Counterion Exchange Selectivity in Detergent–Polymer Aggregates

In aqueous solution, the interaction between sodium dodecyl sulfate (SDS) and poly(ethylene glycol) (PEG) results in the formation of small aggregates or clusters of SDS attached to the PEG polymer chain. Selectivity coefficients for exchange of two monovalent (N-methyl-4-cyanopyridinium cation and Tl⁺) and two divalent (methylviologen cation and Cu²⁺) counterions at the surface of SDS–PEG clusters, determined employing photophysical techniques, are similar, but not identical, to those for exchange at the surface of SDS micelles in the absence of PEG. The principal factor affecting ion exchange selectivity in SDS–PEG clusters does not appear to be aggregate size or surface charge density but rather the presence of poly(oxyethylene) subunits at the aggregate surface.     

Counterion exchange selectivity coefficients at water-in-oil microemulsion interface

The counterion binding at a water/Aerosol-OT (AOT)/heptane microemulsion interface was treated in the context of the pseudo-phase ion exchange formalism. Two approaches were used to determine the selectivity coefficient for copper/sodium counterion binding at the AOT microemulsion interface: measurements of the Cu(II) concentration taken up by the reverse micelle in a Winsor II microemulsion system and steady-state emission quenching measurements of an anionic water-solubilized probe, the tris-(4,4'-dicarboxy-2,2'-bipyridine) ruthenium (II) ion. In addition, the selectivity coefficient for methyl viologen/sodium at the microemulsion surface was determined by the same photophysical technique. The value for copper (II)/sodium exchange (K(Cu/Na)) is 1.1+/-0.3 and that for methyl viologen/sodium (K(MV/Na)) is 0.9+/-0.3. The results show that the pseudo-phase ion exchange model can be used to obtain the selectivity coefficient in a microemulsion system.     

A hybrid SEA/modal technique for modeling structural-acoustic interior noise in rotorcraft

This paper describes a hybrid technique that combines Statistical Energy Analysis (SEA) predictions for structural vibration with acoustic modal summation techniques to predict interior noise levels in rotorcraft. The method was applied for predicting the sound field inside a mock-up of the interior panel system of the Sikorsky S-92 helicopter. The vibration amplitudes of the frame and panel systems were predicted using a detailed SEA model and these were used as inputs to the model of the interior acoustic space. The spatial distribution of the vibration field on individual panels, and their coupling to the acoustic space were modeled using stochastic techniques. Leakage and nonresonant transmission components were accounted for using space-averaged values obtained from a SEA model of the complete structural-acoustic system. Since the cabin geometry was quite simple, the modeling of the interior acoustic space was performed using a standard modal summation technique. Sound pressure levels predicted by this approach at specific microphone locations were compared with measured data. Agreement within 3 dB in one-third octave bands above 40 Hz was observed. A large discrepancy in the one-third octave band in which the first acoustic mode is resonant (31.5 Hz) was observed. Reasons for such a discrepancy are discussed in the paper. The developed technique provides a method for modeling helicopter cabin interior noise in the frequency mid-range where neither FEA nor SEA is individually effective or accurate.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.