Type II Anion Relay Chemistry: Exploiting Bifunctional Weinreb Amide Linchpins for the One‐Pot Synthesis of Differentiated 1,3‐Diketones,Pyrans, and Spiroketals

The design, synthesis, and validation of new highly effective bifunctional linchpins for type II anion relay chemistry (ARC) has been achieved. The mechanistically novel negative‐charge migration that comprises the Brook rearrangement is now initiated by a stabilized tetrahedral intermediate, which is generated by nucleophilic addition to a Weinreb amide, rather than by a simple oxyanion that is generated from an epoxide. As a result, the linchpin preserves the carbonyl functionality in the ARC adducts, thus permitting access to functionally complex systems in a single flask without the need for further chemical manipulations. This tactic was validated with the one‐pot preparation of monoprotected 1,3‐diketones as well as pyran and spiroketal scaffolds, depending on the choice of nucleophile, electrophile, and work‐up conditions.     

Synthesis, characterization, and cytotoxicity of a novel highly charged trinuclear platinum compound. Enhancement of cellular uptake with charge

Charge delocalization (6+ to 8+) in "noncovalent" linear trinuclear platinum complexes produces compounds with cytotoxicity in some cases equivalent to cisplatin. The cellular uptake of a novel 8+ compound is greater than that of neutral cisplatin as well as other multinuclear Pt compounds.     

The anhydride structure of several previously reported stable areneselenenic acids1

The compounds previously reported² to be the stable areneselenenic acids, $\text{o}$-nitro-($\text{la}$ and $\text{+o}$-benzoylbenzeneselenenic acid ($\text{lb}$), are shown actually to be the corresponding selenenic anhydrides (ArSeOSeAr). Solutions of the selenenic acids (ArSeOH), however, can be easily generated from the anhydrides byacid-catalyzed hydrolysis.     

The Farrell-Jones Isomorphism Conjecture for finite covolume hyperbolic actions and the algebraic -theory of Bianchi groups

We prove the Farrell-Jones Isomorphism Conjecture for groups acting properly discontinuously via isometries on (real) hyperbolic -space with finite volume orbit space. We then apply this result to show that, for any Bianchi group , , , and vanish for .

     

Asymptotically liberating sequences of random unitary matrices

A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asymptotic liberation” under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdú.     

On a general class of graph polynomials

Let $\text{F}$ be a family of connected graphs. With each element α ∈ $\text{F}$, we can associate a weight w_α. Let G be a graph. An F-cover of G is a spanning subgraph of G in which every component belongs to $\text{F}$. With every F-cover we can associate a monomial π(C) = Π_αw_α, where the product is taken over all components of the cover. The F-polynomial of G is Σπ(C), where the sum is taken over all F-covers in G. We obtain general results for the complete graph and complete bipartite graphs, and we show that many of the well-known graph polynomials are special cases of more general F-polynomials.     

Examples of Non-Homeomorphic Harmonic Maps Between Negatively Curved Manifolds

Let M and N be closed non-positively curved manifolds, and letf:MN be a smooth map. Results of Eells and Sampson [1] showthat f is homotopic to a harmonic map , and Hartman [6] showedthat this is unique when N is negatively curved and f_*(₁ M)is not cyclic. Lawson and Yau conjectured that if f:MN is ahomotopy equivalence, where M and N are negatively curved, thenthe unique harmonic map homotopic to f would be a diffeomorphism.Counterexamples to this conjecture appeared in [2], and laterin [7] and [5]. There remains the question of whether a ‘topological’Lawson–Yau conjecture holds. 1991 Mathematics SubjectClassification 53C20, 55P10, 57C25, 58E20.     

Nonlinear dynamics of charged particles interacting with combined ac-dc electromagnetic fields

A nonlinear Lorenz model describing interactions between charged particles and combined ac-dc electromagnetic fields is studied for various combinations of frequencies, field strengths and relative angle (θ) between the ac and dc magnetic fields. Strong directional effects on the magnitude and location of resonant particle motion are observed when θ is varied and the regular resonance windows in the aligned field (θ = 0) and linear version of the model studied previously by Durney etaal., break up to form irregular and less well pronounced regions of large and small particle displacements when nonlinearities are taken into account. The length of time takne to achieve resonant behaviour also becomes larger and more variable when nonlinearities are present. The possible relevance of these effects to interactions between electromagnetic fields and biological media is briefly discussed.