It is shown, that the model is able to reproduce a broad class of various temperature dependencies of relaxation times, lying between the extremal cases represented by the Arrhenius relation on one and by the Vogel-Fulcher-Tamman (VFT) relation on the other hand.
While political divisions began to emerge after a period of exceptional unity, a notable improvement in Russian-Polish relations brought on by the tragedy was still very much in evidence.
Now we denote as a relation on defined by, for any, (I).
Then the relation on defined by (1.3). is a partial ordering.
We introduce a relation on X by x ⪯ y if and only if y ≤ x.
In what follows, we define the binary relation # on (mathbb{K}^{n}) by x mathbin y quad Leftrightarrow quad x_{i} ne y_{j}quad text{for all } i,j in I_{n} text{ with } i ne j. (1.15).
Let ⊲ be the binary relation on X defined by ( x, y ) ∈ X × X, x ⊲ y ⟺ x ⪯ y or y ⪯ x.
Let ≼ be the binary relation on (mathbb{R}) given by xpreccurlyeq y quadLeftrightarrow quad (x=y mbox{ or } x< y leqslant0).
It is clear that the relation ~ is an equivalent relation on I. Denote by I /~ as the quotient set, and I s 's, which is called index sets of ζ, as the elements of I/~.
Hence, we get the following imprimitive Γ-invariant equivalence relation on Q ˆ by Γ 1 ( n ) : r s ∼ x y if and only if g − 1 h ∈ Γ 1 ( n ), where g = ( r ∗ s ∗ ) and h is similar.
