Zhang Y.,Hexi University
Journal of Computational and Nonlinear Dynamics | Year: 2013
This paper presents the formulation of the time-fractional Camassa-Holm equation using the Euler-Lagrange variational technique in the Riemann-Liouville derivative sense and derives an approximate solitary wave solution. Our results witness that He's variational iteration method was a very efficient and powerful technique in finding the solution of the proposed equation. Copyright © 2013 by ASME.
Yan Z.,Hexi University
IMA Journal of Mathematical Control and Information | Year: 2013
In this paper, we prove the approximate controllability of control systems governed by a class of partial fractional neutral integro-differential inclusions with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the fixed-point theorem for discontinuous multi-valued operators due to Dhage with the α-resolvent operator. An example is provided to illustrate the main results. © 2012 The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
He Y.-L.,Hexi University
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011
We have applied a nonperturbative resonant theory to study the Rabi frequency of microwave multiphoton transitions between two Rydberg states of potassium in a static electric field. The Stark electric dipole moments used to calculate the Rabi frequency are determined by the Stark states' wave functions, which are obtained by the diagonalization method. The frequencies of the Rabi oscillations are in good agreement with either experimental ones or ones calculated by the time-dependent close-coupling method and the Floquet theory. Furthermore, we are able to show that the size of avoided crossings between the (n+2)s and (n,3) states can be predicted from the Stark electric dipole moment and the difference of the two Stark states' energy at a given resonance. © 2011 American Physical Society.
He Y.-L.,Hexi University
Journal of Physics B: Atomic, Molecular and Optical Physics | Year: 2012
We have presented a novel method to calculate the widths of the avoided crossings of Rydberg states in a static electric field. The widths of avoided crossings can be decided not directly connected by scanning the static field, but indirectly connected through the Stark electric dipole moments. The method is restricted to the case in which both the two relevant states have linear Stark shifts or only one of the two involved states has linear Stark shifts, but another has no Stark shift. As test examples, we calculated the widths of avoided crossings of Li, Na and K. The Stark electric dipole moments are determined by using the Stark state wavefunctions which are obtained from the diagonalization method at a fixed static electric field amplitude. The results are in excellent agreement with experimental and other theoretical data.
Zeng X.,Hexi University |
Tong D.,China University of Petroleum - East China
Shiyou Kantan Yu Kaifa/Petroleum Exploration and Development | Year: 2011
To solve the problem of optimal horizontal length design, reasonable hypothesis and simplification were conducted for the flow in horizontal wells in reservoirs using the filtration mechanic theory. Based on the model proposed by Fan Zifei, et al., fully considering the effects of various drilling costs and petroleum prices on horizontal length design, a new model to calculate the optimal length of horizontal section was derived. At the same time, productivity calculation error is introduced into Fan Zifei's method, and according to case calculation, the effects of horizontal length, flow rate in well, wellbore coarse degree, fluid viscosity, reservoir permeability, wellbore diameter on the horizontal well production and productivity calculation error were analyzed. The results indicate that, for a given reservoir, the main factors affecting horizontal well production and productivity error are horizontal length, wellbore coarse degree and wellbore diameter; for a particular horizontal well, the main factors affecting horizontal well production and productivity calculation error are fluid viscosity, reservoir permeability and flow rate in the well.
Yan Z.,Hexi University |
Yan X.,Hexi University
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2013
This paper discusses a class of impulsive nonlocal stochastic functional integrodifferential inclusions in a real separable Hilbert space. The existence of mild solutions of these inclusions is determined under the mixed continuous and Carathéodory conditions by using Bohnenblust-Karlin's fixed point theorem and fractional operators combined with approximation techniques. An example is provided to illustrate the theory. © 2012 Springer Basel AG.
Li J.,Hexi University
Journal of Networks | Year: 2014
In this paper, I consider nonlinear parabolic problems under nonlinear boundary conditions. I establish respectively the conditions on nonlinearities to guarantee that u(x,t) exists globally or blows up at some finite time. If blow-up occurs, an upper bound for the blow-up time is derived, under somewhat more restrictive conditions, lower bounds for the blow-up time are also derived. © 2014 ACADEMY PUBLISHER.
Yang C.-F.,Hexi University
Computers and Mathematics with Applications | Year: 2011
In this paper, the notions of fuzzy soft semigroup and fuzzy soft (left, right) ideal are given, and the α-level set, union and intersection of them were studied for each α∈[0,1]. Finally, fuzzy soft image and fuzzy soft inverse image of fuzzy soft semigroup (ideal) are discussed. © 2010 Elsevier Ltd. All rights reserved.
Yan Z.,Hexi University
Journal of the Franklin Institute | Year: 2011
In this paper, a sufficient condition is established for the controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay in Banach spaces. The approach used is analytic semigroups and fractional powers of closed operators and nonlinear alternative of LeraySchauder type for multivalued maps due to D. ORegan. © 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Yan Z.,Hexi University
International Journal of Control | Year: 2012
We prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the Krasnoselskii-Schaefer type fixed point theorem with the fractional power of operators. An example is provided to illustrate the main results. © 2012 Taylor & Francis.