While it is known that any $c$-spanner is also both a weak $C_1$-spanner and a $C_2$-power spanner (for appropriate $C_1,C_2$ depending only on $c$ but not on the graph under consideration), we show that the converse fails: There exists a family of $c_1$-power spanners that are no weak $C$-spanners and also a family of weak $c_2$-spanners that are no $C$-spanners for any fixed $C$ (and thus no uniform spanners, either). However the deepest result of the present work reveals that, surprisingly, any weak spanner is also a uniform power spanner. We further generalize the latter notion by considering $(c,delta)$-power spanners where the sum of the $delta$-th powers of the lengths has to be bounded; so $(cdot,2)$-power spanners coincide with the usual power spanners and $(cdot,1)$-power spanners are classical spanners. Interestingly, these $(cdot,delta)$-power spanners form a strict hierarchy where the above results still hold for any $deltageq2$; some even hold for $delta>1$ while counterexamples reveal others to fail for $delta<2$. In fact we show that in general every self-similar curve of fractal dimension $d>delta$ is no $(C,delta)$-power spanner for any fixed $C$. }, author = {Schindelhauer, Christian and Volbert, Klaus and Ziegler, Martin}, booktitle = {Proc. of 15th Annual International Symposium on Algorithms and Computation (ISAAC'04)}, isbn = {9783540241317}, issn = {0302-9743}, pages = {805--821}, publisher = {Springer }, title = {{Spanners, Weak Spanners, and Power Spanners for Wireless Networks}}, doi = {10.1007/978-3-540-30551-4_69}, volume = {3341}, year = {2004}, } @article{18281, author = {Tophinke, Doris}, journal = {Infodienst. Kulturpädagogische Nachrichten }, pages = {26--27}, title = {{Quatschwörterverse und Satzklötze. Sprachförderung im Kindergarten}}, volume = {71}, year = {2004}, } @misc{18495, author = {Peckhaus, Volker}, booktitle = {Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1033.03002]}, title = {{Newen, Albert/Nortmann, Ulrich/Stuhlmann-Laeisz, Rainer (Hgg.), Building on Frege. New Essays on Sense, Content, and Concept, CSLI Publications: Standford, CA 2001}}, year = {2004}, } @misc{18488, author = {Peckhaus, Volker}, booktitle = {Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1030.01030]}, title = {{Takeuti, Gaisi, Memoirs of a Proof Theorist. Gödel and other Logicians, ed. Mariko Yasugi/Nicholas Passell, World Scientific: New Jersey u.a. 2003}}, year = {2004}, } @misc{18483, author = {Peckhaus, Volker}, booktitle = {Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1026.03006]}, title = {{Tomassi, Paul, “Logic after Wittgenstein,” Nordic Journal of Philosophical Logic 6 (2001), 43–70}}, year = {2004}, }