Catalytic Generation and Chemoselective Transfer of Nucleophilic Hydrides from Dihydrogen

Copper(I)–N-heterocyclic-carbene (NHC) complexes enabled the catalytic generation of nucleophilic hydrides from dihydrogen (H₂) and their subsequent transfer to allylic chlorides. The highly chemoselective catalyst displayed no concomitant hydrogenation reactivity; in fact, the terminal double bond formed in the hydride transfer remained intact. Switching to deuterium gas (D₂) allowed for regioselective monodeuteration with excellent isotope incorporation.     

Realization of 2-solvable nilpotent groups as groups of classes of homotopy self-equivalences

Let X be a 1-connected CW-complex of finite type and ε_?(X) be the group of homotopy classes of self-equivalences of X which induce the identity on homotopy groups. In this paper, we prove that every finitely generated 2-solvable rational nilpotent group is realizable as ε_?(X) where X is the rationalization of a 1-connected CW-complex of finite type.     

On the complexity of enumerating pseudo-intents

We investigate whether the pseudo-intents of a given formal context can efficiently be enumerated. We show that they cannot be enumerated in a specified lexicographic order with polynomial delay unless P=NP. Furthermore we show that if the restriction on the order of enumeration is removed, then the problem becomes at least as hard as enumerating minimal transversals of a given hypergraph. We introduce the notion of minimal pseudo-intents and show that recognizing minimal pseudo-intents is polynomial. Despite their less complicated nature, surprisingly it turns out that minimal pseudo-intents cannot be enumerated in output-polynomial time unless P=NP.     

Curve following in illiquid markets

In this article the problem of curve following in an illiquid market is addressed. The optimal control is characterised in terms of the solution to a coupled FBSDE involving jumps via the technique of the stochastic maximum principle. Analysing this FBSDE, we further show that there are buy and sell regions. In the case of quadratic penalty functions the FBSDE admits an explicit solution which is determined via the four step scheme. The dependence of the optimal control on the target curve is studied in detail.     

Gompertz zero-inflated cure rate regression models applied to credit risk data

In the financial market, it is important to consider that there is a proportion of customers that have settled their debt in time zero, immediately recovering their ability to pay. In this context, in this paper, we propose a survival analysis methodology that allows the insertion of times equal to zero in scenarios where credit risk is observed. The proposed model addresses the survival analysis model of the zero-inflated cure rate which incorporates the heterogeneity of three subgroups (individuals having events in the initial time, and individuals not susceptible and susceptible to the event). In our proposal, all available survival data of customers are modeled considering that the number of competitive causes follows a Poisson distribution and the baseline risk function follows a Gompertz distribution. The model parameter estimation is obtained by the maximum likelihood estimation procedure and simulation studies are conducted to evaluate the estimators' performance. The studied methodology will be applied to a credit database provided by a financial institution in Brazil.     

A higher-order large-scale regularity theory for random elliptic operators

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale C^k,α-regularity theory, which in the present work is developed in the form of a corresponding C^k,α-“excess decay” estimate: For a given a-harmonic function u on a ball B_R, its energy distance on some ball B_r to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r₀.

Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.