Hochschild and cyclic (co)homology of superadditive categories

We define the Hochschild and cyclic (co)homology groups for superadditive categories and show that these (co)homology groups are graded Morita invariants. We also show that the Hochschild and cyclic homology are compatible with the tensor product of superadditive categories.     

Quantum McKay Correspondence for Disc Invariants of Toric Calabi–Yau 3-orbifolds

We announce a result on quantum McK ay correspondence for disc invariants of outer legs in toric Calabi–Yau 3-orbifolds, and illustrate our method in a special example [C3/Z5(1, 1, 3)].     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Homoclinic orbits for first order Hamiltonian systems with some twist conditions

In this paper, we study the nonperiodic first-order Hamiltonian system ù = J L(t)u +J H(t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation,we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin.     

Frontispiz: Mild and Versatile Nitrate‐Promoted C?H Bond Fluorination

A novel and facile C H bond fluorination proceeds under remarkably mild conditions (close to room temperature in most cases). Both aromatic and olefinic C(sp²) H bonds with a wide range of electronic properties are selectively fluorinated in the presence of a catalytic amount of simple, cheap, and nontoxic nitrate as the promoter. A Pd^II/Pd^IV catalytic cycle that is initiated by an in situ generated cationic [Pd(NO₃)]⁺ species was proposed based on preliminary mechanistic studies.     

Determination of six polyynes in Oplopanax horridus and Oplopanax elatus using polyethylene glycol modified reversed migration microemulsion electrokinetic chromatography

A PEG‐modified reversed migration MEEKC method was developed for simultaneous determination of six polyynes, including oplopandiol, falcarindiol, oplopandiol acetate, (11S, 16S, 9Z)‐9,17‐octadecadiene‐12,14‐diyne‐1,11,16‐triol,1‐acetate, oplopantriol B, and oplopantriol A, in Oplopanax horridus and Oplopanax elatus. The running buffer containing 0.8% v/v ethyl acetate, 3.8% w/v SDS, 6.6% v/v n‐butanol in 20 mM phosphate buffer (pH 2.5), followed by mixing with propan‐2‐ol at 30% v/v and PEG‐1000 at 15% w/v, was applied in the analysis. The proposed method was successfully applied to determine the six polyynes in five samples of Oplopanax horridus and one of O. elatus. The result showed that the types and amounts of polyynes present were obviously different when comparing the two herbs. Besides, the developed PEG‐modified reversed MEEKC method might be suitable for the analysis of hydrophobic analytes in herbal medicines.