We extend a result of Minsky to show that for a map of a surface to a hyperbolic 3-manifold which is not necessarily π1-injective but is 2-incompressible rel a geodesic link with a definite tube radius, the set of noncontractible simple loops with a bounded length representatives is quasi-convex in the complex of curves.

In this paper, we prove a logarithmic convexity that reflects an observability estimate at single point of time for 1-D heat equation with dynamic boundary conditions. Consequently, establish the impulse approximate controllability impulsive Moreover, obtain explicit upper bound cost control. At end, give constructive algorithm computing control minimal $L^2$-norm. We also present some numerica...

In the parallel variable distribution framework for solving optimization problems (PVD), the variables are distributed among parallel processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining “secondary” variables to change in a restricted fashion along some easily computable directions. For constrained nonlinear programs c...

This paper presents an analysis of the problem of aggregating preference orderings under subjective uncertainty. Individual preferences, or opinions, agree on the ranking of risky prospects, but are quite general because we do not specify the perception of ambiguity or the attitude towards it. A convexity axiom for the ex-ante preference characterizes a (collective) decision rule that can be in...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of the induced paths is associated with the monophonic convexity ; and there are many other examples. Besides reviewing the path convexities in the literature, ...

In this paper, we propose a new combined scalarization method of multi-objective optimization problems by using the surplus variables and generalized Tchebycheff norm then use it to obtain some equivalent characterizations (weakly, strictly, properly) efficient solutions adjusting range parameters. These results do not need any convexity assumption conditions object...

We study the existence of Stackelberg equilibrium points on strategy sets which are geodesic convex in certain Riemannian manifolds by using metric projection arguments. The present results extend those obtained in Nagy [J. Global Optimization (2013)] in the Euclidean context.

The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. support function can be used in order to approximate solutions such problems by finite dimensional various constraints. We propose a framework dimensions two and three we present applications from the field convex geometry. consider depending on volume, perimeter Dirichlet L...

The main features of the fuzzy sets and their corresponding membership functions were presented in terms fuzzification process further by de-fuzzification operation. convexity α -(alfa) cuts is used decomposition sets. alfa defined precisely pair lowest upper greatest lower bounds. convex combination intervals sub-regions function considered as points defuzzified values methods to crisp formula...