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Due to the high number of integrals and the complexity and unknown behaviour of the functions to be integrated , Monte Carlo integration provides a viable method of computing the global illumination in a three-dimensional scene . Given a set of n points in the plane , we consider the problem of computing the circular ordering of the points about a viewpoint q and efficiently maintaining this ordering information as q moves . Checking specific header fields before computing the integrity / authentication value not only may waste time and resources , but also may lead to incorrect diagnoses of a validation failure . This thesis discusses algorithms for computing the subalgebra and congruence lattices of finite multi-sorted algebras and presents a design and implementation of software for creating finite multi-sorted algebras and computing the lattices . The forecast error variance decomposition is used to determine the degree of exogeneity of a set of variables relative to another set of variables by computing the percentage of the k-steps ahead squared prediction error of a particular variable produced by an innovation in another variable ( Hakkio and Morris ( 1984 ) ) . The subgroup N is obtained by computing the coset table of the trivial subgroup in the group defined by the relations of G together with relators corresponding to the words generating H. For a sample application of this function , see Example H22E17 . Paragraph ( b ) of this section provides rules for computing the principal balance of a section 467 loan at the beginning of any rental period . As a rule , the game should stop after it completes a screen update , before computing the next generation . We demonstrate the applicability of the method by computing the feedback capacity of partial response channels and the feedback capacity of run-length-limited ( RLL ) sequences over binary symmetric channels ( BSCs ) . The Board affirmed the ALJ 's conclusions but modified the ALJ 's ruling by utilizing a different method of computing the compensation award . The Lagrange method is more complex because it includes the 61 additional coupling equations.The " consistency test " was used to test the accuracy of both methods for computing the power in uninstrumented assemblies , i.e ., one-by-one , each of the detectors is considered not available , and the remaining detectors are used to compute the powers in the uninstrumented assemblies.There is potential for expanding the Lagrange method to a three-dimensional approach that could produce even better results , and that is a consideration . The bonds , if issued by any new district , shall be considered a liability of the new district for purposes of computing the bonding capacity of the new district when applying the State School Building Aid Law of 1952 , Chapter 8 ( commencing with Section 16000 ) of Part 10 . If computing the DFT of a 256-sample array , select 257 samples in the DFT to produce a set of output frequencies " symmetric " about 0 . Instead of computing the margins across the entire data set , the procedure computes separate margins for each level of the LS-mean effect in question . Unless the user also provides a code for computing the ( sub ) gradient of the objective function , these ( sub ) gradients are calculated by the program itself using finite differences . The comparison is made by computing the ratio of the recorded motion to the reference rock motion , where the Sadigh et al. ( 1994 ) rock attenuation relation is used as the reference . This is a great first-order approximation , and can be improved by computing the aforementioned matrices B_2 , B_3 , etc. Quantum Mechanics , at its core , theorizes that the universe is made up of objects that can be represented as waves . Given a boolean equation system ( E ) and one of its bound variables X_init , we propose a local algorithm for computing the solution delta ( X_init ) of ( E ) .