In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple group divisible designs are useful in constructing other types of super-simple designs which can be applied to codes and designs. In this article, the existence of a super-simple (5, 4)-GDD of group type g^u is investigated and it is shown that such a design exists if and only if u≥5, g(u - 2)≥12, and u(u - 1)g² ≡ 0 (mod 5) with some possible exceptions.

We establish some strong limit theorems for a sequence of pair-wise extended lower/upper negatively dependent random variables and give some new examples of dependent random variables.

We establish the additive theorem of L²-decay rate for multidimensional Markov process with independent marginal processes. Using this and the decomposition method, we obtain explicit upper and lower bounds for decay rate of non-ergodic Jackson network. In some cases, we get the exact decay rate.

We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces ?+n+1. The characterization of the boundedness and compactness of the generalized area operator from L^p(?n) to L^q(?n) is investigated in terms of s-Carleson measures with 1<p, q<+∞. In the case of p = q = 1, the weak type estimate is also obtained.

We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.

Let E be a Banach space with the c¹-norm || ? || in E\{0}, and let S(E) = {e∈E: ||e|| = 1}. In this paper, a geometry characteristic for E is presented by using a geometrical construct of S(E). That is, the following theorem holds: the norm of E is of c¹ in E\{0} if and only if S(E) is a c¹ submanifold of E, with codim S(E) = 1. The theorem is very clear, however, its proof is non-trivial, which shows an intrinsic connection between the continuous differentiability of the norm || ? || in E\{0} and differential structure of S(E).

We study class of finite-dimensional Cantan-type Lie superalgebras HO(m) over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO(m).

We prove that each sufficiently large odd integer N can be written as sum of the form N=p13+p23+?+p93 with |pj-(N/9)1/3|≤N(1/3)-θ, where p_j, j = 1, 2, … , 9, are primes and θ=(1/51)-?.

The definitions of θ-ray pattern matrix and θ-ray matrix are firstly proposed to establish some new results on nonsingularity/singularity and convergence of general H-matrices. Then some conditions on the matrix A\in {\mathbb{C}}^{\mathit{n}\times \mathit{n}} and nonempty \alpha \subset 〈\mathit{n}〉=\{\mathrm{1},\mathrm{2},\cdots ,n\} are proposed such that A is an invertible H-matrix if A(α) and A/α are both invertible H-matrices. Furthermore, the important results on Schur complement for general H-matrices are presented to give the different necessary and sufficient conditions for the matrix A\in H_n^M and the subset \alpha \subset 〈\mathit{n}〉 such that the Schur complement matrix A/\alpha \in H_{n-\left|\alpha \right|}^I\hspace{0.17em}\mathrm{o}\mathrm{r}\hspace{0.17em}A/\alpha \in H_{n-\left|a\right|}^M\hspace{0.17em}\mathrm{o}\mathrm{r}\hspace{0.17em}\mathit{A}/\alpha \in H_{n-\left|\alpha \right|}^S.

We classify finite p-groups all of whose nonnormal subgroups have orders at most p³, podd prime. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3.

We introduce the notion of omni-Lie superalgebras as a super version of an omni-Lie algebra introduced by Weinstein. This algebraic structure gives a nontrivial example of Leibniz superalgebras and Lie 2-superalgebras. We prove that there is a one-to-one correspondence between Dirac structures of the omni-Lie superalgebra and Lie superalgebra structures on a subspace of a super vector space.

We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.