Acta Mathematicae Applicatae Sinica, English Series最新文献

Let G be a simple connected graph with vertex set V(G). For S ⊆ V(G), let π_G(S) denote the maximum cardinality of internally disjoint S-paths in G. For an integer k with k ≥ 2, the k-path-connectivity π_k(G) is defined as the minimum π_G(S) over all k-subsets S of V(G). It is proved that deciding whether π_G(S) ≥ r is NP-complete problem [Graphs Combin. 37 (2021) 2521–2533]. The hypercube Q_n is the famous Cayley graph, which is widely studied in the research of developing multiprocessor systems. The hierarchical cubic network HCN_n is given in [IEEE TPDS 6 (1995) 427–435] which takes Q_n as building clusters and emulates the desirable properties very efficiently. In this paper, we consider the 3-path-connectivity of HCN_n and prove that (pi_{3}(HCN_{n})=lfloor {3n+2 over 4}rfloor) by constructing multiple internally disjoint S-paths. This result improves the 3-tree-connectivity [Discrete Appl. Math. 322 (2022) 203–209] from trees to paths.

In this paper, we present some new regularity criteria for suitable weak solutions to the 3D co-rotational Beris-Edwards system. First, we prove that suitable weak solutions are regular if the scaled L^p;q-norm of the velocity field or gradient of velocity is small with ({2over p}+{3over q}=2,1 < p leq infty). Next, we give ε-regularity criteria in terms of velocity field u and director field Q in Lorentz spaces, which extends the results obtained by Wang et al (J. Evol. Equ. 21: 1627–1650, 2021) for Navier-Stokes equations.

In this paper, we study bimagnetic monopoles which are topological solitons in three space dimensions. We prove the existence and uniqueness of solution of a static and radially symmetric Bogomol’nyi-Prasad-Sommerfield (BPS) bimagnetic monopoles formulated and presented in a recent study of Bazeia, Marques and Menezes. Our method is based on a dynamical shooting approach depending on two shooting parameters which provides an effective framework for constructing the BPS equations in magnetic core and magnetic shell. Furthermore, we obtain the relation between the BPS and non-BPS monopoles solutions, and properties of static BPS monopoles solutions.

We propose an exact explicit closed-form Laguerre series expansion formula to compute the q-scale function of a spectrally negative Lévy process (SNLP), and other functions associated to the scale function for the first time. The proposed closed-form formula for the scale function has many applications in applied probability and in particular in the Lévy insurance risk theory. We shall show that the new series expansion formulas can be used to express the expected discounted penalty functions, the moments of the present value of total dividend payments as well as the time value of Parisian ruin in the Lévy risk models.

The paper focuses on the ergodicity of a ϕ-irreducible Markov chain {X_n, n ≥ 0} that is generated iteratively through the expression X_n+1 = f(X_n) + ϵ_n+1. Here, {ϵ_n, n ≥ 1} is a sequence of independent identically distributed centered random variables, f(·) is an ℝ-valued continuous function, and X₀ is arbitrary but independent of {ϵ_n, n ≥ 1}. Our main contribution is to provide necessary and sufficient conditions for the ergodicity of this special class of Markov chains. We also present a generalized approach for f(·) in the end.

We propose two nonmonotone retraction-based proximal gradient methods for solving a class of nonconvex nonsmooth optimization problems over the Stiefel manifold. The proposed methods are equipped with the descent direction obtained by a proximal mapping restricted in tangent space of the manifold and the Barzilai-Borwein stepsizes determined by two recent iteration points and the corresponding descent directions. By employing, respectively, the Grippo-Lampariello-Lucidi nonmonotone line search strategy and the Dai-Fletcher nonmonotone line search strategy, our proposed methods are proved to be globally convergent. Analysis on the iteration complexity for obtaining an ϵ-stationary solution is provided. Numerical results on the sparse principle component analysis problems demonstrate the efficiency of our methods.

In this paper, an HIV-1 infection model with intracellular delay, humoral immunity and immune impairment is investigated, in which both virus-to-cell infection and cell-to-cell transmission are considered. The basic reproduction ratio is calculated and the existence of feasible equilibria is established. By analyzing the distributions of roots of the corresponding characteristic equations, the local asymptotic stability of each of feasible equilibria is established. With the help of appropriate Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable, and the virus is eventually eliminated; if the basic reproduction ratio is greater than unity, the chronic-infection equilibrium is globally asymptotically stable. Finally, numerical simulations are carried out to illustrate the effects of some parameters on HIV-1 infection dynamics.

The eccentricity matrix ℰ(G) of a connected graph G is obtained from the distance matrix of G by leaving unchanged the largest nonzero entries in each row and each column, and replacing the remaining ones with zeros. In this paper, we consider the set (cal{C}cal{T}) of clique trees whose blocks contain at most two cut-vertices of the clique tree. Along with studying the structural properties of a clique tree in (cal{C}cal{T}), we prove its eccentricity matrix to be irreducible, and then determine its inertia showing that every graph in (cal{C}cal{T}) with more than four vertices and odd diameter has two positive and two negative ℰ-eigenvalues. Positive ℰ-eigenvalues and negative ℰ-eigenvalues turn out to be equal in number even for graphs in (cal{C}cal{T}) with even diameter; that shared cardinality also counts the ‘diametrally distinguished’ vertices. Finally, we prove that the spectrum of the eccentricity matrix of a clique tree G in (cal{C}cal{T}) is symmetric with respect to the origin if and only if G has an odd diameter and exactly two adjacent central vertices. Our results generalize those achieved on trees by I. Mahato and M. R. Kannan in 2022.

Let τ ∈ ℂ {0}; let p and q be distinct positive integers, and let a; b; c be meromorphic functions such that at least one of b and c is not identically equal to zero. The main purpose of this paper is to study the logistic delay differential equations of the Lotka-Volterra type

We prove that any admissible meromorphic solution w of the equation satisfies that the counting function N(r; w) of poles and the characteristic function T(r; w) have the same growth category. Furthermore, we obtain that “most” of admissible meromorphic solutions of a more general delay differential equation

have a pole at least.

This paper studies a model of n insiders with perfect information trading on a risky asset with value normally distributed and disclosed at a random deadline. We propose a concept of information protocol equilibrium under semi-strong efficient pricing, consisting of an n–profile of insider trading strategies with terminal residual information protocols, and find that if a common protocol on terminal residual information before trading is obeyed by all insiders, then, in the market with more than two insiders there exists a uique equilibrium only when it requires to release common partial information eventually, or it does not exist if it requires to release all or not any; but in the market with a single insider, the insider may release all private information eventually to make a maximal profit. Thereby, the existence and uniqueness of information protocol equilibrium among n insiders are deduced. Finally, numerical results illustrate some market characteristics of equilibria with different information protocols required before trading.