The synthesis and cyclization of acyclic quinoxaline, pyridine, and pyrimidine enediynes (1-3) are described. These compounds were prepared using palladium(0) coupling of trimethylsilyl acetylene to o-dihaloor o-halotriflic heteroarenes. All compounds were prepared in modest to good yields. The enediynes prepared were shown to undergo Bergman cyclization. Kinetics over a minimum of 3 half-lives...

We study the positive Bergman complex B(M) of an oriented matroid M , which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid M . The positive Bergman complex is defined so that given a linear ideal I with associated oriented matroid MI , the positive tropical variety associated to I is equal to the fan over B(MI). Our main result is that a certain “fine” ...

This is a short survey paper based on the topics of the author’s research along with his collaborators. Main topics presented in the paper are on the regularity and rigidity theorems for the solutions of the elliptic differential equations. In particular, the author poses several open problems in these topics for further study. The paper contains six sections. Regularity theorems for the ellipt...

Let M 1 and M 2 be two Kähler manifolds. We call M 1 and M 2 relatives if they share a non-trivial Kähler submanifold S, namely, if there exist two holomorphic and isometric immersions (Kähler immersions) h 1 : S → M 1 and h 2 : S → M 2. Moreover, two Kähler manifolds M 1 and M 2 are said to be weakly relatives if there exist two locally isometric (not necessarily holomorphic) Kähler manifolds ...

We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold M , i.e. the critical points of the functional PYM(D) = 1 2 ∫ M ‖πHR‖θ∧(dθ), where D is a connection in a Hermitian CR-holomorphic vector bundle (E, h) → M . Let Ω = {φ < 0} ⊂ C be a smoothly bounded strictly pseuodoconvex domain and g the Bergman metric on Ω. We show that boundary valuesDb of Yang-Mills fieldsD on...

A complex of zirconocene with two rq2-alkynyl ligands is described. This complex is the first isolated example of the postulated intermediate in the zirconocene-mediated reductive coupling of alkynes. The development of a Bergman cyclization controlled by metal-ligand interactions is described. Upon complexation with palladium or platinum, phosphine-substituted enediynes rearrange to the aromat...

In a first course in complex analysis, students learn a theorem that states that if an analytic function is zero on a non-discrete set inside a region in the complex plane, then the function must be identically zero. In particular, the values that an analytic function takes in the neighborhood of a single point completely determine the function in the whole region. This, of course, is very usef...

Abstract Let $$B_n$$ B n be the unit ball in "Equation missing" with Bergman metric g and h is on $$B_m$$ m . $$u: (B_n, g)\rightarrow (B_m, h)$$ u : ( ...

Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in C, n > 1, with Lipschitz boundary, but it holds for domains in C1 with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz domains. These include Bergma...

The paper continues the study of a class of holomorphic Besov spaces on bounded symmetric domains which was initiated in [18]. Several new descriptions of these Besov spaces are given in terms of weighted Bergman projections and fractional differential operators. These new characterizations are then applied to obtain results about the duality of, and Hankel operators on, weighted Bergman spaces...