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In spinors, if Ka = ιAoA. ′. then an α-plane distribution is defined by oA′. ,

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l1a,b=0. q2ab Ka Kb, ν = u = v = 1l. ... l1m=0. q2 m2. ) l1n,a=0. (q q1)n. [n; q2]!q(l1)(na1). 2/2 En Ka F n ,. where RK is defined in (5). It is also known

SET THEORETIC SOLUTIONS OF THE YANG-BAXTEREQUATION, GRAPHS AND COMPUTATIONS. TATIANA GATEVA-IVANOVA AND SHAHN MAJID. Abstract. We extend our recent work on set-theoretic solutions of the Yang-Baxter or braid relations with new results about their

s1λN1. kA(s), where N1. kA is the IDS of the. rescaled adjacency operator 1kA. ... s11kλN1. kA(s) it is clear that Nper(λ) = F(λ/k). Thus it is sufficient to prove.

x ka|. For initial time t = 0, the previous expression simplies tou(x, 0) = c. ... Indeed, when the time t tends to ollision time, the energy density (u2 u2x)(x, t) tends towards a Dira , E k δ a2 ka(x)or E k δka(x),

Then,defining ψ := Skφ and ψ̃(u) := ψ((u/k, 0)), 0 u κ := ka, it holds that. ... A1k,η‖ C (ka)9/10(. 1 |η|k. )1. (5.1). The proof of the theorem is given below.

aXa dYiYi),. 〈j, Ka〉 = 1Y 2 (X2 Y 2)dXa 2Y 2 Xa(dX. ... 2.22a). Similarly, one obtains (ηacηcb = δa. b). 〈j j, Lab〉 = 2ηcd〈j, Lac〉 〈j, Ldb〉 〈j, Pa〉 〈j, Kb〉 〈j, Pb〉 〈j, Ka〉= 2.

We write. x =. N. a=1. ǫaeikawikaw. ab. Gab(ka, kb)ǫaǫbei(kakb)wi(kakb)w. where ǫa, a = 1, 2,. ,

Examining the derivation of (4.2), we see that this approximation is accurate providedk|x1| 1 and k(R′ R) 1; this certainly holds for x SH,A if kA 1 ... Thus, if kAand kA/(kH)2 are large enough then, from (4.2), for x SH,A,.