Simple formulas for the number of different cyclic and dihedral necklaces containing nj beads of the j-th color, and , are derived, using the Pólya enumeration theorem.
In this paper,for 1<p<∞,the authors show that the coarse l^(p)-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s Property(H).
Fractional linear maps have played a key role in mathematical biology,population dynamics,and other research areas.In this paper,a special kind of Ricatti map is studied in detail in order to determine the asymptotica...Fractional linear maps have played a key role in mathematical biology,population dynamics,and other research areas.In this paper,a special kind of Ricatti map is studied in detail in order to determine the asymptotical behaviors of fixed points and periodic solutions.Making use of composition operation of maps and the methods of dynamical systems and qualitative theory,fixed points or periodic orbits are expressed precisely,average value of periodic solution is estimated concretely,and several different bounds are obtained for periodic solutions of the Beverton⁃Holt map when both intrinsic growth rate and carrying capacity change periodically.In addition,some sufficient conditions are given about the attenuation of periodic solution of the non⁃autonomous Beverton⁃Holt equation.Compared with present works in literature,our results about bounds of periodic solutions are more precise,and our proofs about the attenuation of periodic solution are more concise.展开更多
文摘Simple formulas for the number of different cyclic and dihedral necklaces containing nj beads of the j-th color, and , are derived, using the Pólya enumeration theorem.
基金supported by the National Natural Science Foundation of China(Nos.12171156)the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014)。
文摘In this paper,for 1<p<∞,the authors show that the coarse l^(p)-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu’s Property(H).
文摘Fractional linear maps have played a key role in mathematical biology,population dynamics,and other research areas.In this paper,a special kind of Ricatti map is studied in detail in order to determine the asymptotical behaviors of fixed points and periodic solutions.Making use of composition operation of maps and the methods of dynamical systems and qualitative theory,fixed points or periodic orbits are expressed precisely,average value of periodic solution is estimated concretely,and several different bounds are obtained for periodic solutions of the Beverton⁃Holt map when both intrinsic growth rate and carrying capacity change periodically.In addition,some sufficient conditions are given about the attenuation of periodic solution of the non⁃autonomous Beverton⁃Holt equation.Compared with present works in literature,our results about bounds of periodic solutions are more precise,and our proofs about the attenuation of periodic solution are more concise.
