Accurate a posteriori error evaluation in the reduced basis method

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this Note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.     

Multidimensional extension of the Morse–Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence x$x$ over a finite alphabet is ultimately periodic if and only if, for some n$n$, the number of different factors of length n$n$ appearing in x$x$ is less than n+1$n+1$. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let d≥2$d\ge 2$. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of Z^d${\mathbb{Z}}^d$ definable by a first order formula in the Presburger arithmetic 〈Z;<,+〉$〈\mathbb{Z};<,+〉$. With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse–Hedlund theorem to an arbitrary dimension d$d$ and characterize sets of Z^d${\mathbb{Z}}^d$ definable in 〈Z;<,+〉$〈\mathbb{Z};<,+〉$ in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often.     

Superacid-Mediated Late-Stage Aromatic Polydeuteration of Pharmaceuticals

The field of medicinal chemistry is currently witnessing a deuterium rush owing to the remarkable properties of this element as bioisoster of hydrogen atom. Aromatic hydrogen isotope exchange (HIE) is one of the most studied strategies nowadays as it promises to access deuterium-modified drugs directly from their non-labeled parents. While most of the recent studies focus on metal-catalyzed C−H activation strategy, the use of superacidic conditions has been largely overlooked. This study shows that the use of TfOD as reaction medium allows the late-stage polydeuteration of a broad library of pharmaceuticals bearing a wide array of functional groups, complementing existing procedures.     

Copper-catalyzed functionalization of enynes

The copper-catalyzed functionalization of enyne derivatives has recently emerged as a powerful approach in contemporary synthesis. Enynes are versatile and readily accessible substrates that can undergo a variety of reactions to yield densely functionalized, enantioenriched products. In this perspective, we review copper-catalyzed transformations of enynes, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations. Particular attention is given to the regiodivergent functionalization of 1,3-enynes, and the current mechanistic understanding of such processes.

The copper-catalyzed functionalization of enynes is a powerful approach to yield densely functionalized products. This review covers various transformations, such as boro- and hydrofunctionalizations, copper-mediated radical difunctionalizations, and cyclizations.     

Hexacyanometalate molecular chemistry: di-, tri-, tetra-, hexa- and heptanuclear heterobimetallic complexes; control of nuclearity and structural anisotropy

Following a bottom-up approach to nanomaterials, we present a rational synthetic route to high-spin and anisotropic molecules based on hexacyanometalate [M(CN)(6)](3-) cores. Part 1 of this series was devoted to isotropic heptanuclear clusters; herein, we discuss the nuclearity and the structural anisotropy of nickel(II) derivatives. By changing either the stoichiometry, the nature of the terminal ligand, or the counterion, it is possible to tune the nuclearity of the polynuclear compounds and therefore to control the structural anisotropy. We present the synthesis and the characterisation by mass spectrometry, X-ray crystallography and magnetic susceptibility of bi-, tri-, tetra-, hexa- and heptanuclear species [M(CN)(n)(CN-M'L)(6-n)](m+) (with n=0-5; M=Cr(III), Co(III), M'=Ni(II); L=pentadentate ligand). Thus, with M=Cr(III), d(3), S=3/2, a dinuclear complex [Cr(III)(CN)(5)(CN-NiL(n))](9+), (L(n)=polydentate ligand) was built and characterised, showing a spin ground state, S(G)=5/2, with a ferromagnetic interaction J(Cr,Cu)=+18.5 cm(-1). With M=Co(III) (d(6), S=0) were built di-, tri-, tetra-, hexa and hepanuclear CoNi species: CoNi, CoNi(2), CoNi(3), CoNi(5) and CoNi(6). By a first approximation, they behave as one, two, three, five and six isolated nickel(II) complexes, respectively, but more accurate studies allow us to evaluate the weak antiferromagnetic coupling constant between two next-nearest neighbours M'-Co-M'.     

Control of an external-cavity laser diode operating in the regular pulse package regime with a frequency shift of the optical feedback

I demonstrate numerically that the regular pulse package regime observed in an external-cavity laser diode can be controlled by means of an adequate shift of the optical feedback frequency. This control leads to a stable pulsed behavior.     

Current Status and New Perspectives on Chitin and Chitosan as Functional Biopolymers

The natural biopolymer chitin and its deacetylated product chitosan are found abundantly in nature as structural building blocks and are used in all sectors of human activities like materials science, nutrition, health care, and energy. Far from being fully recognized, these polymers are able to open opportunities for completely novel applications due to their exceptional properties which an economic value is intrinsically entrapped. On a commercial scale, chitosan is mainly obtained from crustacean shells rather than from the fungal and insect sources. Significant efforts have been devoted to commercialize chitosan extracted from fungal and insect sources to completely replace crustacean-derived chitosan. However, the traditional chitin extraction processes are laden with many disadvantages. The present review discusses the potential bioextraction of chitosan from fungal, insect, and crustacean as well as its superior physico-chemical properties. The different aspects of fungal, insects, and crustacean chitosan extraction methods and various parameters having an effect on the yield of chitin and chitosan are discussed in detail. In addition, this review also deals with essential attributes of chitosan for high value-added applications in different fields and highlighted new perspectives on the production of chitin and deacetylated chitosan from different sources with the concomitant reduction of the environmental impact.     

Predicting ductile fracture of low carbon steel sheets: Stress-based versus mixed stress/strain-based Mohr–Coulomb model

Two distinct implementations of the Mohr–Coulomb failure model are used in conjunction with a non-associated quadratic plasticity model to describe the onset of fracture in low carbon steel sheets. The stress-based version corresponds to the original Mohr–Coulomb model in stress space. For the mixed stress/strain-based version, the Mohr–Coulomb failure criterion is first transformed into the space of stress triaxiality, Lode angle parameter and equivalent plastic strain and then used as stress-state dependent weighting function in a damage indicator model. Basic fracture experiments including tensile specimens of different notch radii and a punch test are performed to calibrate the material parameters of the respective models. Subsequently, the models are used to predict the crack initiation in a Hasek test and during the stamping of an anticlastic structure. Unlike for the calibration experiments, the loading history during stamping is highly non-linear. Both models can be calibrated with similar accuracy, but the strain-based model predicts the instant of onset of fracture with greater accuracy in the stamping experiment which is an advantage of the empirical damage accumulation rule.     

Phosphino-(α-sulfinylalkyl)phosphonium ylide complexes (Rh,Pd) with a configurationally stable asymmetric ylidic carbon

The synthesis and structure of Rh(I) and Pd(II) complexes of chiral P,C-chelating phosphino-(α-sulfinylalkyl)phosphonium ylide ligands with a trisubstituted asymmetric ylidic center P⁺–C1R(S1(O)p-Tol)–M (R = alkyl group) have been investigated, and compared to those of the analogous disubstituted ylide complexes (R = H). Reaction of the ethyl onium ylide of o-bis(diphenylphosphino)benzene with (?)-menthyl-(S)-p-tolylsulfinate afforded the corresponding racemic erythro phosphino-(α-sulfinylethyl)phosphonium in 90% de (R = Me). The racemization process is interpreted by a Berry-like pseudorotation mechanism driven by the steric repulsion between the α-methyl substituent and the bulky menthyloxy S-substituent or sulfur lone pair in the intermediate ylide-sulfinyl adduct. The ylide of phosphino-(α-sulfinylethyl)phosphonium reacts with [Rh(cod)₂][PF₆] and PdCl₂(MeCN)₂ to afford the corresponding P,C1-chelated threo-Rh(I) and erythro-Pd(II) mononuclear complexes in 70% yield and total diastereoselectivity. These respective complexes act as efficient catalytic precursors for the hydrogenation of (Z)-α-acetamidocinnamic acid and allylic substitution of 3-acetoxy-1,3-diphenyl-1-propene with sodium dimethyl malonate. The bonding features of the erythro-Pd(II) complex exhibiting a sulfinyl O?Pd interaction are studied theoretically at the DFT level using ELF and MESP analyses. The η²-P,C haptomeric form of the ylide ligand is estimated to compete at 19% with the η¹-C haptomeric form dominating at 81%.