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1. A note on tight projective 2‐designs

   https://doi.org/10.1002/jcd.21804  

   Iverson, Joseph W.; King, Emily J.; Mixon, Dustin G. (September 2021, Journal of Combinatorial Designs)

   Abstract We study tight projective 2‐designs in three different settings. In the complex setting, Zauner's conjecture predicts the existence of a tight projective 2‐design in every dimension. Pandey, Paulsen, Prakash, and Rahaman recently proposed an approach to make quantitative progress on this conjecture in terms of the entanglement breaking rank of a certain quantum channel. We show that this quantity is equal to the size of the smallest weighted projective 2‐design. Next, in the finite field setting, we introduce a notion of projective 2‐designs, we characterize when such projective 2‐designs are tight, and we provide a construction of such objects. Finally, in the quaternionic setting, we show that every tight projective 2‐design for determines an equi‐isoclinic tight fusion frame of subspaces of of dimension 3. 

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2. Hydrogenation reactions catalyzed by HN(CH ₂ CH ₂ PR ₂ ) ₂ -ligated copper complexes

   https://doi.org/10.1039/d1qi00776a  

   Ekanayake, Dewmi A.; Chakraborty, Arundhoti; Krause, Jeanette A.; Guan, Hairong (October 2021, Inorganic Chemistry Frontiers)

   null (Ed.)

   HN(CH 2 CH 2 PR 2 ) 2 -ligated copper borohydride complexes, ( R PN H P)Cu(BH 4 ) (R = i Pr, Cy, t Bu), which can be prepared from ( R PN H P)CuBr and NaBH 4 , are capable of catalyzing the hydrogenation of aldehydes in an alcoholic solvent. More active hydrogenation catalysts are ( R PN H P)CuBr mixed with KO t Bu, allowing various aldehydes and ketones to be efficiently reduced to alcohols except those bearing a nitro, N -unprotected pyrrole, pyridine, or an ester group, or those prone to aldol condensation ( e.g. , 1-heptanal). Modifying the catalyst structure by replacing the NH group in ( i Pr PN H P)CuBr with an NMe group results in an inferior catalyst but preserves some catalytic activity. The hexanuclear copper hydride cluster, ( i Pr PN H P) 3 Cu 6 H 6 , is also competent in catalyzing the hydrogenation of aldehydes such as benzaldehyde and N -methyl-2-pyrrolecarboxaldehyde, albeit accompanied by decomposition pathways. The catalytic performance can be enhanced through the addition of a strong base or i Pr PN H P. The three catalytic systems likely share the same catalytically active species, which is proposed to be a mononuclear copper hydride ( R PN H P)CuH with the NH group bound to copper. 

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3. A Construction of a 3/2‐Tough Plane Triangulation With No 2‐Factor

   https://doi.org/10.1002/jgt.23209  

   Shan, Songling (May 2025, Journal of Graph Theory)

   ABSTRACT In 1956, Tutte proved the celebrated theorem that every 4‐connected planar graph is Hamiltonian. This result implies that every more than ‐tough planar graph on at least three vertices is Hamiltonian and so has a 2‐factor. Owens in 1999 constructed non‐Hamiltonian maximal planar graphs of toughness arbitrarily close to and asked whether there exists a maximal non‐Hamiltonian planar graph of toughness exactly . In fact, the graphs Owens constructed do not even contain a 2‐factor. Thus the toughness of exactly is the only case left in asking the existence of 2‐factors in tough planar graphs. This question was also asked by Bauer, Broersma, and Schmeichel in a survey. In this paper, we close this gap by constructing a maximal ‐tough plane graph with no 2‐factor, answering the question asked by Owens as well as by Bauer, Broersma, and Schmeichel. 

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4. Achieving a series of solid-state [2 + 2] cycloaddition reactions involving 1,2-bis(2-pyridyl)ethylene within halogen-bonded co-crystals

   https://doi.org/10.1039/D4CE00097H  

   Andren, Max; Bosch, Eric; Krueger, Herman R; Groeneman, Ryan H (March 2024, CrystEngComm)

   The formation of a halogen-bonded co-crystal based upon 1,2-bis(2-pyridyl)ethylene along with iodoperchlorobenzene is reported. The co-crystal undergoes a nearly quantitative [2 + 2] cycloaddition reaction in the organic solid state. 

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5. Bioresponsive Microneedles with a Sheath Structure for H ₂ O ₂ and pH Cascade‐Triggered Insulin Delivery

   https://doi.org/10.1002/smll.201704181  

   Zhang, Yuqi; Wang, Jinqiang; Yu, Jicheng; Wen, Di; Kahkoska, Anna_R; Lu, Yue; Zhang, Xudong; Buse, John_B; Gu, Zhen (February 2018, Small)

   Abstract Self‐regulating glucose‐responsive insulin delivery systems have great potential to improve clinical outcomes and quality of life among patients with diabetes. Herein, an H₂O₂‐labile and positively charged amphiphilic diblock copolymer is synthesized, which is subsequently used to form nano‐sized complex micelles (NCs) with insulin and glucose oxidase of pH‐tunable negative charges. Both NCs are loaded into the crosslinked core of a microneedle array patch for transcutaneous delivery. The microneedle core is additionally coated with a thin sheath structure embedding H₂O₂‐scavenging enzyme to mitigate the injury of H₂O₂toward normal tissues. The resulting microneedle patch can release insulin with rapid responsiveness under hyperglycemic conditions owing to an oxidative and acidic environment because of glucose oxidation, and can therefore effectively regulate blood glucose levels within a normal range on a chemically induced type 1 diabetic mouse model with enhanced biocompatibility. 

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