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1. 21-Component compositionally complex ceramics: Discovery of ultrahigh-entropy weberite and fergusonite phases and a pyrochlore-weberite transition

   https://doi.org/10.1007/s40145-022-0575-5  

   Qin, Mingde; Vega, Heidy; Zhang, Dawei; Adapa, Sarath; Wright, Andrew J.; Chen, Renkun; Luo, Jian (April 2022, Journal of Advanced Ceramics)

   Abstract Two new high-entropy ceramics (HECs) in the weberite and fergusonite structures, along with the unexpected formation of ordered pyrochlore phases with ultrahigh-entropy compositions and an abrupt pyrochlore-weberite transition, are discovered in a 21-component oxide system. While the Gibbs phase rule allows 21 equilibrium phases, 9 out of the 13 compositions examined possess single HEC phases (with ultrahigh ideal configurational entropies: ∼2.7 k B per cation or higher on one sublattice in most cases). Notably, (15RE 1/15 )(Nb 1/2 Ta 1/2 )O 4 possess a single monoclinic fergusonite (C2/ c ) phase, and (15RE 1/15 ) 3 (Nb 1/2 Ta 1/2 ) 1 O 7 form a single orthorhombic (C222 1 ) weberite phase, where 15RE 1/15 represents Sc 1/15 Y 1/15 La 1/15 Pr 1/15 Nd 1/15 Sm 1/15 Eu 1/15 Gd 1/15 Tb 1/15 Dy 1/15 Ho 1/15 Er 1/15 Tm 1/15 Yb 1/15 Lu 1/15 . Moreover, a series of eight (15RE 1/15 ) 2+ x (Ti 1/4 Zr 1/4 Ce 1/4 H 1/4 ) 2−2 x (Nb 1/2 Ta 1/2 ) x O 7 specimens all exhibit single phases, where a pyrochlore-weberite transition occurs within 0.75 < x < 0.8125. This cubic-to-orthorhombic transition does not change the temperature-dependent thermal conductivity appreciably, as the amorphous limit may have already been achieved in the ultrahigh-entropy 21-component oxides. These discoveries expand the diversity and complexity of HECs, towards many-component compositionally complex ceramics (CCCs) and ultrahigh-entropy ceramics. 

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2. Hydrocortisone/cyclodextrin complex electrospun nanofibers for a fast-dissolving oral drug delivery system

   https://doi.org/10.1039/c9md00390h  

   Celebioglu, Asli; Uyar, Tamer (February 2020, RSC Medicinal Chemistry)

   The electrospinning of hydrocortisone/cyclodextrin complex nanofibers was performed in order to develop a fast-dissolving oral drug delivery system. Hydrocortisone is a water-insoluble hydrophobic drug, yet, the water solubility of hydrocortisone was significantly enhanced by inclusion complexation with hydroxypropyl-beta-cyclodextrin (HP-β-CyD). In this study, hydrocortisone/HP-β-CyD complexes were prepared in aqueous solutions having molar ratios of 1/1, 1/1.5 and 1/2 (hydrocortisone/HP-β-CyD). Highly concentrated aqueous solutions of HP-β-CyD (180%, w/v) were used for hydrocortisone/HP-β-CyD systems (1/1, 1/1.5 and 1/2) in order to perform electrospinning without the use of an additional polymer matrix. The turbidity of hydrocortisone/HP-β-CyD (1/1 and 1/1.5) aqueous solutions indicated the presence of some uncomplexed crystals of hydrocortisone whereas the aqueous solution of hydrocortisone/HP-β-CyD (1/2) was homogeneous indicating that hydrocortisone becomes totally water-soluble by inclusion complexation with HP-β-CyD. Nonetheless, the electrospinning of hydrocortisone/HP-β-CyD systems (1/1, 1/1.5 and 1/2) successfully yielded defect-free uniform nanofibrous structures. Moreover, the electrospinning process was quite efficient that hydrocortisone was completely preserved without any loss yielding hydrocortisone/HP-β-CyD nanofibers having the initial molar ratios (1/1, 1/1.5 and 1/2). The structural and thermal characterization of the hydrocortisone/HP-β-CyD nanofibers revealed that hydrocortisone was totally inclusion complexed with HP-β-CyD and was in the amorphous state in hydrocortisone/HP-β-CyD (1/2) nanofibers whereas some uncomplexed crystalline hydrocortisone was present in hydrocortisone/HP-β-CyD (1/1 and 1/1.5) nanofibers. Nevertheless, hydrocortisone/HP-β-CyD (1/1, 1/1.5 and 1/2) complex aqueous systems were electrospun in the form of nanofibrous webs having a free-standing and flexible nature. The hydrocortisone/HP-β-CyD (1/1, 1/1.5 and 1/2) nanofibrous webs have shown fast-dissolving behavior in water or when they were in contact with artificial saliva. Yet, the hydrocortisone/HP-β-CyD (1/2) nanofibrous web dissolved more quickly than the hydrocortisone/HP-β-CyD (1/1 and 1/1.5) nanofibrous webs due to the full inclusion complexation and the amorphous state of hydrocortisone in this sample. In short, the results suggest that polymer-free electrospun nanofibrous webs produced from hydrocortisone/HP-β-CyD could be quite applicable for fast-dissolving oral drug delivery systems. 

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3. Categorical Primitive Forms and Gromov–Witten Invariants of An Singularities

   https://doi.org/10.1093/imrn/rnz315  

   Căldăraru, Andrei; Li, Si; Tu, Junwu (December 2019, International Mathematics Research Notices)

   Abstract We introduce a categorical analogue of Saito’s notion of primitive forms. For the category $$\textsf{MF}(\frac{1}{n+1}x^{n+1})$$ of matrix factorizations of $$\frac{1}{n+1}x^{n+1}$$, we prove that there exists a unique, up to non-zero constant, categorical primitive form. The corresponding genus zero categorical Gromov–Witten invariants of $$\textsf{MF}(\frac{1}{n+1}x^{n+1})$$ are shown to match with the invariants defined through unfolding of singularities of $$\frac{1}{n+1}x^{n+1}$$. 

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4. On lower bounds for Erdős-Szekeres products

   https://doi.org/10.1090/proc/15503  

   Billsborough, C.; Freedman, M.; Hart, S.; Kowalsky, G.; Lubinsky, D.; Pomeranz, A.; Sammel, A. (October 2021, Proceedings of the American Mathematical Society)

   Let { s j } j = 1 n \left \{ s_{j}\right \} _{j=1}^{n} be positive integers. We show that for any 1 ≤ L ≤ n , 1\leq L\leq n, ‖ ∏ j = 1 n ( 1 − z s j ) ‖ L ∞ ( | z | = 1 ) ≥ exp ⁡ ( 1 2 e L ( s 1 s 2 … s L ) 1 / L ) . \begin{equation*} \left \Vert \prod _{j=1}^{n}\left ( 1-z^{s_{j}}\right ) \right \Vert _{L_{\infty }\left ( \left \vert z\right \vert =1\right ) }\geq \exp \left ( \frac {1}{2e}\frac {L}{\left ( s_{1}s_{2}\ldots s_{L}\right ) ^{1/L}}\right ) . \end{equation*} In particular, this gives geometric growth if a positive proportion of the { s j } \left \{ s_{j}\right \} are bounded. We also show that when the { s j } \left \{ s_{j}\right \} grow regularly and faster than j ( log ⁡ j ) 2 + ε j\left ( \log j\right ) ^{2+\varepsilon } , some ε > 0 \varepsilon >0 , then the norms grow faster than exp ⁡ ( ( log ⁡ n ) 1 + δ ) \exp \left ( \left ( \log n\right ) ^{1+\delta }\right ) for some δ > 0 \delta >0 . 

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5. Universal features of higher-form symmetries at phase transitions

   https://doi.org/10.21468/SciPostPhys.11.2.033  

   Wu, Xiao-Chuan; Jian, Chao-Ming; Xu, Cenke (January 2021, SciPost Physics)

   We investigate the behavior of higher-form symmetries at variousquantum phase transitions. We consider discrete 1-form symmetries, whichcan be either part of the generalized concept “categorical symmetry”(labelled as \tilde{Z}_N^{(1)} Z ̃ N ( 1 ) )introduced recently, or an explicit Z_N^{(1)} Z N ( 1 ) 1-form symmetry. We demonstrate that for many quantum phase transitionsinvolving a Z_N^{(1)} Z N ( 1 ) or \tilde{Z}_N^{(1)} Z ̃ N ( 1 ) symmetry, the following expectation value \langle \left( O_\mathcal{C}\right)^2 \rangle ⟨ ( O 𝒞 ) 2 ⟩ takes the form \langle \left( \log O_\mathcal{C} \right)^2 \rangle \sim - \frac{A}{\epsilon} P + b \log P ⟨ ( log O 𝒞 ) 2 ⟩ ∼ − A ϵ P + b log P , where O_\mathcal{C} O 𝒞 is an operator defined associated with loop \mathcal{C} 𝒞 (or its interior \mathcal{A} 𝒜 ),which reduces to the Wilson loop operator for cases with an explicit Z_N^{(1)} Z N ( 1 ) 1-form symmetry. P P is the perimeter of \mathcal{C} 𝒞 ,and the b \log P b log P term arises from the sharp corners of the loop \mathcal{C} 𝒞 ,which is consistent with recent numerics on a particular example. b b is a universal microscopic-independent number, which in (2+1)d ( 2 + 1 ) d is related to the universal conductivity at the quantum phasetransition. b b can be computed exactly for certain transitions using the dualitiesbetween (2+1)d ( 2 + 1 ) d conformal field theories developed in recent years. We also compute the"strange correlator" of O_\mathcal{C} O 𝒞 : S_{\mathcal{C}} = \langle 0 | O_\mathcal{C} | 1 \rangle / \langle 0 | 1 \rangle S 𝒞 = ⟨ 0 | O 𝒞 | 1 ⟩ / ⟨ 0 | 1 ⟩ where |0\rangle | 0 ⟩ and |1\rangle | 1 ⟩ are many-body states with different topological nature. 

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