Observation of the h(c)(1P) Using e+ e- collisions above the DD threshold

Using 586 pb(-1) of e+ e- collision data at E(c.m.) = 4170 MeV, produced at the Cornell Electron Storage Ring collider and collected with the CLEO-c detector, we observe the process e+ e- → π+ π- h(c)(1P). We measure its cross section to be 15.6±2.3±1.9±3.0 pb, where the third error is due to the external uncertainty on the branching fraction of ψ(2S) → π0 h(c)(1P), which we use for normalization. We also find evidence for e+ e- → ηh(c)(1P) at 4170 MeV at the 3σ level and see hints of a rise in the e+ e- → π+ π- h(c)(1P) cross section at 4260 MeV.     

Phase behavior of some polyamic acid plus ether systems

Polyamic acids, prepared by reacting 3,3′,4,4′-benzophenone tetracarboxylic acid dianhydride with 3,3′-diaminobenzophenone and with 4,4′-diaminobenzophenone, were dissolved in tetrahydrofuran and in bis(2-methoxyethyl) ether at concentrations up to 40 wt %. Reversible phase separation was observed when these systems were heated. Evidence cited indicates that all observed phases are isotropic, notwithstanding the fact that a number of aromatic polyamides are mesogenic.     

Why the square root function is not linear

Six proofs are given for the fact that for each integer n?2, the nth root function, viewed as a function from the set of non-negative real numbers to itself, is not linear. If p is a prime number, then ?/p? is characterized, up to isomorphism, as the only integral domain D of characteristic p such that D admits a pth root function D→D which is linear. The first part of this note could find classroom use in courses on precalculus or calculus; the second part, in courses on abstract algebra.     

Polynomial asymptotes

This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and the elementary limit theorems from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.     

Light-fluorous TEMPO: reagent, spin trap and stable free radical

The synthesis of two light-fluorous TEMPO derivatives is reported, along with their fluorous-organic solvent partition coefficients and their ESR spectra. Applications of the fluorous-TEMPO reagents in oxidation reactions and as radical traps are discussed.     

On almost-divided domains

Let B be a domain, Q a maximal ideal of B, π: B → B/Q the canonical surjection, D a subring of B/Q, and A:=π ⁻¹(D). If both B and D are almost-divided domains (resp., n-divided domains), then A = B × _B/Q D is an almost-divided domain (resp., an n-divided domain); the converse holds if B is quasilocal. If 2 ≤ d ≤ ∞, an example is given of an almost-divided domain of Krull dimension d which is not a divided domain.