Many key verification problems such as bounded model-checking, circuit verification and logical cryptanalysis are formalized with combined clausal and affine logic (i.e. clauses with xor as the connective) and cannot be efficiently (if at all) solved by using CNF-only provers. We present a decision procedure to efficiently decide such problems. The GaussDPLL procedure is a tight integration in ...

New Gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method. For discontinuous functions, we construct Gauss-like quadrature rules over arbitrarily-shaped elements in two dimensions without the need for partitioning the finite element. A point elimination algorithm is used in the construction of the quadra...

The de Sitter thermodynamics of cosmological models with a modified Friedmann equation is considered, with particular reference to high-energy Randall-Sundrum and Gauss-Bonnet braneworlds. The Friedmann equation can be regarded as the first law of thermodynamics of an effective gravitational theory in quasi de Sitter spacetime. The associated entropy provides some selection rules for the range ...

Each of these rules will be called a Gauss-Christoffel quadrature formula if it has maximum degree of exactness, i.e. if (1.1) is an exact equality whenever / is a polynomial of degree 2n — 1. It is a well-known fact, due to Christoffel [3], that such quadrature formulas exist uniquely, provided the weight function w(x) is nonnegative, integrable with /* w(x)dx > 0, and such that all its moments

We study integration in a class of Hilbert spaces of analytic functions defined on the Rs. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite integration rules and show that the errors of our algorithms decay exponentially fast. Furthermore, we study tractability in terms of s and log ε−1 and give necessary and sufficie...

Abstract. A one-parameter generalisation Rλ(X; b) of the symmetric Macdonald polynomials and interpolations Macdonald polynomials is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry, principal specialisation formula and q-difference equation for Rλ(X; b). We also prove a new multiple q-Gauss summation formula and several further results for sl...

To compute integrals on bounded or unbounded intervals we propose a new numerical approach by using weights and nodes of the classical Gauss quadrature rules. An account of the error and the convergence theory is given for the proposed quadrature formulas which have the advantage of reducing the condition number of the linear system arising when applying Nyström methods to solve integral equati...

In this paper it is proposed to compute the volume integral of certain functions whose antiderivates with respect to one of the variates (say either x or y or z) is available. Then by use of the well known Gauss Divergence theorem, it can be shown that the volume integral of such a function is expressible as sum of four integrals over the unit triangle. The present method can also evaluate the ...

It is advisable to refer to the publisher's version if you intend to cite from the work. Abstract. Galerkin discretizations of integral operators in R d require the evaluation of integrals S (1) S (2) f (x, y) dydx,w h e r eS (1) ,S (2) are d-dimensional simplices and f has a singularity at x = y. In [A. Chernov, T. von Petersdorff, and C. Schwab, M2A NM a t h .M o d e l .N u m e r .A n a l. , ...