40,639 research outputs found
Strongly intersecting integer partitions
We call a sum a1+a2+⢠⢠â˘+ak a partition of n of length k if a1, a2, . . . , ak and n are positive integers such that a1 ⤠a2 ⤠⢠⢠⢠⤠ak and n = a1 + a2 + ⢠⢠⢠+ ak. For i = 1, 2, . . . , k, we call ai the ith part of the sum a1 + a2 + ⢠⢠⢠+ ak. Let Pn,k be the set of all partitions of n of length k. We say that two partitions a1+a2+⢠⢠â˘+ak and b1+b2+⢠⢠â˘+bk strongly intersect if ai = bi for some i. We call a subset A of Pn,k strongly intersecting if every two partitions in A strongly intersect. Let Pn,k(1) be the set of all partitions in Pn,k whose first part is 1. We prove that if 2 ⤠k ⤠n, then Pn,k(1) is a largest strongly intersecting subset of Pn,k, and uniquely so if and only if k ⼠4 or k = 3 ⤠n ̸â {6, 7, 8} or k = 2 ⤠n ⤠3.peer-reviewe
Properties of Fermion Mixings in Intersecting D-brane Models
We consider the Yukawa couplings for quarks and leptons in the context of
Pati-Salam model using intersecting D-brane models where the Yukawa coupling
matrices are rank one in a simple choice of family replication. The CKM mixings
can be explained by perturbing the rank 1 matrix using higher order terms
involving new Higgs fields available in the model. We show that the near
bi-large neutrino mixing angles can be naturally explained, choosing the light
neutrino mass matrix to be type II seesaw dominant. The predicted value of
U_{e3} is in the range \simeq 0.05-0.15. In the quark sector, V_{cb} is
naturally close to the strange/bottom quark mass ratio and we obtain an
approximate relation V_{ub} V_{cb} \simeq (m_s/m_b)^2 V_{us}. The geometrical
interpretations of the neutrino mixings are also discussed.Comment: 17 pages, 3 figure
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