By Lennart Råde, Bertil Westergren (auth.)

ISBN-10: 3662035561

ISBN-13: 9783662035566

ISBN-10: 3662035588

ISBN-13: 9783662035580

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**Extra info for Mathematics Handbook: for Science and Engineering**

**Sample text**

164 511353 Mersenne primes: If 2P- 1 is prime then pis prime. Fermat primes: If 2P + 1 is prime then pis a power of 2. The following are some prime Mersenne numbers. M6 1 =2305 843 009213 693 951 M89 =618 970019 642690137 449 562111 M 107 = 162 259 276 829 213 363 391 578 010 288 127 M 127 =17014118346046923 173168730371588410 5727 M 139 8269 is the (1996) largest known prime number. 2 Fibonacci numbers The nth Fibonacci number is denoted by Fn- These numbers are defined by the formulas F 1 =I Fz= 1 Fn+z=Fn+Fn+ I• n~ 1 (Cf.

0 in a. z; --t Z~, n ~ m 2. An (m, n)-code K is a one-to-one function K: X c --t z~ is a matrix code if X= x'A, where the matrix A is of type (m, n). 3. A code K: z; 4. The range of K is the set of code words. 5. A code K: z; --t z; is a group code if the code words in Z~ form an additive group. 6. The weight of a code is the minimum distance between the code words= the minimal number of rows in the control (decoding) matrix C whose sum is the zero vector. 7. A code detects k errors if the minimum distance between the code words (the weight) is at least k+ I.

The level of a node is the length of its path from the root. 5 Weighted digraphs A weighted digraph is a digraph in which each directed edge (v;, vj) is assigned a positive number (the weight) wij= w(v;, v). If there is no edge from v; to vj then wij= oo. The graph can be represented by a weighted'adjacency matrix W= (wij). The weight of a path is the sum b of the weights of the edges occuring in the path. 00 2 6 5 00 oooo4oo7 W= 00 00 00 00 00 00 00 00 00 1 2 00 1 00 00 a = v, b = vz c = v3 d = v4 z = v5 d Dijkstra's algorithm for finding the shortest path To find the shortest path from a to z.

### Mathematics Handbook: for Science and Engineering by Lennart Råde, Bertil Westergren (auth.)

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