The Bergman kernel function: Explicit formulas and zeroes

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in defined by the inequality , have zeroes.

     

Efficient algorithms for a family of matroid intersection problems

Consider a matroid where each element has a real-valued cost and a color, red or green; a base is sought that contains q red elements and has smallest possible cost. An algorithm for the problem on general matroids is presented, along with a number of variations. Its efficiency is demonstrated by implementations on specific matroids. In all cases but one, the running time matches the best-known algorithm for the problem without the red element constraint: On graphic matroids, a smallest spanning tree with q red edges can be found in time O(n log n) more than what is needed to find a minimum spanning tree. A special case is finding a smallest spanning tree with a degree constraint; here the time is only O(m + n) more than that needed to find one minimum spanning tree. On transversal and matching matroids, the time is the same as the best-known algorithms for a minimum cost base. This also holds for transversal matroids for convex graphs, which model a scheduling problem on unit-length jobs with release times and deadlines. On partition matroids, a linear-time algorithm is presented. Finally an algorithm related to our general approach finds a smallest spanning tree on a directed graph, where the given root has a degree constraint. Again the time matches the best-known algorithm for the problem without the red element (i.e., degree) constraint.     

Tiebout and sympathy

In its simplest form the Tiebout hypothesis suggests that redistribution by local government is not sustainable because individuals, when confronted by negative net fiscal benefits, will vote with their feet, changing their residential locations to jurisdictions which offer a more favorable fiscal balance. It is usually thought, moreover, that they will move (e.g. from central city to suburbs) in descending order of income.Recognition of extended preference modifies this simple characterization of the tiebout process, in which the process of relocation is like ‘peeling an onion’. Any relocation sequence is possible, with either sympathy or antipathy. Even for sympathetic individuals with identical tastes, restrictive and unrealistic assumptions are required to predict, with certainty, that individuals with higher incomes would be the first to move. In particular the marginal tax rate must exceed unity. With antipathy, individuals with lower incomes may move before those with higher incomes, even if net fiscal benefits decrease with income, if they become more willing to begrudge transfers to others as their incomes increase.     

Electron-transfer polymers. XXXIX. Redox polymers based on duroquinonyl glycol

Redox polyurethanes, polyesters, and alternate copolyurethanes and copolycarbonates from two kinds of benzoquinonyl glycol were prepared based on 2-(duroquinonyl)-propan-1,3-diol. The oxidized polymer is stable. When the fully reduced polymer in solution is exposed to air the durohydroquinonyl residues are oxidized to the quinone form while the less substituted hydroquinonyl glycol residues remain stable in the reduced form. There is thus prepared polymer with oxidized and reduced groups alternating along the chain.     

Precision infrared spectroscopy in CF379Br by means of infrared-microwave double resonance

From the observation of double resonance effects on the microwave spectrum two coincidences between 9.4 μm CO₂ laser lines and infrared transitions of the ν₆ → (ν₆ + ν₁) band of CF₃⁷⁹Br have been determined: R(30) laser line coincident with ^qR₂(7), F = 17/2→17/2 transition, R(28) laser line coincident with all four ΔF = 0 hyperfine components of the ^qQ₈(13) transition. In both cases other infrared transitions lay within the tuning range of the laser. The frequencies of these two laser lines allowed calculations of the band center frequency ν₀ = 1083.530 ± 0.001cm^?1 and α_A = 11.93 ± 0.3MHz, for the ν₆ → (ν₆ + ν₁) band.α_B constants were determined for the vibrational states v₆, (v₆ + v₁), v₁, and v₃.