This paper addresses the quasilinear Schrödinger equation with critical growth in the zero-mass case:−Δu−uΔ(u2)=λg(x)|u|p−2u+|u|2·2*−2u,x∈RN,where N ≥ 3, λ > 0, p ∈ (4, 2 · 2*) or p ∈ (1, 2) with 2*=2NN−2 the critical Sobolev exponent, and g∈Lp0(RN), wherep0=2·2*2·2*−pifp∈(4,2·2*),p0=2*2*−pifp∈(1,2).To address the inherent lack of compactness in the zero-mass case, we develop a perturbative variational framework inspired by established techniques. For the case p ∈ (4, 2 · 2*), we establish the existence of a positive-energy ground state solution when λ is sufficiently large. For the case p ∈ (1, 2), we prove that for small λ > 0, the equation admits a ground state solution with negative energy. Additionally, for p ∈ (1, 2), we show the multiplicity of solutions to the above equation for small λ.
In this study, we explored the photoinduced dynamics of a zinc tetraphenylporphyrin-subphthalocyanine dyad (ZnTPP-SubPcH) and its fluorinated analogue (ZnTPP-SubPcF) in toluene and benzonitrile. This was achieved by combining the optimally tuned screened range-separated hybrid (OT-SRSH) functional, the polarizable continuum model (PCM), and nonadiabatic molecular dynamics (NAMD) simulations based on restricted full linear-response time-dependent density functional theory (LR-TDDFT). The results show that ZnTPP-SubPcH in toluene predominantly exhibits energy transfer from SubPcH to ZnTPP, in qualitative agreement with the experimentally proposed SubPc → ZnTPP energy-transfer pathway. In benzonitrile, however, the system evolves into a charge-transfer (CT) state. In contrast, ZnTPP-SubPcF exhibits a much stronger tendency toward charge separation in toluene and benzonitrile. This work elucidates the microscopic mechanism by which substituent effects and the solvent environment act in concert to govern the photodynamic behavior of ZnTPP-SubPc systems.
Emotional situations in real life are highly diverse, yet existing emotion regulation training approaches often lack adaptivity to such diversity. Self-compassion, an emotion regulation strategy characterized by kindness and non-judgmental understanding toward one's own suffering, has demonstrated emotional benefits. However, its effectiveness is constrained by cognitive demands, limiting its applicability among individuals with emotional disorders or cognitive impairments. Implementation intention, specifying how to response in a given situation based on the goal with a typical structure as "if + situation, then + reaction", can effectively reduce the cognitive demands of self-regulation and enhance its regulatory effect. To improve the emotional regulation efficacy of self-compassion, this study integrated implementation intention with self-compassion to establish a standardized sentence collection (Experiment 1) and evaluated its effectiveness in regulating negative emotions among college students with depressive tendencies (Experiment 2 similar to 3). In Experiment 1, situational and response sentences were prepared following the "if + situation, then + reaction" structure. Forty negative and forty neutral situational sentences were developed, along with 120 implementation intention-based self-compassion (II-SC) statements and 120 implementation intention-based neutral (II-N) statements. A total of 106 participants (age: 20.17 +/- 1.90 years; 66 females) evaluated these sentences on dimensions such as emotional valence, arousal, and relevance to self-compassion. By presenting negative situational sentences to induce negative emotions, followed by II-SC statements, a substantial increase in pleasure was observed, supporting the efficacy of II-SC in emotion regulation. Experiment 2 employed a 2 (measuring time: pre-test vs. post-test) x 3 (group: II-SC vs. TSC vs. Control) mixed factorial design to examine the effect of II-SC on negative emotion regulation. Ninety college students with depressive tendencies (age: 20.07 +/- 1.80 years; 82 females) were randomly assigned to one of the three groups (II-SC, TSC or Control group). After baseline assessments of emotional state, participants received either II-SC, TSC (traditional self-compassion) guidance, or no guidance (Control group). Negative emotions were then induced through negative self-evaluation sentences accompanied by sad music, followed by post-test on emotional measures. Building upon Experiment 2, Experiment 3 incorporated physiological indicators including heart rate and electrodermal activity to more comprehensively and objectively assess emotional responses. Sixty-nine college students with depressive tendencies (age: 20.01 +/- 1.38 years; 65 female) participated. In this experiment, negative emotions were elicited through challenging arithmetic tasks to test whether the II-SC sentences produced increased emotion regulation effects compared with TSC under conditions of cognitive resource depletion. Results indicate that (1) II-SC sentence collection can significantly alleviate negative emotions, and showed a satisfactory reliability and validity. (2) When negative emotions were induced by negative self-evaluation, both II-SC and TSC sentences effectively reduced negative affect, with no significant difference in efficacy; however II-SC required less cognitive effort. (3) When negative emotions were elicited through frustrating tasks that depleted cognitive resources, both II-SC and TSC alleviated negative affect, but the resource dependence of TSC reduced its effectiveness, resulting in better regulatory effects for II-SC. Nevertheless, no significant group differences were found in perceived regulation effort, and neither physiological activation associated with negative emotion induction. In conclusion, the current study developed a standardized and valid self-compassion sentence collection based on implementation intention, and demonstrated its effectiveness in regulating negative emotions. These II-SC sentences enable individuals with depressive tendencies to engage in automatic and efficient emotion regulation through self-compassion, thereby enhancing its regulatory efficacy and offering a potential approach for coping with the diverse stressors encountered in daily life.
Understanding the soil nitrogen (N) cycling during vegetation succession is critical for effective ecosystem restoration and management. However, a comprehensive view of the dynamics of both the entire N-cycling functional microbial community and gross N mineralization/nitrification rates during secondary succession remains a key knowledge gap, limiting the optimization of restoration strategies. We investigated N-cycling functional gene profiles using metagenomics and gross N mineralization/nitrification rates by 15N pool dilution techniques, along a complete secondary succession chronosequence (grassland-shrubland-secondary forest-primary forest). The abundance of functional genes involved in N fixation, organic N synthesis, mineralization, nitrification, dissimilatory/assimilatory nitrate reduction to nitrite and denitrification increased by 27%-98% from grassland to shrubland, then declined by 13%-80% towards primary forest. The N-cycling microbial community composition shifted significantly along the secondary succession. Functional genes were mainly distributed in Pseudomonadota, Acidobacteriota and Verrucomicrobiota phyla. The abundance of dominant phyla and the complexity of the functional gene co-occurrence network were highest in the shrubland stage. The trend of the soil gross N mineralization rate was parallel to that of the mineralization functional gene abundance. Soil total carbon (C)/N pools exhibited greater effects on the N-cycling microbial community and gross N mineralization rate than labile C/N fractions. Specifically, total C/N pools altered the gross N mineralization rate by changing the abundance of key mineralization genes, that is ureA/B/C and glsA. Synthesis and applications. These findings establish a microbial mediation framework for ecosystem recovery and suggest shrubland acts as a biogeochemical catalyst accelerating N cycling. By linking soil C/N pools to microbial N-cycling potential and key N transformation rates, we provide a mechanistic basis for optimizing ecosystem restoration strategies.
Intentional emotional contagion, the conscious transmission of emotions between individuals, has unclear neurobehavioral mechanisms in naturalistic dyadic communications. Experiment 1 demonstrated that conscious engagement enhanced sad emotional contagion between strangers. Using the fNIRS pseudo-hyperscanning technique, Experiment 2 showed a behavioral-neural dissociation in intentional sadness contagion: Behavioral findings revealed increased interpersonal intimacy and listener altruism. Neurocognitive findings demonstrated reduced activation in the left frontopolar cortex, bilateral dorsolateral prefrontal cortex (dlPFC), and angular/supramarginal gyri. While weaker interpersonal neural synchronization emerged between the speaker’s left frontopolar/dlPFC and listener’s right dlPFC. Mediation analysis indicated that intentional emotional contagion mediated emotional communication and self-other overlap, extending Emotions as Social Information Model. Findings suggest that intentional sadness contagion based on dyadic story sharing has an adaptive neurocognitive reorganization which facilitates prosocial behavior.
