Shift-invariant spaces on LCA groups

In this article we extend the theory of shift-invariant spaces to the context of LCA groups. We introduce the notion of H-invariant space for a countable discrete subgroup H of an LCA group G, and show that the concept of range function and the techniques of fiberization are valid in this context. As a consequence of this generalization we prove characterizations of frames and Riesz bases of these spaces extending previous results, that were known for Rd and the lattice Zd.     

X-Ray Structural Analysis of Ethyl [2,2-dimethyl-6-(Δ2-thiazolin-2-yl)-4H-1,4-benzoxazin-3-one-4-yl]butyrate

With the aim of discovering new molecules with K⁺ channel modulating properties, we have synthesized analogues of cromakalim, an important molecule which shows specific affinity toward the K⁺ channels, by replacing the benzopyrane ring with a benzoxazine moiety. As a part of this study, we have synthesized and characterized, in solution and in the solid state as well, the compound ethyl [2,2-dimethyl-6-(²-thiazolin-2-yl)-4H-l,4-benzoxazin-3-one-4-yl]butyrate (V). This compound exhibits in the solid state the following parameters: molecular formula C₁₉H₂₄N₂O₄S, triclinic, space group , M_w = 376.5, a = 12.581(3) Å, b = 5.485(4) Å, c = 14.612(2) Å, = 91.85(2), = 108.9(3), = 82.04(4), V = 944.7 ų, Z = 2, d = 1.323 g·cm^–3. We describe here the synthesis and discuss the solid-state conformation of this new molecule; when tested on rat aorta ring precontracted with phenylephrine, the compound showed a concentration-dependent relaxation comparable to that measured for cromakalin taken as reference drug.     

Synthesis of 2-Cycloalkenones (Parts of 1,4-Diacyl-1,3-butadiene Systems) and of a Heterocyclic Analogue by Metal-Catalyzed Decomposition of 2-Diazoacylfurans

Furans with side-chains at C(2) of various lengths terminating in diazomethyl keto groups are shown to undergo Rh₂(OAc)₄-catalyzed furan unravelling with the production of 2-cyclopentenone, 2-cyclohexenone, and 2-cycloheptenone to each of whose olefinic C(β) is attached an acrylaldehyde unit. Interposition of a cyclohexane or a methylaminomethylene moiety between the furan and diazoketo functions leads to the formation of a hydroindenone and pyrrolone, respectively. Replacement of the diazomethylketo terminus by an α-diazoethylketo system or a α-diazo-β-keto-ester function produces 2-substituted 2-cycloalkenones. A furan with a C₄, diazo-methylketo-terminating side-chain at C(3) is described to be transformed into a 4-formylmethylidene-2-cyclohe-xenone.     

Conformational properties and homolytic bond cleavage of organic peroxides. I. An empirical approach based upon molecular mechanics and ab initio calculations

The conformational features of a large number of hydroperoxides ROOH and peroxides ROOR′, where R and R′ are alkyl groups of different and increasing size and phenyl rings, including ortho substituted derivatives, were obtained from molecular mechanics calculations by employing a standard package. For the molecules of small molecular size, comparison was carried out with the results of ab initio calculations. Heats of formation were also obtained from molecular mechanics for hydroperoxides and peroxides: The values are, in general, overestimated. For the molecules containing the CF₃ group, the calculated values are subject to large errors and heats of formation were obtained from ab initio total energies in the “atom equivalents” scheme. To estimate the homolytic dissociation energies of the different bonds in the peroxide molecules, heats of formation of R·, ·OR, and ·OOR radicals were employed and several of them had to be calculated. Different approaches were employed—molecular mechanics calculations, ab initio energies within the atom equivalent and isodesmic reaction schemes, and Benson's group additivity rule; values consistent within the different calculation methods were chosen for estimating dissociation energies. The bond dissociation energies indicate different trends in these molecules as a function of the nature of the R and R′ groups and the possible electronic effects operating in these molecules are discussed. © 1993 John Wiley & Sons, Inc.     

1H NMR spectra of the 2-trifluoroacetyl derivatives of benzo[b]furan and benzo[b]thiophene

The ¹H NMR spectra of the 2-trifluoroacetyl derivatives of benzo[b]furan and benzo[b]thiophene were recorded at 200MHz in two solvents, chloroform and acetone. A long-range coupling constant, 5J(HF), between the fluorine nuclei of the trifluoroacetyl group and H-3, of a value higher than 1 Hz, was measured. From the comparison of the ¹H chemical shifts of, and the solvent effects on, the trifluoroacetyl compounds and those of the corresponding 2-acetyl derivatives, and on the basis of an empirical interpretation of the ⁵J(HF) coupling constant, a predominant Z conformation was tentatively assigned to these derivatives.     

Overlaps help: Improved bounds for group testing with interval queries

Given a finite ordered set of items and an unknown distinguished subset P of up to p positive elements, identify the items in P by asking the least number of queries of the type ‘‘does the subset Q intersect P?”, where Q is a subset of consecutive elements of {1,2,…,n}. This problem arises, e.g., in computational biology, in a particular method for determining splice sites in genes. We consider time-efficient algorithms where queries are arranged in a fixed number s of stages: In each stage, queries are performed in parallel. In a recent bioinformatics paper, we proved optimality (subject to lower-order terms) with respect to the number of queries, of some strategies for the special cases p=1 or s=2. Exploiting new ideas, we are now able to provide improved lower bounds for any p?2 and s?3 and improved upper bounds for larger s. Most notably, our new bounds converge as s grows. Our new query scheme uses overlapping query intervals within a stage, which is effective for large enough s. This contrasts with our previous results for s?2 where optimal strategies were implemented by disjoint queries. The main open problem is whether overlaps help already in the case of small s?3. Anyway, the remaining gaps between the current upper and lower bounds for any fixed s?3 amount to small constant factors in the main term. The paper ends with a discussion of practical implications in the case that the positive elements are well separated.     

Semi-empirical MO calculations of nuclear spin coupling constants

The results obtained using different semi-empirical approaches, namely EHMO, IEHMO, CNDO/2 and INDO, in the calculation of spin–spin coupling constants within the framework of the one-electron MO approximation are systematically compared in the case of several classes of organic molecules. While, at a semi-empirical level SCF methods normally provide satisfactory wave function, the use of the simple EHMO seems better able to satisfy the problem connected with the calculation of spin–spin coupling constants, expecially when an appropriate set of AO's is chosen, in order to avoid parametrisation of Dirac monocentric integrals. Charge iteration (IEHMO) seems to improve the results slightly only when heteroatoms are present, but the complexity introduced into the calculations and the greatly increased computer time do not justify the slight improvement achieved, particularly as the method is applied to large molecules and organometallic compounds.     

One-pot synthesis of benzo[e]1,4-oxathiepin-5-ones under solvent-free condition via self-promoted thiolysis of 1,2-epoxides

Under solvent-free conditions, thiosalicylic acid (2) efficiently self-promotes the thiolysis of 1,2-epoxides 1, anti-stereoselectively and generally totally beta-regioselectively. The resulting beta-hydroxysulfide products 3 have been obtained in very good yields. Benzo[e]1,4-oxathiepin-5-ones 4 have been easily prepared in a regio- and diasteroselective manner and in satisfactory yields under SFC by a one-pot protocol including nucleophilic ring opening of 1,2-epoxides 1 by thiosalicylic acid (2) and thermally induced lactonization of beta-hydroxy arylsulfides 3. Solvent-free condition and the absence of any catalyst make this procedure atom-economical and environmentally friendly.     

"Green"-enzymatic synthesis of pegylated phenolic macromer and polymer

Environmentally benign synthesis of novel pegylated polyphenolics, by combining the extraordinary selectivities of a lipase and an oxidase to develop polymeric electrolytes for applications in dye sensitised solar cells.