A p‐Order signed integer‐valued autoregressive (SINAR(p)) model

In this article, we propose an extension of integer‐valued autoregressive INAR models. Using a signed version of the thinning operator, we define a larger class of ‐valued processes, called SINAR, which can have positive as well as negative correlations. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. In particular, it is shown that the autocorrelation function of any real‐valued AR process can be recovered with a SINAR process, which improves INAR modeling.     

A New Covariance Function and Spatio‐Temporal Prediction (Kriging) for A Stationary Spatio‐Temporal Random Process

Consider a stationary spatio‐temporal random process and let be a sample from the process. Our object here is to predict, given the sample, for all t at the location s _o. To obtain the predictors, we define a sequence of discrete Fourier transforms using the observed time series. We consider these discrete Fourier transforms as a sample from the complex valued random variable . Assuming that the discrete Fourier transforms satisfy a complex stochastic partial differential equation of the Laplacian type with a scaling function that is a polynomial in the temporal spectral frequency ω, we obtain, in a closed form, expressions for the second‐order spatio‐temporal spectrum and the covariance function. The spectral density function obtained corresponds to a non‐separable random process. The optimal predictor of the discrete Fourier transform is in terms of the covariance functions. The estimation of the parameters of the spatio‐temporal covariance function is considered and is based on the recently introduced frequency variogram method. The methods given here can be extended to situations where the observations are corrupted by independent white noise. The methods are illustrated with a real data set.     

Non‐stationary autoregressive processes with infinite variance

Consider an AR(p) process , where {?_t} is a sequence of i.i.d. random variables lying in the domain of attraction of a stable law with index 0<α<2. This time series {Y_t} is said to be a non‐stationary AR(p) process if at least one of its characteristic roots lies on the unit circle. The limit distribution of the least squares estimator (LSE) of for {Y_t} with infinite variance innovation {?_t} is established in this paper. In particular, by virtue of the result of Kurtz and Protter (1991) of stochastic integrals, it is shown that the limit distribution of the LSE is a functional of integrated stable process. Simulations for the estimator of β and its limit distribution are also given.     

Identification of Persistent Cycles in Non‐Gaussian Long‐Memory Time Series

Abstract. Asymptotic distribution is derived for the least squares estimates (LSE) in the unstable AR(p) process driven by a non‐Gaussian long‐memory disturbance. The characteristic polynomial of the autoregressive process is assumed to have pairs of complex roots on the unit circle. In order to describe the limiting distribution of the LSE, two limit theorems involving long‐memory processes are established in this article. The first theorem gives the limiting distribution of the weighted sum, is a non‐Gaussian long‐memory moving‐average process and (c_n,k,1 ≤ k ≤ n) is a given sequence of weights; the second theorem is a functional central limit theorem for the sine and cosine Fourier transforms      

Least tail‐trimmed squares for infinite variance autoregressions

We develop a robust least squares estimator for autoregressions with possibly heavy tailed errors. Robustness to heavy tails is ensured by negligibly trimming the squared error according to extreme values of the error and regressors. Tail‐trimming ensures asymptotic normality and super‐‐convergence with a rate comparable to the highest achieved amongst M‐estimators for stationary data. Moreover, tail‐trimming ensures robustness to heavy tails in both small and large samples. By comparison, existing robust estimators are not as robust in small samples, have a slower rate of convergence when the variance is infinite, or are not asymptotically normal. We present a consistent estimator of the covariance matrix and treat classic inference without knowledge of the rate of convergence. A simulation study demonstrates the sharpness and approximate normality of the estimator, and we apply the estimator to financial returns data. Finally, tail‐trimming can be easily extended beyond least squares estimation for a linear stationary AR model. We discuss extensions to quasi‐maximum likelihood for GARCH, weighted least squares for a possibly non‐stationary random coefficient autoregression, and empirical likelihood for robust confidence region estimation, in each case for models with possibly heavy tailed errors.     

Transition Metal‐Free Approach to Propynenitriles and 3‐Chloropropenenitriles

A transition metal‐free, facile and efficient one‐pot protocol for the synthesis of propynenitriles from readily available 3‐chloropropenals is disclosed. The reaction conditions have also been optimized for the exclusive formation and isolation of 3‐chloropropenenitriles which are important building blocks in general and are intermediates in the synthesis of propynenitriles. The hallmark of the methodology is the use of non‐toxic reagents, milder, metal‐free and economically benign reaction conditions avoiding a harsh dehydration step while achieving excellent yields.

     

Synthesis of Free NH 2‐(Aminomethyl)indoles through Copper‐Catalyzed Reaction of 3‐(ortho‐Trifluoroacetamidophenyl)‐1‐propargylic Alcohols with Amines and Palladium/Copper‐ Cocatalyzed Domino Three‐Component Sonogashira Cross‐Coupling/Cyclization/Substitution Reactions

Free NH 2‐(aminomethyl)indoles have been prepared via copper‐catalyzed cyclization of 3‐(ortho‐trifluoroacetamidophenyl)‐1‐propargylic alcohols in the presence of primary or secondary amines. The synthesis has been developed into a simple and very efficient domino three‐component Sonogashira cross‐coupling/cyclization/substitution process that, omitting the isolation of 3‐(ortho‐trifluoroacetamidophenyl)‐1‐propargylic alcohols, provides access to this class of compounds by treating 2‐iodotrifluoroacetanilides, propargylic alcohols, and primary or secondary amines with a copper/palladium catalyst system.

     

Robust and Recyclable Self‐Supported Chiral Nickel Catalyst for the Enantioselective Michael Addition

A simple chemical modification of a chiral diamine ligand may produce a robust and recyclable enantioselective catalyst. Metallopolymers based on chiral cyclohexyldiamine‐containing ditopic ligands and nickel(II) complexes have been readily prepared and applied in catalytic enantioselective Michael additions of 1,3‐dicarbonyl compounds to nitroalkenes. High yields and good enantioselectivities have been obtained and the catalytic systems have been recycled up to 11 times without loss of either activity or enantioselectivity at a low catalyst loading of 0.75 mol%. Moreover, the nickel metallopolymers were found to be air‐ and moisture‐stable, which enabled this chemistry to be carried out on the bench without the use of any air‐free techniques and with non‐degassed solvents. Finally, the nature of the catalyst was studied by non‐linear effect experiments, giving a negative non‐linear effect (NLE) as a consequence of an in situ decrease in the ee of the active species consistent with the trapping of homochiral aggregates.

     

High‐frequency sampling of a continuous‐time ARMA process

Continuous‐time autoregressive moving average (CARMA) processes have recently been used widely in the modelling of non‐uniformly spaced data and as a tool for dealing with high‐frequency data of the form ,n = 0, 1, 2,…, where Δ is small and positive. Such data occur in many fields of application, particularly in finance and in the study of turbulence. This article is concerned with the characteristics of the process , when Δ is small and the underlying continuous‐time process is a specified CARMA process.     

Stationary bootstrapping for non‐parametric estimator of nonlinear autoregressive model

We consider stationary bootstrap approximation of the non‐parametric kernel estimator in a general kth‐order nonlinear autoregressive model under the conditions ensuring that the nonlinear autoregressive process is a geometrically Harris ergodic stationary Markov process. We show that the stationary bootstrap procedure properly estimates the distribution of the non‐parametric kernel estimator. A simulation study is provided to illustrate the theory and to construct confidence intervals, which compares the proposed method favorably with some other bootstrap methods.     

Nickel‐ or Iron‐Catalyzed Cross‐Coupling of Aryl Carbamates with Arylsilanes

Aryl carbamates were for the first time applied as electrophiles in the cross‐coupling with arylsilanes via nickel or iron catalysis to construct valuable biaryl compounds. This new coupling reaction features a good group tolerance and non‐sensitivity to steric hindrance on both aryl carbamates and arylsilanes.

     

Inhibition of Peroxidase‐Catalyzed Iodination by Cephalosporins: Metallo‐β‐Lactamase‐Induced Antithyroid Activity of Antibiotics

Broad‐spectrum antibiotics with heterocyclic side chains strongly inhibit peroxidase‐catalyzed iodination in the presence of metallo‐β‐lactamase. This suggests that antibiotic resistance due to hydrolysis of the β‐lactam ring in antibiotics would have negative effects on thyroid activity.

     

Enhanced Exfoliation of Organoclay in Partially End‐Functionalized Non‐Polar Polymer

We found that enhanced exfoliation of clay up to 20 wt.‐% in non‐polar polybutadiene (PB) if the PB was blended with a relatively small fraction of hydroxyl‐terminated PB (HTPB). The choice of an intermediate polymer composition to enhance exfoliation was motivated by theoretical predictions of end‐functionalizing effects of Balazs, Farmer, and coworkers. A combination of X‐ray diffraction and rheological measurements were used to optimize HTPB content for enhanced exfoliation. We also observed the competition of the kinetic and thermodynamic processes during the ripening of the exfoliated clay structure.

     

Time‐ and Temperature‐Dependent Fracture Mechanics of Polymers: General Aspects at Monotonic Quasi‐Static and Impact Loading Conditions

Well‐defined correlations exist between the maxima in mechanical loss factor and the local maxima in temperature‐ or loading‐speed‐dependent fracture toughness. The non‐linear viscoelastic fracture processes and small‐strain deformations are characterised by the same Arrhenius‐type activation enthalpies. The local increase in toughness is linearly correlated with the relaxation strength of molecular relaxation processes. Stable crack propagation can be understood as a three‐phase process resulting in steady‐state stable crack growth. The normalised steady‐state crack‐tip‐opening displacement is independent of matrix material, temperature and loading speed.

     

Discovery of a Potent,CNS‐Penetrant Orexin Receptor Antagonist Based on an N,N‐Disubstituted‐1,4‐diazepane Scaffold that Promotes Sleep in Rats

Silent Night : Antagonism of the orexin (or hypocretin) system has recently been identified as a novel mechanism for the treatment of insomnia. Herein, we describe discovery of a dual (OX₁R/OX₂R) orexin receptor antagonist featuring a 1,4‐diazepane central constraint that blocks orexin signaling in vivo. In telemetry‐implanted rats, oral administration of this antagonist produced a decrease in wakefulness, while increasing REM and non‐REM sleep.

     

Zinc Iodide‐Mediated Direct Synthesis of 2,3‐Dihydroisoxazoles from Alkynes and Nitrones

A zinc diiodide (ZnI₂)‐mediated direct synthesis of 2,3‐dihydroisoxazoles via a [3+2] cycloaddition reaction of the nitrones and non‐electron‐deficient terminal alkynes has been developed. This method was applied in the formal synthesis of HPA‐12 and aminoglucose.

     

Non‐Heme Imine‐Based Iron Complexes as Catalysts for Oxidative Processes

Non‐heme iron complexes are emerging as powerful and versatile catalysts in several oxidative transformations. The most investigated iron complex structures are based on aminopyridine ligands, but a number of imine‐based ligands have been also tested. In this review a collection of recent results obtained in oxidation catalysis with non‐heme imine‐based iron complexes is presented. Their catalytic performances in C H, CC and  S oxidation are spread over a wide range of efficiency, going from very low to quite high. Such performances are discussed, whenever possible, in light of the operating reaction mechanisms and of catalyst stability. In order to facilitate the discussion, an initial survey of the most useful mechanistic tools widely applied to distinguish a metal‐based oxidation from a radical‐chain process is also reported. Imine‐based catalysts are divided into two classes: (i) salen‐Fe complexes, and (ii) imine‐Fe complexes. In some cases clues for free‐radical oxidation mechanisms have been reported while in other cases evidence for metal‐based mechanisms has been collected. The preferred mechanistic pathway is shown to be a function of catalyst structure and features. Interestingly, some imine‐based iron complexes are able to perform stereospecific oxidation reactions, demonstrating that the imine functionality can be incorporated in ligands designed for oxidation catalysis.

     

Titanium‐Catalyzed,One‐Pot Synthesis of 2‐Amino‐3‐cyano‐ pyridines

Earth‐abundant and inexpensive titanium can catalyze alkyne iminoamination, which generates tautomers of 1,3‐diimines. Upon treatment with base (DBU) and malononitrile, the multicomponent coupling product is converted to 2‐amino‐3‐cyanopyridines in a one‐pot procedure in good to modest yields. There is substantial control of regioselectivity for the substituents on the pyridine ring and on the 2‐amino group. Several studies were done that provide significant evidence for a Dimroth rearrangement mechanism for 2‐aminopyridine formation, including isolation of a 2‐imino‐1,2‐dihydropyridine intermediate that undergoes rearrangement under the reaction conditions.

     

Sodium Iodide/Hydrogen Peroxide‐Mediated Oxidation/Lactonization for the Construction of Spirocyclic Oxindole‐Lactones

The sodium iodide/hydrogen peroxide‐mediated oxidation/lactonization of indolepropionic acids was achieved, affording the corresponding spirocyclic oxindole‐lactones in moderate to high yields. This metal‐free procedure features mild reaction conditions, non‐toxicity and easy handling, with hydrogen peroxide (H₂O₂) as a clean oxidant.

     

Palladium‐Catalyzed Divergent Arylation with Triazolopyridines: One‐Pot Synthesis of 6‐Aryl‐2‐α‐styrylpyridines

We have developed a new strategy for palladium‐catalyzed arylation reactions with triazolopyridines, wherein two different chemical transformations (C‐3 vs. C‐7) are observed by differentiating the substrates using different bases. The reactive palladium carbenoids were directly generated from triazolopyridines and underwent denitrogenative arylations with aryl bromides. Intriguingly, when potassium carbonate was replaced with potassium tert‐butoxide, direct C H arylation occurred at the most acidic position (C‐7). Moreover, two different catalytic arylation events were successfully performed in a one‐pot sequence, providing a convenient access to 6‐aryl‐2‐α‐styrylpyridines.