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The closed finite-to-one mappings and their applications
YANG Jie, LIN Shou
Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 149-.
https://doi.org/10.1007/s11766-019-3557-7
In this paper, we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications. It is proved that point-G properties, @0-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings. By the relationships between the weak first-countabilities, we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability, quasi-first-countability, snf-countability, gf- countability and sof-countability. Furthermore, these results are applied to the study of symmetric products of topological spaces.
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Wiener Index, Hyper-Wiener Index, Harary Index and Hamiltonicity Properties of graphs
YU Gui-dong, REN Li-fang, LI Xing-xing
Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 162-.
https://doi.org/10.1007/s11766-019-3565-9
In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we first give some sufficient conditions for a nearly balance bipartite graph with given minimum degree to be traceable. Secondly, we establish some conditions for a k-connected graph to be Hamilton-connected and traceable for every vertex, respectively.
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The geometrical properties of parity and time reversal operators in two dimensional spaces
HUANG Min-yi, YANG Yu, WU Jun-de, CHO Min-Hyung
Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 173-.
https://doi.org/10.1007/s11766-017-3568-6
The parity operator P and time reversal operator T are two important operators in the quantum theory, in particular, in the PT -symmetric quantum theory. By using the concrete forms of P and T , we discuss their geometrical properties in two dimensional spaces. It is showed that if T is given, then all P links with the quadric surfaces; if P is given, then all T links with the quadric curves. Moreover, we give out the generalized unbroken PT -symmetric condition of an operator. The unbroken PT -symmetry of a Hermitian operator is also showed in this way.
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Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion
FEI Chen, FEI Wei-yin, YAN Li-tan
Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 184-.
https://doi.org/10.1007/s11766-019-3619-x
Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper, by using Peng’s G-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by G-Brownian motion (G-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.
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Econometric modeling of risk measures: A selective review of the recent literature
TIAN Ding-shi, CAI Zong-wu, FANG Ying
Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 205-.
https://doi.org/10.1007/s11766-019-3628-9
Since the financial crisis in 2008, the risk measures which are the core of risk management, have received increasing attention among economists and practitioners. In this review, the concentration is on recent developments in the estimation of the most popular risk measures, namely, value at risk (VaR), expected shortfall (ES), and expectile. After introducing the concept of risk measures, the focus is on discussion and comparison of their econometric modeling. Then, parametric and nonparametric estimations of tail dependence are investigated. Finally, we conclude with insights into future research directions.
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7 articles
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