Reactivity of divalent germanium alkoxide complexes is in sharp contrast to the heavier tin and lead analogues

The chemistry of β-diketiminate germanium alkoxide complexes has been examined and shown to be in sharp contrast to its heavier congeners. For instance, (BDI)GeOR (BDI = [{N(2,6-(i)Pr(2)C(6)H(3))C(Me)}(2)CH], R = (i)Pr, (s)Bu, (t)Bu) does not react with carbon dioxide to form a metal carbonate complex. Addition of aliphatic electrophiles, such as methyl iodide or methyl triflate, results in the net oxidative addition to the germanium, giving cationic tetravalent germanium complexes, [(BDI)Ge(Me)OR][X] (X = I, OTf). An examination of the contrasting reactivities of the alkoxide ligand and the germanium loan pair with Lewis acids yielded the unusual germanium(II)-copper(I) adduct, {μ(2)-Cu(2)I(2)}[(BDI)GeO(t)Bu](2). This complex not only displays a rare example of a divalent Ge-Cu bond, but is the first example in which a planar Cu(2)I(2) diamond core possesses a three-coordinate copper bound to another metal center.     

Aircraft proximity termination conditions in the planar turn centric modes

Closed-form analytic solutions for proximity management strategies are of great importance as a design benchmark when validating both automated systems and procedures associated with the design of air traffic rules. Merz (1973) first presented a solution for a set of optimal strategies for resolving co-planar co-operative encounters between two aircraft (or ships) with identical linear and rotational speeds. This paper extends the solution domain for turning aircraft beyond that of identical aircraft by presenting a rigorous analysis of the problem through a generalised optimisation approach. This analysis provides a dependable method for determining the location of the point of closest approach. This is achieved by using a vector form of Fermat’s equation for stationary points. A characteristic of this solution is the identification of a fixed reference point lying on the vector between the aircraft turn centres or on one of its extensions. This point is then used to determine where the location of the minima in the relative range between the aircraft will occur. Bounds for the domain of the solution are constructed in terms of the rotational angles of the aircraft on their turn circles. Four distinct topologies are required to characterise the types of minima that can occur. The methodology has applications in an operational context permitting a more detailed and precise specification of proximity management functions when developing algorithms for aircraft avionics and air traffic management systems.     

Synthesis of Bioactive Side‐Chain Analogues of TAN‐2483B

The fungal metabolite TAN‐2483B has a 2,6‐trans‐relationship across the pyran ring of its furo[3,4‐b]pyran‐5‐one core, which has thwarted previous attempts at its synthesis. We have now developed a chiral pool approach to this core and prepared side‐chain analogues of TAN‐2483B. The synthesis relies on ring expansion of a reactive furan ring‐fused dibromocyclopropane and alkynylation of the resulting pyran. The furan ring is constructed by palladium‐catalysed carbonylative lactonisation. Various side‐chains are appended through Wittig‐type chemistry. The prepared analogues showed micromolar activity towards cancer cell lines HL‐60, 1A9 and MCF‐7 and certain human disease‐relevant kinases, including Bruton's tyrosine kinase (Btk).     

Total synthesis of violaceimides A–E and consideration of the reported stereochemistry

Here we report the first total synthesis of violaceimides A–E, a family of sulfur-containing metabolites from Aspergillus violaceus, a sponge-associated fungus. A concise, convergent and enantioselective synthesis was developed for all five family members, from a common advanced intermediate. However, while the NMR spectral data matched that of the reported natural products, the optical rotations were of opposite sign. This result prompted the enantioselective synthesis of all four diastereomeric pairs of violaceimide E, and suggests that the stereochemistry might have been misassigned.     

Sturm-Liouville Operators with Singularities and Generalized Nevanlinna Functions

The Titchmarsh–Weyl function, which was introduced in Fulton (Math Nachr 281(10):1418–1475, 2008) for the Sturm-Liouville equation with a hydrogen-like potential on (0, ∞), is shown to belong to a generalized Nevanlinna class N_k{bf N_kappa}. As a consequence, also in the case of two singular endpoints for the Fourier transformation defined by means of Frobenius solutions there exists a scalar spectral function. This spectral function is given explicitly for potentials of the form dfracq₀x²+dfracq₁x, -dfrac 14 ￡ q₀ < ￥{dfrac{q_0}{x^2}+dfrac{q_1}{x},,-dfrac 14le q_0 < infty}.