This paper gives the existence of a relatively stable duck solution in a slow-fast system in R2＋2 with an invariant manifold. The slow-fast system in R2＋： has a 2-dimensional slow vector field and a 2-dimensional f...This paper gives the existence of a relatively stable duck solution in a slow-fast system in R2＋2 with an invariant manifold. The slow-fast system in R2＋： has a 2-dimensional slow vector field and a 2-dimensional fast vector field. The fast vector field restricts a feasible region of the slow vector field strictly. In the case of the slow-fast system in R2＋1 , that is, the fast vector field is l-dimension, it is classified according to its sign, because it gives only negative（-）, positive（＋） or zero sign. Then it is attractive, repulsive or stationary. On the other hand, in R2~2 , the fast vector field has combinatorial cases. It causes a complex state to analyze the system. First, we introduce a local model near the pseudo singular point on which we classify the fast vector field attractive（-,-）, attractive-repulsive（-,＋） or repulsive（＋,＋）, simply as possible. We prove the existence of a 4-dimensional duck solution in the local model. Secondarily, we assume that the slow-fast system has an invariant manifold near the pseudo singular point. When the invariant manifold has a homoclinic point near the pseudo singular point, we show that the slow-fast sytem has a 4-dimensional duck solution having a relatively stable region.展开更多
The strained cyclopropane and/or cyclobutane subunits occurred in many complex natural products including terpenoids, steroids and alkaloids. Natural products with cyclopropane and/or cyclobutane motifs not only furni...The strained cyclopropane and/or cyclobutane subunits occurred in many complex natural products including terpenoids, steroids and alkaloids. Natural products with cyclopropane and/or cyclobutane motifs not only furnished fascinating structures, but also exhibited versatile biological activities, such as cytotoxic, anti-HIM antimicrobial, antiviral, and immunosuppressive effects. This review covered a large array of structurally unique natural products with strained cyclopropane and/or cyclobutane motifs and summarized their structural features, distributions, biological activities, as well as biogenetic considerations.展开更多
Disentangling the influence of multiple signal components on receivers and elucidating general processes influencing complex signal evolution are difficult tasks. In this study we test mate preferences of female squir...Disentangling the influence of multiple signal components on receivers and elucidating general processes influencing complex signal evolution are difficult tasks. In this study we test mate preferences of female squirrel treefrogs Hyla squirella and female tungara frogs Physalaemus pustulosus for similar combinations of acoustic and visual components of their multimodal courtship signals. In a two-choice playback experiment with squirrel treefrogs, the visual stimulus of a male model significantly increased the attractivness of a relatively unattractive slow call rate. A previous study demonstrated that faster call rates are more attractive to female squirrel treefrogs, and all else being equal, models of male frogs with large body stripes are more attractive. In a similar experiment with female tungara frogs, the visual stimulus of a robotic frog failed to increase the attractiveness of a relatively unattractive call. Females also showed no preference for the distinct stripe on the robot that males commonly bear on their throat. Thus, features of conspicuous signal components such as body stripes are not universally important and signal function is likely to differ even among species with similar ecologies and communication systems. Finally, we discuss the putative information content of anuran signals and suggest that the categorization of redundant versus multiple messages may not be sufficient as a general explanation for the evolution of multimodal signaling. Instead of relying on untested assumptions concerning the information content of signals, we discuss the value of initially collecting comparative empirical data sets related to receiver responses.展开更多
Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exac...Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.展开更多
文摘This paper gives the existence of a relatively stable duck solution in a slow-fast system in R2＋2 with an invariant manifold. The slow-fast system in R2＋： has a 2-dimensional slow vector field and a 2-dimensional fast vector field. The fast vector field restricts a feasible region of the slow vector field strictly. In the case of the slow-fast system in R2＋1 , that is, the fast vector field is l-dimension, it is classified according to its sign, because it gives only negative（-）, positive（＋） or zero sign. Then it is attractive, repulsive or stationary. On the other hand, in R2~2 , the fast vector field has combinatorial cases. It causes a complex state to analyze the system. First, we introduce a local model near the pseudo singular point on which we classify the fast vector field attractive（-,-）, attractive-repulsive（-,＋） or repulsive（＋,＋）, simply as possible. We prove the existence of a 4-dimensional duck solution in the local model. Secondarily, we assume that the slow-fast system has an invariant manifold near the pseudo singular point. When the invariant manifold has a homoclinic point near the pseudo singular point, we show that the slow-fast sytem has a 4-dimensional duck solution having a relatively stable region.
基金supported by the National Natural Science Foundation of China (21532007)
文摘The strained cyclopropane and/or cyclobutane subunits occurred in many complex natural products including terpenoids, steroids and alkaloids. Natural products with cyclopropane and/or cyclobutane motifs not only furnished fascinating structures, but also exhibited versatile biological activities, such as cytotoxic, anti-HIM antimicrobial, antiviral, and immunosuppressive effects. This review covered a large array of structurally unique natural products with strained cyclopropane and/or cyclobutane motifs and summarized their structural features, distributions, biological activities, as well as biogenetic considerations.
文摘Disentangling the influence of multiple signal components on receivers and elucidating general processes influencing complex signal evolution are difficult tasks. In this study we test mate preferences of female squirrel treefrogs Hyla squirella and female tungara frogs Physalaemus pustulosus for similar combinations of acoustic and visual components of their multimodal courtship signals. In a two-choice playback experiment with squirrel treefrogs, the visual stimulus of a male model significantly increased the attractivness of a relatively unattractive slow call rate. A previous study demonstrated that faster call rates are more attractive to female squirrel treefrogs, and all else being equal, models of male frogs with large body stripes are more attractive. In a similar experiment with female tungara frogs, the visual stimulus of a robotic frog failed to increase the attractiveness of a relatively unattractive call. Females also showed no preference for the distinct stripe on the robot that males commonly bear on their throat. Thus, features of conspicuous signal components such as body stripes are not universally important and signal function is likely to differ even among species with similar ecologies and communication systems. Finally, we discuss the putative information content of anuran signals and suggest that the categorization of redundant versus multiple messages may not be sufficient as a general explanation for the evolution of multimodal signaling. Instead of relying on untested assumptions concerning the information content of signals, we discuss the value of initially collecting comparative empirical data sets related to receiver responses.
文摘Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.
