For a given braid group representation (BGR), a process of the Yang-Baxterization is formulated to generate solutions of the Yang-Baxter equation (YBE). When a BGR admits the Birman-Wenzl (BW) algebraic structure, this process can be explicitly passed through and two types of trigonometric solutions of YBE are generated from such a BGR. These two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given BGR has. By taking certain reduction on the BW algebra, the rational solution is also generated. A practical condition to judge whether a BGR satisfies the BW algebra is given, from which one finds that not only the familiar BGRs of [5,7,9], but also some new ones obtained recently in [12] have the BW structure. Thus they can be explicitly Yang-Baxterized to solutions of the YBE.

Polymer dielectrics with excellent processability and high breakdown strength (Eb) enable the development of high‐energy‐density capacitors. Although the improvement of dielectric constant (K) of polymer dielectric has been realized by adding high‐K inorganic fillers with high contents (>10 vol%), this approach faces significant challenges in scalable film processing. Here, the incorporation of ultralow ratios (<1 vol%) of low‐K Cd1−xZnxSe1−ySy nanodots into a ferroelectric polymer is reported. The polymer composites exhibit substantial and concurrent increase in both K and Eb, yielding a discharged energy density of 26.0 J cm−3, outperforming the current dielectric polymers and nanocomposites measured at ≤600 MV m−1. The observed unconventional dielectric enhancement is attributed to the structural changes induced by the nanodot fillers, including transformation of polymer chain conformation and induced interfacial dipoles, which have been confirmed by density function theory calculations. The dielectric model established in this work addresses the limitations of the current volume‐average models on the polymer composites with low filler contents and gives excellent agreement to the experimental results. This work provides a new experimental route to scalable high‐energy‐density polymer dielectrics and also advances the fundamental understanding of the dielectric behavior of polymer nanocomposites at atomistic scales.

Abstract. In this paper we generalize the Sato theory to the extended bigraded Toda hierarchy (EBTH). We revise the definition of the Lax equations, give the Sato equations, wave operators, Hirota bilinear identities (HBI) and show the existence of tau function τ (t). Meanwhile we prove the validity of its Fay-like identities and Hirota bilinear equations (HBEs) in terms of vertex operators whose coefficients take values in the algebra of differential operators. In contrast with HBEs of the usual integrable system, the current HBEs are equations of product of operators involving e ∂x and τ (t).

Insulin-like growth factor 2 mRNA binding protein 2 (IGF2BP2) is a member of the IGF2BP protein family consisting of IGF2BP1~3 with the capacity of binding to many transcripts and regulating RNA stability, localization, and translation. In this study, we discovered that expression of IGF2BP2 was upregulated and led to a poor prognosis in pancreatic ductal adenocarcinoma (PDAC). IGF2BP2 protein was gradually elevated from normal pancreas, pancreatic intraepithelial neoplasia to PDAC in an LSL-KrasG12D/+;LSL-Trp53R172H/+;Pdx1-Cre mouse model. Furthermore, we demonstrated that IGF2BP2 promoted aerobic glycolysis and PDAC cell proliferation through directly binding to and stabilizing GLUT1 mRNA. In summary, our study unveiled an important role of IGF2BP2 in PDAC development by modulating aerobic glycolysis and as a potential therapeutic target for PDAC treatment.