Asymptotic stability and other properties of trajectories and transfer sequences leading to the bargaining sets

The foundation of a dynamic theory for the bargaining sets started withStearns, when he constructed transfer sequences which always converge to appropriate bargaining sets. A continuous analogue was developed byBillera, where sequences where replaced by solutions of systems of differential equations. In this paper we show that the nucleolus is locally asymptotically stable both with respect toStearns' sequences andBillera's solutions if and only if it is an isolated point of the appropriate bargaining set. No other point of the bargaining set can be locally asymptotically stable. Furthermore, it is always stable in these processes. As by-products of the study we derive the results ofBillera andStearns in a different fashion. We also show that along the non-trivial trajectories and sequences, the vector of the excesses of the payoffs, arranged in a non-increasing order, always decreases lexicographically, thus each bargaining set can be viewed as resulting from a certain monotone process operating on the payoff vectors.     

The rotational and vibrational spectra of 1,3-dithiole- 2-one

Microwave spectra of 1,3-dithiole-2-one show that the molecule has a planar equilibrium conformation. IR and Raman spectra are analysed to give the normal modes of vibration.     

pH-dependent intracellular quenching of the indicator carboxy-SNARF-1

Carboxy-SNARF-1 is an emission-changing, pH-sensitive probe for measurements of intracellular pH. However, the protonated and deprotonated forms of the dye interact differently with intracellular constituents, and this imposes new requirements on the calibration of the system. Whole spectra of intracellular and extracellular C.SNARF-1 were analyzed and showed (1) intracellular quenching which was significantly greater for the deprotonated form of the dye than for the protonated state and (2) a detectable change in pK _a. Importantly for avoiding damage to cells, this mathematical analysis allowed reference spectra for fully protonated and fully deprotonated dye to be obtained without a need for spectra measured at extreme values of pH. It is not known what constituent(s) of the intracellular milieu might be responsible for the changes in dye behavior in the cell. To address this question, preliminary experiments with cell-free buffers compared the pattern seen inside the cell with quenching by a protein (bovine serum albumin; BSA) or that due to ethanol. The BSA result was completely unlike the intracellular case in that the protonated form of the dye was quenched. Buffer containing ethanol, on the other hand, was able to mimic the essential features of the intracellular spectra.     

Synthesis of perazine

A novel synthesis of perazine (10-(4-methylpiperazinyl-3-propyl)phenothiazine), likely to be applicable to 10-dialkylaminopropyl phenothiazines generally, is described.     

A new upper limit for the branching ratio for the decay η → π0e+e−

We have looked for the decay η → π⁰e⁺e^? in an optical spark chamber experiment at the Rutherford Laboratory. Our observations are consistent with no events being seen and give an upper limit rate (η → π⁰e⁺e^?)/ rate (η → all) < 4.5 × 10^?5 (90% C.L.).     

Infrared spectra and rotational isomerism of ethyl fluoroformate and ethyl propiolate

The infrared absorption spectra of ethyl fluoroformate and ethyl propiolate have been examined in the vapour, solution and solid states. For both esters evidence is found of rotational isomerism arising from internal rotation about the O-C₂H₅ bond, in close agreement with previous work on other ethyl esters.     

A measurement of the electromagnetic form factor of the eta meson and of the branching ratio for the eta Dalitz decay

In an optical spark chamber experiment we have obtained a sample of 80 eta Dalitz decays (η → e⁺e^?γ) and have measured the eta electromagnetic form factor to be F(X) = 1.0?(0.22 ±0.45)X, where X=M_ee²/M_η², and the branching ratio (η→e⁺e^?γ/(η→π⁺π^?π⁰)= (0.0082 ± 0.0020).