ISSN 1439-8516 CN 11-2039/O1
We classify all Leibniz conformal algebras of rank two.
For stochastic reaction-diffusion equations with Lévy noises and non-Lipschitz reaction terms, we prove that W1H transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the L1-metric. The proofs are based on the Galerkin approximations.
This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively. The sets of limit points of those Gaussian random fields are obtained. The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.
This paper is concerned with one-dimensional derivative quintic nonlinear Schrödinger equation,
iut-uxx + i(|u|4u)x=0, x ∈ T.
The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established. The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem. We mention that in the present paper the mean value of u does not need to be zero, but small enough, which is different from the assumption (1.7) in Geng-Wu[J. Math. Phys., 53, 102702 (2012)].
Combining the dual least action principle with Mountain-pass lemma, we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.
As a special case of experimental design, locating array is useful for locating interaction faults in component-based systems. In this paper, bipartite locating array is proposed to locate interaction faults between two specific groups. Such arrays are especially suitable for antagonism tests. Based on the definition of bipartite locating array, the lower bound on run sizes are established to measure the optimality for specific parameters. When a single fault is to be located, optimal bipartite locating arrays are proved to be equivalent to certain specific combinatorial configurations. As a result, approaches to constructing optimal bipartite locating arrays are proposed and some infinite classes of optimal bipartite locating arrays are obtained using the corresponding construction method.
Any bounded tile of the field Qp of p-adic numbers is a compact open set up to a set of zero Haar measure. In this note, we present two simple and direct proofs of this fact.
The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the two-term exponential sums, and give several interesting identities and asymptotic formulae for them.
