ISSN 1439-8516 CN 11-2039/O1
We find a new representation of the simple Lie algebra of type E6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen's idea of mixed product, we construct a new functor from D5-Mod to E6-Mod. A condition for the functor to map a finite-dimensional irreducible D5-module to an infinite-dimensional irreducible E6-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant's characteristic identities plays a key role.
In this paper, we study the large deviation for a supercritical branching process with immigration controlled by a sequence of non-negative integer-valued independently identical distributed random variables, improving the previous results for non immigration processes. We rely heavily on the detail description and limit property of the generating function of immigration processes.
We propose a conjecture on the generating series of Chern numbers of tautological bundles on symmetric products of curves and establish the rank 1 and rank -1 case of this conjecture. Thus we compute explicitly the generating series of integrals of Segre classes of tautological bundles of line bundles on curves, which has a similar structure as Lehn's conjecture for surfaces.
We consider the Cauchy-Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain. The coefficients supposed to be only measurable in one of the space variables and small BMO with respect to the others. We obtain Calder′on-Zygmund type estimate for the gradient of the solution in generalized weighted Morrey spaces with Muckenhoupt weight.
In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn-1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.
The paper explores the connection of Graph-Lagrangians and its maximum cliques for 3-uniform hypergraphs. Motzkin and Straus showed that the Graph-Lagrangian of a graph is the Graph-Lagrangian of its maximum cliques. This connection provided a new proof of Turán classical result on the Turán density of complete graphs. Since then, Graph-Lagrangian has become a useful tool in extremal problems for hypergraphs. Peng and Zhao attempted to explore the relationship between the Graph-Lagrangian of a hypergraph and the order of its maximum cliques for hypergraphs when the number of edges is in certain range. They showed that if G is a 3-uniform graph with m edges containing a clique of order t-1, then λ(G) = λ([t-1](3)) provided (3 t-1) ≤ m ≤ (3 t-1) + (2 t-2). They also conjectured: If G is an r-uniform graph with m edges not containing a clique of order t-1, then λ(G) < λ([t-1](r)) provided (r t-1) ≤ m ≤ (r t-1) + (r-1 t-2). It has been shown that to verify this conjecture for 3-uniform graphs, it is sufficient to verify the conjecture for left-compressed 3-uniform graphs with m = (3 t-1) +(2 t-2). Regarding this conjecture, we show: If G is a left-compressed 3-uniform graph on the vertex set [t] with m edges and |[t-1](3)\E(G)| = p, then λ(G) < λ([t-1](3)) provided m = (3 t-1) + (2 t-2) and t ≥ 17p/2 + 11.
Let q1 = 1, and qn be the largest value of (k + 1)(n-qk) for all integers 1 ≤k≤n-1 with n ≥ 2. The sequence Q = {q1, q2, q3, . . .} is called Levine-O'Sullivan sequence. In this paper, we use the combinational and analysis skill and the mathematical induction to study the asymptotic properties of qn, and give an interesting asymptotic formula for it. This solved a conjecture proposed by Professor Chen Yonggao.
Graph coloring is an important tool in the study of optimization, computer science, network design, e.g., file transferring in a computer network, pattern matching, computation of Hessians matrix and so on. In this paper, we consider one important coloring, vertex coloring of a total graph, which is also called total coloring. We consider a planar graph G with maximum degree Δ(G) ≥ 8, and proved that if G contains no adjacent i, j-cycles with two chords for some i, j ∈ {5, 6, 7}, then G is total-(Δ + 1)-colorable.
Let f : Md → Md(d ≥ 2) be a diffeomorphism on a compact C∞ manifold on M. If a diffeomorphism f belongs to the C1-interior of the set of all diffeomorphisms having the barycenter property, then f is Ω-stable. Moreover, if a generic diffeomorphism f has the barycenter property, then f is Ω-stable. We also apply our results to volume preserving diffeomorphisms.
We show that if for every prime p, the normalizer of a Sylow p-subgroup of a finite group G admits a p-solvable supplement, then G is solvable. This generalizes a solvability criterion of Hall which asserts that a finite group G is solvable if and only if G has a Hall p'-subgroup for every prime p.
