Correlation relations between the parameters of the empirical dependences of some strength and diffusion characteristics on test conditions

Experimental data are often approximated by two-parameter relations in the form of a power or an exponential function. When a number of similar objects are considered, the parameters of these relations are connected by a correlation dependence. The examples of empirical relations where this dependence is observed are considered. In all cases of this correlation dependence, the value of an approximating function changes by several orders of magnitude when its argument varies by several times, and the initial data for the calculation of the empirical-equation parameters are located in a relatively narrow band in the coordinate space. This behavior is always accompanied by a linear relationship between the empirical coefficients of the equations obtained for a number of similar objects.     

An orthogonal basis for the hyperbolic hybrid polynomial space

Motivated by the wide usage of the Tchebyshev basis and Legendre basis in the algebra polynomial space, we construct an orthogonal basis with the properties of the H-Bézier basis in the hyperbolic hybrid polynomial space, which is similar to the Legendre basis and holds remarkable properties. Moreover, we derive the transformation matrices that map the H-Bézier basis and the orthogonal basis forms into each other. An example for approximating the degree reduction of the H- Bézier curves is sketched to illustrate the utility of the orthogonal basis.     

The research seminar on computer algebra in 2005–2006

An annual report on meetings of the scientific research seminar on computer algebra is presented.     

Test of the KÉ-250-ShS machine for twisting acetate yarn

Conclusions An attempt has been made to use the KÉ-250-ShS machine for twisting acetate yarns.It has been found that in developing a new twisting machine it is advisable to use a checkerboard disposition of the spindles in its lower part with the objective of reducing the noise level, and also to use pedal braking to stop the spindles. This helps increase the productivity of twister labor, and mechanization and automation of operations associated with transfer in removing packages of weight not less than 3 kg.Translated from Khimicheskie Volokna, No. 6, pp. 40–41, November–December, 1985.