The use of temporary tethers in the meta photocycloaddition reaction

The use of temporary tethers in facilitating meta photocycloaddition reactions between phenol and allyl alcohol derivatives has been investigated. The merits of silicon, carbonate and methylene acetal tethers were assessed, whilst considering strategies for the preparation of the natural products gymnomitrol and gelsemine. The photoadducts were epoxidised, and then subjected to acid catalysed fragmentation with concomitant cleavage of the tether. Depending on whether water or methanol was used during the fragmentation stage of the methylene tethers, the methylene group was either removed altogether or transformed into a MOM group.     

Ein allgemeiner Satz über die Integrirbarkeit von Functionen integrirbarer Functionen

Ohne ZusammenfassungAbgedruckt aus den Sitzungsberichten der math.-phys. Classe der k. b. Akadem. d. Wiss. zu München.     

Equivalence of inverse Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter

Three inverse problems for a Sturm-Liouville boundary value problem −y″+qy=λy, y(0)cosα=y′(0)sinα and y′(1)=f(λ)y(1) are considered for rational f. It is shown that the Weyl m-function uniquely determines α, f, and q, and is in turn uniquely determined by either two spectra from different values of α or by the Prüfer angle. For this it is necessary to produce direct results, of independent interest, on asymptotics and oscillation.     

On subgroups of finite index in compact Hausdorff groups

Let G be a compact Hausdorff group and n a positive integer. It is proved that all subnormal subgroups of G of index dividing n are open if and only if there are only finitely many such subgroups, and that all subgroups of finite index in G are open if and only if there are only countably many such subgroups.     

Synthesis of all diastereomeric methyl 2,5-anhydro-3-deoxy-hexonates: precursors to C-2-deoxynucleosides and THF-templated γ- and δ-amino acids

Efficient syntheses of all diastereomers of methyl 2,5-anhydro-3-deoxy-hexonate from mannono- or gulono-lactones provide precursors for C-nucleosides of 2-deoxyribose and for THF-templated γ- and δ-amino acids.     

Search during decision making

Nearly four hundred non-routine organizational decisions were investigated to discover search approaches––determining the frequency of use and success of each search approach uncovered. A “search approach” is made up of a direction and a means to uncover solution ideas. Direction indicates desired results and it can be either implicit or explicit, with an explicit direction offering either a problem or a goal-like target. Solutions can be uncovered by opportunity, bargaining, and chance as well as by rational approaches. Defining a search approach as a direction coupled with a means of search, search approaches were linked with indicators of success, measured by the decision's adoption, value and timeliness, noting frequency. A rational, goal-directed, search approach was more apt to produce successful outcomes. Bargaining with stakeholders to uncover solutions was always combined some of the search approaches in this study, and this merger improved the prospects of success. Searches with an opportunistic or chance (emergent opportunity) features and rational searches with a problem target were more apt to produce unsuccessful outcomes. The means used to come up with a solution had less bearing on success than did the type of direction, with goal-directed searches leading to the best outcomes. Each search approach is discussed to reveal best practices and to offer suggestions to improve practice.     

tert‐Butyl (6S)‐4‐hydroxy‐6‐isobutyl‐2‐oxo‐1,2,5,6‐tetra­hydropyridine‐1‐carboxyl­ate and tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxopiperidine‐1‐carboxyl­ate

X‐ray studies reveal that tert‐butyl (6S)‐6‐iso­butyl‐2,4‐dioxo­piperidine‐1‐carboxyl­ate occurs in the 4‐enol form, viz. tert‐butyl (6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo‐1,2,5,6‐tetra­hydropyri­dine‐1‐carboxyl­ate, C₁₄H₂₃NO₄, when crystals are grown from a mixture of di­chloro­methane and pentane, and has an axial orientation of the iso­butyl side chain at the 6‐position of the piperidine ring. Reduction of the keto functionality leads predominantly to the corresponding β‐hydroxy­lated δ‐lactam, tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo­piperidine‐1‐car­boxyl­ate, C₁₄H₂₅NO₄, with a cis configuration of the 4‐hydroxy and 6‐iso­butyl groups. The two compounds show similar molecular packing driven by strong O—H⋯O=C hydrogen bonds, leading to infinite chains in the crystal structure.     

The Orevkov invariant of an affine plane curve

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.

     

On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.