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, æ ¸$ 3 Ó þ ú × !. Virtual Strain Energy Caused by Shear L V UK dx ⎛⎞ν =∫ ⎜⎟ 0 S ⎝⎠GA ν= internal virtual shear in the member caused by the external virtual unit load V = internal shear in the member caused by the real load G= shear modulus of elasticity for the material A = crosssectional area of the member K = form factor for the crosssectional area K=12 for rectangular cross sections. Editions of the word board game Scrabble in different languages have differing letter distributions of the tiles, because the frequency of each letter of the alphabet is different for every language As a general rule, the rarer the letter, the more points it is worth Many languages use sets of 102 tiles, since the original distribution of one hundred tiles was later augmented with two blank.
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Proof lnexy = xy = lnex lney = ln(ex ·ey) Since lnx is onetoone, then exy = ex ·ey 1 = e0 = ex(−x) = ex ·e−x ⇒ e−x = 1 ex ex−y = ex(−y) = ex ·e−y = ex · 1 ey ex ey • For r = m ∈ N, emx = e z }m { x···x = z }m { ex ···ex = (ex)m • For r = 1 n, n ∈ N and n 6= 0, ex = e n n x = e 1 nx n ⇒ e n x = (ex) 1 • For r rational, let r = m n, m, n ∈ N. Gt¤*y Ã^g*k g t¤ 6c¤ {g* f*z0 &±* gt¤ g*k gtmy g* Îh¤0c g* h political parties and democracy in theoretical and practical perspectives. Department of Computer Science and Engineering University of Nevada, Reno Reno, NV 557 Email Qipingataolcom Website wwwcseunredu/~yanq I came to the US.
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