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Abstract: Abstract In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The k-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered. In addition, we also consider two other clustering methods, k-centres surface clustering methods based on product functional principal component analysis or double functional principal component analysis. Simulation results indicate that the proposed methods have a nice performance in terms of both the correct classification rate and the adjusted rand index. The approaches are further illustrated through empirical analysis of human mortality data. PubDate: 2024-01-03

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Abstract: Abstract We consider the relation between the direction of the vorticity and the global regularity of 3D shear thickening fluids. It is showed that a weak solution to the non-Newtonian incompressible fluid in the whole space is strong if the direction of the vorticity is \({{11 - 5p} \over 2}\) -Hölder continuous with respect to the space variables when \(2 < p < {{11} \over 5}\) . PubDate: 2024-01-01

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Abstract: Abstract In this paper, we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations. That is, the paper deals with a singular limit problem of $$\left\{ \begin{gathered} \begin{array}{*{20}{c}} {u_t^\varepsilon+ {u^\varepsilon } \cdot \nabla {u^\varepsilon } - \Delta {u^\varepsilon } + \nabla {P^\varepsilon } = \Delta {\phi ^\varepsilon }\nabla {\phi ^\varepsilon },}&{in{\text{ }}{\mathbb{R}^3} \times (0,\infty )} \\ {\nabla\cdot {u^\varepsilon } = 0,}&{in{\text{ }}{\mathbb{R}^3} \times (0,\infty )} \end{array} \hfill \\ \begin{array}{*{20}{c}} {n_t^\varepsilon+ {u^\varepsilon } \cdot \nabla {n^\varepsilon } - \Delta {n^\varepsilon } =- \nabla\cdot ({n^\varepsilon }\nabla {\phi ^\varepsilon }),}&{in{\text{ }}{\mathbb{R}^3} \times (0,\infty )} \\ {c_t^\varepsilon+ {u^\varepsilon } \cdot \nabla {c^\varepsilon } - \Delta {c^\varepsilon } = \nabla\cdot ({c^\varepsilon }\nabla {\phi ^\varepsilon }),}&{in{\text{ }}{\mathbb{R}^3} \times (0,\infty )} \end{array} \hfill \\ \begin{array}{*{20}{c}} {{\varepsilon ^{ - 1}}\phi _t^\varepsilon= \Delta {\phi ^\varepsilon } - {n^\varepsilon } + {c^\varepsilon },}&{in{\text{ }}{\mathbb{R}^3} \times (0,\infty )} \\ {({u^\varepsilon },{n^\varepsilon },{c^\varepsilon },{\phi ^\varepsilon })\left {_{t = 0 = ({u_0},{n_0},{c_0},{\phi _0})},} \right.}&{in{\text{ }}{\mathbb{R}^3}} \end{array} \hfill \\ \end{gathered}\right.$$ involving with a positive, large parameter ϵ. The present work show a case that (uϵ, nϵ, cϵ) stabilizes to (u∞, n∞, c∞):= (u, n, c) uniformly with respect to the time variable as ϵ → + ∞ with respect to the strong topology in a certain Fourier-Herz space. PubDate: 2024-01-01

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Abstract: Abstract A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that \(\sum\limits_{z \in {E_G}(u) \cup \{u\}} {\phi (z) \ne} \sum\limits_{z \in {E_G}(v) \cup \{v\}} {\phi (z)} \) for each edge uv ∈ E(G), where EG(u) is the set of edges incident with a vertex u. In 2015, Pilśniak and Woźniak conjectured that every graph with maximum degree Δ has an NSD total (Δ + 3)-coloring. Recently, Yang et al. proved that the conjecture holds for planar graphs with Δ ≥ 10, and Qu et al. proved that the list version of the conjecture also holds for planar graphs with Δ ≥ 13. In this paper, we improve their results and prove that the list version of the conjecture holds for planar graphs with Δ ≥ 10. PubDate: 2024-01-01

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Abstract: Abstract In this paper, we consider a susceptible-infective-susceptible (SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique, the uniform boundedness of solution is established. In addition, the spatial-temporal risk index \({{\cal R}_0}(\rho)\) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of \({{\cal R}_0}(\rho)\) with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention. PubDate: 2024-01-01

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Abstract: Abstract An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in G. The acyclic chromatic index \(\cal{X}_{\alpha}^{\prime}(G)\) of G is the smallest k such that G has an acyclic edge coloring using k colors. It was conjectured that every simple graph G with maximum degree Δ has \(\cal{X}_{\alpha}^{\prime}(G)\le\Delta+2\) . A 1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every 1-planar graph G without 4-cycles has \(\cal{X}_{\alpha}^{\prime}(G)\le\Delta+22\) . PubDate: 2024-01-01

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Abstract: Abstract In this paper, we are concerned with the problem of the pathwise uniqueness of one-dimensional reflected stochastic differential equations with jumps under the assumption of non-Lipschitz continuous coefficients whose proof are based on the technique of local time. PubDate: 2024-01-01

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Abstract: Abstract In the determination of the Earth gravity field in satellite geodesy, the inclination functions represent the projection of data observed along the orbital plane of a satellite orbit into the sphere in the terrestial reference frame. The inclination functions in this work is studied from a group theoretical perspective. The inclination functions are proved to generate a representation of the SO(3) group. An orthogonal relation of the inclination functions is derived and some recurrence relations for the inclination functions are given, based on which an algorithm to calculate the inclination functions is proposed. PubDate: 2024-01-01

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Abstract: Abstract Let Ω be a bounded smooth domain in ℝN (N ≥ 3). Assuming that 0 < s < 1, \(1 < p,q \le {{N + 2s} \over {N - 2s}}\) with \((p,q) \ne ({{N + 2s} \over {N - 2s}},{{N + 2s} \over {N - 2s}})\) , and a, b > 0 are constants, we consider the existence results for positive solutions of a class of fractional elliptic system below, $$\left\{{\matrix{{(a + b[u]_s^2){{(- \Delta)}^s}u = {v^p} + {h_1}(x,u,v,\nabla u,\nabla v),} \hfill & {x \in \Omega,} \hfill \cr {{{(- \Delta)}^s}v = {u^q} + {h_2}(x,u,v,\nabla u,\nabla v),} \hfill & {x \in \Omega,} \hfill \cr {u,v > 0,} \hfill & {x \in \Omega,} \hfill \cr {u = v = 0,} \hfill & {x \in {\mathbb{R}^N}\backslash \Omega.} \hfill \cr}}\right.$$ Under some assumptions of hi(x, u, v, ∇u, ∇v)(i = 1, 2), we get a priori bounds of the positive solutions to the problem (1.1) by the blow-up methods and rescaling argument. Based on these estimates and degree theory, we establish the existence of positive solutions to problem (1.1). PubDate: 2024-01-01

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Abstract: Abstract In this paper, we have introduced the concepts of pseudomonotonicity properties for nonlinear transformations defined on Euclidean Jordan algebras. The implications between this property and other P-properties have been studied. More importantly, we have solved the solvability problem of the nonlinear pseudomonotone complementarity problems over symmetric cones. PubDate: 2024-01-01

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Abstract: Abstract We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous Markov-Feller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior, then the e-property is satis ed on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups. PubDate: 2024-01-01

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Abstract: Abstract The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in ℝ2 and it is well-known that by using linear combinations of these basic estimates, modern extrapolation techniques can greatly speed up the approximation process. Similarly, when n vertices are randomly selected on the circle, the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n → ∞, and by further applying extrapolation processes, faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random polygons. In this paper, we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such polygons. We focus on two types of extrapolation estimates of the forms \({{\cal X}_n} = {\cal S}_n^\alpha {\cal A}_n^\beta \) and \({{\cal Y}_n}(p) = {(\alpha {\cal S}_n^p + \beta {\cal A}_n^p)^{1/p}}\) where α + β = 1, p ≠ 0, and \({{\cal S}_n}\) and \({{\cal A}_n}\) respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in ℝ2, and \({{\cal X}_n}\) may be viewed as the limit of \({{\cal Y}_n}(p)\) when p → 0. By deriving probabilistic asymptotic expansions with carefully controlled error estimates for \({{\cal X}_n}\) and \({{\cal Y}_n}(p)\) , we show that the choice α = 4/3, β= −1/3 minimizes the approximation error in both cases, and their distributions are also asymptotically normal. PubDate: 2024-01-01

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Abstract: Abstract In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case. PubDate: 2024-01-01

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Abstract: Abstract This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density, velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞. PubDate: 2024-01-01

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Abstract: Abstract The traditional simple random sampling (SRS) design method is ine cient in many cases. Statisticians proposed some new designs to increase e ciency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more e cient than the SRS and MERSS methods for usual symmetric distributions (normal and uniform). For asymmetric distributions considered in this study, the DMERSS has a small bias and it is more e cient than SRS for usual asymmetric distribution (exponential) for small sample sizes. PubDate: 2024-01-01

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Abstract: Abstract Let G be a simple graph and Gσ be the oriented graph with G as its underlying graph and orientation σ. The rank of the adjacency matrix of G is called the rank of G and is denoted by r(G). The rank of the skew-adjacency matrix of Gσ is called the skew-rank of Gσ and is denoted by sr(Gσ). Let V(G) be the vertex set and E(G) be the edge set of G. The cyclomatic number of G, denoted by c(G), is equal to ∣E(G)∣ − ∣V(G)∣+ ω(G), where ω(G) is the number of the components of G. It is proved for any oriented graph Gσ that −2c(G) ⩽ sr(Gσ) − r(G) ⩽ 2c(G). In this paper, we prove that there is no oriented graph Gσ with sr(Gσ) − r(G) = 2c(G)−1, and in addition, there are in nitely many oriented graphs Gσ with connected underlying graphs such that c(G) = k and sr(Gσ)−r(G) = 2c(G)−ℓ for every integers k, ℓ satisfying 0 ⩽ ℓ ⩽ 4k and ℓ≠ 1. PubDate: 2024-01-01

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Abstract: Abstract Given two graphs G and H, the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of KN in red or blue yields a red G or a blue H. Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G. Let s(G) denote the chromatic surplus of G, the number of vertices in a minimum color class among all proper χ(G)-colorings of G. Burr showed that \(R(G,H) \ge (v(G) - 1)(\chi (H) - 1) + s(H)\) if G is connected and \(v(G) \ge s(H)\) . A connected graph G is H-good if \(R(G,H) = (v(G) - 1)(\chi (H) - 1) + s(H)\) . Let tH denote the disjoint union of t copies of graph H, and let \(G \vee H\) denote the join of G and H. Denote a complete graph on n vertices by Kn, and a tree on n vertices by Tn. Denote a book with n pages by Bn, i.e., the join \({K_2} \vee \overline {{K_n}} \) . Erdős, Faudree, Rousseau and Schelp proved that Tn is Bm-good if \(n \ge 3m - 3\) . In this paper, we obtain the exact Ramsey number of Tn versus 2B2- Our result implies that Tn is 2B2-good if n ≥ 5. PubDate: 2023-12-29

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Abstract: Abstract For an integer r ≥ 2 and bipartite graphs Hi, where 1≤ i ≤ r the bipartite Ramsey number br(H1, H2, …, Hr) is the minimum integer N such that any r-edge coloring of the complete bipartite graph KN,N contains a monochromatic subgraph isomorphic to Hi in color i for some 1 ≤ i ≤ r. We show that if \(r \ge 3,{\alpha _1},{\alpha _2} > 0,{\alpha _{j + 2}} \ge [(j + 2)! - 1]\sum\limits_{i = 1}^{j + 1} {{\alpha _i}} \) for j = 1, 2, …, r −2, then \(br({C_{2\left\lfloor {{\alpha _1}\,n} \right\rfloor }},{C_{2\left\lfloor {{\alpha _2}\,n} \right\rfloor }}, \cdots ,{C_{2\left\lfloor {{\alpha _r}\,n} \right\rfloor }}) = (\sum\limits_{j = 1}^r {{\alpha _j} + o(1))n} \) . PubDate: 2023-12-29

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Abstract: Abstract In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results. PubDate: 2023-11-30

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Abstract: Abstract This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that D-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models. PubDate: 2023-10-01 DOI: 10.1007/s10255-023-1089-9