By Lennart Rade, Bertil Westergren, Visit Amazon's Peter Vachenauer Page, search results, Learn about Author Central, Peter Vachenauer,

Der schnelle und präzise Zugriff auf Daten und Fakten der Mathematik für Ingenieure, Informatiker, Naturwissenschaftler und Wirtschaftswissenschaftler, für Studenten und Anwender!

Dieses völlig neu konzipierte Handbuch bietet in moderner, besonders übersichtlicher Aufmachung mathematische Formeln, Tabellen, Definitionen und Sätze. Kurz, prägnant und stets in Verbindung mit konkreten Beispielen präsentiert es klassische wie aktuelle Gebiete, zugeschnitten auf die Bedürfnisse des Anwenders und Praktikers.
"Springers Mathematische Formeln" ist obendrein die ideale Ergänzung zur "Höheren Mathematik" von Meyberg/Vachenauer.

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Additional resources for Springers Mathematische Formeln: Taschenbuch für Ingenieure, Naturwissenschaftler, Informatiker, Wirtschaftswissenschaftler

Example text

B) z =yC= (101)=r2 (2. Zeile von C). Yt=e2 =(010000) fi YtC= (101). Daher ist y+y,= (001111) und x'=(OOI). (e) z=yC=(Ol1)=r, +rz =r5 + r6. Kein Codewort vom Gewicht 1 hat dieses Fehlersyndrom. Der Fehler hat Gewicht ~ 2. Keine "sichere" Korrektur möglich. B. (1 +x+~)+(l +x+x3 ) = ~+~ und (I +x+~)(1 +x+x3)= I +x4+~]. Man identifiziert jedes Polynom b(x)EZ2[x] mit dem binären Vektor seiner Koeffizienten b(x)=bo+b,x+ ... +bP" 'f-? b = (bob, ... b k) . Die polynomiale Codierung K: Z~ ~ Z~ (n=m+k) mit dem Generatorpolynom g(x)=ao+atx+ ...

Keine "sichere" Korrektur möglich. B. (1 +x+~)+(l +x+x3 ) = ~+~ und (I +x+~)(1 +x+x3)= I +x4+~]. Man identifiziert jedes Polynom b(x)EZ2[x] mit dem binären Vektor seiner Koeffizienten b(x)=bo+b,x+ ... +bP" 'f-? b = (bob, ... b k) . Die polynomiale Codierung K: Z~ ~ Z~ (n=m+k) mit dem Generatorpolynom g(x)=ao+atx+ ... +ap" f-? (aOat ... ak) bildet X=p(X)EZ; auf y=q(x)=g(X)p(X)E Z~ ab. In Matrixschreibweise bedeutet dies (qoq, ... qn-') = (PoP, ... Pm_,)G mit der mxn-Matrix ao a, ............ ak 0 .....

6. (i) Der Körper E ist eine Erweiterung des Körpers F. wenn E einen zu F isomorphen Unterkörper enthält. (ii) Ist STeilmenge von E, dann bezeichnet F(S) den kleinsten Unterkörper von E, der S und F enthält. Zum Beispiel: (a) R(z)=C. (b) Q(J2) ={a+b,J2; a. bE Q} (e) Q(lt) ={(aO+allt +a2lt2+ ... +anltn)/(bo+b1lt +b2lt 2+... +bmlt m) ; ai' biE Q, nicht alle bj=O} 5. • k-2n, k-n. k, k+n. k+2n, ... }. 1. [k]=[m] ~ k-m ist ganzahliges Vielfaches von n. Daher ist Zn={[O]. [I], ... ,[n-I]}. 2. Verknüpfungen: [kt1+n[k 2]=[k1+k2] , [kt1 x n [k2] = [k 1k2] 3.

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