with n, m > 2, Ω ⊂ R, m < p <∞ and a compact set A ⊂ R with nonempty interior. In the case of a convex integrand f(s, ξ, · ) and a convex restriction set A = K, the global minimizers of (1.1) − (1.3) satisfy optimality conditions in the form of Pontryagin’s principle 01) even though the usual regularity condition for the equality operator (1.2) fails. 02) The question arises whether the Pontrya...

with n, m > 2, Ω ⊂ R, m < p < ∞ and a compact set K ⊂ R with nonempty interior. In the case of a convex integrand f(s, ξ, · ) and a convex restriction set K, the global minimizers of (1.1) − (1.3) satisfy optimality conditions in the form of Pontryagin’s principle 01) even though the usual regularity condition for the equality operator (1.2) fails. 02) The question arises whether the Pontryagin...

For a finite-dimensional operator A with spectrum σ(A), the following conditions on the Davis–Wielandt shell DW (A) of A are equivalent: (a) A is normal. (b) DW (A) is the convex hull of the set {(λ, |λ|) : λ ∈ σ(A)}. (c) DW (A) is a polyhedron. These conditions are no longer equivalent for an infinite-dimensional operator A. In this note, a thorough analysis is given for the implication relati...

Lovász and Schrijver (1991) described a semi-definite operator for generating strong valid inequalities for the 0-1 vectors in a prescribed polyhedron. Among their results, they showed that n iterations of the operator are sufficient to generate the convex hull of 0-1 vectors contained in a polyhedron in n-space. We give a simple example, having Chvátal rank 1, that meets this worst case bound ...

Choosing the right hull shape is important in designing a ship, for example, U-section or V-section of hull. The will affect various aspects, such as design, resistance, seakeeping, structure and production. ship must be properly designed so that it can operate according to ship’s mission. From seakeeping aspect ship's motion at sea, difference result different motions dynamic effects slamming ...

In this paper, we first extend the concept of arity in crisp convex spaces to case fuzzification and give some related properties. From view hull operator, study relations between disjoint sum M-fuzzifying its factor spaces. We also examine additivity degree separability (S0,S1,S2,S3,S4). Finally, show that every space is JHC iff corresponding JHC.

Finding a good classifier is a multiobjective optimization problem with different error rates and the costs to be minimized. The receiver operating characteristic is widely used in the machine learning community to analyze the performance of parametric classifiers or sets of Pareto optimal classifiers. In order to directly compare two sets of classifiers the area (or volume) under the convex hu...

Strong normalization results are obtained for a general language for collection types. An induced normal form for sets and bags is then used to show that the class of functions whose input has height (that is, the maximal depth of nestings of sets/bags/lists in the complex object) at most i and output has height at most o de nable in a nested relational query language without powerset operator ...

Later a bouquet of Krasnosel 'skii-type theorems was discovered; see [1,2, 3, 4,16,17]. Apart from the usual line segment visibility and starshapedness several other notions of starshaped set and visibility have been investigated in the past years: d-starshaped sets in metric and normed spaces [14,15,16,17], starshaped sets in graphs [14,171, staircase visibility [5,10,12], rectangular visibili...