fifty years ago warren and root have introduced the shape factor. this fundamental parameter for modeling of naturally fractured reservoirs has been discussed stormily ever since. different definitions for shape factor have been suggested which all of them are heuristically based. recently, heinemann and mittermeir mathematically derived - based on the dual-continuum theorem assuming pseudo-ste...

C Elementary and special functions (search also class L5 ) C1 Integer-valued functions (e.g., factorial, binomial coefficient, permutations, combinations, floor, ceiling) C06GXFP Factorizes a positive integer n as n = n1 × n2. This routine may be used in conjunction with C06MCFP D Linear Algebra D1 Elementary vector and matrix operations D1a Elementary vector operations D1a1 Set to constant D1a...

This note explores sparse matrix dense matrix (SMDM) multiplications, useful in block Krylov or block Lanczos methods. SMDM computations are AU , and V A, multiplication of a large sparse matrix m × n matrix A by a matrix V of k rows of length m or a matrix U of k columns of length k, k << m, k << n . In a block Lanczos or Krylov algorithm, matrix matrix multiplications with the ”tall” U and ”w...

a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...