3,794 research outputs found
Statistical-grey consistent grey differential equation modelling
Includes abstract.
Includes bibliographical references (p. 152-156)
Contributions to statistical machine learning algorithm
This thesis's research focus is on computational statistics along with DEAR (abbreviation of differential equation associated regression) model direction, and that in mind, the journal papers are written as contributions to statistical machine learning algorithm literature
On the zeros of solutions of any order of derivative of second order linear differential equations taking small functions
In this paper, we investigate the hyper-exponent of convergence of zeros of , where is a solution of second or order linear differential equation, is an entire function satisfying or . We obtain some precise results which improve the previous results in [3, 5] and revise the previous results in [11, 13]. More importantly, these results also provide us a method to investigate the hyper-exponent of convergence of zeros of
The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron transfer rate processes
In this work, we revisit the electron transfer rate theory, with particular
interests in the distinct quantum solvation effect, and the characterizations
of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first
present a full account for the quantum solvation effect on the electron
transfer in Debye solvents, addressed previously in J. Theore. & Comput. Chem.
{\bf 5}, 685 (2006). Distinct reaction mechanisms, including the quantum
solvation-induced transitions from barrier-crossing to tunneling, and from
barrierless to quantum barrier-crossing rate processes, are shown in the fast
modulation or low viscosity regime. This regime is also found in favor of
nonadiabatic rate processes. We further propose to use Kubo's motional
narrowing line shape function to describe the Markovian character of the
reaction. It is found that a non-Markovian rate process is most likely to occur
in a symmetric system in the fast modulation regime, where the electron
transfer is dominant by tunneling due to the Fermi resonance.Comment: 13 pages, 10 figures, submitted to J. Phys. Chem.
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