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Given the matrices and vectors above, their solution is found via standard least-squares methods; e.g., forming the normal matrix and applying Cholesky decomposition, applying the QR factorization directly to the Jacobian matrix, iterative methods for very large systems, etc.
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In topographic surveying, to determine slope to horizontal distance calculation, contour tracing and relative heights. [9] In forestry, for tree height measurement. [10] In mining and mine safety inspection, to measure the grades of haulage roads. [11] In geology, in measurements of rock outcrops and fault scarps. [12] [13] [14]
Clifford's theorem states that for an effective special divisor D, one has: 2 ( ℓ ( D ) − 1 ) ≤ d {\displaystyle 2(\ell (D)-1)\leq d} , and that equality holds only if D is zero or a canonical divisor, or if C is a hyperelliptic curve and D linearly equivalent to an integral multiple of a hyperelliptic divisor.
A probable mineral reserve is the economically mineable part of an Indicated and, in some circumstances, a Measured Mineral Resource demonstrated by at least a Preliminary Feasibility Study. This Study must include adequate information on mining, processing, metallurgical, economic, and other relevant factors that demonstrate, at the time of ...
J. M. Tienstra [] (1895-1951) was a professor of the Delft university of Technology where he taught the use of barycentric coordinates in solving the resection problem. It seems most probable that his name became attached to the procedure for this reason, though when, and by whom, the formula was first proposed is unknown.
Clifford analysis has analogues of Cauchy transforms, Bergman kernels, Szegő kernels, Plemelj operators, Hardy spaces, a Kerzman–Stein formula and a Π, or Beurling–Ahlfors, transform. These have all found applications in solving boundary value problems, including moving boundary value problems, singular integrals and classic harmonic ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.