In our studies on the catalytic activity of Group IVB transition metal Lewis acids, Hf(OTf)4 was identified as a highly potent catalyst for ”one-pot, three-component” Biginelli reaction. More importantly, it was found that solvent-free conditions, in contrast to solvent-based conditions, could dramatically promote the Hf(OTf)4-catalyzed formation of 3,4-dihydro-pyrimidin-2-(1H)-ones. To provide a mechanistic explanation, we closely examined the catalytic effects of Hf(OTf)4 on all three potential reaction pathways in both “sequential bimolecular condensations” and “one-pot, three-component” manners. The experimental results showed that the synergistic effects of solvent-free conditions and Hf(OTf)4 catalysis not only drastically accelerate Biginelli reaction by enhancing the imine route and activating the enamine route but also avoid the formation of Knoevenagel adduct, which may lead to an undesired byproduct. In addition, 1H-MMR tracing of the H-D exchange reaction of methyl acetoacetate in MeOH-d4 indicated that Hf(IV) cation may significantly accelerate ketone-enol tautomerization and activate the β-ketone moiety, thereby contributing to the overall reaction rate.

Hf(OTf)4 was identified as a highly potent catalyst (0.1–0.5 mol%) for three-component Mannich reaction under solvent-free conditions. Hf(OTf)4-catalyzed Mannich reaction exhibited excellent regioselectivity and diastereoselectivity when alkyl ketones were employed as substrates. 1H NMR tracing of the H/D exchange reaction of ketones in MeOH-d4 indicated that Hf(OTf)4 could significantly promote the keto-enol tautomerization, thereby contributing to the acceleration of reaction rate.

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As investment fever rises, investment strategy is a critical choice for investors. In this paper, based on the price data of gold and bitcoin from 9/11/2016 to 9/10/2021, the corresponding mathematical models are established by the LSTM, evaluation model, and single-objective optimization model in an attempt to obtain the optimal investment strategy. Firstly, the price is predicted by the LSTM model after data cleaning. The evaluation system is constructed from three perspectives: market trading intention, price stability and market environment trend. Based on the scores and thresholds of the evaluation system, the trading directions (buy, sell, hold) are obtained qualitatively. Then, based on the corrected predicted price, a single-objective optimization is established for maximizing total assets, obtaining the final investment strategy, where an initial $1,000 asset is able to reach a final total asset of $134,226 after five years. Secondly, we establish the evaluation system of investment strategies and establish three evaluation indexes of Sharpe Value, Max Drawdown, and Interest Rate in terms of both return and risk. We construct four new investment strategies with different types of investment product and model selection. Comparing the five investment strategies, we can find that our investment strategy has the highest Interest Rate, higher Sharpe Value, and smaller Max Drawdown compared with other investment strategies. Thirdly, we test the impact of transaction costs on the model and learn that the model is more sensitive to the change of bitcoin transaction costs and not sensitive to the change of gold transaction cost.

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