In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and nonlinear memory source term. For 1, will be considered on bounded domain ℝ d . By some Sobolev embeddings properties Mittag-Leffler function, give results existence uniqueness mild solution (1.1) below. When = introduce L p −...

In this paper, we will use the Kohn’s ∂̄b-theory on CRhypersurfaces to derive some new results in CR-geometry. Main Theorem. LetM2n−1 be the smooth boundary of a bounded strongly pseudo-convex domain Ω in a complete Stein manifold V 2n. Then: (1) For n ≥ 3, M2n−1 admits a pseudo-Einstein metric. (2) Forn ≥ 2,M2n−1 admits a Fefferman metric of zero CRQ-curvature. (3) In addition, for a compact st...

In this paper we derive the evolution equation of first nonzero eigenvalue (p,q)-Laplace system under unnormalized Hk-flow. By imposing some conditions on mean curvature prove monotonicity

Abstract The p -Laplacian for graphs, as well the vertex Laplace operator and hyperedge general setting of oriented hypergraphs, are generalized. In particular, both a defined all ? 1. Several spectral properties these operators investigated.

Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high-dimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.