加州大学

In recent work, the author, in collaboration with Allen, Long, and Tu, developed the Explicit Hypergeometric Modularity Method (EHMM), which establishes the modularity of a large class of hypergeometric Galois representations in dimensions two and three. One important application of the EHMM is the construction of an explicit family of eta-quotients, which we call the K2 functions, from the hypergeometric background. In this article, we introduce an analogous family of eta-quotients, which we call the K3 functions. These K3 functions are constructed using the theory of weight one cubic theta functions originally developed by Jonathan and Peter Borwein. We then use the K3 functions in the EHMM to resolve several hypergeometric modularity conjectures of Dawsey and McCarthy. Further, we provide applications to special L-values of the K3 functions and to the study of generalized Paley graphs.

Power systems face increasing weather-driven variability and, therefore, increasingly rely on flexible but energy-limited storage resources. Energy storage can buffer this variability, but its value depends on intertemporal decisions under uncertain prices. Without accounting for the future reliability value of stored energy, batteries may act myopically, discharging too early or failing to preserve reserves during critical hours. This paper introduces a stopping-time reward that, together with a state-of-charge (SoC) range target penalty, aligns arbitrage incentives with system reliability by rewarding storage that maintains sufficient SoC before critical hours. We formulate the problem as an online optimization with a chance-constrained terminal SoC and embed it in an end-to-end (E2E) learning framework, jointly training the price predictor and control policy. The proposed design enhances reachability of target SoC ranges, improves profit under volatile conditions, and reduces its standard deviation.

The importance of using a control in the testing of a new drug or a new procedure is discussed, and we see how this often results in comparisons between parameters of two different populations. We show how to test that two normal populations have the same population mean, both when the population variances are known and when they are unknown. We show how to test the equality of two population proportions.

Watercore is a physiological disorder that reduces fruit quality in durian, yet its underlying mechanism remains poorly understood. This study compared the tolerant cultivar ‘Monthong’ (MT) and the susceptible cultivar ‘Chanee’ (CN) to identify structural, physiological, biochemical, and molecular traits associated with watercore development. CN developed watercore symptoms earlier and reached nearly 100% incidence at the overripe stage, whereas MT exhibited only mild symptoms. These differences were not associated with fruit maturity, transpiration, fruit surface water uptake, or vascular structure. Instead, CN exhibited higher specific gravity and lower intercellular gas content in both the whole fruit and central axis, indicating smaller intercellular air spaces. Ripening was accompanied by greater accumulation of glucose, fructose, and total sugars in the central axis of CN than in MT, although these changes were not consistently associated with the expression of DzSUC2, DzN3, or DzCWINV1. Osmotically driven water uptake was evident following vacuum infiltration, whereas apoplastic soluble solids concentration did not differ between cultivars in healthy fruit. During watercore progression, only apoplastic fructose increased significantly with symptom severity. Membrane deterioration occurred only during advanced ripening. Collectively, these findings suggest that limited intercellular air space is the primary factor associated with watercore susceptibility, while ripening-associated changes in sugar composition may contribute to symptom development.

Leveraging the synergistic effects of bimetallic atoms in dual single-atom catalysts (DACs) and the efficient charge transfer of S-scheme heterojunctions, we have designed and systematically evaluated a series of DACsupported carbon nitride/black TiO2 S-scheme heterojunctions (DAC-TCN) for photocatalytic glucose reforming to hydrogen. Among these catalysts, CuNi 0.5-TCN3 exhibited the highest hydrogen evolution rate of 1104.15 mu mol center dot g-1 center dot h-1, which is 34 times higher than pristine carbon nitride and 3.6 times higher than TiO2-X. This superior performance arises from the atomic-level dispersion of bimetallic species and the intimate S-scheme interface, which effectively suppresses electron-hole recombination and extends the lifetime of charge carriers. The catalyst retained over 80% of its activity after four consecutive cycles, demonstrating excellent stability. Density functional theory (DFT) calculations revealed enhanced water adsorption on CuNi-TCN, further stabilizing the system. This work opens up a promising strategy for high-performance hydrogen generation by rationally tuning the structure to combine DACs with S-scheme heterojunctions, which effectively enhances both the efficiency and durability of photocatalytic hydrogen production.