The total dissipation rate for magnetohydrodynamic ~MHD! flows in plane geometry with both velocity and magnetic shear is studied. For some boundary conditions it is shown that the lower bound on the dissipation rate is achieved by the equivalent of Stokes flow for MHD. Using the background method @Doering and Constantin, Phys. Rev. Lett. 69, 1648 ~1992!# upper bounds for the dissipation rate a...

In this article, three economic dispatch examples will be given to show the philosophy and general steps on cutting plane methods (Bender’s decomposition and Branch and Bound (B&B) algorithm). Bender’s decomposition employs duality to generate cuts, while B&B employs linear programming (LP) relaxation to find lower bound for a minimization problem and generate subregions. We will show a continu...

We revisit two natural reconfiguration models for systems of disjoint objects in the plane: translation and sliding. Consider a set of n pairwise interior-disjoint objects in the plane that need to be brought from a given start (initial) configuration S into a desired goal (target) configuration T , without causing collisions. In the translation model, in one move an object is translated along ...

Semidefinite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as finding a point in a nonempty bounded convex body Γ in the cone of symmetric positive semidefinite matrices. Assume that Γ is defined by an oracle, which for any given m ×m symmetric positive semidefinite matrix Ŷ either confirms that Ŷ ∈ Γ or returns a cut, i.e....

Slab method of analysis has been used for solving metal forming problems for a long time. However it has been restricted to plane strain and axisymmetric problems due to limitations in its formulations. In this paper a new formulation has been proposed so that it could be applied to three dimensional problems in metal forming. A parametric slab has been considered in this analysis and the force...

We describe several objects and problems of homological combinatorics, arising naturally in the theory of discriminants and plane arrangements, in particular the homology groups of complexes of connected and two-connected graphs and hypergraphs. Knot-theoretical motivations and applications are indicated, as well as first results of related calculations of homology groups of spaces of knots and...

statement of problem: considering the importance of the occlusal plane orientation in complete denture prostheses, a study was conducted on the relationship between this plane with ala-tragus and camper’s lines in soft tissue among individuals with class iii malocclusion, in mashhad school of dentistry. purpose: the aim of the present study was to define the best soft tissue index by which the ...