The p-primary v1-periodic homotopy groups, v −1 1 π∗(X; p), of a topological space X, as defined in [13], are a localization of the portion of the actual homotopy groups of X detected by K-theory. In [10, 4, 6], v−1 1 π∗(X; p) was calculated for classical groups X and primes p in all cases except (SO(n), 2). In this paper we make a first step toward the calculation of v−1 1 π∗(SO(n); 2), which ...

In this paper we compute the 3-primary v1-periodic homotopy groups of the exceptional Lie group E7. The p-primary v1-periodic homotopy groups of a space X, denoted v −1 1 π∗(X; p) or just v 1 π∗(X), were defined in [21]. They are a localization of the actual homotopy groups, telling roughly the portion which is detected by K-theory and its operations. If X is a compact Lie group, each v 1 πi(X;...

and the end conditions bx(0, t) = bx(`, t) = cx(0, t) = cx(`, t) = 0. Our task is to recover p ≡ {Db, Dc, k−, r, u} from knowledge of b(xj , ·) and Kd = k−/k+. Let us explicitly track the dependence of of b upon p by writing b = b(x, t; p) and write the IBVP above as R([b, c], p) = 0. Now differentiating R([b(p), c(p)], p) = 0 wrt p reveals ∂[b,c]R∂p[b, c] + ∂pR = 0 or ∂p[b(p), c(p)] = −∂[b,c]R...

Rabern and Rabern (2008) and Uzquiano (2010) have each presented increasingly harder versions of 'the hardest logic puzzle ever' (Boolos 1996), and each has provided a BLOCKIN BLOCKIN two-­‐question BLOCKIN BLOCKIN solution BLOCKIN BLOCKIN to BLOCKIN BLOCKIN his BLOCKIN BLOCKIN predecessor's BLOCKIN BLOCKIN puzzle. BLOCKIN BLOCKIN But BLOCKIN BLOCKIN Uzquiano's BLOCKIN BLOCKIN puzzle BLOCKIN BL...

Linguistic Resources for Text Planning M a r i e W . M e t e e r BBN Systems & Technologies Corporation 10 Moulton Street Cambridge, Massachusetts 02138 [email protected]

We investigate oscillatory properties of the second order half-linear differential equation ðrðtÞFðy 0ÞÞ 0 þ cðtÞFðyÞ 1⁄4 0; FðsÞ :1⁄4 jsj s; p > 1; ð*Þ viewed as a perturbation of a nonoscillatory equation of the same form ðrðtÞFðy 0ÞÞ 0 þ ~ cðtÞFðyÞ 1⁄4 0: Conditions on the di¤erence cðtÞ ~ cðtÞ are given which guarantee that equation ð*Þ becomes oscillatory (remains nonoscillatory).

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A computer p rogram w h i c h s o l v e s p h y s i c s p r o b lems s t a t e d i n E n g l i s h i s d e s c r i b e d i n terms o f t h e knowledge w h i c h i s used t o t r a n s f o r m one t y p e o f r e p r e s e n t a t i o n i n t o a n o t h e r . The E n g l i s h s e n t e n c e s o f t h e p r o b l e m s t a t e m e n t a re p r o g r e s s i v e l y t r a n s f o r m e d i n t ...