Q p G Qp Q G Q p Ramanujan 12 q- (q) : (q) = q n=1 (1 qn ) 24 S 12 (SL 2 (Z))., p (ordinary) (, q- p a p ( ) p ). p = 11 a p ( ) p. p 11 p a p

Corollary 24 In a P Q-tree which represents a given hypergraph, a cluster that has an ancestor which is an ancestor-P -node and spans all its vertices, has at most C vertices for

F igueiredo , Positive solution for a class of p&q-singular elliptic equation, Nonlinear Anal.. Real

Secondly, once we have established the solvability of SPDEs within the stochastic parabolic weighted Sobolev spaces H γ,q p,θ (O, T ) , we have to exploit the L q (L p ) –regularity

We devote Section 3 to show two distinct nontrivial weak solutions for problem (1.1) by using the mountain pass theorem and Ekeland variational principle.. In Section 4,

In Sections 8.1–8.3, we give some explicit formulas on the Jacobi functions, which are key to the proof of the Parseval–Plancherel-type formula of branching laws of

8.1 In § 8.1 ∼ § 8.3, we give some explicit formulas on the Jacobi functions, which are key to the proof of the Parseval-Plancherel type formula of branching laws of

In this paper, we take some initial steps towards illuminating the (hypothetical) p-adic local Langlands functoriality principle relating Galois representations of a p-adic field L

These recent studies have been focused on stabilization of the lowest equal-order finite element pair P 1 − P 1 or Q 1 − Q 1 , the bilinear function pair using the pressure