Functional Equations and Weierstrass Transforms

The purpose of this article is to illustrate the utility of the Weierstrass transform in the study of functional equations (and systems) of the form 1 $${\mathop \sum^N\limits_{k=0}}\alpha_{k}f(x+r_{k})=f_{0}(x)\ \ \ \, x\in\ {\rm R}.$$ One may think of α₀, α₁,…, α_N as given complex numbers, r₀, r₁,…, r_N as given real numbers, ?₀: ? → C as a given function and ? as the unknown.     

An explicit computation of the Bergman kernel function

We give an explicit computation of the Bergman kernel function on the domain

Infinite period and Hopf bifurcations for the pH-regulated oscillations in a semibatch reactor (H(2)O(2)-Cu(2+)-S(2)O(2-) (3)-NaOH system)

Dynamic behavior of the pH-regulated oscillations has been studied for the hydrogen peroxide oxidation of thiosulfate ions in the presence of trace amounts of copper(II) ions in a semibatch reactor. A solution of 0.08 M Na(2)S(2)O(3) and 0.112 M NaOH was flowed at 0.160 mL/min into 300 mL of solution containing the H(2)O(2) and Cu(2+) in a vessel. There exists a critical value of the H(2)O(2) or Cu(2+) concentrations below which the system does not oscillate. The oscillations appear due to an infinite period bifurcation at low initial concentrations of the H(2)O(2). The initial concentration of Cu(2+) may be considered as a bifurcation parameter in this case. Increase of the initial hydrogen peroxide concentration causes the pH-regulated oscillations through a nondegenerate supercritical Hopf bifurcation. The classification of bifurcations is based on the analysis of the behavior of oscillation amplitude and period at different initial concentrations of the H(2)O(2) and Cu(2+). Our results show a possibility to distinguish different scenarios for the appearance of transient oscillations in semibatch experiments. (c) 1996 American Institute of Physics.     

K − and\bar p Production in Au + Pb Collisions at 11.5 A GeV/cProduction in Au + Pb Collisions at 11.5 A GeV/c

I will present the first results from the E864 collaboration on the production of negative kaons and antiprotons in 10% central 11.5 A GeV/c Au+Pb nucleus collisions at the Brookhaven AGS. E864 is a high rate, open geometry spectrometer, capable of measuring particle production in a range of rapidities and transverse momenta at a single setting of the spectrometer magnets. The results are derived from the analysis of over 20 million central interactions collected in the Fall 1994 run. I will report onK ^? production in a rapidity range from 1.9<y<2.2 (y _cm=1.6) and 25<pT<150 MeV/c, and $\bar p$ production from 1.2<y<2.2 and 50<pT<400 MeV/c. A comparison with previously published results from E878 is presented and the implications for $\bar \Lambda $ production are discussed.     

On a functional equation of Luce

Summary In a recent communication to J. Aczél, R. Duncan Luce asked about the functional equationU(x)U(G(x)F(y)) = U(G(x))U(xy) forx, y > 0, (1) which has arisen in his research on certainty equivalents of gambles. He was particularly interested in cases in which the unknowns (U, F andG) are strictly increasing functions from (0, + ) into (0, + ). In this paper we solve (1) in the case whereU, F andG are continuously differentiable with everywhere positive first derivatives. Our solution is perhaps novel in that in certain cases (1) reduces to a functional equation in a single variable and in other cases to a functional equation in several variables; see [1] for the terminology.     

Polynomial rings over Goldie-Kerr commutative rings II

An overlooked corollary to the main result of the stated paper (Proc. Amer. Math. Soc. 120 (1994), 989--993) is that any Goldie ring of Goldie dimension 1 has Artinian classical quotient ring , hence is a Kerr ring in the sense that the polynomial ring satisfies the on annihilators . More generally, we show that a Goldie ring has Artinian when every zero divisor of has essential annihilator (in this case is a local ring; see Theorem ). A corollary to the proof is Theorem 2: A commutative ring has Artinian iff is a Goldie ring in which each element of the Jacobson radical of has essential annihilator. Applying a theorem of Beck we show that any ring that has Noetherian local ring for each associated prime is a Kerr ring and has Kerr polynomial ring (Theorem 5).

     

Greenhouse gas abatement — toward Pareto-optimal decisions under uncertainty

This paper examines the economic logic of integrated assessment — balancing the costs against the benefits of greenhouse gas abatement. Stylized facts are employed in a multiregion computable general equilibrium model with a public good. The percentage shares of global emissions are determined outside the model — based upon some form of international agreement — and emission rights are tradeable between regions. The analysis is confined to Pareto-optimal (cooperative) solutions. We focus on the sensitivity of initial decisions to low-probability, high-consequence scenarios associated with cumulative emissions. For simplicity, there are only two regions, two tradeable goods, two time periods, and two states-of-world. With the particular form of public good model adopted here (production rather than utility function impacts), it turns out that a Pareto-optimal hedging strategy is indepedent of the emission shares allocated to each region. Equity issues may be separated from those of economic efficiency. Similar results extend to cases in which there are additional regions, tradeable goods, time periods, and states-of-world.Presented at the Conference on the Economics of Global Environmental Change, Birmingham University, May 9–11, 1994. This research was funded by the Electric Power Research Institute (EPRI). The views presented here are solely those of the individual authors, and do not necessarily represent the views of EPRI or its members.     

Cohomology of groups with metacyclic Sylow -subgroups

We determine the cohomology algebras for all groups with a metacyclic Sylow -subgroup. The complete -local stable decomposition of the classifying space is also determined.