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Utjtj. (n2j. (ti tj)2U2tiU2tjU2titjU2tj 1tj ti. UtitjUtj. ). n2i2(ti tj)3. UtjUti. ... 2(ti tj)(tj tk)U2tj+. n2k2(tj tk)(tk ti)U2tk. (4.10a). or(ti tj)UtkUtitj (tj tk)UtiUtjtk (tk ti)UtjUtkti = 0.

Fh,R contains a disjoint copy Tj of the tree T (j), for each j {0,. , ... A |= rooth(t) t is the root of one of the trees Tj.

11] Tj. C. Koopmans, Optimum utilization of the transportation system, in D.

to repay at some later stage at most qj[x]. Moreover at stage x a string of weightqj[x] is used to describe A tj [x] via Nj. ... 5) we get that tj[y] tj[x] for all y [x,r].

fBos[xj,. ] (1)j1fFer[xj,. ] = I4,sl [vj, wj, tj, yj] (2.39). ... where. I4, :=[DU]e. j=1. 1jI4,sl. (vj,wj,tj,yj) TrUjTrU†j. = TrH(1)F x2{Q,S}vR1wR2t2(HJ31 )y2J.

Quadratic Weyl Sums, Automorphic Functions,. and Invariance Principles. Francesco Cellarosi, Jens Marklof†. February 25, 2015. Abstract. Hardy and Littlewood’s approximate functional equation for quadratic Weyl sums. (theta sums) provides, by

tn,q) =n. j=1 G(tj,q) =n. j=1. i(1 q. itj ). The classical Boson-Fermion correspondence is an. isomorphism between two representations of the Heisenberg algebra, namely

tj kj (w). (O. (1. k(w). ))dk(w), w P. (9). Here we assume that only finite number of variables tn are different from 0. ... exp[i. j. tj. zw. j. ](11). Here j are meromorphic differentials with an unique pole at the point P ,. j = d(kj) regular tems.

σ(uv) = (si(u) v, (1)iu tj(v))in (Pi1 k Qi) (Pi k Qj1). ... The homotopy σ sends uv tothe element. (si(u) v, (1)iu tj(v))in (Pi1 k Qj) (Pi k Qj1).

Tj Pj1Y1+ Pj1T. †j , T. †j1Pj1YPj1Tj1 AW. By Prop. 5 Pj Y1Pj AW. ... Lemma 3.2 (Lemma W for XW ;nW ). Let Vj, Tj, j = 1,. ,