A new integration technique is presented for systems of linear partial differential equations (PDEs) for which syzygies can be formulated that obey conservation laws. These syzygies come for free as a by-product of the differential Gröbner Basis computation. Compared with the more obvious way of integrating a single equation and substituting the result in other equations the new technique integ...

Conditions are found for the convergence of interpolatory product integration rules and the corresponding companion rules for the class of Riemann-integrable functions. These conditions are used to prove convergence for several classes of rules based on sets of zeros of orthogonal polynomials possibly augmented by one or both of the endpoints of the integration interval.

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Lower case letters are used to represent functions from R to N, and capital letters are used to represent functions from R x R to N, where R denotes the set of real numbers and N denotes a ring which has a multiplicative identity element represented by 1 and a norm | • | with respect to which N is complete and |l| = 1. For a subdivision \x.\n. of an interval [a, b], we use G. and /. to denote G...

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