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Conflicts between resource names residing within the same logical subnet or workgroup can be resolved by partitioning the namespace through the use of a NetBIOS scope identifier (Figure 3.4). This is a character string used in conjunction with the NetBIOS name to enforce uniqueness in the namespace. The total length of the NetBIOS scope plus the NetBIOS name cannot exceed 256 characters. Note that the use of NetBIOS scopes effectively isolates resources from communicating with each other.

Combinatorica` letters={a, b, c, d, e}; KSubsets[letters, 3]

{{a, b, c}, {a, b, d}, {a, b, e}, {a, c, d}, {a, c, e}, {a, d, e}, {b, c, d}, {b, c, e}, {b,

d, e}, {c, d, e}}

i 2 2 1 z lim by L Hospital s rule. z! i=2 z! i=2 6z 10i 3 3z2 10iz 3 4i 2 dz 1 2 i Then , the required value. 2 10iz 3 4i 2 C 3z

Length[%] 10

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Mathematica represents tables and matrices as nested lists. Internally, there is no difference in the way they are stored, but they are represented differently using the functions MatrixForm and TableForm. It is often more convenient to use //MatrixForm or //TableForm to the right of the matrix or table name.

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z z 1 e3i e 3i z3 z 3 ; cos 3 ; dz iz d . 2 2 2 2 cos 3 z3 z 3 =2 dz ! d 5 4 cos 0 C z z 1 iz 5 4 2 1 z6 1 dz 3 2i C z 2z 1 z 2

MatrixForm[list] prints double nested lists as a rectangular array enclosed within parentheses. The innermost lists are printed as rows. Single nested lists are printed as columns enclosed within parentheses. TableForm[list] prints list the same way as MatrixForm except the surrounding parentheses are omitted.

Matrices and tables can be entered directly as nested lists. A matrix or table having m rows and n columns would be a nested list of m sublists, each containing n entries.

list = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}; MatrixForm[list] 1 2 3 4 5 6 7 8 9 10 11 12 or list //MatrixForm

Each application registers its presence in the namespace by making a NetBIOS Add Name or Add Group Name call. The service or group name is then reserved in the namespace until specifically released by a Delete call or the machine on which the service resides is shut down. Registered names and resource types can be queried by invoking the Windows nbtstat command. In Example 3.1, nbstat is used to display the registered NetBIOS resource table for a machine named Wizard. The listing indicates that Wizard is a member of the group Eyrie and it has one connected user, DeRoest. The reserved name _MSBROWSE_ delineates Wizard as the registered master browser for the group. Example 3.1 NetBIOS Machine Listing C:\nbtstat a Wizard NetBIOS Remote Machine Name Table Name Type Status ----------------------------------------------------WIZARD <00> UNIQUE Registered EYRIE <00> GROUP Registered WIZARD <03> UNIQUE Registered

(a) absolutely convergent,

list = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}};

{{1,

MatrixForm[list] 1 2 3 4 5 6 7 8 9 10 11 12

(b) uniformly convergent for jzj @ 1.

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Two special matrix-generating commands are worth remembering because of their frequency in applications. These generate a nested list. Use MatrixForm to get a matrix.

IdentityMatrix[n] produces an n n matrix with 1s on the main diagonal and 0s elsewhere. DiagonalMatrix[list] creates a diagonal matrix whose diagonal entries are the elements of list.

IdentityMatrix[3] //MatrixForm 1 0 0 0 1 0 0 0 1 DiagonalMatrix[{1, 2, 3}] //MatrixForm 1 0 0 0 2 0 0 0 3

16.61. Locate in the nite z plane all the singularities, if any, of each function and name them: a z 2 ; 2z 1 4 b z ; z 1 z 2 2 c z2 z2 1 ; 2z 2 1 d cos ; z e sin z =3 ; 3z f cos z : z2 4 2

Once defined, matrices can be combined using the operations of addition, subtraction, scalar, and matrix multiplication. The operation of matrix multiplication is represented by a period (.). Matrices are discussed in greater detail in 12.

WIZARD EYRIE DEROEST EYRIE .._MSBROWSE__..

1 2 3 A = 4 5 6 7 8 9

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