Arithmetic degree and associated graded modules

We prove that the arithmetic degree of a graded or local ring A is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideal I in A. In particular, if Spec(A) is equidimensional and has an embedded component (i.e., A has an embedded associated prime ideal), then the normal cone of Spec(A) along V(I) has an embedded component too. This extends a result of W. M. Ruppert about embedded components of the tangent cone.Mathematics Subject Classification (2000): Primary 13H15, 13A30; Secondary 13D45, 14Q99     

Hopf Algebra Extensions of Group Algebras and Tambara-Yamagami Categories

We determine the structure of Hopf algebras that admit an extension of a group algebra by the cyclic group of order 2. We study the corepresentation theory of such Hopf algebras, which provide a generalization, at the Hopf algebra level, of the so called Tambara-Yamagami fusion categories. As a byproduct, we show that every semisimple Hopf algebra of dimension < 36 is necessarily group-theoretical; thus 36 is the smallest possible dimension where a non group-theoretical example occurs.     

On the Classification of Almost Square-Free Modular Categories

Let \(\mathcal {C}\) be a modular category of Frobenius-Perron dimension d q ⁿ , where q >?2 is a prime number and d is a square-free integer. We show that \(\mathcal {C}\) must be integral and nilpotent and therefore group-theoretical. In the case where q =?2, we describe the structure of \(\mathcal {C}\) in terms of equivariantizations of group-crossed braided fusion categories.     

Ubiquitin Associates with the N‐Terminal Domain of Nerve Growth Factor: The Role of Copper(II) Ions

Many biochemical pathways involving nerve growth factor (NGF), a neurotrophin with copper(II) binding abilities, are regulated by the ubiquitin (Ub) proteasome system. However, whether NGF binds Ub and the role played by copper(II) ions in modulating their interactions have not yet been investigated. Herein NMR spectroscopy, circular dichroism, ESI‐MS, and titration calorimetry are employed to characterize the interactions of NGF with Ub. NGF_1–14, which is a short model peptide encompassing the first 14 N‐terminal residues of NGF, binds the copper‐binding regions of Ub (K_D=8.6 10^?5 m ). Moreover, the peptide undergoes a random coil–polyproline type II helix structural conversion upon binding to Ub. Notably, copper(II) ions inhibit NGF_1–14/Ub interactions. Further experiments performed with the full‐length NGF confirmed the existence of a copper(II)‐dependent association between Ub and NGF and indicated that the N‐terminal domain of NGF was a valuable paradigm that recapitulated many traits of the full‐length protein.     

The preparation of perfluoroaryl substituted isoxazoles via nucleophilic aromatic substitution with lithioalkylisoxazoles

The lithioalkylisoxazoles obtained from C-5 lateral metalation of alkylisoxazoles, 1 , add to hexafluorobenzene. When the C-4 substituent was an electron withdrawing tertiary amide moiety, the yields were highest for mono-perfluoroarylation to give 5-pentafluorophenylmethylisoxazoles, 2 .     

Zinc Interactions with a Soluble Mutated Rat Amylin to Mimic Whole Human Amylin: An Experimental and Simulation Approach to Understand Stoichiometry,Speciation and Coordination of the Metal Complexes

Islet amyloid polypeptide (IAPP) is a hormone co-secreted with insulin and zinc from pancreatic β-cells. To overcome the low solubility of human IAPP, we characterized zinc complexes species formed with 1) a mutated form of rat-IAPP(1–37; R18 H) able to mimic the human IAPP, 2) the r-IAPP(1–37) and the IAPP(1–8) fragment. Stoichiometry, speciation and coordination features of zinc(II) complexes were unveiled by ESI-MS, potentiometry and NMR measurements combined with DFT and free-energy simulations. Mononuclear species start to form around pH 6; Zn²⁺ binds both His18 and N-amino terminus in rat-IAPP(1–37; R18 H). The in silico study allows us to assess not only a structured turn compact domain in r-IAPP(1–37) and r-IAPP(1–37; R18 H) featured by a different free energy barrier for the transition from the compact to elongated conformation upon the coordination of Zn²⁺, but also to bring into light a coordination shell further stabilized by noncovalent interactions.