Different Degrees Of Smoothness Research Articles

Geometric angle for rotated rotators, and the Hannay angle of the world

A simple formula is derived for the shift in angle variable (Hannay angle) arising from a slow (adiabatic) cycle of a parameter in a one-dimensional classical system. The formula is illustrated by numerical computations for different degrees of smoothness of the adiabatic driving. If the driving is smooth enough, the adiabatic invariant is sufficiently well conserved to enable fluctuations in the frequency to be neglected when computing the dynamical angle contribution to the final angle. If not (e.g. if the driving is uniform over a finite time), these fluctuations must be taken into account. The Hannay angle appears as a small change in period of a celestial body (Earth) rotating about another body (Sun) caused by the slow revolution of a third body (Jupiter).

Analysis of the pion form factor in the space-like and time-like region

We discuss an analytic parametrization of the pion form factor which is only weakly model dependent. Its model dependence comes from a preference of those analytic functions that are smooth in a certain well-defined sense. Different solutions for different values ofχ 2 corresponding to different degrees of smoothness can be constructed. All available space-like and time-like data are taken into account simultaneously. Our approach allows conclusions on an incompatibility of space-like with time-like data sets and on the significance of the occurrence of higher coupled resonances. We discuss the asymptotic behaviour which is consistent with QCD and give the relevant low energy and resonance parameters.

A method for analysis of experimental data on spherical irradiation of laser target

An application is considered of the authors' algorithm for the solution of the Abel equation, stable on the right-hand side, in an analysis of the experimental data obtained as a result of contactless diagnostics of spherically symmetric plasma objects. Examples are given of calculations of laser plasma parameters whose distribution functions have different degrees of smoothness. A comparison is made of the proposed method with the techniques used currently in the solution of the Abel equation.

Study of Improvement of Smoothness of Cotton Fabrics

An exploratory research has sought the most promising ways of imparting a high degree of durable smoothness to cotton cloth. This work, limited to laboratory pro cedures, has resulted in finishes characterized by different degrees of smoothness, of luster or glaze, and of durability. Smoothness was very well retained in the best of these finishes and can be considered permanent, although luster decreased gradually upon washing. Some of these finishes seem readily adaptable to lining and other apparel fabrics. The work was based on the use of an experimental calender and largely upon the calendering of cloth while it was wet, in a state of swelling greater than that from mere wetting with water. There would be difficulties in practical opera tion if the water in the cloth contained dissolved finishing agents or if the cloth was too wet. Objections have been partially met by preswelling, washing, padding the wet cloth in a softening and fixing agent, and then drying before calendering. Promising for further investigation is close control of moisture content of the cloth at the time of calendering, at levels between those of present practice and values attained in this re search. A range of 15-40% regain in cottons treated as described, but only partially dried before calendering, is suggested. Higher calender temperatures and pressures should also be considered.