Molecular Design Principles for Near‐Infrared Absorbing and Emitting Indolizine Dyes

Desirable components for dye‐sensitzed solar cell (DSC) sensitizers and fluorescent imaging dyes include strong donating building blocks coupled with well‐balanced acceptor functionalities for absorption beyond the visible range. We have evaluated the effects of increasing acceptor strengths and incorporation of dye morphology controlling groups on molar absorptivity and absorption breadth with indolizine donor‐based dyes. Indolizine‐based D –A and D –π–A sensitizers incorporating bis‐rhodanine, tricyanofuran (TCF), and cyanoacrylic acid functionalities were analyzed for performance in DSC devices. The TCF derivatives were also evaluated as near‐infrared (NIR)‐emissive materials with the AH25 emissions extending past 1000 nm.     

When the dual of an ideal is a ring

Let R be a commutative integral domain with identity with quotient field K, and let I be a nonzero ideal of R. We analyze several general and particular instances when I^–1 is a subring of K. We then apply some of our results to show that certain non-maximal prime ideals in Prüfer domains are divisorial.     

Hilbert Coefficients and the Depths of Associated Graded Rings

This work was motivated in part by the following general question:given an ideal I in a Cohen–Macaulay (abbreviated to CM)local ring R such that dim R/I=0, what information about I andits associated graded ring can be obtained from the Hilbertfunction and Hilbert polynomial of I? By the Hilbert (or Hilbert–Samuel)function of I, we mean the function H_I(n)=(R/Iⁿ) for all n1,where denotes length. Samuel [23] showed that for large valuesof n, the function H_I(n) coincides with a polynomial P_I(n) ofdegree d=dim R. This polynomial is referred to as the Hilbert,or Hilbert–Samuel, polynomial of I. The Hilbert polynomialis often written in the form where e₀(I), ..., e_d(I) are integers uniquely determined byI. These integers are known as the Hilbert coefficients of I.     

Quotient rings of polynomial rings

Let R be a commutative ring with identity. The multiplicatively closed sets U₂={fR[X]: c(f)–1=R}, (U₂)={fU₂: f is regular} and S={fR[X]: c(f)=R} are studied. By considering various equalities between these sets, many characterizations of Noetherian rings are found. In particular, a Noetherian ring R has depth 1 if and only if S=(U₂): and each maximal ideal of a Noetherian ring is regular if and only if U₂=(U₂).The theory of Prüfer v-multiplication rings (PVMR's) is developed for rings with zero divisors. Six equivalent conditions are given to the statement that an additively regular v-ring R is a PVMR.     

Inkjet-Printed TiO2/Fullerene Composite Films for Planar Perovskite Solar Cells

Perovskite solar cells have garnered and held international research interest, due to ever-climbing power conversion efficiency values, now >25 %. Some high efficiency configurations utilize a compact TiO₂ layer underneath a mesoporous TiO₂ layer, both of which require high temperature annealing steps that could hinder perovskite commercialization. To address the high thermal budget, we chose to use inkjet-printing to combine the two layers into a single TiO₂ film, which incorporates both nanoparticle and molecular precursor as well as organic fullerene additives. We printed the ink on fluorine-doped tin oxide, and after annealing at various temperatures, we found that 400 °C was the optimum annealing temperature for the inkjet-printed electron transport layers, which is significantly lower than the 500 °C required to anneal typical mesoporous TiO₂ films.     

M-Canonical ideals in integral domains

We prove that a Priifer domain R has an m-canonical ideal J, that is, an ideal I such that J: (I: J) = J for every ideal J of R, if and only if R is h-local with only finitely many maximal ideals that are not finitely generated; moreover, if these conditions are satisfied, then the product of the non-finitely generated maximal ideals is an m-canonical ideal of R