General Synthetic Route to Monosubstituted Cycloheptadienes from Organometallic Compounds

An examination of the literature reveals that only a limited number of monosubstituted cycloheptadiene compounds have been reported. An obvious synthetic route to 5-substituted -1, 3-cycloheptadiene derivatives would be the reaction of nucleophiles with the cycloheptadienyl cation, but this pathway is generally unsuccessful due to the limited stability of the cation. On the other hand, the iron tricarbonyl complex of this cation shows remarkable stability¹ and an ability to react with nucleophiles². If the -Fe(CO)₃ group could be removed easily, a facile route to this family of organic compounds would be available. This work reports our investigation of the range of nucleophiles that can be utilized and the oxidizing agents that can remove efficiently the -Fe(CO)₃ group.     

Determining angular frequency from images of rotating objects via a generalized fast Fourier transform

In certain real-world applications, one needs to estimate the angular frequency of a spinning object. We consider the image processing problem of estimating this rate of rotation from a video of the object taken by a camera aligned with the axis of rotation. For many types of spinning objects, this problem can be addressed with existing techniques: simply register two consecutive video frames. We focus, however, on objects whose shape and intensity changes greatly from frame to frame, such as spinning plumes of plasma that emerge from a certain type of spacecraft thruster. To estimate the angular frequency of such objects, we introduce the Geometric Sum Transform (GST), a new rotation-based generalization of the discrete Fourier transform (DFT). Taking the GST of a given video produces a new sequence of images, the most coherent of which corresponds to the object’s true rate of rotation. After formally demonstrating this fact, we provide a fast algorithm for computing the GST which generalizes the decimation-in-frequency approach for performing a Fast Fourier Transform (FFT). We further show that computing a GST is, in fact, mathematically equivalent to computing a system of DFTs, provided one can decompose each video frame in terms of an eigenbasis of a rotation operator. We conclude with numerical experimentation.     

The (S−1,S) inventory model and its counterparts in queueing theory

We explore the relationship between the ($S?1,S$) inventory model and three well-known queueing models: the Erlang loss system, the machine-repair model and a two-node Jackson network. Exploiting this relationship allows us to obtain key performance measures of the ($S?1,S$) model, like the so-called virtual outdating time, the number of items on the shelf in steady state, the long-run rate of unsatisfied demands and the distribution of the empty shelf period.     

Dabco-Catalysed Reactions of Salicylaldehydes with Acrylate Derivatives

Treatment of salicylaldehydes with acrylate derivatives in the presence of 1,4-diazabicyclo[2.2.2]octane (DABCO) has been shown to afford both coumarin and chromene derivatives, and factors influencing the product distributions have been investigated.     

Composite Likelihood Inference in a Discrete Latent Variable Model for Two-Way “Clustering-by-Segmentation” Problems

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g., exchangeable observational units or features) and contiguous groups, or segments, along the other (e.g., consecutively ordered times or locations). The model relies on a hidden Markov structure but, given its complexity, cannot be estimated by full maximum likelihood. Therefore, we introduce a composite likelihood methodology based on considering different subsets of the data. The proposed approach is illustrated by simulation, and with an application to genomic data.     

Regioselective A-Ring Chlorination of Benzodiazepine Analogues Using tert-Butyl Hypochlorite

Treatment of 2-phenyl-2,3-dihydro-1,4-benzodiazepin-5(4H)-one and a series of 1,4-benzoxazepinone analogues with tert-butyl hypochlorite affords products shown, by NMR and MS spectroscopy, to be chlorinated exclusively in the A-ring at positions 7 and/or 9.     

Preparation of Nitriles by Dehydration of Primary Carboxawides with a Supported phosphorus pentoxide reagent

The use of a supported phosphorus pentoxide reagent in the synthesis of selected nitriles is discussed.     

Rapid Aqueous Borohydride Reduction of Carbonyls Under Sealed-Tube Microwave Conditions

Ketones and aldehydes are conveniently and rapidly reduced to the corresponding alcohols in good yields using sodium borohydride under sealed-tube microwave conditions in either 95% ethanol or water. In purely aqueous systems, highly aliphatic substrates are sluggish, but this can be overcome by introducing sodium dodecyl sulfate (SDS) at the critical micelle concentration. With a 2:1 substrate/borohydride ratio and a reaction temperature of 100 °C, reduction is typically complete within 1 min in 95% ethanol and 5 min in water/SDS. The methodology is well suited for parallel and combinatorial synthetic approaches.     

A Convenient Preparation of Carboxylic Acid Anhydrides Using a “Supported” Phosphorus Pentoxide Reagent

Treatment of carboxylic acids with a “supported” phosphorus pentoxide reagent provides a convenient route to the corresponding anhydrides.