A study of helix formation in polydimethysiloxane by Raman scattering

Depolarization ratios ρ of the Raman bands due to CH₃ stretching at 2907 cm^?1 and the Si? O skeletal mode at 491 cm^?1 have been measured in polydimethylsiloxane gum as a function of temperature from 100°C to ?45°C. Below 0°C the changes in p have been interpreted in terms of the formation of helical regions in the gum. The enthalpy of helix formation ΔH has been determined as 3200 ± 600 cal/mole. An upper limit on the entropy change, ΔS, of 16 ± 3 e.u./mole and minimum values of helix content at different temperatures have been found. The Raman spectrum of crystalline polydimethylsiloxane is presented.     

Coulomb excitation of radioactive 132,134,136Te beams and the low B(E2) of 136Te

The B(E2;0(+)-->2+) values for the first 2+ excited states of neutron-rich 132,134,136Te have been measured using Coulomb excitation of radioactive ion beams. The B(E2) values obtained for 132,134Te are in excellent agreement with expectations based on the systematics of heavy stable Te isotopes, while that for 136Te is unexpectedly small. These results are discussed in terms of proton-neutron configuration mixing and shell-model calculations using realistic effective interactions.     

Regular 4-polytopes from the Livingstone graph of Janko’s first group

The Janko group J ₁ has, up to duality, exactly two regular rank four polytopes, of respective Schl?fli types {5,3,5} and {5,6,5}. The aim of this paper is to give geometric constructions of these two polytopes, starting from the Livingstone graph.     

A Frequency-Domain Approach to Optimal Fractional-Order Damping

In this paper, we will consider the single term optimal fractional-order damper for an otherwise undamped oscillator. First, we will find the single term damper that minimizes the time domain integral of the squared step error (2-norm) and the integral of the time-weighted squared error (Hilbert–Schmidt–Hankel norm). Next we will consider a more intuitive frequency domain approach that insures the maximally flat magnitude response. Time and frequency domain plots are given for comparison with the integer-order solutions. Further improvements in performance are shown to be possible using multiple active fractional-order dampers.     

Fractional Trigonometry and the Spiral Functions

This paper develops two related fractional trigonometries based on the multi-valued fractional generalization of the exponential function, the R-function. The trigonometries contain the traditional trigonometric functions as proper subsets. Also developed are relationships between the R-function and the new fractional trigonometric functions. Laplace transforms are derived for the new functions and are used to generate solution sets for various classes of fractional differential equations. Because of the fractional character of the R-function, several new trigonometric functions are required to augment the traditional sine, cosine, etc. functions. Fractional generalizations of the Euler equation are derived. As a result of the fractional trigonometry a new set of phase plane functions, the Spiral functions, that contain the circular functions as a subset, is identified. These Spiral functions display many new symmetries.