A quark meson coupling model with density- and temperature- dependent quark masses

Based on the quark mass density- and temperature- dependent model we suggest a model for nuclear matter where the meson field is introduced to be directly coupled to the quarks. The dynamic formation of the nucleon bag, the saturation properties of nuclear matter as well as equation of state for this model are studies.Comment: 4 pages, 2 figure

Topological Crystalline Insulator Nanomembrane with Strain-Tunable Band Gap

The ability to fine-tune band gap and band inversion in topological materials is highly desirable for the development of novel functional devices. Here we propose that the electronic properties of a free-standing nanomembrane of topological crystalline insulator (TCI) SnTe and Pb$_{1-x}$Sn$_x$(Se,Te) are highly tunable by engineering elastic strain and controlling membrane thickness, resulting in tunable band gap and giant piezoconductivity. Membrane thickness governs the hybridization of topological electronic states on opposite surfaces, while elastic strain can further modulate the hybridization strength by controlling the penetration length of surface states. We propose a frequency-resolved infrared photodetector using force-concentration induced inhomogeneous elastic strain in TCI nanomembrane with spatially varying width. The predicted tunable band gap accompanied by strong spin-textured electronic states will open up new avenues for fabricating piezoresistive devices, thermoelectrics, infrared detectors and energy-efficient electronic and optoelectronic devices based on TCI nanomembrane.Comment: 10 pages, 9 figure

Backward stochastic dynamics on a filtered probability space

We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation formulate are needed. This approach provides new tools for the study of BSDE, and is particularly useful for the study of BSDE with partial information. The approach allows us to study the following type of backward stochastic differential equations: $$dY_t^j=-f_0^j(t,Y_t,L(M)_t) dt-\sum_{i=1}^df_i^j(t,Y_t), dB_t^i+dM_t^j$$ with $Y_T=\xi$, on a general filtered probability space $(\Omega,\mathcal{F},\mathcal{F}_t,P)$, where $B$ is a $d$-dimensional Brownian motion, $L$ is a prescribed (nonlinear) mapping which sends a square-integrable $M$ to an adapted process $L(M)$ and $M$, a correction term, is a square-integrable martingale to be determined. Under certain technical conditions, we prove that the system admits a unique solution $(Y,M)$. In general, the associated partial differential equations are not only nonlinear, but also may be nonlocal and involve integral operators.Comment: Published in at http://dx.doi.org/10.1214/10-AOP588 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation.Comment: 26 page