Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs has been extensively studied, due to both its interesting structure and its numerous applications (in bioinformatics, constrained-based temporal reasoning, resource allocation, and scheduling problems, among others). Several efficient al...

Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in O∗(23k) time given a boolean-decomposition of width k, hence for all graph classes where a boolean-decomposition of width O(log n) can be found in polynomial time, MWDS can be solved...

BACKGROUND AND PURPOSE Open-wedge osteotomies of the distal radius create a void that is usually filled with either iliac crest bone graft or bone substitute. Previous studies have suggested that this is unnecessary. We investigated the safety of omitting the filling procedure. PATIENTS AND METHODS We included 15 patients with a dorsal malunion of a distal radius fracture. A palmar approach a...

In this paper, we establish some generalizations of weighted trapezoid inequality for mappings of bounded variation, and give several applications for r − moment, the expectation of a continuous random variable and the Beta mapping.

An approximation of the Stieltjes integral of bounded integrals and continuous integrators via the Darst-Pollard inequality is given. Applications for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation are also provided.

Utilising the Beesack version of the Darst-Pollard inequality, some error bounds for approximating the Riemann-Stieltjes integral are given. Some applications related to the trapezoid and mid-point quadrature rules are provided.

Some generalizations and refinements of Hermite-Hadamard type inequalities related to [Formula: see text]-convex functions are investigated. Also applications for trapezoid and mid-point type inequalities are given.

Generalizations of the classical and perturbed trapezoid inequalities are developed using a new mean value theorem for the remainder in Taylor’s formula. The resulting inequalities for N -times differentiable mappings are sharp.