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Global Attractivity Of A Circadian Pacemaker Model In A Periodic Environment, Yuming Chen, Lin Wang
Global Attractivity Of A Circadian Pacemaker Model In A Periodic Environment, Yuming Chen, Lin Wang
Mathematics Faculty Publications
In this paper, we propose a delay differential equation with continuous periodic parameters to model the circadian pacemaker in a periodic environment. First, we show the existence of a positive periodic solution by using the theory of coincidence degree. Then we establish the global attractivity of the periodic solution under two su±cient conditions. These conditions are easily verifiable and are independent of each other. Some numerical simulations are also performed to demonstrate the main results.
Accounting For Nonlinearities In Mathematical Modelling Of Quantum Dot Molecules, Roderick V.N. Melnik, Benny Lassen, L.C. Lew Yan Voon, Morten Willatzen, Calin Galeriu
Accounting For Nonlinearities In Mathematical Modelling Of Quantum Dot Molecules, Roderick V.N. Melnik, Benny Lassen, L.C. Lew Yan Voon, Morten Willatzen, Calin Galeriu
Mathematics Faculty Publications
Nonlinear mathematical models are becoming increasingly important for new applications of low-dimensional semiconductor structures. Examples of such structures include quasi-zero-dimensional quantum dots that have potential applications ranging from quantum computing to nano-biological devices. In this contribution, we analyze presently dominating linear models for bandstructure calculations and demonstrate why nonlinear models are required for characterizing adequately opto- electronic properties of self-assembled quantum dots.
A General Treatment Of Deformation Effects In Hamiltonians For Inhomogeneous Crystalline Materials, Benny Lassen, Morten Willatzen, Roderick V.N. Melnik, L.C. Lew Yan Voon
A General Treatment Of Deformation Effects In Hamiltonians For Inhomogeneous Crystalline Materials, Benny Lassen, Morten Willatzen, Roderick V.N. Melnik, L.C. Lew Yan Voon
Mathematics Faculty Publications
In this paper, a general method of treating Hamiltonians of deformed nanoscale systems is proposed. This method is used to derive a second-order approximation both for the strong and weak formulations of the eigenvalue problem. The weak formulation is needed in order to allow deformations that have discontinuous first derivatives at interfaces between different materials. It is shown that, as long as the deformation is twice differentiable away from interfaces, the weak formulation is equivalent to the strong formulation with appropriate interface boundary conditions. It is also shown that, because the Jacobian of the deformation appears in the weak formulation, …
Jordan Decomposition In Bilinear Forms, Dragomir Ž. Đokovic, Kaiming Zhao
Jordan Decomposition In Bilinear Forms, Dragomir Ž. Đokovic, Kaiming Zhao
Mathematics Faculty Publications
No abstract provided.