Browsing by Author "Ma, J."

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    Set-valued backward stochastic differential equations
    (Institute of Mathematical Statistics, 2023-10) Ararat, Çağın; Ma, J.; Wu, W.
    In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of the Hukuhara difference between sets, in order to compensate the lack of “inverse” operation of the traditional Minkowski addition, whence the vector space structure in set-valued analysis. While proving the well-posedness of a class of set-valued BSDEs, we shall also address some fundamental issues regarding generalized Aumann–Itô integrals, especially when it is connected to the martingale representation theorem. In particular, we propose some necessary extensions of the integral that can be used to represent set-valued martingales with nonsingleton initial values. This extension turns out to be essential for the study of set-valued BSDEs.
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    Tailoring insoluble nanobelts into soluble anti-UV nanopotpourris
    (Royal Society of Chemistry, 2011) Wang, J.; Sun, X. W.; Jiao, Z.; Khoo, E.; Lee, P. S.; Ma, J.; Demir, Hilmi Volkan
    Soluble, transparent and anti-UV nanopotpourris have been prepared by tailoring long nanobelts. The strains and layered structures facilitate the breaking of the as-synthesized nanobelts under an applied mechanical action. The developed tailoring process of nanobelts is a general top-down secondary processing of layered nanostructures at the nanoscale level, which can be expended to the modifications of layered nanowires, nanotubes and hierarchical nanostructures. By tailoring, the size, morphology and solubility are modified, which may open up an area of advanced processing of nanomaterials and hint at some potential applications. Because of the excellent solubility of the tailored nanopotpourris, they are easily dispersed in cosmetics or polymer films, which are quite useful for some anti-UV protection applications, such as anti-UV sunscreen creams and anti-UV window films for vehicles and buildings.