Tempered distributions in infinitely many dimensions

The space of testing functions for tempered distributions is characterized in an abstract way as the maximal space in a certain class of locally convex topological vector-spaces. The main characteristic of this class is stability under the differentiation and multiplication operators.The ensuing characterization of tempered distributions may readily be generalized to the case of infinitely many dimensions, and a certain class of such generalizations is studied. The spaces of testing elements are required to be stable under the action of the canonical field operators of the quantum theory of free fields, and it is shown that extreme spaces of testing elements exist and have simple properties. In fact, the maximal space is a Montel space, and the minimal complete space is a direct sum of such spaces.The formalism is applied to the problem of extending the canonical field operators, and a number of extension theorems are derived. In a forthcoming paper the theory of tempered distributions in infinitely many variables will be applied to a structurally simple linear operator equation.     

Photocurrent decay in silicon at low temperatures

We report measurements performed at low temperatures in silicon of the transient photovoltaic current following excitation by an intense laser light pulse. They show the occurrence of a delayed minor current peak, which we suggest is related to the free carriers obtained, when electron-hole droplets after drift in an exciton density gradient are destroyed by heating.     

The Singular Set of Lipschitzian Minima of Multiple Integrals

The singular set of any Lipschitzian minimizer of a general quasiconvex functional is uniformly porous and hence its Hausdorff dimension is strictly smaller than the space dimension     

Extended verification of scaling behavior in split-ring resonators

We present an expanded LC-model for nanoscale split-ring resonators (SRR), including the influence of dielectric host materials. The LC-model is experimentally verified by changing the geometry of the SRR unit cell as well as by optofluidic tuning, where the SRR samples are covered with index oil. The extended model can be used as a general guideline for metal SRR structures with arbitrary dielectric host materials.     

Enhanced stability of a protein with increasing temperature

The unusual stability of a structured but locally flexible protein, human growth hormone (hGH) at pH 2.7, was investigated using the temperature dependence of the nanosecond-picosecond dynamics of the backbone amide groups obtained from (15)N NMR relaxation data. It is found that the flexibility of the backbone of the helices decreases with temperature in the range from 24 °C to ～40 °C, corresponding to an increasing stability. A concomitant increase with temperature of the electrostatic interactions between charged residues forming an interhelical network of salt bridges at the center of the four-helix core suggests that these interactions give rise to the decreasing flexibility and increasing stability of the protein. However, numerous hydrophobic interactions in the interior of the four-helix core may also contribute. Above ～40 °C, where the thermal energy overcomes the electrostatic and hydrophobic interactions, a substantial increase in the flexibility of the helix backbones results in a highly positive contribution from the local conformational heat capacity, C(p,?conf), of the helix backbones to the total heat capacity, C(p), of the protein. This reduces the change in heat capacity upon unfolding, ΔC(p), increases the change in the Gibbs free energy, ΔG(unfold), and stabilizes the protein at high temperatures. A similar decrease in flexibility is found near other salt bridges in hGH and in Calmodulin and may be of general importance for the thermostability of proteins and, in particular, of the salt bridge intensive thermophilic proteins.     

Preparation, structural analysis and dielectric properties of Bi x La1−x FeO3 perovskite

Rare earth element substituted bismuth ferrites (BiFeO₃) are of enormous importance as magnetoelectric materials. The polycrystalline samples of Bi _x La_1−x FeO₃ (x=0, 0.2, 0.4, 0.6, 0.8) were prepared by solid-state reaction using standard ceramic method. The single-phase formation of these compounds was confirmed by X-ray diffraction (XRD) studies. The samples with x=0, 0.2, 0.4, 0.6 are found to be orthorhombic while the sample with x=0.8 is triclinic. The dielectric constant (ε′) and dissipation factor (tan δ) were measured in the frequency range 100 Hz to 1 MHz at room temperature and as a function of temperature at certain fixed frequencies (1 kHz, 10 kHz, 100 kHz, 1 MHz). All the samples showed dielectric dispersion. The dielectric constant with temperature shows a broad peak; the peak temperature shifts with frequency which reflects the relaxor-type behavior. The peak above 600 K in the measured temperature range corresponds to antiferromagnetic ordering temperature (Néel temperature). The broadness of the peak changes with composition. The ac conductivity as well as ε′ are found to be maximum for the sample x=0.2 at room temperature.