数学季刊

李伟平, 戈文旭, 王天泽

2013, 28(3): 317-322.

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_{The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x21+λ2x22+λ3x43 are prime infinitely often for natural numbers x1, x2, x3.}

图2Cn的点可区别全染色

陈祥恩, 马彦荣

2013, 28(3): 323-330.

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Let f be a proper total k-coloring of a simple graph G. For any vertex x∈V(G), let Cf(x)denote the set of colors assigned to vertex x and the edges incident with x. If Cf(u)=Cf(v)for all distinct vertices u and v of V(G), then f is called a vertex-distinguishing total k-coloring of G. The minimum number k for which there exists a vertex-distinguishing total k-coloring of G is called the vertex-distinguishing total chromatic number of G and denoted by χ_vt(G). The vertex-disjoint union of two cycles of length n is denoted by 2Cn.We will obtain χ_vt(2Cn) in this paper.

完备L-模糊偏序集范畴中的自由对象

周异辉

2013, 28(3): 331-337.

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The free object generated by a set in the category of complete L-fuzzy posets is discussed in this paper. The construction of a free complete L-fuzzy poset generated by a set is obtained, which is a generalization of the free complete lattice generated by a set.

具有de Morgan骨架的Ockham代数的同余关系与核理想

方捷, 王雷波

2013, 28(3): 338-344.

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In this note, we study of those congruences on an Ockham algebra with de Morgan skeleton that the quotient algebras belong to the class of de Morgan algebras. We particularly give a description of those kernel ideals that generate these congruences.

具P-Laplacian算子的二阶微分系统奇异边值问题正解的存在性

赵霞, 胡卫敏, 蒋达清

2013, 28(3): 345-354.

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In this paper we present some new existence results for singular boundary value problems by Arzela-Ascoli theorem.In particular our nonlinearity may be singular in its dependent variable.

二部图补图的Wiener指数

邢抱花, 邵云

2013, 28(3): 355-359.

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The Wiener index W(G) of a graph G is defined as the sum of distances between all pairs of vertices of the graph. Let Gc is the set of the complements of bipartite graphs with order n. In this paper, we characterize the graphs with the maximum and second-maximum Wiener indices among all the graphs in Gc, respectively.

数学无穷与中介逻辑(下)——关于△y/△y有意义dy/dx是切线的斜率在中介逻辑中的逻辑数学解读与逻辑分析

朱梧槚, 宫宁生, 杜国平

2013, 28(3): 360-365.

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Ref [5] provides a logical-mathematical explanation of the incompatibility of Leibniz’s secant and tangent lines in medium logic. However, the expression(*)(Δy/Δx is meaningful and dy/dx is the tangent slope) derived from 7 and 8 in §4 of Ref [5] is unimaginable within the framework of two-valued logic, why shouldn’t the same conflicting conclusion be reached in the medium logic calculus? This paper has subjected these questions to careful logical analysis, and approached them from the perspective of logical mathematics. As the two approaches have led to the identical conclusion, the paper thereby rigorously and thoroughly answers these questions.

Richards 模型的最优捕获问题

曾志军

2013, 28(3): 366-375.

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In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for autonomous and periodic exploited Richards model. Further, when the functions in the exploited Richards model are stably bounded functions, we study the ultimately optimal harvesting policy and obtain the corresponding average limiting maximum sustainable yield.

原-对偶伪样条及其性质

袁德辉, 冯岩, 沈延峰, 杨守志

2013, 28(3): 376-382.

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In this paper, basing on a new family of masks, namely primal-dual-pseudo spline(PDPS), we present basics of PDPSs which include the regularity, asymptotical analysis and approximation order.

斜幂级数诣-Armendariz 环

张万儒, 普昭年

2013, 28(3): 383-389.

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For a ring endomorphismα,in this paper we introduce the notion of α-power-serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α-power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.

关于4-循环半群的一些子半群-Ⅱ

商宇, 汪立民

2013, 28(3): 390-396.

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In this paper, we study subsemigroups B_d,0of the 4-cyclic semigroup B_ω2and characterize the Green’s relations of B_d,0. We show that, up to isomorphism, the only fundamental simple inverse ω²-semigroups such that D|_E(S)=M_d are the semigroups B_d,0(d=1,2,3,···).

Q_n Filiform 李代数的导子代数

吴明忠

2013, 28(3): 397-401.

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In this paper, we explicitly determine the maximal torus of the derivation algebra of a Q_n filiform Lie algebra. Using the root space decomposition of DerQ_n, we prove that the derivation algebra of a Q_n filiform Lie algebra is complete.

不取零点的亚纯函数族的正规性

刘丹, 邓炳茂, 杨德贵

2013, 28(3): 402-407.

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Let F be a family of zero-free meromorphic functions in a domain D, let h(z)≡0 be a holomorphic function in D and let k be a positive integer.If,for each f∈F, P(f)(z)-h(z) has at most k distinct zeros(ignoring multiplicity)in D, where P(f)=f(k)(z)+a1(z)f(k-1)(z)+···+ak(z)f(z) is a diferential polynomial of f and aj(z)(j=1,2,···,k) are holomorphic functions in D, then F is normal in D. This extends the results due to Deng[2], Chang[1], Gu[3], Yang[12], etc.

具有非标准增长条件的反应扩散方程组的熄灭估计

刘丙辰, 洪真真

2013, 28(3): 408-416.

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This paper deals with reaction-diffusion equations involving nonstandard growth conditions, subject to homogeneous Neumann boundary conditions. The complete classification is established for simultaneous and non-simultaneous quenching under suitable assumptions on initial data. Moreover, quenching sets and quenching rates are obtained.

Factor-critical 图的阈值

郇潇, 鲁红亮, 于青林

2013, 28(3): 417-427.

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A connected graph G is said to be k-extendable if it has a set of k independent edges and each set of k independent edges in G can be extended to a perfect matching of G. A graph G is k-factor-critical if G-S has a perfect matching for any k-subset S of V(G). The basic properties of k-extendable and k-factor-critical graphs have been investigated in [11] and [13]. In this paper, we determine thresholds for k-factor-critical graphs and k-extendable bipartite graphs. For non-bipartite k-extendable graphs, we find a probability sequence, which acts the same way like a threshold.

对于Cox’s 比例风险模型基于自适应LASSO 的惩罚经验似然

侯文, 黄荣

2013, 28(3): 428-436.

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Penalized empirical likelihood inferential procedure is proposed for Cox’s proportional hazards model with adaptive LASSO(ALASSO).Under reasonable conditions, we show that the proposed method has oracle property and the limiting distribution of a penalized empirical likelihood ratio via ALASSO is a chi-square distributions. The advantage of penalized empirical likelihood is illustrated in testing hypothesis and constructing confidence sets by simulation studies and a real example.

二阶非齐次微分方程解的增长性与不动点

冯斌, 刘慧芳

2013, 28(3): 437-446.

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In this paper, we investigate the growth and the fixed points of solutions and their 1st,2nd derivatives of second order non-homogeneous linear differential equation and obtain the estimation of the order and the exponent of convergence of fixed points of solutions of the above equations.

一类非扩张型迭代方程的连续可微解

梁英, 米玉珍, 林雪梅

2013, 28(3): 447-453.

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By using the Schauder’s fixed point theorem, the existence, uniqueness and stability of the C¹ solutions of a class non-extended iterative equation are discussed.

一阶泛函微分方程正周期解的存在唯一性

韩倩倩, 翟成波

2013, 28(3): 454-461.

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In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y‘(t) =-a(t)y(t) + f(t, y(t-τ(t))) + g(t) by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.

平衡正交不可分多小波的构造

谢长珍

2013, 28(3): 462-467.

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A general method for constructing bidimensional orthogonal nonseparable multiwavelets is presented. Moreover, this construction method can be extended to the construction of n-dimensional multiwavelets. In addition, we also study some properties of the multiwavelets such as balancing. Finally, we give an example to illustrate our method to construct bidimensional nonseparable compactly supported orthogonal multiwavelets.

Banach 空间中推广的一类Roper-Suffridge 算子

王晓凤, 许逸飞

2013, 28(3): 468-474.

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In this paper, by the definition of almost spirallike mappings of type β and orderαand the geometric property of the spirallike mapping of type β, we prove that the generalized Roper-SufFridge extension operator preserves almost spirallikeness of type β and orderαin complex Banach spaces.

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