Explicit congruences modulo 2048 for overpartitions

The Ramanujan Journal - Let $${\bar{p}}(n)$$ denote the number of overpartitions of n. Recently, a number of congruences modulo powers of 2, 3 and 5 have been discovered. The moduli for these...     

Preparation of polymer-supported Ru-TsDPEN catalysts and use for enantioselective synthesis of (S)-fluoxetine

Polymer-supported chiral ligands 9 and 17 were prepared based on Noyori's (1S,2S)- or (1R,2R)-N-(p-tolylsulfonyl)-1,2-diphenylethylenediamine. The combination with [RuCl2(p-cymene)]2 has been shown to exhibit high activities and enantioselectivities for heterogeneous asymmetric transfer hydrogenation of aromatic ketones (19a-c) with formic acid-triethylamine azeotrope as the hydrogen donor, whereby affording the respective optically active alcohols 20a-c, the key precursors of chiral fluoxetine. As exemplified by ligand 17 for substrate 19c, the catalysts can be recovered and reused in three consecutive runs with no significant decline in enantioselectivity. The procedure avoids the plausible contamination of fluoxetine by the toxic transition metal species.     

Proofs of some conjectures on the reciprocals of the Ramanujan–Gordon identities

The Ramanujan Journal - Recently, Lin and Wang introduced two special partition functions $$RG_1(n)$$ and $$RG_2(n)$$ , the generating functions of which are the reciprocals of two identities due...     

Few-Layer MoS2 Nanosheets Encapsulated in N-Doped Carbon Hollow Spheres as Long-Life Anode Materials for Lithium-Ion Batteries

Two-dimensional molybdenum disulfide (MoS₂) has been recognized as a promising anode material for lithium-ion batteries (LIBs) due to its high theoretical capacity, but its rapid capacity decay owing to poor conductivity, structure pulverization, and polysulfide dissolution presents significant challenges in practical applications. Herein, triple-layered hollow spheres in which MoS₂ nanosheets are fully encapsulated between inner carbon and outer nitrogen-doped carbon (NC) were fabricated. Such an architecture provides high conductivity and efficient lithium-ion transfer. Moreover, the NC shell prevents aggregation and exfoliation of MoS₂ nanosheets and thus maintains the integrity of the nanostructure during the charge/discharge process. As anode materials for LIBs, the C@MoS₂@NC hollow spheres deliver a high reversible capacity (747 mA h g⁻¹ after 100 cycles at 100 mA g⁻¹) and excellent long-cycle performance (650 mA h g⁻¹ after 1000 cycles at 1.0 A g⁻¹), which confirm its potential for high-performance LIBs.