A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.
In this paper,we address the existence and asymptotic analysis of higher-dimensional contrast structure of singularly perturbed Dirichlet problem.Based on the existence,an asymptotical analysis of a steplike contrast structure (i.e.,an internal transition layer solution) is studied by the boundary function method via a proposed smooth connection.In the framework of this paper,we propose a first integral condition,under which the existence of a heteroclinic orbit connecting two equilibrium points is ensured in a higher-dimensional fast phase space.Then,the step-like contrast structure is constructed,and the internal transition time is determined.Meanwhile,the uniformly valid asymptotical expansion of such an available step-like contrast structure is obtained.Finally,an example is presented to illustrate the result.
The impulsive solution for a semi-linear singularly perturbed differential-difference equation is studied. Using the methods of boundary function and fractional steps, we construct the formula asymptotic expansion of the problem. At the same time, Based on sewing techniques, the existence of the smooth impulsive solution and the uniform validity of the asymptotic expansion are proved.
Functional magnetic resonance imaging（fMRI）is one of the most commonly used methods in cognitive neuroscience on humans.In recent decades,fMRI has also been used in the awake monkey experiments to localize functional brain areas and to compare the functional differences between human and monkey brains.Several procedures and paradigms have been developed to maintain proper head fixation and to perform motion control training.In this study,we extended the application of fMRI to awake cats without training,receiving a flickering checkerboard visual stimulus projected to a screen in front of them in a block-design paradigm.We found that body movement-induced non-rigid motion introduced artifacts into the functional scans,especially those around the eye and neck.To correct for these artifacts,we developed two methods：one for general experimental design,and the other for studies of whether a checkerboard task could be used as a localizer to optimize the motioncorrection parameters.The results demonstrated that,with proper animal fixation and motion correction procedures,it is possible to perform fMRI experiments with untrained awake cats.
Manxiu MaChencan QianYanxia LiZhentao ZuoZuxiang Liu
The human visual system is tuned to the motions of biological entities, which provide potentially vital information for survival. The current study examines the interplay between motion speed and motion direction perception. Following a brief presentation of a point-light walker walking straight ahead or slightly leftward or rightward, observers were asked to quickly judge the walking direction (left or right). Participants showed better direction discrimination when the walker walked at a fast pace compared to a natural or slow pace, and this was not simply due to a difference in motion cycles. Moreover, walking direction sensitivity could be enhanced by increasing the feet motion speed alone, so long as the direction of feet movement was consistent with that of the other body parts. These findings demonstrate that our perception of walking direction is influenced by local motion speed, and highlight the role of the feet in biological motion perception.
