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Freezing limits for Calogero–Moser–Sutherland particle models

∶= 𝜉 −1∕2 𝑛 ̂𝑛) ∞ 𝑛=0 with ̃0 = 1, ̃1(𝑥) = 𝑏 −1 1 (𝑥 − 𝑎0), 𝑥̃𝑛(𝑥) = 𝑏𝑛+1̃𝑛+1(𝑥) + 𝑎𝑛̃𝑛(𝑥) + 𝑏𝑛̃𝑛−1(𝑥) (𝑛 ≥ 1) (87) with 𝑏𝑛 = 𝑢𝑛 √ 𝜉𝑛−1∕𝜉𝑛 = √ 𝜉𝑛∕𝜉𝑛−1 for 𝑛 ≥ 1. In [...] (5.1.6)90). By (24), we may form 𝐿 (−1) 𝑁 for 𝑁 ≥ 0 where, by (5.2.1) of Ref. 90, 𝐿 (−1) 𝑁 (𝑥) = − 𝑥 𝑁 𝐿 (1) 𝑁−1(𝑥) (𝑁 ≥ 1). (25) If 𝑧1 > … > 𝑧𝑁−1 are the𝑁 − 1 zeros of 𝐿 (1) 𝑁−1, we [...] introduce the measures 𝜇𝑁,𝜈 ∶= 1 𝑁(𝑁 + 𝜈 − 1) ( 𝑧 (𝜈−1) 1,𝑁 𝛿 𝑧 (𝜈−1) 1,𝑁 +⋯+ 𝑧 (𝜈−1) 𝑁,𝑁 𝛿 𝑧 (𝜈−1) 𝑁,𝑁 ) . (71) As ∑𝑁 𝑘=1 𝑧 (𝜈−1) 𝑘,𝑁 = 𝑁(𝑁 + 𝜈 − 1) by Appendix C of Ref. 6, these …

σ̂ · √ 1/n1 +1/n2 +1/n3 +1/n4 , (1) where σ̂2 = ∑4 i=1 wis2 i is a pooled estimator of the constant variance, and wi = (ni−1)/∑4 j=1(n j− 1). For a given split s, G(s) = t2(s) converges to a χ2(1) distribution [...] trt+2Z1 +2Z2 + ε N (0,1) B Y = 2+2 · trt+2Z1 +2Z2 +2 · trt ·Z1 Z2 + ε N (0,1) C Y = 2+2 · trt+2Z1 +2Z2 +2 · trt ·Z1 +2 · trt ·Z2 + ε N (0,1) D Y = 10+10 · trt · exp{(X1−0.5)2 +(X2−0.5)2}+ ε N (0,1) E Y [...] provided by Theorem 1 in the appendix. For a given node t, a split s yields the following 2×2 table: 143 SU, TSAI, WANG, NICKERSON AND LI child node treatment tL tR 1 µL 1 ȳL 1 s2 1 n1 µR 1 ȳR 1 s2 2 n2 0 µL …

Forming Al99.5, 50 µm 1.4301, 50 µm 1.4301, 25 µm Al99.5, 10 µm Al99.5, 50 µm 1 mm 1 mm 1 mm 1 mm 1 mm Comparison forming results 1 mm 1.4301, 50 µm 0 40 80 120 200 µm 0 500 1000 µm 2000 1.4301, 50 µm Al99 [...] conductor depth of cups cutting 2 mm Ądown to 1.4 mm diameter! © bime | University of Bremen | Lasse Langstädtler | slide 7 Joining by forming foil 1 foil 2 1 mm 1 mm inductor sheet tool © bime | University [...] processing 00000 metal strip micro part functional element tool package tool (2) - inductor tool (1) - die (1) (2) (1) (2) 5 mm example © bime | University of Bremen | Lasse Langstädtler | slide 9 Summary and …

aus: Phasen : p1<p2> p2<m> q1<0> q2<0> q3<1> v1<s> v2<F> Bere iche : b1 : ( p1 p2 ) b2 : ( q1 q2 q3 ) b3 : ( v1 v2 ) Kopplungsre la t ion : PxP = { (p1 , v1 ) ( v1 , p1 ) ( q1 , v1 ) ( v1 , q1 ) } Er r egung [...] geschrieben. Beispiel 1 Ein ISystem Gegeben sei ein ISystem IS = (P, B, B, K, E) mit 1. P = {p1, p2, v1, v2, q1, q2, q3} 2. B = {b1, b2, b3} 3. B = {b3} 4. K = {(p1, v1), (q1, v1)} 5. E = {(p1, q1), (q3, v2)} Die [...] addBereich ( ber1 ) ; pbbke1 . addBereich ( ber2 ) ; pbbke1 . addBereich ( ber3 ) ; pbbke1 . couplePhases (p1 , v1 ) ; pbbke1 . couplePhases ( q1 , v1 ) ; pbbke1 . exc i t ePhase (p2 , q1 ) ; pbbke1 . exc i t …

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