The optimal power-flow problem (OPF) has always played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations (e.g., of the network model) that render the problem convex, but that consequently yield ...

The optimal power-flow problem (OPF) has always played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations (e.g., of the network model) that render the problem convex, but that consequently yield ...

A 1-combing for a finitely presented group consists of a continuous family of paths based at the identity and ending at points x in the 1-skeleton of the Cayley 2-complex associated to the presentation. We define two functions (radial and ball tameness functions) that measure how efficiently a 1-combing moves away from the identity. These functions are geometric in the sense that they are quasi...

where B = {x ∈ Rn : |x| < } is the unit ball in Rn and Du = ( ∂u ∂xi∂xj ) is the Hessian of u, λ is a nonnegative parameter and f : R→ R is a continuous function. The study of problem (.) in general domains of Rn may be found in [, ]. Kutev [] investigated the existence of strictly convex radial solutions of problem (.) when f (u) = up. Delanoë [] treated the existence of convex radi...

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...

The convex hull of X,,. . ., X., a sample of independent identically distributed Rd-valued random vectors with density f is called a random convex hull with parameters f and II. In this paper, we give an a orithm for the computer generation of random convex hulls when f is radial, i.e. when j(x) = g(ll $ l)Tor some function g. Then we look at the average time E(r) of the algorithm under a conve...

In this study the effects of machining parameters such as shearing speed, feed rate, tool diameter and machining depth on different milling strategies i.e. 3D offset, spiral, raster and radial to produce the convex surface made of epoxy/glass composites is investigated. The effects of mentioned strategies on output parameters such as surface roughness and milling removal rate is also studied. T...

Abstract. We consider the class of semi-stable solutions to semilinear equations −∆u = f(u) in a bounded smooth domain Ω of R (with Ω convex in some results). This class includes all local minimizers, minimal, and extremal solutions. In dimensions n ≤ 4, we establish an priori L∞ bound which holds for every semi-stable solution and every nonlinearity f . This estimate leads to the boundedness o...

This paper presents a mixed-integer quadratically-constrained programming (MIQCP) model to solve the distribution system expansion planning (DSEP) problem. The DSEP model considers the construction/ reinforcement of substations, the construction/reconductoring of circuits, the allocation of fixed capacitors banks and the radial topology modification. As the DSEP problem is a very complex mixed-...