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A set of integral elements of higher order jet spaces

Shibuya K.

Demonstratio Mathematica

2010

Vol. 43, nr 2

473-486

We will consider prolongations of the canonical systems on Jet spaces for multi independent variables. We will characterize appearances of singularities obtained from the prolongations.

New approach to a theoretical study of some of the parameters in the knitting process, and their influence on knit-fabric stitch density

Charalambus A.

Autex Research Journal

2007

Vol. 7, no. 2

95--99

This paper proves relations, which concern the structure of knitted fabric by using a simple geometrical model. In addition, a series of graphics are made which allow fast, simple and effective analysis of the relations between some of the parameters of the knitting process and these of the ready-knit fabric. The quantity "relative geometrical prolongation of the thread length in the stitch", introduced by me plays a significant role in this study. The relations given below allow the machine gauge to be defined; this helps to produce knit fabric with precisely calculated density by choosing appropriate values for the thread's sinking depth and acceptable average geometrical prolongation.

On stability in impulsive dynamical systems

Ciesielski K.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 1

81-91

Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.