High-order harmonics are generated by coherent interaction of an intense laser and atoms or molecules[1]. With the development of the intense ultrashort pulse laser, the research of high-order harmonic generation has reached the water-window in spectral region[2] and subfemtosecond in time domain[3]. Especially, the generation and application of subfemtosecond pulse led the study of high-order harmonic generation into a completely new world[4, 5]. It has made the study of ultrafast science fro… 相似文献
In 1990, Gutman and Mizoguchi conjectured that all roots of the -polynomial (G,C,x) of a graph G are real. Since then, there has been some literature intending to solve this conjecture. However, in all existing literature, only classes of graphs were found to show that the conjecture is true; for example, monocyclic graphs, bicyclic graphs, graphs such that no two circuits share a common edge, graphs without 3-matchings, etc, supporting the conjecture in some sense. Yet, no complete solution has been given. In this paper, we show that the conjecture is true for all graphs, and therefore completely solve this conjecture. 相似文献
A theorem of M. F. Driscoll says that, under certain restrictions, the probability that a given Gaussian process has its sample paths almost surely in a given reproducing kernel Hilbert space (RKHS) is either or . Driscoll also found a necessary and sufficient condition for that probability to be .
Doing away with Driscoll's restrictions, R. Fortet generalized his condition and named it nuclear dominance. He stated a theorem claiming nuclear dominance to be necessary and sufficient for the existence of a process (not necessarily Gaussian) having its sample paths in a given RKHS. This theorem - specifically the necessity of the condition - turns out to be incorrect, as we will show via counterexamples. On the other hand, a weaker sufficient condition is available.
Using Fortet's tools along with some new ones, we correct Fortet's theorem and then find the generalization of Driscoll's result. The key idea is that of a random element in a RKHS whose values are sample paths of a stochastic process. As in Fortet's work, we make almost no assumptions about the reproducing kernels we use, and we demonstrate the extent to which one may dispense with the Gaussian assumption.
Accurate control of vocal pitch (fundamental frequency) requires coordination of sensory and motor systems. Previous research has supported the relationship between perceptual accuracy and vocal pitch matching accuracy. The purpose of this study was to investigate the role of memory for pitch in pitch matching and pitch discrimination ability. Three experimental tasks were used. First, a pitch matching task was completed, in which the participants listened to target tones and vocally matched the pitch of the tones. The second task was a pitch discrimination task that required the participants to judge the pitch (same or different) of complex tone pairs. The third task was pitch discrimination with memory interference task that was similar to the pitch discrimination task except interference tones were added. Results of the pitch matching and pitch discrimination tasks yielded a significant correlation between these values. When there was memory interference, pitch discrimination ability was poorer, and there was no significant correlation between pitch discrimination and pitch matching. These results support earlier findings of a relationship between pitch discrimination and pitch matching abilities. The results also suggest a possible role of pitch memory in both tasks. These findings may have implications for abilities related to accurate pitch control. 相似文献