla gaoxworb po pexdmh ow nomwal nmissmA yhsbM as A

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Mathematics Undergraduate

ベクトル解析の初歩です。 数学苦手過ぎて高校生レベルで躓いています。 例題1.2(2)ですが式を展開すると2枚目最後のように2(X1Y1+X2Y2)が残ってしまい1枚目教科書のように展開できません。 数学に2年ほど触れておらず本当にできなくなっているので誰か助けて下さい。お... Read More

となることが分かります。 なお, 等号が成立するのは, 3点2,y,zが同一直 例題1.2:(1) R° 上の2点A(12,3), B(1, -1)の間の距離 ABを求めなさ い。 (2) = (21, 2), 9 = (y, 32), 2 = (21, 22) e R° とするとき, d2(2, z) S de(m,y) + d2(y,2) ん が成り立つことを確認しなさい。 解:(1) AB=v(1+ 2)? + (-1-3)? =D v9 + 16 =5. (2) de(z, 9) = V(E1-1)+ (12 - y2)?であるから, 示すことは V(21 - 2)?+ (T2 -- 2)?V(21-)? + (22- y2)2+V(y1- )? + (2-22 です。1 - 1 = Xi, 22 - y2 = X2,yi - 21 = Yi, Y2 - 22 = Y2 とおいてみ ると, C1- 21 = - (21 - 1) + (1 - 21)=D Xi+ Yi 02 - 22 = (22 - y2) + (y2 - 22) = X2 + Y2 となりますから V(X) + Y)? +(X2 +Y)?VX+X}+VY?+Y を示せばよいことが分かります。 一般に, 実数 A,Bに対して0SASBで あるとき, A°< B° なら ASBが成り立ちますから, 2 2 (Vx+ X3+ \?+) - (V(X)+Y) + (Xa+ Ya)}) 20 を示せばよいことになります。 平方根の中身はすべて0以上ですから, 上の 不等式の左辺を展開すると = 2V(X?+X3)(Y? ++Y})20 となることが分かります。 なお、 等号が成立するのは, 3点c,y,2" 線上にあるときであることも分かります。

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Mathematics Undergraduate

問題としてはこのURLのやつでexercise2.2.9の問題です。 2.2.9. Define T : ℓ^2(Zn ) → ℓ^2(Zn ) by (T(z))(n) =z(n + 1) − z(n). Find all eigenvalues of T.... Read More

16:22マ l 全 の Exerc: 164/520 matrices, convolution operators, and Fourier r operators. 2.2.9. Define T:l'(Zn) - → e°(ZN) by ニ Find all eigenvalues of T. 2.2.10. Let T(m):e'(Z4) → '(Z) be the Fourier multipliei (mz)' where m = (1,0, i, -2) defined by T (m)(2) = i. Find be l(Z4) such that T(m) is the convolutior Tb (defined by Th(Z) = b*z). ii. Find the matrix that represents T(m) with resp standard basis. 2.2.11. i. Suppose Ti, T2:l(ZN) → e(ZN) are tra invariant linear transformations. Prove that th sition T, o T, is translation invariant. ii. Suppose A and B are circulant NxN matric directly (i.e., just using the definition of a matrix, not using Theorem 2.19) that AB is Show that this result and Theorem 2.19 imp Hint: Write out the (m + 1,n+1) entry of the definition of matrix multiplication; compare hint to Exercise 2.2.12 (i). iii. Suppose b,, bz e l'(Zn). Prove that the cor Tb, o Tb, of the convolution operators Tb, and convolution operator T, with b = 2 bz * b.. E Exercise 2.2.6. iv. Suppose m,, mz € l"(Z). Prove that the cor T(m2) ° T(m) and T(m) is the Fourier multiplier operator T) m(n) = m2(n)m」(n) for all n. v. Suppose Ti, T2:l"(Zw) → e'(Zn) are linear tra tions. Prove that if Ti is represented bya matri respect to the Fourier basis F (i.e., [T; (z)]F =A Tz is represented by a matrix Az with respect t the composition T20T, is represented by the ma with respect to F. Deduce part i again. Remark:ByTheerem 2.19, we have just proved of the Fourier multiplier operat Aresearchgate.net - 非公開

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