An N-heterocyclic carbene (NHC) catalyzed dihalomethylenation of enals is described. It is a rare example of merging NHC catalysis with single-electron chemistry, a challenging topic with limited previous success. The versatile carbon-centered trihalomethyl radicals have been demonstrated, for the first time, to be compatible with an NHC-bound intermediate, thus leading to efficient and regiose...

Haisheng Li showed that given a module (W,YW (·, x)) for a vertex algebra (V, Y (·, x)), one can obtain a new V -module W = (W,YW (Δ(x)·, x)) if Δ(x) satisfies certain natural conditions. Li presented a collection of such Δ-operators for V = L(k, 0) (a vertex operator algebra associated with an affine Lie algebra, k a positive integer). In this paper, for each irreducible L(k, 0)-module W , we ...

In this paper we consider Artinian modules over power series rings endowed with a Frobenius map. We describe a method for finding the set of all prime annihilators of submodules which are preserved by the given Frobenius map and on which the Frobenius map is not nilpotent. This extends the algorithm by Karl Schwede and the first author, which solved this problem for submodules of the injective ...

a f(x) dx (which one would use for instance to compute the work required to move a particle from a to b). For simplicity we shall restrict attention here to functions f : R → R which are continuous on the entire real line (and similarly, when we come to differential forms, we shall only discuss forms which are continuous on the entire domain). We shall also informally use terminology such as “i...

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...

let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

In this paper we study the effects of bounded rationality in mechanism design problems. We model bounded rationality by assuming that in the presence of an incentive compatible mechanism, players behave as if their types were in a δ-neighborhood of their true types. In our results, we explore what are the effects of such bounded rationality in the outcomes of the mechanism design problem. To su...