On the concept of point value in the infinite-dimensional realization theory

In this article, we study the effect of the chosen representation of a point value (and point evaluation) on the class of periodic signals realizable using a certain type of infinite-dimensional linear system. By suitably representing the point evaluation at the origin in a Hilbert space, we are able to give a complete characterization of its extensions. These extensions involve a new concept called δ-sequence, the use of which as an observation operator of an infinite-dimensional linear system is studied in this article. In particular, we consider their use in the realization of periodic signals. We also investigate how the use of δ-sequences affects the convergence properties of such realizations; we consider the rate and character of convergence and the removal of the Gibbs phenomenon. As still a further demonstration of the significance of the chosen concept of a point value, we discuss the use of distributional point values in the realization of periodic distributions. The possible applications of this work lie in regulator problems of infinite-dimensional control theory, as is indicated by the well-known internal model principle.     

Enzymatic synthesis of optically active α-chloro-δ-hydroxy-β-ketoalkanephosphonates and reactions thereof

A novel and enzymatic approach to α-chloro-δ-hydroxy-β-ketoalkanephosphonates was developed via enantioselective CALB-catalyzed acetylation and CRL-catalyzed hydrolysis. The resultant optically active compounds provide, via Horner-Wadsworth-Emmons (HWE) reaction, chiral α,β-unsaturated ketones that are building block with potential application in organic synthesis.     

Defect clusters and precipitation/oxidation of MgO-Co1−xO solid solution

MgO and Co_1−xO powders in 9:1 and 1:9 molar ratio (denoted as M₉C₁ and M₁C₉, respectively) were sintered and homogenized at 1600°C followed by annealing at 850°C and 800°C, respectively to form defect clusters and precipitates. Analytical electron microscopic observations indicated the protoxide remained as rock salt structure with complicated planar diffraction contrast for M₉C₁ sample, however with spinel paracrystal precipitated from the M₁C₉ sample due to the assembly of charge- and volume-compensating defects of the 4:1 type, i.e., four octahedral vacant sites surrounding one Co³⁺-filled tetrahedral interstitial site. The spacing of such defect clusters is 4.5 times the lattice spacing of the average spinel structure of Mg-doped Co_3−δO₄, indicating a higher defect cluster concentration than undoped Co_3−δO₄. The {111} faulting of Mg-doped Co_3−δO₄/Co_1−xO in the annealed M₁C₉ sample implies the possible presence of zinc blend-type defect clusters with cation vacancies assembled along oxygen close packed (111) plane.     

Metalloporphyrin Cr(TPP)Cl-catalyzed Claisen rearrangement of simple aliphatic allyl vinyl ethers and its unique stereoselectivity

The catalytic Z-selective Claisen rearrangement of simple aliphatic allyl vinyl ethers can be achieved using a chromium(III) porphyrin complex, Cr(TPP)Cl, as a catalyst: Cr(TPP)Cl significantly enhances reversal of E-Z selectivity in the thermal Claisen rearrangement of allyl vinyl ethers, especially, 4,5- and 4,6-disubstituted derivatives, at low catalyst loading.     

The first example of γ-chloromagnesio γ-lactones: their generation from γ-tolylsulfinyl γ-lactones with isopropylmagnesium chloride, stability, and reaction with electrophiles

The treatment of γ-lactones having a sulfinyl group at the γ-position, which were synthesized from 1-chlorovinyl p-tolyl sulfoxides with lithium enolate of carboxylic esters, with isopropyl magnesium chloride in THF at −78 °C gave γ-chloromagnesio γ-lactones by the sulfoxide-magnesium exchange reaction in high yields. The generated γ-chloromagnesio γ-lactones were found to be stable at below −50 °C for at least 2 h. The reaction of these γ-chloromagnesio γ-lactones with electrophiles and the stereochemistry of the reactions were investigated.     

A highly efficient synthesis of antiobestic ligand GW501516 for the peroxisome proliferator-activated receptor δ through in situ protection of the phenol group by reaction with a Grignard reagent

A new synthesis of an agonist for the peroxisome proliferator-activated receptor δ (PPARδ) GW501516 as a potential antiobesity drug is described. The synthetic route involves the in situ protection of the phenol group with a Grignard reagent and a regio-controlled one-pot reaction for the formation of a sulfide bond as the key step. Starting from commercially available 4-iodo-2-methylphenol, this approach affords GW501516 with an overall yield of 87%.     

Combustibles,fuels and their combustion products: A view through carbon isotopes

Stable (i.e. non-radioactive) carbon-isotope composition (δ¹³C) in fuels has been extensively used as an indicator of the processes leading to the generation of their parent crude-oil. With the example of those used in Paris (France), this preliminary study isotopically characterizes fuels and combustibles, as well as the isotopic relations existing with their combustion by-products, i.e. gases (CO₂) and particles (bulk carbon). Results show that δ¹³C in fuels is clearly related to their physical state, with natural gas being strongly depleted in ¹³C while coal yields the highest δ¹³C, and liquid fuels display intermediate values. This relation is also valid for combustion gases, although δ¹³C values of combustion particles form a homogeneous range within which no clear distinction is observed. Combustion processes are accompanied by carbon-isotope fractionation (noted Δ¹³C) resulting from the combustion being incomplete. Carbon-isotope fractionation is strictly negative (Δ¹³C = ?1.3‰) during the formation of combustion gases, but generally positive in particle formation even if values close to zero are observed. Using simple mixing equations for describing the closed system formed by fuel, CO₂ and carbonaceous particles, we discuss the carbon budget for spark-ignition (unleaded gasoline) and diesel engines. Stable carbon isotopes corroborate the already-proved superior efficiency of diesel combustion mode compared with spark ignition, as carbon is preferentially transformed into CO₂.     

A new approach to the synthesis of lactams of muramic,isomuramic and normuramic acids via intramolecular O-alkylation: Stereochemical features of the intramolecular nucleophilic substitution

The title compounds were synthesized from the selectively protected N-acylated d-glucosamine derivatives, containing α-halo carboxylic acid moieties, via intramolecular 3-O-alkylation. It was found that if the starting compound contains asymmetric electrophilic center, isomuramic acid derivatives were mainly formed, regardless of the configuration of the electrophilic carbon atom. An explanation for the observed stereochemical results was proposed on the basis of the analysis of steric interactions in the molecules of the starting compounds, as well as using the concept of anchimeric assistance. It was shown that N-acetylation of the obtained lactam derivatives and subsequent methanolysis under mild conditions led to the selective cleavage of δ-lactam ring resulting in the formation of the corresponding ester derivatives of N-acetylmuramic acid or its analogues in high yields.     

Acetate anion-selective encapsulation in the ellipsoidal cavity of symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril

Four symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril-based compounds have been prepared and characterised by X-ray crystallography. Their crystal structures displayed the acetate anion-selective encapsulating capability of symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril. The host–guest interaction between the symmetrical α,α′,δ,δ′-tetramethyl-cucurbit[6]uril and the acetate anion in aqueous solution has also been observed by variable temperature ¹H NMR spectroscopy.