Determination of structure of weak scatterers from holographic images

For a weak scatterer a three dimensional Fourier transform of the image formed by a generalized hologram is shown to yield directly the Fourier transform of the scattering potential evaluated on the Ewald sphere. The entire scattering potential can be approximately determined if the object is illuminated from all directions in a series of experiments and if the scattering potential is essentially bandlimited to within a sphere of radius 4π/λ.     

QCD asymptotics and kinematic thresholds in deep inelastic scattering

The Nachtmann moments of deep inelastic scattering structure functions are required by kinematics to contain a so far neglected threshold factor which is dependent on both n and q². Its presence significantly affects the “moment analysis” in the usual QCD phenomenology and it resolves the difficulties connected with improper threshold behavior of the “ξ-scaling” analysis of structure functions.     

Rheological properties of poly(2,6-dimethylphenylene oxide)—polystyrene blends

The viscoelastic (VE) response of freeze-dried blends of polystyrene (PS) and poly-(2,6-dimethyl phenylene oxide) (PPO) has been studied as a function of composition, frequency, and temperature to examine the degree of rheological compatibility. When blended together, the relaxation processes of both molecular species exhibit the same temperature dependence. However, the temperature dependence of the VE response is a function of composition. It is shown that this behavior can be predicted from the measured glass transition temperatures by assuming the additivity of the free volumes of the components. The properties of the blends are compared at equal free volumes. The effective segmental friction factor is found to be independent of composition while the modulus of the rubbery plateau increases with PPO concentration. This result is interpreted as a change in the entanglement molecular weight M_e of the blends. When the changes in M_e are considered, the relationship between the zero-shear viscosity η0 and the 3.4 power of the weight-average molecular weight, commonly found for high molecular weight homopolymers, predicts the compositional dependence of η0 for the PPO–PS blends. It is concluded that the PPO–PS system forms a rheologically compatible blend.     

DNA sequence-enabled reassembly of the green fluorescent protein

We describe a general methodology for the direct detection of DNA by the design of a split-protein system that reassembles to form an active complex only in the presence of a targeted DNA sequence. This approach, called SEquence Enabled Reassembly (SEER) of proteins, combines the ability to rationally dissect proteins to construct oligomerization-dependent protein reassembly systems and the availability of DNA binding Cys2-His2 zinc-finger motifs for the recognition of specific DNA sequences. We demonstrate the feasibility of the SEER approach utilizing the split green fluorescent protein appended to appropriate zinc fingers, such that chromophore formation is only catalyzed in the presence of DNA sequences that incorporate binding sites for both zinc fingers.     

Causality structure and the Weierstrass theorem

In a recent paper P. M. Prenter has shown that the Weierstrass theorem can be lifted up to a real separable Hilbert space H. In this paper H is equipped with an identity resolving orthoprojector chain. The Weierstrass type result of Prenter, namely, if ? is any continuous function on H, then there exists a finite order approximating polynomic operator on every compact K ? H, is sharpened by the extension: if ? is strictly causal (strictly anticausal) then the polynomic approximation can also be strictly causal (strictly anticausal). Other extensions in the same spirit are developed and the results are interpreted in the setting of Volterra operators on L₂.     

A polynomial energy-gap model for molecular linewidths

A simple phenomenological model for predicting high-temperature linewidths is described. The rotationally inelastic relaxation time is calculated by using a polynomial inverse-energy-gap model. From this time, the linewidths may be calculated and ambient pressure linewidths may then be used to determine the polynomial coefficients and predict high-temperature linewidths. A detailed comparison with known nitrogen linewidths is given. The relaxation rates obtainable from the model may also be used to calculate pressure-narrowing effects for vibrational Q branches.