Let L be a congruence-uniform lattice. In this note, we investigate the shard order on L that was introduced by N. Reading. When L is a poset of regions of a hyperplane arrangement the shard order always is a lattice. For general L, however, this fails. We provide a necessary condition for the shard order to be a lattice, and we show how to construct a congruence-uniform lattice L′ from L such ...

We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The functional is extended to the space of measures. obtained derivatives contain integrals on lower-dimensional manifolds. proofs utilize pre-conjugate, which an continuous functions. Applications optimal control problems are given.

We propose a new parametrization for the quark and lepton mixing matrices: the two 12-mixing angles (the Cabibbo angle and the angle responsible for solar neutrino oscillations) are at zeroth order π/12 and π/5, respectively. The resulting 12-elements in the CKM and PMNS matrices, Vus and Ue2, are in this order irrational but simple algebraic numbers. The difference between π/5 and the observed...

Abstract : The object of this paper is to give several properties and applications of the multiple p-adic q-L-function of two variables L (r) p,q (s, z, χ). The explicit formulas relating higher order qBernoulli polynomials, which involve sums of products of higher order q-zeta function and higher order Dirichlet q-L-function are given. The value of higher order Dirichlet p-adic q-L-function fo...