Let a, b and k be nonnegative integers with a ≥ 2 and b ≥ a(k + 1) + 2. A graph G is called a k-Hamiltonian graph if after deleting any k vertices of G the remaining graph of G has a Hamiltonian cycle. A graph G is said to have a k-Hamiltonian[a, b]-factor if after deleting any k vertices of G the remaining graph of G admits a Hamiltonian[a, b]-factor. Let G is a k-Hamiltonian graph of order n with n ≥ a + k + 2. In this paper, it is proved that G contains a k-Hamiltonian[a, b]-factor if δ(G) ≥ a + k and δ(G) ≥ I(G) ≥ a-1 + ((a(k+1))/b-2).
In survival analysis, data are frequently collected by some complex sampling schemes, e.g., length biased sampling, case-cohort sampling and so on. In this paper, we consider the additive hazards model for the general biased survival data. A simple and unified estimating equation method is developed to estimate the regression parameters and baseline hazard function. The asymptotic properties of the resulting estimators are also derived. Furthermore, to check the adequacy of the fitted model with general biased survival data, we present a test statistic based on the cumulative sum of the martingale-type residuals. Simulation studies are conducted to evaluate the performance of proposed methods, and applications to the shrub and Welsh Nickel Refiners datasets are given to illustrate the methodology.
In this paper, we deduced an iteration formula for the computation of central composite discrepancy. By using the iteration formula, the computational complexity of uniform design construction in flexible region can be greatly reduced. And we also made a refinement to threshold accepting algorithm to accelerate the algorithm's convergence rate. Examples show that the refined algorithm can converge to the lower discrepancy design more stably.
This paper evaluates the performance of the F_{W} -test for testing part of p-regression coefficients in linear panel data model when p is divergent. The asymptotic power of the F_{W} -statistic is obtained under some regular conditions. The theoretical development are challenging since the number of covariates increases as the sample size increases. It is worth noting that the inference approach does not require any specification of the error distribution. Some simulation comparisons are conducted and show that the simulated power coincide with theoretical power well. The method is also illustrated using a renal cancer data example.
A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G is the least number of colors such that G has an acyclic edge coloring and denoted by χ'_{a}(G). An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. In this paper, it is proved that χ'_{a}(G) ≤ △(G) + 10, if G is an IC-planar graph without adjacent triangles and χ'_{a}(G) ≤ △(G) + 8, if G is a triangle-free IC-planar graph.
Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the Catalan-Larcombe-French sequence {P_{n}}_{n ≥ 0} and the Fennessey-Larcombe-French sequence {V_{n}}_{n ≥ 0} respectively. In this paper, we first establish some criteria for determining log-behavior of a sequence based on its three-term recurrence. Then we prove the log-convexity of {V_{n}^{2}-V_{n-1}V_{n+1}}_{n ≥ 2} and {n!V_{n}}_{n ≥ 1}, the ratio log-concavity of {P_{n}}_{n ≥ 0} and the sequence {A_{n}}_{n ≥ 0} of Apéry numbers, and the ratio log-convexity of {V_{n}}_{n ≥ 1}.
Hartsfield and Ringel conjectured that every connected graph other than K_{2} is antimagic. Since then, many classes of graphs have been proved to be antimagic. But few is known about the antimagicness of lexicographic product graphs. In this paper, via the construction of a directed Eulerian circuit, the Siamese method, and some modification on graph labeling, the antimagicness of lexicographic product graph G[P_{n}] is obtained.
In 2005, Flandrin et al. proved that if G is a k-connected graph of order n and V(G)=X_{1} ∪ X_{2} ∪ … ∪ X_{k} such that d(x)+ d(y) ≥ n for each pair of nonadjacent vertices x, y ∈ X_{i} and each i with i=1, 2, …, k, then G is hamiltonian. In order to get more sufficient conditions for hamiltonicity of graphs, Zhu, Li and Deng proposed the definitions of two kinds of implicit degree of a vertex v, denoted by id_{1}(v) and id_{2}(v), respectively. In this paper, we are going to prove that if G is a k-connected graph of order n and V (G)=X_{1} ∪ X_{2} ∪ … ∪ X_{k} such that id_{2}(x) + id_{2}(y) ≥ n for each pair of nonadjacent vertices x, y ∈ X_{i} and each i with i=1, 2, …, k, then G is hamiltonian.
In this paper, Wang's Harnack and shift Harnack inequality for a class of stochastic differential equations driven by G-Brownian motion are established. The results generalize the ones in the linear expectation setting. Moreover, some applications are also given.
Let H=(V, E) be an n-balanced k-partite k-graph with partition classes V_{1}, …, V_{k}. Suppose for every legal (k-1)-tuple f contained in V \ V_{1} and for every legal (k-1)-tuple g contained in V \ V_{k} such that f ∪ g∉ E(H), we have d(f) + d(g) ≥ n + 1. In this paper, we prove that under this condition H must have a perfect matching. Another result of this paper is about the perfect matching in 3-uniform hm-bipartite hypergraphs. Let G be a 3-uniform hm-bipartite hypergraph with one of whose sides V_{1} has the size n, the another side V_{2} has size 2n. If for all the legal 2-tuple f with|f ∩ V_{1}|=1 and for all the legal 2-tuple g with|g ∩ V_{1}|=0, we have d(f) ≥ n-2 and d(g) > n/2, then G has a perfect matching.
Published auxiliary information can be helpful in conducting statistical inference in a new study. In this paper, we synthesize the auxiliary information with semiparametric likelihood-based inference for censoring data with the total sample size is available. We express the auxiliary information as constraints on the regression coefficients and the covariate distribution, then use empirical likelihood method for general estimating equations to improve the efficiency of the interested parameters in the specified model. The consistency and asymptotic normality of the resulting regression parameter estimators established. Also numerical simulation and application with different supposed conditions show that the proposed method yields a substantial gain in efficiency of the interested parameters.
This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion. By applying the detailed spectral analysis and in virtue of the bifurcating direction to the limiting system as the cross diffusion rate tends to infinity, it is proved the stability/instability of the nontrivial positive steady states with some special bifurcating structure. Further, the existence and stability/instability of the corresponding nontrivial positive steady states for the original cross-diffusion system are proved by applying perturbation argument.
Under the framework of sub-linear expectation initiated by Peng, motivated by the concept of extended negative dependence, we establish a law of logarithm for arrays of row-wise extended negatively dependent random variables under weak conditions. Besides, the law of logarithm for independent and identically distributed arrays is derived more precisely and the sufficient and necessary conditions for the law of logarithm are obtained.
In this paper, we make use of stochastic theta method to study the existence of the numerical approximation of random periodic solution. We prove that the error between the exact random periodic solution and the approximated one is at the 1/4 order time step in mean sense when the initial time tends to ∞.
Matching is a routinely used technique to balance covariates and thereby alleviate confounding bias in causal inference with observational data. Most of the matching literatures involve the estimating of propensity score with parametric model, which heavily depends on the model specification. In this paper, we employ machine learning and matching techniques to learn the average causal effect. By comparing a variety of machine learning methods in terms of propensity score under extensive scenarios, we find that the ensemble methods, especially generalized random forests, perform favorably with others. We apply all the methods to the data of tropical storms that occurred on the mainland of China since 1949.
In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear semidefinite programming. At each iteration, two systems of linear equations with the same coefficient matrix are solved to determine search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for traditional filter methods. The proposed algorithm is globally convergent under some mild conditions. Preliminary numerical results indicate that the proposed algorithm is comparable.
A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most once. It is known that the list edge chromatic number χ'_{l}(G) of any outer-1-planar graph G with maximum degree △(G) ≥ 5 is exactly its maximum degree. In this paper, we prove χ'_{l}(G)=△(G) for outer-1-planar graphs G with △(G)=4 and with the crossing distance being at least 3.
In this paper, we present a primal-dual interior point algorithm for semidefinite optimization problems based on a new class of kernel functions. These functions constitute a combination of the classic kernel function and a barrier term. We derive the complexity bounds for large and small-update methods respectively. We show that the best result of iteration bounds for large and small-update methods can be achieved, namely O(q√n(log √n) ^{q+1/q} log n/ε) for large-update methods and O(q^{3/2} (log √q)^{q+1/q} √n log n/ε) for small-update methods. We test the efficiency and the validity of our algorithm by running some computational tests, then we compare our numerical results with results obtained by algorithms based on different kernel functions.