Experimental realisations of the fractional Schr\"{o}dinger equation in the temporal domain

The fractional Schr\"{o}dinger equation (FSE) -- a natural extension of the standard Schr\"{o}dinger equation -- is the basis of fractional quantum mechanics. It can be obtained by replacing the kinetic-energy operator with a fractional derivative. Here, we report the experimental realisation of an optical FSE for femtosecond laser pulses in the temporal domain. Programmable holograms and the single-shot measurement technique are respectively used to emulate a \textit{L\'evy waveguide} and to reconstruct the amplitude and phase of the pulses. Varying the L\'evy index of the FSE and the initial pulse, the temporal dynamics is observed in diverse forms, including solitary, splitting and merging pulses, double Airy modes, and ``rain-like'' multi-pulse patterns. Furthermore, the transmission of input pulses carrying a fractional phase exhibits a ``fractional-phase protection'' effect through a regular (non-fractional) material. The experimentally generated fractional time-domain pulses offer the potential for designing optical signal-processing schemes.Comment: This manuscript reports on experimental progress in fractional Schrodinger equations. Welcome to your comments and suggestions

Investigation and Study on the "Dragon Boat Race" of Ankang Folk Sports

This paper investigates and studies the "dragon boat race" of folk sports activities in Ankang city to understand the cultural connotation of dragon boat race and the development history of "dragon boat race" in this region. In this paper, the literature review, questionnaire survey, field visits, and statistics and analysis of data are used to investigate and study the current situation of the development of the "dragon boat race" in Ankang. It aims to provide a valuable and meaningful reference for the inheritance and development of the "dragon boat race" movement in Ankang

Age-related modulation of the nitrogen resorption efficiency response to growth requirements and soil nitrogen availability in a temperate pine plantation

Nitrogen (N) resorption is a key strategy for conserving N in forests, and is often affected by soil nutrient condition and N sink strength within the plant. However, our understanding of the age-related pattern of N resorption and how increasing N deposition will affect this pattern is limited. Here, we investigated N resorption along a chronosequence of stands ranging in age from 2 to 100 years old, and conducted a 4-year exogenous N input experiment in stands at age class 11, 20, and 45 in a Larix Principis-rupprechtii plantation in north China. We found a logarithmic increase in leaf N resorption efficiency (NRE) and green leaf N concentration, and a logarithmic decrease in senesced-leaf N concentration along the stand-age chronosequence. Leaf NRE was negatively correlated with plant-available N concentration. Stand-level N resorption was positively correlated with the annual N requirement for tree growth. N resorption contributed to 45, 62, and 68% of the annual N supply in the 11-, 20-, and 45-year-old stands, respectively. Our exogenous N input experiment showed that leaf NRE in the 11- and 20-year-old stands decreased 17 and 12% following a 50-kg N ha¯¹ y¯¹ input. However, leaf NRE was not affected in the 45-year-old stand. The increases in leaf NRE and the contribution of N resorption to annual N supply along stand ages suggested that, with stand development, tree growth depends more on N resorption to supply its N need. Furthermore, the leaf NRE of mature stand was not decreased under exogenous N input, suggesting that mature stands can be stronger sinks for N deposition than young stands due to their higher capacity to retain the deposited N within plants via internal cycle. Ignoring age-related N use strategies can lead to a bias in N cycle models when evaluating forest net primary production under increasing global N deposition