Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains

Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored. This paper aims at developing accurate spectral methods using rational basis (or modified mapped Gegenbauer functions) for such models in unbounded domains. The main building block of the spectral algorithms is the explicit representations for the Fourier transform and fractional Laplacian of the rational basis, derived from some useful integral identites related to modified Bessel functions. With these at our disposal, we can construct rational spectral-Galerkin and direct collocation schemes by pre-computing the associated fractional differentiation matrices. We obtain optimal error estimates of rational spectral approximation in the fractional Sobolev spaces, and analyze the optimal convergence of the proposed Galerkin scheme. We also provide ample numerical results to show that the rational method outperforms the Hermite function approach

How do firms in strategic emerging industries influence their peers’ innovation strategies?

Drawing on signaling theory, peer effect, and the awarenessmotivation-capability (AMC) framework, we examine the role of strategic emerging industries (SEI) firms in raising the awareness and motivation of non-SEI firms’ R&D activities, including gaining government R&D subsidies and adopting internal R&D investment, while considering the moderate effect of non-SEI firms’ capability factor. Based on the data of Chinese listed firms from SEI and non-SEI, the empirical results reveal that (a) the number of SEI firms funded by government R&D has an inverted U-shape relationship with the amount that non-SEI firms gain from government R&D subsidies, and has a positive relationship with the investment of non-SEI firms on internal R&D. (b) The financial performance of SEI firms funded by government R&D motivates nonSEI firms to gain government R&D subsidies and invest in internal R&D. (c) These relationships are strengthened by the relative scale of the non-SEI firms

THE KINEMATIC ANALYSIS ON THOMAS ENQVIST’S FOREHAND TOPSPIN TECHNIQUE

This paper presents knowledge on kinematic feature of an outstanding athlete who uses forehand topspin technique during a tennis match. Thomas Enqvist had used forehand topspin technique to receive for three times in the ATP Championship Round-robin Tournament Semifinal, which was held in Chengdu, China. The technique of forehand topspin has been further analyzed by three-dimensional video. Through study, the kinematic technical feature has been obtained, resulting in not only providing referential statistics for the technical training of the athletes, but also enriching the technical theory of tennis

Dynamically Assisted Schwinger Effect at Strong Coupling with Its Holographic Extension

At strong-coupling and weak-field limit, the scalar Schwinger effect is studied by the field-theoretical method of worldline instantons for dynamic fields of single-pulse and sinusoidal types. By examining the Wilson loop along the closed instanton path, corrections to the results obtained from weak-coupling approximations are discovered. They show that this part of contribution for production rate becomes dominant as Keldysh parameter increases, it makes the consideration at strong coupling turn out to be indispensable for dynamic fields. Moreover a breaking of weak-field condition similar to constant field also happens around the critical field, defined as a point of vacuum cascade. In order to make certain whether the vacuum cascade occurs beyond the weak-field condition, following Semenoff and Zarembo's proposal, the Schwinger effects of dynamic fields are studied with an $\mathcal{N}=4$ supersymmetric Yang--Mills theory in the Coulomb phase. With the help of the gauge/gravity duality, the vacuum decay rate is evaluated by the string action with instanton worldline as boundary, which is located on a probe D3-brane. The corresponding classical worldsheets are estimated by perturbing the integrable case of a constant field.Comment: 13 pages, 7 figures, two columns. Revision according to review. Appendices for proofs adde

Trait rumination in post-stress growth among Chinese college students: the chain mediating effect of distress disclosure and perceived social support

BackgroundRumination has emerged as a significant factor contributing to personal growth following periods of stress or trauma. The present study aimed to investigate the relationship between trait rumination and post-stress growth (PSG) within the context of Chinese college students who encounter mild stressors in their daily lives. Moreover, we aim to evaluate the potential mediating roles played by both distress disclosure and perceived social support in this dynamic relationship.MethodAll participants completed assessments using the Adolescent Self-Rating Life Events Checklist, Rumination Response Scale, Post-Stress Growth Inventory, Distress Disclosure Index, and Perceived Social Support Scale. Correlation and mediation analyses were conducted using SPSS PROCESS 4 MACRO.ResultsAll students reported experiencing mild psychological impacts as a result of negative life events in the past year and displayed moderate levels of PSG. There was no significant correlation observed between the effects of negative life events and PSG. Significant negative correlations were found between trait rumination and distress disclosure, perceived social support, and PSG. Distress disclosure and perceived social support jointly operated as sequential mediators in the relationship between trait rumination and PSG among all the participants. Qualitative analyses revealed different correlation patterns of high- versus low-ruminator.ConclusionTrait rumination affects PSG both directly and indirectly, through its influence on distress disclosure and perceived social support. Our results emphasize the significance of actively participating in distress disclosure and nurturing a robust sense of social support to counteract the detrimental effects of rumination on post-stress growth among Chinese college students