Table of Content

30 September 2013, Volume 28 Issue 3

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The Integer Parts of a Nonlinear Form with Integer Variables and Mixed Powers 2 and 4

LI Wei-ping, GE Wen-xu, WANG Tian-ze

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.





Vertex-distinguishing Total Colorings of 2Cn

CHEN Xiang- en, MA Yan-rong

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. 

The Free Abjects in the Category of Complete L-fuzzy Posets

ZHOU Yi-hui

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.



Congruences and Ideals of Ockham Algebras with de Morgan Skeleton

FANG Jie, WANG Lei- bo

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.



Existence Theory for Single and Multiple Positive Solutions to Singular Boundary Value Problems for Second-order Differential Systems P-Laplacian

ZHAO Xia, HU Wei-min, JIANG Da- qing

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.



On the Wiener Index of the Complements of Bipartite Graphs

XING Bao-hua, SHAO Yun

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.





Mathematical Infinity and Medium Logic (II)——Logical-mathematical Interpretation and Logical Analysis of...

ZHU Wu-jia, GONG Ning-sheng, DU Guo-ping

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.

The Harvesting Optimal Problem of Richards Model

ZENG Zhi-jun

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.



Primal-dual-pseudo Spline and Its Properties

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.



On Skew Power-serieswise nil-Armendariz Rings

ZHANG Wan-ru, PU Zhao-nian

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.

On Some Subsemigroups of the 4-cyclic Semigroup-II

SHANG Yu, WANG Li-min

2013, 28(3):  390-396. 

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In this paper, we study subsemigroups B_d,0 of the 4-cyclic semigroup B_ω2 and 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)=Md are the semigroups B_d,0(d=1,2,3,···).





The Derivation Algebra of Q_n Filiform Lie Algebra

WU Ming-zhong

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.





Normal Families of Zero-free Meromorphic Functions

LIU Dan, DENG Bing-mao, YANG De-gui

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.

Quenching Estimates for Reaction-diffusion Equations with Nonstandard Growth Conditions

LIU Bing- chen, HONG Zhen-zhen

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.

Threshold Functions for Factor-critical Graphs

HUAN Xiao, LU Hong-liang, YU Qing-lin

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. 





Penalized Empirical Likelihood Via Adaptive LASSO for Cox’s Proportional Hazards Model

HOU Wen, HUANG Rong

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.





On the Growth and the Fixed Points of Solutions of Second Order Non-homogeneous Differential Equations

FENG Bin, LIU Hui-fang

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.





The C¹  Solutions of a Class of a Non-extended Iterative Equation

LIANG Ying, MI Yu-zhen, LIN Xue-mei

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.

Existence and Uniqueness of Positive Periodic Solutions for First-order Functional Differential Equations

HAN Qian- qian, ZHAI Cheng- bo

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.



Construction of Balanced Orthogonal Nonseparable Multiwavelets

XIE Chang-zhen

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.





One Roper-Suffridge Extension Operator in Complex Banach Spaces

WANG Xiao-feng, XU Yi-fei

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.