中国科学院数学与系统科学研究院期刊网

15 January 2020, Volume 63 Issue 1
    

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  • Gui Ping SUN, Cheng Bo LI, Yong ZHOU
    Acta Mathematica Sinica, Chinese Series. 2020, 63(1): 1-18. https://doi.org/10.12386/A2020sxxb0001
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    We use the quantile residual lifetime models to analyze the length-biased data that are often encountered in observational studies. Ignoring sampling bias may lead to substantial estimation bias and fallacious inference. We consider a conditional log-linear regression model on the residual lifetimes at a fixed time point under right-censored and length-biased data for both covariate-independent censoring and covariate-dependent censoring. Consistency and asymptotically normalities of the regression estimators are established. Simmulation studies are performed to assess finite sample properties of the regression parameter estimator. Finally, we analyze the Oscar real data by the proposed method.

  • Tao XIONG
    Acta Mathematica Sinica, Chinese Series. 2020, 63(1): 19-26. https://doi.org/10.12386/A2020sxxb0002
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    It is well known that a domain R is a Prüfer domain if and only if every divisible module is FP-injective; if and only if every h-divisible module is FP-injective. In this paper, we introduce the concept of Gorenstein FP-injective modules, and show that a domain R is a Gorenstein Prüfer domain if and only if every divisible module is Gorenstein FP-injective; if and only if every h-divisible module is Gorenstein FPinjective.

  • Jian Quan LIAO, Bi Cheng YANG
    Acta Mathematica Sinica, Chinese Series. 2020, 63(1): 27-44. https://doi.org/10.12386/A2020sxxb0003
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    By means of the way of real analysis and the weight functions, introducing some parameters and intermediate variables, a few equivalent statements of a Hilberttype integral inequality with the general nonhomogeneous kernel in the whole plane are obtained. The constant factor is proved to be the best possible. As applications, a few equivalent statements of a Hilbert-type integral inequality with the general homogeneous kernel in the whole plane are deduced. We also consider some particular cases, the operator expressions and a few examples.

  • Yun Zhang LI, Ya Hui WANG
    Acta Mathematica Sinica, Chinese Series. 2020, 63(1): 45-60. https://doi.org/10.12386/A2020sxxb0004
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    This paper addresses a class of dilation-and-modulation (MD) systems in the space L2(R+) of square integrable functions defined on the right half real line R+. In practice, the time variable cannot be negative. L2(R+) models the causal signal space, but it admits no wavelet and Gabor systems due to R+ being not a group under addition. We study the dilation-and-modulation systems in L2(R+) generated by characteristic functions. We introduce the notion of MD-frame sets in R+. Using "dilation-equivalence" and "cardinality function" methods we characterize MD-Bessel and complete sets; obtain two sufficient conditions for MD-Riesz basis sets; and prove that an arbitrary finite and measurable decomposition of an MD-Riesz basis set leads to an MD-frame set.

  • Jun Na BI, Min Han LI
    Acta Mathematica Sinica, Chinese Series. 2020, 63(1): 61-76. https://doi.org/10.12386/A2020sxxb0005
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    We study the optimal investment and optimal reinsurance problem for an insurer under the criterion of mean-variance. The insurer's risk process is modeled by a compound Poisson process and the insurer can invest in a risk-free asset and a risky asset whose price follows a jump-diffusion process. In addition, the insurer can purchase new business (such as reinsurance). The controls (investment and reinsurance strategies) are constrained to take nonnegative values due to nonnegative new business and no-shorting constraint of the risky asset. We control the risk by the new Basel regulation and use the stochastic linear-quadratic (LQ) control theory to derive the optimal value and the optimal strategy. The corresponding Hamilton-Jacobi-Bellman (HJB) equation no longer has a classical solution. With the framework of viscosity solution, we give a new verification theorem, and then the efficient strategy (optimal investment strategy and optimal reinsurance strategy) and the efficient frontier are derived explicitly.

  • Xin MA, Xiao Yan YANG
    Acta Mathematica Sinica, Chinese Series. 2020, 63(1): 77-88. https://doi.org/10.12386/A2020sxxb0006
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    Let X be a subcategory of an abelian category A. We proceed by generalizing the homotopy resolutions of complexes to the relative version, which is important basis making the relative derived category operational. We prove that every bounded above complex has a dg X resolution. Furthermore, we also show that the existence of resolutions for any unbounded complex when A=R-Mod and X is a particular subcategory. Finally, we establish a colocalization sequence of the homotopy category K(A) involving the relative derived category DX (A) under some condition.

  • Na Na LUAN
    Acta Mathematica Sinica, Chinese Series. 2020, 63(1): 89-96. https://doi.org/10.12386/A2020sxxb0007
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    Let XH={XHt, t ∈ R+} be a subfractional Brownian motion in Rd. We establish sharp Hölder conditions and tail probability estimates for the local times of XH in one-parameter case. We also give the existence and the L2-representation for the local time of XH in multi-parameter case.