A note on generating <Emphasis Type="Italic">P</Emphasis>-matrices

We prove that for any \({A,B\in\mathbb{R}^{n\times n}}\) such that each matrix S satisfying min(A, B) ≤ S ≤ max(A, B) is nonsingular, all four matrices A ^?1 B, AB ^?1, B ^?1 A and BA ^?1 are P-matrices. A practical method for generating P-matrices is drawn from this result.     

On unique solvability of the absolute value equation

It is proved that the singular value condition σ _max(|B|) < σ _min(A) implies unique solvability of the absolute value equation Ax + B|x| = b for each right-hand side b. This is a generalization of an earlier result by Mangasarian and Meyer proved for the special case of B = −I. Supported by the Czech Republic Grant Agency under grants 201/09/1957 and 201/08/J020, and by the Institutional Research Plan AV0Z10300504.     

关于3-正则图的路分解

本文讨论了3-正则图的路分解问题,证明了任意的3-正则图都有{P3,P4}分 解,其中Rk指包含k个顶点的路.     

Effect of SBS on Rheological Properties of Different Base Asphalts

In this note rheological properties of two different polymer modified asphalts (PMA) are compared. PMAs were prepared from two different base asphalts, a soft one (200/300 Pen grade) and a hard one (70/100 Pen grade), by addition of 4% by weight of radial SBS as modifier. Dynamic mechanical properties were determined in a wide temperature range for bases and modified asphalts both before and after artificial aging. As expected, the moduli of the soft base are more sensitive to polymer addition and the two PMAs attain similar maximum values after aging. However a significant difference in the frequency at which the maxima of the loss modulus are reached is maintained within the two materials irrespectively of aging or polymer addition.     

Blends and composites based on fluoropolymers

Fluoropolymers represent a rather unique group of polymeric materials. Essentially, current most widely used commercial fluoropolymers are derivatives of ethylene and propylene, also known as fluorocarbon polymers. Other, more complex fluorinated polymers are also important technically, but these are used in considerably smaller amounts. Because of the unique chemistry and properties, fluorocarbon polymers rarely form good blends. The only exceptions are homopolymers and copolymers of vinylidene fluoride, which form blends based on thermodynamic compatibility with certain polymers, such as acrylates and methacrylates. However, most known fluoropolymers can be used to produce fiber and fabric reinforced composites as well as composite films and coatings.