ar X iv : 1 10 8 . 28 74 v 1 [ m at h . Q A ] 1 4 A ug 2 01 1 THERMODYNAMIC SEMIRINGS

ar X iv : m at h / 98 08 06 5 v 1 [ m at h . Q A ] 1 4 A ug 1 99 8 QUANTUM DETERMINANTS AND QUASIDETERMINANTS

ar X iv : 0 90 8 . 27 37 v 1 [ m at h . G R ] 1 9 A ug 2 00 9 On Bruck Loops of 2 - power Exponent , II ∗

As anounced in [BSS], we show that the non-passive finite simple groups are among the PSL2(q) with q − 1 ≥ 4 a 2-power.

ar X iv : m at h / 01 04 17 8 v 1 [ m at h . N T ] 1 8 A pr 2 00 1 Arithmetic theory of q - difference equations

Part II. p-adic methods §3. Considerations on the differential case §4. Introduction to p-adic q-difference modules 4.1. p-adic estimates of q-binomials 4.2. The Gauss norm and the invariant χv(M) 4.3. q-analogue of the Dwork-Frobenius theorem §5. p-adic criteria for unipotent reduction 5.1. q-difference modules having unipotent reduction modulo ̟v 5.2. q-difference modules having unipotent redu...

ar X iv : h ep - e x / 04 08 01 4 v 1 6 A ug 2 00 4 Plans for Kaon Physics at BNL

ar X iv : 0 80 8 . 01 63 v 1 [ cs . D S ] 1 A ug 2 00 8 Twice - Ramanujan Sparsifiers ∗

We prove that for every d > 1 and every undirected, weighted graph G = (V, E), there exists a weighted graph H with at most ⌈d |V |⌉ edges such that for every x ∈ IR , 1 ≤ x T LHx x LGx ≤ d + 1 + 2 √ d d + 1 − 2 √ d , where LG and LH are the Laplacian matrices of G and H , respectively.