This paper is concerned with the existence and stability of a type of blowing-up positive steady states for a shadow system of the Shigesada–Kawasaki–Teramoto (SKT) two-species competition model and for the perturbed SKT system with a sufficiently large cross-diffusion parameter and bounded random diffusion parameters. The asymptotic behavior of coexistence steady states of the SKT model as one of the cross-diffusion parameters tends to infinity was studied by Lou and Ni [1], who showed that almost all coexistence states can be characterized by one of three shadow systems. In [2], the first author of the present paper studied one of these shadow systems with one cross-diffusion term in one space dimension and proved that one component along a bifurcation branch blows up as the bifurcation parameter approaches the least positive eigenvalue of −Δ under the homogeneous Neumann boundary condition. Using a different approach from that in [2], based on suitable transformations and the Lyapunov-Schmidt reduction, we establish the existence and detailed asymptotic structure of several branches of positive steady states near the blow-up points for shadow systems with one or two cross-diffusion terms in one- and multi-dimensional domains. We further prove that all the large steady states obtained near the blow-up points are spectrally unstable. Finally, by perturbation arguments, we establish the existence and instability of corresponding branches of positive steady states for the original SKT system when one of the cross-diffusion parameters is sufficiently large.
We investigated the adsorption behavior and fluorescence properties of 7-methylguanosine (m7Guo), a cationic nucleoside, on clay minerals under acidic conditions. The fluorescence quantum yield Φf was 0.011 in water and 0.126 in a clay dispersion. We observed Surface-fixation-induced emission (S-FIE)—a phenomenon in which fluorescence is enhanced upon adsorption of molecules onto clay mineral surfaces—in this nucleic acid-related molecule. Analysis of the factors contributing to fluorescence enhancement revealed that suppression of the nonradiative decay rate constant knr plays a key role. The value of knr decreased to approximately 1/27 of that in water, indicating that strong immobilization on the clay surface suppresses nonradiative relaxation and stabilizes the excited state.
The power-law relationship between large language model (LLM) performance and the scale of pre-training corpora has driven remarkable advances, while raising serious ethical and legal concerns. Pre-training corpora often contain sensitive personal information, copyrighted content, or benchmark test data, and the opacity of pre-training corpora further exacerbates these concerns. Consequently, detecting pre-training data has become a significant research challenge. Most existing detection methods rely on intermediate outputs of LLMs (activations, token probabilities, or model loss), which are inaccessible in commercial LLMs, where only final outputs are available. Only a few early-stage attempts rely solely on final outputs by measuring lexical or semantic similarity between reproduced and original texts at the sentence or token level. Yet, these attempts overlook the dynamic nature of reproducibility: reproducibility fluctuates differently across reproduction positions, contextual spans, and expressions, between seen and unseen texts. This oversight narrows the gap of reproduction similarity, ultimately degrading detection performance. To address this limitation, we propose RADS-PDD (reproducibility-aware dynamic similarity–based pre-training data detection), which shifts black-box pre-training data detection from static similarity comparison to reproducibility-aware dynamic similarity modeling. RADS-PDD incorporates three reproducibility-aware mechanisms, positional gain weight, continual gain weight, and triplet occurrence probability, to quantify varying reproducibility by dynamic similarity, amplifying the reproduction similarity gap between seen and unseen texts. Extensive experiments across two representative datasets, multiple data domains, and diverse LLMs demonstrate that RADS-PDD consistently outperforms detection methods that rely solely on final outputs and achieves performance comparable to detection methods that require intermediate outputs.
Modern test methods for air conditioners and heat pumps must reconcile two competing demands: accurately reflecting real operating behavior and ensuring practicality, repeatability, and interlaboratory comparability. Conventional fixed-speed, steady-state rating procedures fall short of this objective, as they exclude control dynamics and interactions with buildings and distribution systems, thereby limiting their representativeness of in-use performance.This review critically examines the limitations of current testing standards and synthesizes recent research and technical advances aimed at improving performance characterization and seasonal efficiency assessment. Emphasis is placed on load-based testing methodologies, emulator-based approaches, and hardware-in-the-loop (“field test in the lab”) concepts, which enable active-control operation under reproducible yet realistic conditions. Evidence from laboratory demonstrations, interlaboratory comparisons, and emerging standardization efforts is consolidated to assess the technical maturity, robustness, and scalability of these methods. The discussion also reflects ongoing international initiatives, including International Energy Agency Annex 88, “Evaluation and Demonstration of Actual Energy Efficiency of Heat Pump Systems in Buildings,” and the International Organization for Standardization Informal Meeting on “Load-based Test Methods.”Based on the reviewed methods, the paper identifies pathways toward next-generation testing frameworks that better recognize advanced system architectures and control strategies, support evidence-based policy and standardization, and provide consumers with performance metrics that more closely align with real-world energy outcomes.
High-electron-mobility transistors (HEMTs) based on wide bandgap (WBG) materials like gallium nitride (GaN) are vital for next-generation power electronics and high-frequency applications, offering high breakdown voltage, electron mobility, and power density. The global shift toward electrification and sustainability is driving demand for GaN and silicon carbide (SiC) power devices. However, challenges such as current collapse and increased channel resistance under high-power conditions hinder performance. To address these limitations, numerous solutions have been explored, with simulation emerging as an indispensable starting point. Technology Computer-Aided Design (TCAD) simulations play a critical role by enabling accurate modeling, performance optimization, and reduced experimental effort. This paper reviews key and advanced physical models in TCAD simulations of GaN HEMTs, covering mechanisms such as carrier transport, thermal effects, and impact ionization. Mobility models—FLDMOB, Albrecht, Gansat, Yamaguchi, Brooks-Herring, and Conwell-Weisskopf—are analyzed for capturing velocity saturation and nonlocal transport. Recombination models like Shockley-Read-Hall and Auger are discussed in relation to carrier lifetime, while impact ionization models, including van-Overstraeten-de-Man, Selberherr, and Okuto-Crowell, are evaluated for breakdown prediction. Emphasis is placed on choosing models suited to specific structures and conditions to ensure simulation accuracy. Advanced modeling enhances TCAD’s predictive power, supporting innovation in GaN-based power electronics.
