Reprint of: Minimal affinizations as projective objects

We prove that the specialization to q=1$q=1$ of a Kirillov–Reshetikhin module for an untwisted quantum affine algebra of classical type is projective in a suitable category. This yields a uniform character formula for the Kirillov–Reshetikhin modules. We conjecture that these results hold for specializations of minimal affinization with some restriction on the corresponding highest weight. We discuss the connection with the conjecture of Nakai and Nakanishi on q$q$-characters of minimal affinizations. We establish this conjecture in some special cases. This also leads us to conjecture an alternating sum formula for Jacobi–Trudi determinants.     

Prime representations from a homological perspective

We explore the relation between self extensions of simple representations of quantum affine algebras and the property of a simple representation being prime. We show that every nontrivial simple representation has a nontrivial self extension. Conversely, we prove that if a simple representation has a unique nontrivial self extension up to isomorphism, then its Drinfeld polynomial is a power of the Drinfeld polynomial of a prime representation. It turns out that, in the $\mathfrak{sl }_2$ -case, a simple module is prime if and only if it has a unique nontrivial self extension up to isomorphism. It is tempting to conjecture that this is true in general and we present a large class of prime representations satisfying this homological property.     

Synthesis of triazolo indazolones using 3D mesoporous aluminosilicate catalyst with nanocage structure

Mesoporous Aluminosilicate (AlKIT-5) has been found to be an efficient catalyst for one-pot synthesis of triazolo[1,2-a]indazole-1,3,8-trione derivatives from dimedone, urazole, and aromatic aldehydes using acetonitrile as a solvent. This new method is simple, effective, ecofriendly, and consistently has the advantage of excellent yields (80-96%) and short reaction time (30-60 min). The effect of the catalyst weight, aluminum content in the catalyst, and the solvents on the synthesis of triazolo[1,2-a]indazole-1,3,8-trione derivatives has been investigated. It has been found that the catalyst can be recycled for several times without much affecting its activity for a variety of organic transformations.     

Heavy Heparin: A Stable Isotope‐Enriched,Chemoenzymatically‐Synthesized,Poly‐Component Drug

Heparin is a highly sulfated, complex polysaccharide and widely used anticoagulant pharmaceutical. In this work, we chemoenzymatically synthesized perdeuteroheparin from biosynthetically enriched heparosan precursor obtained from microbial culture in deuterated medium. Chemical de‐N‐acetylation, chemical N‐sulfation, enzymatic epimerization, and enzymatic sulfation with recombinant heparin biosynthetic enzymes afforded perdeuteroheparin comparable to pharmaceutical heparin. A series of applications for heavy heparin and its heavy biosynthetic intermediates are demonstrated, including generation of stable isotope labeled disaccharide standards, development of a non‐radioactive NMR assay for glucuronosyl‐C5‐epimerase, and background‐free quantification of in vivo half‐life following administration to rabbits. We anticipate that this approach can be extended to produce other isotope‐enriched glycosaminoglycans.     

An alternate approach for the synthesis of 2‐substituted‐arylimidazo[4,5‐b]pyridines and their anti‐bacterial activity

An alternate method for the convenient preparation of the imidazo[4,5‐b]pyridines from 2,3‐pyridinediamine and 2‐aryl‐3(1)‐benzoxazine‐4H‐one has been illustrated. The mechanistic pathway for the formation of the product 4 has been proposed. All the compounds prepared herein were screened for their anti‐ bacterial properties.     

Advancing global chemical education through interactive teaching tools

This perspective highlights our recent efforts to develop interactive resources in chemical education for worldwide usage. First, we highlight online tutorials that connect organic chemistry to medicine and popular culture, along with game-like resources for active learning. Next, we describe efforts to aid students in learning to visualize chemical structures in three dimensions. Finally, we present recent approaches toward engaging children and the general population through organic chemistry coloring and activity books. Collectively, these tools have benefited hundreds of thousands of users worldwide. We hope this perspective promotes a spirit of innovation in chemical education and spurs the development of additional free, interactive, and widely accessible chemical education resources.

This perspective highlights the development of interactive chemical education resources for worldwide usage. We hope to promote a spirit of innovation in chemical education and spur the development of new chemical education resources.     

Investigation of the specificity of Raman spectroscopy in non-invasive blood glucose measurements

Although several in vivo blood glucose measurement studies have been performed by different research groups using near-infrared (NIR) absorption and Raman spectroscopic techniques, prospective prediction has proven to be a challenging problem. An important issue in this case is the demonstration of causality of glucose concentration to the spectral information, especially as the intrinsic glucose signal is smaller compared with that of the other analytes in the blood–tissue matrix. Furthermore, time-dependent physiological processes make the relation between glucose concentration and spectral data more complex. In this article, chance correlations in Raman spectroscopy-based calibration model for glucose measurements are investigated for both in vitro (physical tissue models) and in vivo (animal model and human subject) cases. Different spurious glucose concentration profiles are assigned to the Raman spectra acquired from physical tissue models, where the glucose concentration is intentionally held constant. Analogous concentration profiles, in addition to the true concentration profile, are also assigned to the datasets acquired from an animal model during a glucose clamping study as well as a human subject during an oral glucose tolerance test. We demonstrate that the spurious concentration profile-based calibration models are unable to provide prospective predictions, in contrast to those based on actual concentration profiles, especially for the physical tissue models. We also show that chance correlations incorporated by the calibration models are significantly less in Raman as compared to NIR absorption spectroscopy, even for the in vivo studies. Finally, our results suggest that the incorporation of chance correlations for in vivo cases can be largely attributed to the uncontrolled physiological sources of variations. Such uncontrolled physiological variations could either be intrinsic to the subject or stem from changes in the measurement conditions.     

Square-bounded partitions and Catalan numbers

For each integer k≥1, we define an algorithm which associates to a partition whose maximal value is at most k a certain subset of all partitions. In the case when we begin with a partition λ which is square-bounded, i.e. λ=(λ ₁≥⋅⋅⋅≥λ _k ) with λ ₁=k and λ _k =1, applying the algorithm ℓ times gives rise to a set whose cardinality is either the Catalan number c _ℓ−k+1 (the self dual case) or twice that Catalan number. The algorithm defines a tree and we study the propagation of the tree, which is not in the isomorphism class of the usual Catalan tree. The algorithm can also be modified to produce a two-parameter family of sets and the resulting cardinalities of the sets are the ballot numbers. Finally, we give a conjecture on the rank of a particular module for the ring of symmetric functions in 2ℓ+m variables.