In this short note we present a new Harnack expression for the Gaussian curvature flow, which is modeled from the shrinking self similiar solutions. As applications we give alternate proofs of Chow's Harnack inequality and entropy estimate.
This paper is concerned with an optimal model averaging estimation for linear regression model with right censored data. The weights for model averaging are picked up via minimizing the Mallows criterion. Under some mild conditions, it is shown that the identified weights possess the property of asymptotic optimality, that is, the model averaging estimator corresponding to these weights achieves the lowest squared error asymptotically. Some numerical studies are conducted to evaluate the finite-sample performance of our method and make comparisons with its intuitive competitors, while an application to the PBC dataset is provided to serve as an illustration.
Space-filling designs are widely used in various fields because of their nice space-filling properties. Uniform designs are one of space-filling designs, which desires the experimental points to scatter uniformly over the experimental area. For practical need, the construction and their properties of nine-level uniform designs are discussed via two code mappings in this paper. Firstly, the algorithm of constructing nine-level uniform designs is presented from an initial three-level design by the Type-I code mapping and tripling technique. Secondly, the algorithm of constructing nine-level uniform designs is presented from a three-level base design by the Type-II code mapping and generalized orthogonal arrays. Moreover, relative properties are discussed based on the two code mappings. Finally, some numerical examples are given out for supporting our theoretical results.
A matching is extendable in a graph G if G has a perfect matching containing it. A distance q matching is a matching such that the distance between any two distinct matching edges is at least q. In this paper, we prove that any distance 2k-3 matching is extendable in a connected and locally (k-1)-connected K_{1, k}-free graph of even order. Furthermore, we also prove that any distance q matching M in an r-connected and locally (k-1)-connected K_{1, k}-free graph of even order is extendable provided that M is bounded by a function on r, k and q. Our results improve some results in [J. Graph Theory 93 (2020), 5-C20].
In this paper, we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming (SDP). This add a new type of functions to the class of eligible kernel functions. We prove that the interior-point algorithm based on the new kernel function meets O(n^{3/4} log n/ε) iterations as the worst case complexity bound for the large-update method. This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al. in 2012, and improves with a factor n^{1/4} the obtained iteration bound based on the classic kernel function. We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.
The effectiveness of this paper lies in the influence of the discretization step on the asymptotic stability of the positive two-dimensional fractional linear systems. It aims at investigating whether, how and when this step affects the asymptotically stable two-dimensional positive fractional linear continuous-discrete systems. To accomplish this study, a new test was outlined and used so that the asymptotic stability of the system was measured both before and after being exposed to the sampling step. Furthermore, the conditions of that stability were assessed. As a result, the outcome of the approximation shows that the stability is preserved under a particular set of conditions. On this basis, the newly proposed approach is recommended for testing the intended stability of such systems. A numerical example is tested to show the accuracy and the applicability of the proposed tests.
Several tests for multivariate mean vector have been proposed in the recent literature. Generally, these tests are directly concerned with the mean vector of a high-dimensional distribution. The paper presents two new test procedures for testing mean vector in large dimension and small samples. We do not focus on the mean vector directly, which is a different framework from the existing choices. The first test procedure is based on the asymptotic distribution of the test statistic, where the dimension increases with the sample size. The second test procedure is based on the permutation distribution of the test statistic, where the sample size is fixed and the dimension grows to infinity. Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.
Empirical likelihood in generalized linear models with multivariate responses and working covariance matrix is discussed. Under the weakest assumption on eigenvalues of Fisher's information matrix and some other regular conditions, we prove that the non-parametric Wilk's property still holds, that is, the empirical log-likelihood ratio at the true parameter values converges to the standard chi-square distribution. Numerical simulations are given to verify our theoretical result.
In this paper, we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations. The generalized Navier boundary condition and the relaxation boundary condition are established in order to solve the problem of moving contact lines on the solid boundary by using the principle of minimum energy dissipation. The existence and uniqueness for local strong solution in three dimensional bounded domain for this type of boundary value problem is obtained by the elementary energy method and the maximum principle.
In this paper, we consider the one dimensional third order p-Laplacian equation (Φ_{p}(u"))'+ h(t)f(t, u(t))=0 with integral boundary conditions u(0)-αu'(0)= ∫t_{0}^{1}g_{1}(s)u(s)ds, u(1)+βu'(1)= ∫t_{0}^{1}g_{2}(s)u(s)ds, u"(0)=0. By using kernel functions and the Avery-Peterson fixed point theorem, we establish the existence of at least three positive solutions.
We investigate a diffusive, stage-structured epidemic model with the maturation delay and freelymoving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation. The normal forms of Hopf bifurcations on the center manifold are calculated, and explicit formulae determining the criticality of bifurcations are derived. There are two different kinds of stable oscillations near the first bifurcation: on one hand, we theoretically prove that when the diffusion rate of infected immature individuals is sufficiently small or sufficiently large, the first branch of Hopf bifurcating solutions is always spatially homogeneous; on the other, fixing this diffusion rate at an appropriate size, stable oscillations with different spatial profiles are observed, and the conditions to guarantee the existence of such solutions are given by calculating the corresponding eigenfunction of the Laplacian at the first Hopf bifurcation point. These bifurcation behaviors indicate that spatial diffusion in the epidemic model may lead to spatially inhomogeneous distribution of individuals.
A graph G is said to be p-factor-critical if G-u_{1}-u_{2}-...-u_{p} has a perfect matching for any u_{1}, u_{2}, ..., u_{p}∈ V(G). The concept of p-factor-critical is a generalization of the concepts of factor-critical and bicritical for p=1 and p=2, respectively. Heping Zhang and Fuji Zhang[Construction for bicritical graphs and k-extendable bipartite graphs, Discrete Math., 306(2006) 1415–1423] gave a concise structure characterization of bicritical graphs. In this paper, we present the characterizations of p-factor-critical graphs and minimal p-factor-critical graphs for p ≥ 2. As an application, we also obtain a class of graphs which are minimal p-factor-critical for p ≥ 1.
In this paper a new class of orthogonal arrays (OAs), i.e., OAs without interaction columns, are proposed which are applicable in factor screening, interaction detection and other cases. With the tools of difference matrices, we present some general recursive methods for constructing OAs of such type. Several families of OAs with high percent saturation are constructed. In particular, for any integer λ ≥ 3, such a two-level OA of run 4λ can always be obtained if the corresponding Hadamard matrix exists.
A graph is 1-planar if it can be drawn on the Euclidean plane so that each edge is crossed by at most one other edge. A proper vertex k-coloring of a graph G is defined as a vertex coloring from a set of k colors such that no two adjacent vertices have the same color. A graph that can be assigned a proper k-coloring is k-colorable. A cycle is a path of edges and vertices wherein a vertex is reachable from itself. A cycle contains k vertices and k edges is a k-cycle. In this paper, it is proved that 1-planar graphs without 4-cycles or 5-cycles are 5-colorable.
A spanning subgraph F of a graph G is called a path factor of G if each component of F is a path. A P_{≥k}-factor means a path factor with each component having at least k vertices, where k≥2 is an integer. Bazgan, Benhamdine, Li and Wozniak [C. Bazgan, A. H. Benhamdine, H. Li, M. Wozniak, Partitioning vertices of 1-tough graph into paths, Theoret. Comput. Sci. 263(2001)255--261.] obtained a toughness condition for a graph to have a P_{≥3}-factor. We introduce the concept of a P_{≥k}-factor deleted graph, that is, if a graph G has a P_{≥k}-factor excluding e for every e∈ E(G), then we say that G is a P_{≥k}-factor deleted graph. In this paper, we show four sufficient conditions for a graph to be a P_{≥3}-factor deleted graph. Furthermore, it is shown that four results are best possible in some sense.
For a function ? satisfying some suitable growth conditions, consider the following general dispersive equation defined by{i?_{t}u+?(√-?)u = 0, (x, t)∈ R^{n}×R, u(x, 0)=f(x), f∈S(R^{n}), (*)where ?(√-?) is a pseudo-differential operator with symbol ?(ξ). In the present paper, when the initial data f belongs to Sobolev space, we give the local and global weighted L^{q} estimate for the global maximal operator S_{?}^{**} defined by S_{?}^{**}f(x)=sup_{t∈R}S_{t, ?}f(x), whereS_{t, ?}f(x) = (2π)^{-n}∫_{Rn}e^{ix·ξ+it?(ξ)}f(ξ)dξis a formal solution of the equation (*).
We investigate the family of vertex-transitive graphs with diameter 2. Let Γ be such a graph. Suppose that its automorphism group is transitive on the set of ordered non-adjacent vertex pairs. Then either Γ is distance-transitive or Γ has girth at most 4. Moreover, if Γ has valency 2, then Γ ? C_{4} or C_{5}; and for any integer n ≥ 3, there exist such graphs Γ of valency n such that its automorphism group is not transitive on the set of arcs. Also, we determine this family of graphs of valency less than 5. Finally, the family of diameter 2 circulants is characterized.
A graphic sequence π=(d_{1}, d_{2}, ..., d_{n}) is said to be forciblyk-edge-connected if every realization of π is k-edge-connected. In this paper, we obtain a new sufficient degree condition for π to be forcibly k-edge-connected. We also show that this new sufficient degree condition implies a strongest monotone degree condition for π to be forcibly 2-edge-connected and a conjecture about a strongest monotone degree condition for π to be forcibly 3-edge-connected due to Bauer et al. (Networks, 54(2) (2009) 95-98), and also implies a strongest monotone degree condition for π to be forcibly 4-edge-connected.
The Turán number of a k-uniform hypergraph H, denoted by ex_{k} (n; H), is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph. Let C_{e}^{(k)} denote the family of all k-uniform minimal cycles of length e, S(e_{1}, ..., e_{r}) denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length e_{1}, ..., e_{r}, respectively, and C_{e}^{(k)} denote a k-uniform linear cycle of length e. We determine precisely ex_{k}(n; S(e_{1}, ..., e_{r})) and ex_{k}(n; C_{e1}^{(k)}, ..., C_{er}^{(k)}) for sufficiently large n. Our results extend recent results of Füredi and Jiang who determined the Turán numbers for single k-uniform minimal cycles and linear cycles.