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Theorem 1. For any system of interacting particles/bodies with given interaction φ satisfying conditions i)–iii) and given chemical potentials µ ¯ there exists a trans- lation
We determine for a broad range of different classes of shift spaces if they have property ( ∗ ) and property ( ∗∗ ) and use this to show that Matsumoto’s K 0 -group and the
Theorems such as Theorem 3, Theorem 4, Theorem 5, and Theorem 6 can also be proved for right s -unital rings by the same lines as above employing the necessary variations..
In addition to providing conditions for the existence of double positive solutions of (M 1) and (M 2), we also derive upper and lower bounds for the norms of these solutions..
Using the finite element method we calculated the approximate values of λ 1 for various values of p for different shape of domain.. Ω
However we cannot conclude from this that solutions of (1) with initial values near 0 are integrable, though the equivalence of uniform asymptotic stability and integrability of
Stability and boundedness of Volterra integral and integrodifferential equations have been ex- tensively considered for a long time (see the well-known books [1, 4], recent papers
For the same reasons as previously, these perfor- mance domains will be the reference performance domains used for the coherence analysis in the homogeneous decomposition (i.e.
