Since the D-band center theory was proposed,it has been widely used in the fields of surface chemistry by almost all researchers,due to its easy understanding,convenient operation and relative accuracy.However,with th...Since the D-band center theory was proposed,it has been widely used in the fields of surface chemistry by almost all researchers,due to its easy understanding,convenient operation and relative accuracy.However,with the continuous development of material systems and modification strategies,researchers have gradually found that D-band center theory is usually effective for large metal particle systems,but for small metal particle systems or semiconductors,such as single atom systems,the opposite conclusion to the D-band center theory is often obtained.To solve the issue above,here we propose a bonding and anti-bonding orbitals stable electron intensity difference(BASED)theory for surface chemistry.The newly-proposed BASED theory can not only successfully explain the abnormal phenomena of D-band center theory,but also exhibits a higher accuracy for prediction of adsorption energy and bond length of intermediates on active sites.Importantly,a new phenomenon of the spin transition state in the adsorption process is observed based on the BASED theory,where the active center atom usually yields an unstable high spin transition state to enhance its adsorption capability in the adsorption process of intermediates when their distance is about 2.5Å.In short,the BASED theory can be considered as a general principle to understand catalytic mechanism of intermediates on surfaces.展开更多
Using the radius of gyration from fractal theory, this paper describes the calculation of fractal dimensions for the four tiers of central places in the Jilin Central Urban Agglomeration(JCUA), Jilin Province, China a...Using the radius of gyration from fractal theory, this paper describes the calculation of fractal dimensions for the four tiers of central places in the Jilin Central Urban Agglomeration(JCUA), Jilin Province, China and the structural characteristics of each tier: 1) the 1st tier central place, Changchun Proper(not including Shuangyang District), provides the most service functions and has the most stable primate position; 2) the 2nd tier central places, Jilin Proper, Siping Proper, Liaoyuan Proper and Songyuan Proper have unclear statuses and do not provide certain functions; 3) the 3rd tier central places comprise 23 county-level cities, counties and urban districts(including Shuangyang District of Changchun), exhibiting a dense spatial structure that agrees with theory; 4) the 4th tier contains the largest number of central places(248 designated towns), but they are loosely distributed. In this study, a spatial image of the JCUA was created, based on vectorized data of the urban settlement distribution, which was then modified and abstracted to create a hexagonal network covering the JCUA. Compared to the traditional central place model, the modified spatial image conforms to the K = 3 principle. In reality, however, the growth of some 3rd tier central places should be increased with the cities being upgraded to the 2nd tier so as to overcome that tier′s functional deficiency. The loose distribution in the 4th tier should also be changed. This apparent anomaly can be explained by the fact that the classic hexagon model used to describe the way market areas layout does not exist in the real world. However, this should not be viewed as an obstacle to using central place theory. If its assumptions are properly applied, it can still assist research into the spatial structure of regions.展开更多
The analytic response theory at density functional theory level is applied to investigate onephoton and two-photon absorption properties of a series of recently synthesized pyrene-core derivatives. The theoretical res...The analytic response theory at density functional theory level is applied to investigate onephoton and two-photon absorption properties of a series of recently synthesized pyrene-core derivatives. The theoretical results show that there are a few charge-transfer states for each compound in the lower energy region. The one-photon absorption properties of the five investigated compounds are highly consistent with those given by experimental measurements. The two-photon absorption intensities of the compounds are greatly enhanced with the increments of the molecular sizes, in which the two-photon absorption cross section of the four-branched compound is about 5.6 times of that of the mono-branched molecule. Fhrthermore, it is shown that the two-photon absorption properties are sensitive to the geometrical arrangements.展开更多
The planetary theory in the Great Expansion System(Dayan li大衍历,727 CE)is investigated,with a detailed example of Mars.In ancient Chinese astrology,the position of one planet and the relative positions of different ...The planetary theory in the Great Expansion System(Dayan li大衍历,727 CE)is investigated,with a detailed example of Mars.In ancient Chinese astrology,the position of one planet and the relative positions of different planets had important astrological significance.Thus,planetary theory is an important part of Chinese mathematical astronomy.The Great Expansion System,which was compiled by Yixing一行of the Tang唐dynasty(618–907 CE),provided many innovations in planetary theory.Based on the extant Treatises on Mathematical Harmonics and Astronomy(Lüli zhi律历志)in Chinese official histories,the Great Expansion System was the first Chinese astronomical system to include tables of the planetary equation of center and procedures for correcting the influence of the planetary equation of center on the position of a planet.It was also the first Chinese system to design a table of the planetary phases of motion for calculating the mean position of a planet,which was the basis for calculating the true position of the planet.In addition,Yixing proposed the concept of the precession of planetary perihelion and gave the values of the precession of planetary perihelion for the first time in ancient China.The innovations of the Great Expansion System regarding planetary theory established its important position in the history of Chinese astronomical systems.Mars is taken as a case study to investigate the planetary theory in the Great Expansion System,including the astronomical constants related to Mars,two important astronomical tables,namely the table of the equation of center and the table of the phase motion of Mars in one synodic period,and the procedures for calculating the position of Mars on any given day using the planetary and solar equations of center.Two questions are addressed.First,how did Yixing correct the influence of the equation of center of Mars on the time of mean conjunction and the mean position of Mars?Second,how did Yixing calculate the true position of Mars on any given day?The original text of the Great Expansion System is analyzed to show how Yixing developed the planetary theory in the Sui and early Tang periods and constructed a complete method for predicting the true positions of planets using the planetary and solar equations of center.展开更多
Based on the literature review on learner-centered classroom, this essay is to explore now to create a learner-centered classroom in Chinese context so as to design a workshop for those teaching professionals all over...Based on the literature review on learner-centered classroom, this essay is to explore now to create a learner-centered classroom in Chinese context so as to design a workshop for those teaching professionals all over China to create a learner-centered classroom. The workshop conducted mainly focuses on what is a learner-centered classroom, why and how to create a learner-centered classroom, meanwhile, it aims at helping the participants work out a practical framework which can be eventually put to their everyday teaching.展开更多
Comparing the relativistic and nonrelativistic frame works, we study the effect of the relativistic center-of-mass vector on the electric polarizability of a compound system.
Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding c...Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.展开更多
This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to...This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.展开更多
In Critique of Pure Reason, Kant explains his critical method "as an experiment" in metaphysics. The aim of that "experiment" is to establish "an entire revolution" in philosophical thinking, which was initiated...In Critique of Pure Reason, Kant explains his critical method "as an experiment" in metaphysics. The aim of that "experiment" is to establish "an entire revolution" in philosophical thinking, which was initiated by the Copernican revolution in cosmology in order to find the secure path, and its possibility application to metaphysics. Kant's aim in Critique of Pure Reason is to rescue metaphysics from a "blind groping" by undertaking a revolution in metaphysics as Copernicus has brought to cosmology. Kant's Copernican turn consists in the assertion that the possibility of knowledge requires that "the objects must conform to our cognition." From Kant's view, we can know only what we "construct," "make," or "produce" as a necessary condition of knowledge, but we cannot know the mind--independent external world, i.e., the world which is independent of us. Kant's epistemological constructivism is the central point to his Copernican revolution.展开更多
We study a neutral donor center (D^0) and a negatively charged donor center (D^-) trapped by a quantum dot, which is subjected to a Gaussian potential confinement. Calculations are made by using the method of nume...We study a neutral donor center (D^0) and a negatively charged donor center (D^-) trapped by a quantum dot, which is subjected to a Gaussian potential confinement. Calculations are made by using the method of numerical diagonalization of Hamiltonian within the effective-mass approximation. The dependence of the ground state of the neutral shallow donor and the negatively charged donor on the dot size and the potential depth is investigated. The same calculations performed with the parabolic approximation of the Gaussian potential lead to the results that are qualitatively and quantitatively different from each other.展开更多
The total photodetachment cross section of a linear triatomic anion is derived for arbitrary laser polarization direction. The cross section is ,shown to be strongly oscillatory when the laser polarization direction i...The total photodetachment cross section of a linear triatomic anion is derived for arbitrary laser polarization direction. The cross section is ,shown to be strongly oscillatory when the laser polarization direction is parallel to the axis of the system; the oscillation amplitude decreases and vanishes as the angle between the laser polarization and the anion axis increases and becomes perpendicular to the axis. The average cross section over the orientations of the triatomie system is also obtained. The cross section of the triatomic anion is compared with the cross section of a two-center system. We find there are two oscillation frequencies in the triatomie anion in contrast to only one oscillation frequency in the two-center case. Closed-orbit theory is used to explain the oscillations.展开更多
This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form ...This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form method, it is shown that the model not only undergoes codimension one(flip, Neimark-Sacker) bifurcation, but also undergoes cusp and resonance bifurcation(1:1 and 1:2) of codimension two. Further, it is found that the parity of delay has some effect on bifurcation behaviors. Finally, some numerical simulations are given to support the analytic results and explore complex dynamics, such as periodic orbits near homoclinic orbits, quasiperiodic orbits, and chaotic orbits.展开更多
Adjusting the suitable coupling constants in relativistic mean field(RMF) theory and focusing on thermal effect of an entropy per baryon(S) from 0 to 3, we investigate the composition and structure of massive protoneu...Adjusting the suitable coupling constants in relativistic mean field(RMF) theory and focusing on thermal effect of an entropy per baryon(S) from 0 to 3, we investigate the composition and structure of massive protoneutron stars corresponding PSR J1614-2230 and PSR J0348+0432. It is found that massive protoneutron stars(PNSs) have more hyperons than cold neutron stars. The entropy per baryon will stiffen the equation of state, and the influence on the pressure is more obvious at low density than high density, while the influence on the energy density is more obvious at high density than low density. It is found that higher entropy will give higher maximum mass, higher central temperature and lower central density. The entropy per baryon changes from 0 to 3, the radius of a PNS corresponding PSR J0348+0432 will increase from 12.86 km to 19.31 km and PSR J1612-2230 will increase from 13.03 km to 19.93 km.The entropy per baryon will raise the central temperature of massive PNSs in higher entropy per baryon, but the central temperature of massive PNSs maybe keep unchanged in lower entropy per baryon. The entropy per baryon will increase the moment of inertia of a massive protoneutron star, while decrease gravitational redshift of a massive neutron star.展开更多
A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multip...A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.展开更多
Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with...Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state.Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E* and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.展开更多
文摘Since the D-band center theory was proposed,it has been widely used in the fields of surface chemistry by almost all researchers,due to its easy understanding,convenient operation and relative accuracy.However,with the continuous development of material systems and modification strategies,researchers have gradually found that D-band center theory is usually effective for large metal particle systems,but for small metal particle systems or semiconductors,such as single atom systems,the opposite conclusion to the D-band center theory is often obtained.To solve the issue above,here we propose a bonding and anti-bonding orbitals stable electron intensity difference(BASED)theory for surface chemistry.The newly-proposed BASED theory can not only successfully explain the abnormal phenomena of D-band center theory,but also exhibits a higher accuracy for prediction of adsorption energy and bond length of intermediates on active sites.Importantly,a new phenomenon of the spin transition state in the adsorption process is observed based on the BASED theory,where the active center atom usually yields an unstable high spin transition state to enhance its adsorption capability in the adsorption process of intermediates when their distance is about 2.5Å.In short,the BASED theory can be considered as a general principle to understand catalytic mechanism of intermediates on surfaces.
基金Under the auspices of National Natural Science Foundation of China(No.41201162)
文摘Using the radius of gyration from fractal theory, this paper describes the calculation of fractal dimensions for the four tiers of central places in the Jilin Central Urban Agglomeration(JCUA), Jilin Province, China and the structural characteristics of each tier: 1) the 1st tier central place, Changchun Proper(not including Shuangyang District), provides the most service functions and has the most stable primate position; 2) the 2nd tier central places, Jilin Proper, Siping Proper, Liaoyuan Proper and Songyuan Proper have unclear statuses and do not provide certain functions; 3) the 3rd tier central places comprise 23 county-level cities, counties and urban districts(including Shuangyang District of Changchun), exhibiting a dense spatial structure that agrees with theory; 4) the 4th tier contains the largest number of central places(248 designated towns), but they are loosely distributed. In this study, a spatial image of the JCUA was created, based on vectorized data of the urban settlement distribution, which was then modified and abstracted to create a hexagonal network covering the JCUA. Compared to the traditional central place model, the modified spatial image conforms to the K = 3 principle. In reality, however, the growth of some 3rd tier central places should be increased with the cities being upgraded to the 2nd tier so as to overcome that tier′s functional deficiency. The loose distribution in the 4th tier should also be changed. This apparent anomaly can be explained by the fact that the classic hexagon model used to describe the way market areas layout does not exist in the real world. However, this should not be viewed as an obstacle to using central place theory. If its assumptions are properly applied, it can still assist research into the spatial structure of regions.
文摘The analytic response theory at density functional theory level is applied to investigate onephoton and two-photon absorption properties of a series of recently synthesized pyrene-core derivatives. The theoretical results show that there are a few charge-transfer states for each compound in the lower energy region. The one-photon absorption properties of the five investigated compounds are highly consistent with those given by experimental measurements. The two-photon absorption intensities of the compounds are greatly enhanced with the increments of the molecular sizes, in which the two-photon absorption cross section of the four-branched compound is about 5.6 times of that of the mono-branched molecule. Fhrthermore, it is shown that the two-photon absorption properties are sensitive to the geometrical arrangements.
基金supported by the National Social Science Fund of China for Lesser-Known Traditional Knowledge冷门绝学(Group Project)“Research on the Method to Calculate the Five Planets in Chinese Calendrical Systems”中国古代历法中的“步五星术”研究(20VJXT005)。
文摘The planetary theory in the Great Expansion System(Dayan li大衍历,727 CE)is investigated,with a detailed example of Mars.In ancient Chinese astrology,the position of one planet and the relative positions of different planets had important astrological significance.Thus,planetary theory is an important part of Chinese mathematical astronomy.The Great Expansion System,which was compiled by Yixing一行of the Tang唐dynasty(618–907 CE),provided many innovations in planetary theory.Based on the extant Treatises on Mathematical Harmonics and Astronomy(Lüli zhi律历志)in Chinese official histories,the Great Expansion System was the first Chinese astronomical system to include tables of the planetary equation of center and procedures for correcting the influence of the planetary equation of center on the position of a planet.It was also the first Chinese system to design a table of the planetary phases of motion for calculating the mean position of a planet,which was the basis for calculating the true position of the planet.In addition,Yixing proposed the concept of the precession of planetary perihelion and gave the values of the precession of planetary perihelion for the first time in ancient China.The innovations of the Great Expansion System regarding planetary theory established its important position in the history of Chinese astronomical systems.Mars is taken as a case study to investigate the planetary theory in the Great Expansion System,including the astronomical constants related to Mars,two important astronomical tables,namely the table of the equation of center and the table of the phase motion of Mars in one synodic period,and the procedures for calculating the position of Mars on any given day using the planetary and solar equations of center.Two questions are addressed.First,how did Yixing correct the influence of the equation of center of Mars on the time of mean conjunction and the mean position of Mars?Second,how did Yixing calculate the true position of Mars on any given day?The original text of the Great Expansion System is analyzed to show how Yixing developed the planetary theory in the Sui and early Tang periods and constructed a complete method for predicting the true positions of planets using the planetary and solar equations of center.
文摘Based on the literature review on learner-centered classroom, this essay is to explore now to create a learner-centered classroom in Chinese context so as to design a workshop for those teaching professionals all over China to create a learner-centered classroom. The workshop conducted mainly focuses on what is a learner-centered classroom, why and how to create a learner-centered classroom, meanwhile, it aims at helping the participants work out a practical framework which can be eventually put to their everyday teaching.
基金The project supported by National Natural Science Foundation of China under Grant No.10075056CAS Knowledge Innovation Project No.KC2-SW-N02 of the Institute of Theoretical Physics
文摘Comparing the relativistic and nonrelativistic frame works, we study the effect of the relativistic center-of-mass vector on the electric polarizability of a compound system.
文摘Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.
基金the Natural Science Foundation of China (No. 50075029)
文摘This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.
文摘In Critique of Pure Reason, Kant explains his critical method "as an experiment" in metaphysics. The aim of that "experiment" is to establish "an entire revolution" in philosophical thinking, which was initiated by the Copernican revolution in cosmology in order to find the secure path, and its possibility application to metaphysics. Kant's aim in Critique of Pure Reason is to rescue metaphysics from a "blind groping" by undertaking a revolution in metaphysics as Copernicus has brought to cosmology. Kant's Copernican turn consists in the assertion that the possibility of knowledge requires that "the objects must conform to our cognition." From Kant's view, we can know only what we "construct," "make," or "produce" as a necessary condition of knowledge, but we cannot know the mind--independent external world, i.e., the world which is independent of us. Kant's epistemological constructivism is the central point to his Copernican revolution.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475014 and the Natural Science Foundation of Guangdong Province under Grant No. 04009519
文摘We study a neutral donor center (D^0) and a negatively charged donor center (D^-) trapped by a quantum dot, which is subjected to a Gaussian potential confinement. Calculations are made by using the method of numerical diagonalization of Hamiltonian within the effective-mass approximation. The dependence of the ground state of the neutral shallow donor and the negatively charged donor on the dot size and the potential depth is investigated. The same calculations performed with the parabolic approximation of the Gaussian potential lead to the results that are qualitatively and quantitatively different from each other.
文摘The total photodetachment cross section of a linear triatomic anion is derived for arbitrary laser polarization direction. The cross section is ,shown to be strongly oscillatory when the laser polarization direction is parallel to the axis of the system; the oscillation amplitude decreases and vanishes as the angle between the laser polarization and the anion axis increases and becomes perpendicular to the axis. The average cross section over the orientations of the triatomie system is also obtained. The cross section of the triatomic anion is compared with the cross section of a two-center system. We find there are two oscillation frequencies in the triatomie anion in contrast to only one oscillation frequency in the two-center case. Closed-orbit theory is used to explain the oscillations.
基金supported by the National Priorities Research Program through the Qatar National Research Funda member of Qatar Foundation(Grant No.NPRP 4-1162-1-181)+2 种基金the Natural Science Foundation of China(Grant Nos.6140331361374078&61375102)the Natural Science Foundation Project of Chongqing CSTC(Grant No.cstc2014jcyj A40014)
文摘This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form method, it is shown that the model not only undergoes codimension one(flip, Neimark-Sacker) bifurcation, but also undergoes cusp and resonance bifurcation(1:1 and 1:2) of codimension two. Further, it is found that the parity of delay has some effect on bifurcation behaviors. Finally, some numerical simulations are given to support the analytic results and explore complex dynamics, such as periodic orbits near homoclinic orbits, quasiperiodic orbits, and chaotic orbits.
基金Supported by National Natural Science Foundation of China under Grant No.11175147
文摘Adjusting the suitable coupling constants in relativistic mean field(RMF) theory and focusing on thermal effect of an entropy per baryon(S) from 0 to 3, we investigate the composition and structure of massive protoneutron stars corresponding PSR J1614-2230 and PSR J0348+0432. It is found that massive protoneutron stars(PNSs) have more hyperons than cold neutron stars. The entropy per baryon will stiffen the equation of state, and the influence on the pressure is more obvious at low density than high density, while the influence on the energy density is more obvious at high density than low density. It is found that higher entropy will give higher maximum mass, higher central temperature and lower central density. The entropy per baryon changes from 0 to 3, the radius of a PNS corresponding PSR J0348+0432 will increase from 12.86 km to 19.31 km and PSR J1612-2230 will increase from 13.03 km to 19.93 km.The entropy per baryon will raise the central temperature of massive PNSs in higher entropy per baryon, but the central temperature of massive PNSs maybe keep unchanged in lower entropy per baryon. The entropy per baryon will increase the moment of inertia of a massive protoneutron star, while decrease gravitational redshift of a massive neutron star.
文摘A mathematical model describing the dynamics of toxin producing phytoplankton- zooplankton interaction with instantaneous nutrient recycling is proposed. We have explored the dynamics of plankton ecosystem with multiple delays; one due to gestation period in the growth of phytoplankton population and second due to the delay in toxin liberated by TPP. It is established that a sequence of Hopf bifurcations occurs at the interior equilibrium as the delay increases through its critical value. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined using the theory of normal form and center manifold. Meanwhile, effect of toxin on the stability of delayed plankton system is also established numerically. Finally, numerical simulations are carried out to support and supplement the analytical findings.
文摘Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state.Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E* and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.