Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the gr...Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou＇s direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.展开更多
Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of （2＋1）-dimensional Boussinesq equation. An auto-Backlund transformation and a number of ...Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of （2＋1）-dimensional Boussinesq equation. An auto-Backlund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass ＆ function. Some of them are novel.展开更多
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋1）-dimensional breaking soliton system. By introducing Jacobi elliptic functions in...Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋1）-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.展开更多
A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue ...A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue models are also derivable from birth-death processes. These queue models consist of mathematical formulas and relationships that can be used to determine the operating characteristics （performance measures） for a waiting line. Schematic and transition diagrams of different single server queue models were shown. Relationships between birth-death processes, waiting lines （queues） and transition diagrams were given. While M/M/I/K queue model states was limited by K customers and had （K＋I） states, M/M/1/1 queue model had only two states. M/G/1/∝/∝ and M/M/1/∝/∝ shared similar characteristics. Many ideal queuing situations employ M/M/1 queueing model.展开更多
Infection of human immunodeficiency virus （HIV） is determined through the decay of healthy CD44- T-cells in a well-mixed compartment, such as a bloodstream. A mathe- matical model is considered to illustrate the eff...Infection of human immunodeficiency virus （HIV） is determined through the decay of healthy CD44- T-cells in a well-mixed compartment, such as a bloodstream. A mathe- matical model is considered to illustrate the effects of combined drug therapy, i.e. reverse transcription plus protease inhibitor, on viral growth and T-cell population dynamics. This model is used to explain the existence and stability of infected and uninfected steady states in HIV growth. An analytical technique, called variational iteration method （VIM）, is used to solve the mathematical model. This method is modified to obtain the rapidly convergent successive approximations of the exact solution. These approximations are obtained without any restrictions or the transformations that may change the physical behavior of the problem. Numerical simulations are computed and exhibited to illustrate the effects of proposed drug therapy on the growth or decay of infection.展开更多
In this paper, we revisit the model by Guedj et al. [J. Guedj, R. Thibaut and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics 63 （2007） 198-206; J. Guedj, R. Thibaut and D. Commeng...In this paper, we revisit the model by Guedj et al. [J. Guedj, R. Thibaut and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics 63 （2007） 198-206; J. Guedj, R. Thibaut and D. Commenges, Practical identifiability of HIV dynamics models, Bull. Math. Biol. 69 （2007） 2493 2513] which describes the effect of treatment with reverse transcriptase （RT） inhibitors and incorporates the class of quiescent cells. We prove that there is a threshold value 7 of drug efficiency η such that if η 〉 7, the basic reproduction number R0 〈 1 and the infection is cleared and if η〈 η^-, the infectious equilibrium is globally asymptotically stable. When the drug efficiency function η（t） is periodic and of the bang-bang type we establish a threshold, in terms of spectral radius of some matrix, between the clearance and the persistence of the disease. As stated in related works [L. Rong, Z. Feng and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol. 69 （2007） 2027-2060; P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bull. Math. Biol. 71 （2009） 189-210.], we prove that the increase of the drug efficiency or the active duration of drug must clear the infection more quickly. We illustrate our results by some numerical simulations.展开更多
Circulating leukocytes in trafficking to the inflammatory sites, will be first tether to, and then roll on the vascular surface. This event is mediated through specific interaction of P-selectin and P-selectin glycopr...Circulating leukocytes in trafficking to the inflammatory sites, will be first tether to, and then roll on the vascular surface. This event is mediated through specific interaction of P-selectin and P-selectin glycoprotein ligand-1 （PSGL-1）, and regulated by hemodynamics. Poor data were reported in understanding P-selectin-mediated rolling. With the flow chamber technique, we herein observed HL-60 cell rolling on P-selectin with or without 3% Ficoll at various wall shear stresses from 0.05 to 0.4 dyn/cm：. The results demonstrated that force rather than transport regulated the rolling, similar to rolling on L- and E-selectin. The rolling was accelerated quickly by an increasing force below the optimal shear threshold of 0.15 dyn/cm2 first and then followed by a slowly decelerating phase starting at the optimum, showing a catch-slip transition and serving as a mechanism for the rolling. The catch-slip transition was completely reflected to the tether lifetime and other rolling parameters, such as the mean and fractional stop time. The narrow catch bond regime stabilized the rolling quickly, through steeply increasing frac- tional stop time to a plateau of about 0.85. Data presented here suggest that the low shear stress threshold serves as a mecha- nism for most cell rolling events through P-selectin.展开更多
基金the State Key Basic Research Program of China under Grant No.2004CB318000
文摘Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou＇s direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.
基金National Natural Science Foundation of China under Grant No.10761005the Natural Science Foundation of Inner Mongolia under Grant No.200607010104
文摘Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of （2＋1）-dimensional Boussinesq equation. An auto-Backlund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass ＆ function. Some of them are novel.
基金National Natural Science Foundation of China under Grant No.10272071the Natural Science Foundation of Zhejiang Province under Grant No.Y504111the Scientific Research Foundation of Huzhou University
文摘Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the （2＋1）-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.
文摘A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue models are also derivable from birth-death processes. These queue models consist of mathematical formulas and relationships that can be used to determine the operating characteristics （performance measures） for a waiting line. Schematic and transition diagrams of different single server queue models were shown. Relationships between birth-death processes, waiting lines （queues） and transition diagrams were given. While M/M/I/K queue model states was limited by K customers and had （K＋I） states, M/M/1/1 queue model had only two states. M/G/1/∝/∝ and M/M/1/∝/∝ shared similar characteristics. Many ideal queuing situations employ M/M/1 queueing model.
文摘Infection of human immunodeficiency virus （HIV） is determined through the decay of healthy CD44- T-cells in a well-mixed compartment, such as a bloodstream. A mathe- matical model is considered to illustrate the effects of combined drug therapy, i.e. reverse transcription plus protease inhibitor, on viral growth and T-cell population dynamics. This model is used to explain the existence and stability of infected and uninfected steady states in HIV growth. An analytical technique, called variational iteration method （VIM）, is used to solve the mathematical model. This method is modified to obtain the rapidly convergent successive approximations of the exact solution. These approximations are obtained without any restrictions or the transformations that may change the physical behavior of the problem. Numerical simulations are computed and exhibited to illustrate the effects of proposed drug therapy on the growth or decay of infection.
文摘In this paper, we revisit the model by Guedj et al. [J. Guedj, R. Thibaut and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics 63 （2007） 198-206; J. Guedj, R. Thibaut and D. Commenges, Practical identifiability of HIV dynamics models, Bull. Math. Biol. 69 （2007） 2493 2513] which describes the effect of treatment with reverse transcriptase （RT） inhibitors and incorporates the class of quiescent cells. We prove that there is a threshold value 7 of drug efficiency η such that if η 〉 7, the basic reproduction number R0 〈 1 and the infection is cleared and if η〈 η^-, the infectious equilibrium is globally asymptotically stable. When the drug efficiency function η（t） is periodic and of the bang-bang type we establish a threshold, in terms of spectral radius of some matrix, between the clearance and the persistence of the disease. As stated in related works [L. Rong, Z. Feng and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol. 69 （2007） 2027-2060; P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bull. Math. Biol. 71 （2009） 189-210.], we prove that the increase of the drug efficiency or the active duration of drug must clear the infection more quickly. We illustrate our results by some numerical simulations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11272125,11072080,31170887 and 31200705)Guangdong Natural Science Foundation(Grant No.S2011010005451)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20110172110030)
文摘Circulating leukocytes in trafficking to the inflammatory sites, will be first tether to, and then roll on the vascular surface. This event is mediated through specific interaction of P-selectin and P-selectin glycoprotein ligand-1 （PSGL-1）, and regulated by hemodynamics. Poor data were reported in understanding P-selectin-mediated rolling. With the flow chamber technique, we herein observed HL-60 cell rolling on P-selectin with or without 3% Ficoll at various wall shear stresses from 0.05 to 0.4 dyn/cm：. The results demonstrated that force rather than transport regulated the rolling, similar to rolling on L- and E-selectin. The rolling was accelerated quickly by an increasing force below the optimal shear threshold of 0.15 dyn/cm2 first and then followed by a slowly decelerating phase starting at the optimum, showing a catch-slip transition and serving as a mechanism for the rolling. The catch-slip transition was completely reflected to the tether lifetime and other rolling parameters, such as the mean and fractional stop time. The narrow catch bond regime stabilized the rolling quickly, through steeply increasing frac- tional stop time to a plateau of about 0.85. Data presented here suggest that the low shear stress threshold serves as a mecha- nism for most cell rolling events through P-selectin.
