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Global stability of a delayed viral infection model with latent period and immune response
FU Jin-bo, CHEN Lan-sun, CHENG Rong-fu
Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 379-388.
In this paper, the dynamical behaviors of the time delayed viral infection model with latent period and CTL immune response are studied. The model describes the interaction of viral and two classes of target cells: CD4$^+$T cells and macrophages. By constructing suitable Lyapunov functionals, using the LaSalle invariance principle, it's shown that the basic repro\text{d}uctive amounts $R_{0}$ of CD4$^+$T cells and macrophages and the immune response reproductive $R_{*}$ of CD4$^+$T cells and macrophages CTL determine the global properties of the model. If $R_{0}\leq1$ , the virus is cleared. If $R_{0}>1$ , positive solutions approach to an immune-free equilibrium when $R_{*}\leq1$ , and to a positive equilibrium when $R_{*}>1$ . Thus the sufficient conditions for the global stability of the infection-free equilibrium , the immune-free equilibrium and the positive equilibrium are obtained.
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A forced vibration resonance phenomena with fractional derivative damping
GE Zhi-xin, CHEN Xian-jiang, HOU Wei-gen
Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 410-416.
A forced vibration resonance phenomena with fractional derivative damping is studied in this paper.First, an asymptotic solution is constructed. Then, by the definition and properties of RiemannLiouville fractional derivative, the expression of the fractional derivative item is obtained. Then using the method of multiple scales, the frequency of each resonance is calculated. These resonances include the main resonance and the secondary resonances. For each resonance frequency, the detuning parameter is introduced. The secular terms are eliminated. After drawing the graph of the numerical solutions of amplitude and the relevant variables of initial phase when fractional derivatives are different by mathematical software, the influence of fractional derivatives on resonance is found. The first-order approximate expressions of the asymptotic solution for each resonance frequency is gotten.
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Complete convergence for weighted sums of widely orthant dependent random variables
DING Yang, WU Yi, WANG Xue-jun, XIE Xiu-juan, DU Ling
Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 417-424.
The class of widely orthant-dependent (WOD, in short) random variables includes independent sequence, negatively associated sequence, negatively orthant dependent sequence and extended negatively dependent sequence as special cases. In this paper, the complete convergence for weighted sums of WOD random variables under some mild conditions is established by using the Rosenthal type inequality for WOD random variables and the truncation method. The result obtained in the paper generalizes the corresponding ones for some dependent random variables.
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Least squares estimation for $\alpha$-weighted fractional Brownian bridge
HAN Jing-qi, SHEN Guang-jun, YAN Li-tan
Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 432-444.
In this paper, the asymptotic properties of $\widehat{\alpha}$ are considered, which is a least squares estimator for the parameter $\alpha$ of a weighted fractional bridge $$X_0=0,~~ \text{d}X_t=-\alpha\frac{X_t}{T-t}\text{d}t +\text{d}B^{a,b}_t, \ \ 0\leq t0, T>0$. The estimator has various convergence depending on the value of $\alpha$ as $t\rightarrow T.$ The rate of corresponding convergence is proved as well.
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LI-ideals theory in negative non-involutive residuated lattices
LIU Chun-hui
Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 445-456.
In this paper, the problem of ideals in negative non-involutive residuated lattices is studied by using the principle and method of universal algebras and lattice-order theory. Firstly, the notions of LI-ideals and LI-ideal generated by a non-empty subset are introduced in negative non-involutive residuated $L$, and some their properties are investigated. Secondly, lattice operations $\sqcap$ and $\sqcup$ are defined on the set $\textbf{Id}(L)$ of all LI-ideals in $L$. It is proved that $(\textbf{Id}(L), \subseteq, \sqcap, \sqcup)$ forms a distributive continuous lattice, and particularly forms a frame. Then, the notion of prime LI-ideals is introduced in $L$ and its properties are discussed. The prime LI-ideals theorem is estabLIshed in pre-LInear negative non-involutive residuated lattices. Finally, some equivalent characterizations of prime elements of LI-ideal lattice $(\textbf{Id}(L), \subseteq, \sqcap, \sqcup)$ are obtained by means of prime LI-ideals in pre-LInear negative non-involutive residuated lattice $L$.
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Weighted Shapley value for cooperative games with fuzzy coalition and incomplete information
LIN Jian, ZHANG Qiang
Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 476-484.
With respect to cooperative game with fuzzy coalitions, in which the payoffs information are partially known, the definition of $E$-incompelte fuzzy games is introduced. The $w$-weighted Shapley value, which satisfies linearity and symmetry, is proposed based on the cardinality set of incomplete coalition value. By considering the marginal contribution between coalitions, the equivalent form of $w$-weighted Shapley value is provided. The study showes that the Shapley value for complete fuzzy cooperative games in accordance with the $w$-weighted Shapley value. In the frame of fuzzy coalitions, some desirable properties of $w$-weighted Shapley value, such as coalition monotonicity, zero-normalization, etc, are discussed in detail. Finally, a numerical example is illustrated to show the validity of the $w$-weighted Shapley value.
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14 articles
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