Change point testing for the drift parameters of a periodic mean reversion process

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein–Uhlenbeck process which is defined as the solution of $$\begin{aligned} dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t \end{aligned}$$ and which is observed in continuous time. We derive an explicit representation of the generalized likelihood ratio test statistic assuming that the mean reversion function $L(t)$ is a finite linear combination of known basis functions. In the case of a periodic mean reversion function, we determine the asymptotic distribution of the test statistic under the null hypothesis.     

A non-photochemical route for the regioselective preparation of rtct-pyridylcyclobutanes via hydrothermal isomerisation promoted by polymolybdates

A novel approach for the regioselective preparation of rtct-tpcb (tpcb = tetrapyridylcyclobutanes) compounds promoted by polymolybdates under hydrothermal conditions is reported; these isomers are stabilised as counterions in inorganic-organic hybrid solids and are obtained in high to fair yield.     

Radical cyclization cascades of unsaturated Meldrum's acid derivatives

Unsaturated, differentially substituted Meldrum's acid derivatives undergo cascade cyclizations upon ester reduction with SmI(2)-H(2)O. The cascade cyclizations proceed in good yield and with high diastereocontrol and convert simple, achiral starting materials to complex molecular architectures, bearing up to four stereocenters, in a single operation. The cascades are triggered by the generation and trapping of unusual radical-anions formed by electron transfer to the ester carbonyl.     

Development of Domino Processes by Using 7‐Silylcycloheptatrienes and Its Analogues

7‐Silyl‐ and 7‐silylmethylcycloheptatrienes were shown to react with acylnitroso reagents at room temperature, through their norcaradiene forms, to generate the corresponding cycloadducts 5 a – b and 6 a – b as single diastereomers. The course of the reaction was dramatically modified by changing the reaction conditions. Using a polar medium, functionalized cyclohexa‐1,3‐dienes 7 a – b and bicyclic compounds 13 a – b were instead generated, incorporating one or two amino groups. Similar behavior was observed by using other dienophiles, including triazolinedione, but also activated aldehydes and ketones. A tentative mechanism has been proposed to rationalize the formation of both classes of products that relies on a domino process involving four consecutive elementary steps, in this order: 1) electrocyclic process, 2) hetero‐Diels–Alder reaction, 3) cyclopropane ring opening, and 4) hetero‐Diels–Alder reaction. Trapping of the cationic intermediate and isolation of the primary cycloadduct provide support for this hypothesis. An enantioselective version of the cascade using cycloheptatriene 4 b and aldehydes and ketones, under copper(II) catalysis was also carried out, leading to cyclohexa‐1,3‐dienes 21 , 28 , and 30 with enantioselectivities up to 93 % ee. Finally, elaboration of the intermediates above has been carried out, opening a straightforward access to sugar mimics 42 – 43 and complex polycyclic systems 36 and 39 .     

Long-range effects on the capture and release of a chiral guest by a helical molecular capsule

Helically folded molecular capsules based on oligoamide sequences of aromatic amino acids which are capable of binding tartaric acid in organic solvents with high affinity and diastereoselectivity have been synthesized, and their structures and binding properties investigated by (1)H NMR, X-ray crystallography, circular dichroism, and molecular modeling. We found that elongating the helices at their extremities by adding monomers remote from the tartaric binding site results in a strong increase of the overall helix stability, but it does not influence the host-guest complex stability. The effect of this elongation on the binding and release rates of the guest molecules follows an unexpected non-monotonous trend. Three independent observations (direct monitoring of exchange over time, 2D-EXSY NMR, and molecular modeling) concur and show that guest exchange rates tend to first increase upon increasing helix length and then decrease when helix length is increased further. This investigation thus reveals the complex effects of adding monomers in a helically folded sequence on a binding event that occurs at a remote site and sheds light on possible binding and release mechanisms.     

Mild copper-catalyzed vinylation reactions of azoles and phenols with vinyl bromides

An efficient and straightforward copper-catalyzed method allowing vinylation of N- or O-nucleophiles with di- or trisubstituted vinyl bromides is reported. The procedure is applicable to a broad range of substrates since N-vinylation of mono-, di-, and triazoles as well as O-vinylation of phenol derivatives can be performed with catalytic amounts of copper iodide and inexpensive nitrogen ligands 3 or 8. In the case of more hindered vinyl bromides, the use of the original bidentate chelator 8 was shown to be more efficient to promote the coupling reactions than our key tetradentate ligand 3. The corresponding N-(1-alkenyl)azoles and alkenyl aryl ethers are obtained in high yields and selectivities under very mild temperature conditions (35-110 degrees C for N-vinylation reactions and 50-80 degrees C for O-vinylation reactions). Moreover, to our knowledge, this method is the first example of a copper-catalyzed vinylation of various azoles. Finally, this protocol, practical on a laboratory scale and easily adaptable to an industrial scale, is very competitive compared to the existing methods that allow the synthesis of such compounds.     

Supramolecular isomerism in multivalent metal-templated assemblies with topochemical influence in the regioselective synthesis of tetrakis(2-pyridyl)cyclobutane isomers

An unprecedented example of supramolecular isomerism based on 2D hydrogen-bonded multi-component networks that leads to the preparation of different photoproducts via a topochemical transformation is reported.