ISSN 1439-8516 CN 11-2039/O1
Furthermore, βa can not be replaced by any greater number. As the application, we obtain some weighted Trudinger-Moser inequalities for x-symmetric function on Grushin space.A super-Brauer character theory of a group G and a prime p is a pair consisting of a partition of the irreducible p-Brauer characters and a partition of the p-regular elements of G that satisfy certain properties. We classify the groups and primes that have exactly one super-Brauer character theory. We discuss the groups with exactly two super-Brauer character theories.
Let Gi be closed Lie groups of U(n), Ωi be bounded Gi-invariant domains in Cn which contains 0, and O(Cn)Gi=C, for i=1, 2. It is known that if f:Ω1→Ω2 is a proper holomorphic mapping, and f-1{0}={0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f.
Let G=Hol(H) be the holomorph of a finite group H. If there is a prime q dividing |H| such that every q-central automorphism of H is inner and Z(H)=1, then every Coleman automorphism of G is inner. In particular, the normalizer property holds for G.
Calculating the genus distributions of ladder graphs is a concerned topic in topological graph theory. In this paper, we formulate several ladder-class graphs by using a starting graph iterative amalgamation with copies of a path to construct a base graph and then adding some edges to the appointed root-vertices of the base graph. By means of transfer matrix and a finer partition of the embeddings, the explicit formulas for the genus distribution polynomials of four types of ladder-class graphs are derived.
In this paper, we investigate the time-periodic solution to a coupled compressible Navier- Stokes/Allen-Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in RN. The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory, and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force.
The statistical inference of the Vasicek model driven by small Lévy process has a long history. In this paper, we consider the problem of parameter estimation for Vasicek model dXt=(μ-θXt)dt+εdLtd, t ∈ [0, 1], X0=x0, driven by small fractional Lévy noise with the known parameter d less than one half, based on discrete high-frequency observations at regularly spaced time points {ti=n/i, i=1, 2,…, n}. For the general case and the null recurrent case, the consistency as well as the asymptotic behavior of least squares estimation of unknown parameters μ and θ have been established as small dispersion coefficient ε → 0 and large sample size n → ∞ simultaneously.
A simple graph G is a 2-tree if G=K3, or G has a vertex v of degree 2, whose neighbors are adjacent, and G-v is a 2-tree. Clearly, if G is a 2-tree on n vertices, then |E(G)|=2n -3. A non-increasing sequence π=(d1,…, dn) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices. [Acta Math. Sin. Engl. Ser., 25, 795-802 (2009)] proved that if k ≥ 2, n ≥ (9/2)k2 + (19/2)k and π=(d1,…, dn) is a graphic sequence with Σi=1n di > (k-2)n, then π has a realization containing every 1-tree (the usual tree) on k vertices. Moreover, the lower bound (k-2)n is the best possible. This is a variation of a conjecture due to Erd?s and Sós. In this paper, we investigate an analogue problem for 2-trees and prove that if k ≥ 3 is an integer with k ≡ i (mod 3), n ≥ 20 ?k/3?2 + 31 ?k/3? + 12 and π=(d1,…, dn) is a graphic sequence with Σi=1n di > max{(k-1)(n-1), 2 ?2k/3?n-2n-?2k/3?2 + ?2k/3?+1-(-1)i}, then π has a realization containing every 2-tree on k vertices. Moreover, the lower bound max{(k-1)(n-1), 2 ?2k/3?n-2n-?2k/3?2+ ?2k/3?+1-(-1)i} is the best possible. This result implies a conjecture due to [Discrete Math. Theor. Comput. Sci., 17(3), 315-326 (2016)].
