Linearization of homogeneous Riccati equations

An autonomous system of n coupled homogeneous Riccati equations of the projective type linearizes to its linear part by means of a map which is analytic for almost all initial data. The explicit form of the map is presented.     

Pseudomorphic growth of a single element quasiperiodic ultrathin film on a quasicrystal substrate

An ultrathin film with a periodic interlayer spacing was grown by the deposition of Cu atoms on the fivefold surface of the icosahedral Al70Pd21Mn9 quasicrystal. For coverages from 5 to 25 monolayers, a distinctive quasiperiodic low-energy electron diffraction pattern is observed. Scanning tunneling microscopy images show that the in-plane structure comprises rows having separations of S=4.5+/-0.2 A and L=7.3+/-0.3 A, whose ratio equals tau=1.618... within experimental error. The sequences of such row separations form segments of terms of the Fibonacci sequence, indicative of the formation of a pseudomorphic Cu film.     

Synthesis of acetylenic cyclophanes via intramolecular self-assembly: evidence of perfluorophenyl-phenyl quadrupole interactions in the solution state

Reported herein is an example of a solution-state cross-coupling cyclization with an outcome mediated by perfluorophenyl-phenyl electrostatic interactions.     

Effect of shear on human insulin in zinc suspension

Human insulin in zinc suspension was used as a model protein to test the effect of shear on the settling rate of proteins, a possible inference for protein denaturation. The rate of settling was determined directly in a spectropho-tometer. Shear effects are important in retaining the activity of proteins and are present in bubble, foam, and droplet protein fractionation processes. A sim pletest, such as that conducted here, mayeven be useful for monitoring changes in protein structure caused by commercial shipping of the protein. The settling ratefor insulin was continously monitored in theoriginal bottle by spectrophotometric absorbance changes as a function of time. A settling curve was determined following each shear experiment, which included shaking the “worked” insulin solution in a vortex mixer for different lengths of time. It was determined, when comparing long shaking times with short ones, that the initial settling rate was less for the long-term shaking of the insulin samples and greater for the short-term shaking. The secondary effects of light and heat, along with shaking, a pparently did not produce differences from shaking alone.     

Different approaches for evaluating exponentially weighted nonequilibrium relations

The Kawasaki identity (KI) and the Jarzynski equality (JE) are important nonequilibrium relations. Both of these relations take the form of an ensemble average of an exponential function and can exhibit convergence problems when the average of the exponent differs greatly from the log of the average of the exponential function. In this work, we re-express these relations so that only selected regions need to be evaluated in an attempt to avoid these convergence issues. In the context of measuring free energies, we compare our method to the JE and the literature standard approach, the maximum likelihood estimator (MLE), and show that in a system with asymmetric work distributions it can perform as well as the MLE. For the KI, we derive an analog to the MLE to compare with our relation and show that these two new relations improve on the KI and are complimentary to each other.     

Modification of tricine–SDS–PAGE for online and offline analysis of phosphoproteins by ICP-MS

This study describes a modification to tricine sodium dodecyl sulphate polyacrylamide gel electrophoresis to make it more effective for the separation of low molecular mass proteins and for coupling with inductively coupled plasma mass spectrometry (ICP-MS). The modified method employs low-percentage polyacrylamide gels (7–10%) (w/v) and low reagent concentrations that provide efficient separations, good quantitation and low matrix levels that are compatible with ICP-MS. Using phosphopeptides as a model system, and offline analysis, we obtained recoveries of 73% (w/v) in a 9% gel compared with 55% in a conventional 16% gel. Online coupling was achieved by modification of a standard commercially available gel electroelution apparatus and casting of the gel into a 7.3-cm-long tube. Online separation of a digest of β-casein was demonstrated with recovery of the mono- and tetraphosphopeptides, which were identified by comparison with peptide standards. A mass balance study with the standards yielded recoveries of 95% for tetraphosphopeptides and 48% for monophosphopeptides. The factors affecting the separations and recoveries are discussed in detail. The detection limits for 10-μL samples of the mono- and tetraphosphopeptides were 0.7 μM (7 pmol) and 0.2 μM (2 pmol) respectively.     

Observation of the crystallization and supersaturation of mixed component NaNO3-Na2SO4 droplets by FTIR-ATR and Raman spectroscopy

We present here a study of the phase behavior of mixed component NaNO(3)-Na(2)SO(4) (SNS) droplets with NaNO(3) to Na(2)SO(4) molar ratios of 1:1, 3:1, and 10:1, comparing observations with thermodynamic predictions. Measurements are made by Fourier transform infrared attenuated total reflection and micro-Raman spectroscopy for SNS droplets deposited on ZnSe and quartz substrates, respectively. The conventional deliquescence/efflorescence hysteresis in phase behavior is observed. On drying, heterogeneous crystallization leads to phase behavior that is consistent with bulk solution thermodynamics, with the formation of the mixed salt NaNO(3)·Na(2)SO(4)·H(2)O, Na(2)SO(4) (s), and NaNO(3) (s) all observed to form at relative humidities that coincide with predictions by the aerosol inorganics model. However, conditioning of the droplet at high relative humidity prior to drying is observed to lead to quantitative differences between the fractions of different salts formed. When substrate effects do not influence the crystallization process, supersaturated solutions are formed, and this leads to the observation of contact ion pairs. Such measurements of the phase behavior of mixed component droplets are important for testing the reliability of thermodynamic models.