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We show that pointwise limits of semistatic trading strategies in discrete time are again semistatic strategies. The analysis is carried out in full generality for a two‐period model, and under a probabilistic condition for multiperiod, multistock models. Our result contrasts with a counterexample of Acciaio, Larsson, and Schachermayer, and shows that their observation is due to a failure of integrability rather than instability of the semistatic form. Mathematically, our results relate to the decomposability of functions as studied in the context of Schrödinger bridges.

 

The gas-phase reaction of the methylidyne (CH; X 2 Π) radical with dimethylacetylene (CH 3 CCCH 3 ; X 1 A 1g ) was studied at a collision energy of 20.6 kJ mol −1 under single collision conditions with experimental results merged with ab initio calculations of the potential energy surface (PES) and ab initio molecule dynamics (AIMD) simulations. The crossed molecular beam experiment reveals that the reaction proceeds barrierless via indirect scattering dynamics through long-lived C 5 H 7 reaction intermediate(s) ultimately dissociating to C 5 H 6 isomers along with atomic hydrogen with atomic hydrogen predominantly released from the methyl groups as verified by replacing the methylidyne with the D1-methylidyne reactant. AIMD simulations reveal that the reaction dynamics are statistical leading predominantly to p28 (1-methyl-3-methylenecyclopropene, 13%) and p8 (1-penten-3-yne, 81%) plus atomic hydrogen with a significant amount of available energy being channeled into the internal excitation of the polyatomic reaction products. The dynamics are controlled by addition to the carbon–carbon triple bond with the reaction intermediates eventually eliminating a hydrogen atom from the methyl groups of the dimethylacetylene reactant forming 1-methyl-3-methylenecyclopropene (p28). The dominating pathways reveal an unexpected insertion of methylidyne into one of the six carbon–hydrogen single bonds of the methyl groups of dimethylacetylene leading to the acyclic intermediate, which then decomposes to 1-penten-3-yne (p8). Therefore, the methyl groups of dimethylacetylene effectively ‘screen’ the carbon–carbon triple bond from being attacked by addition thus directing the dynamics to an insertion process as seen exclusively in the reaction of methylidyne with ethane (C 2 H 6 ) forming propylene (CH 3 C 2 H 3 ). Therefore, driven by the screening of the triple bond, one propynyl moiety (CH 3 CC) acts in four out of five trajectories as a spectator thus driving an unexpected, but dominating chemistry in analogy to the methylidyne – ethane system. 

3D facial animation synthesis from audio has been a focus in recent years. However, most existing literature works are designed to map audio and visual content, providing limited knowledge regarding the relationship between emotion in audio and expressive facial animation. This work generates audio‐matching facial animations with the specified emotion label. In such a task, we argue that separating the content from audio is indispensable—the proposed model must learn to generate facial content from audio content while expressions from the specified emotion. We achieve it by an adaptive instance normalization module that isolates the content in the audio and combines the emotion embedding from the specified label. The joint content‐emotion embedding is then used to generate 3D facial vertices and texture maps. We compare our method with state‐of‐the‐art baselines, including the facial segmentation‐based and voice conversion‐based disentanglement approaches. We also conduct a user study to evaluate the performance of emotion conditioning. The results indicate that our proposed method outperforms the baselines in animation quality and expression categorization accuracy.