Numerous problems arising in engineering applications can have several objectives to be satisfied. An important class of problems of this kind is lexicographic multi-objective problems where the first objective is incomparably more important than the second one which, in its turn, is incomparably more important than the third one, etc. In this paper, Lexicographic Multi-Objective Linear Program...

Mathematical Morphology is a powerful non-linear image analysis techniques based on lattice theory. The definitions of morphological operators need an ordered lattice algebraic structure. In order to apply these operators to the colour images it is required, on one hand the choice of a suitable colour space representation and on the other hand, to establish an order in the colour space providin...

We generalize the main result of [K–K–S] concerning the convex embeddings of a chain Γ in a lexicographic power ∆Γ. For a fixed non-empty chain ∆, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functional equations (∆) ≃ Γ , (∆) ≃ Γ and (∆) ≃ Γ .

It is well-known, that the ring C[X1, . . . , Xn]n of polynomial invariants of the alternating group An has no finite SAGBI basis with respect to the lexicographical order for any number of variables n ≥ 3. This note proves the existence of a nonsingular matrix δn ∈ GL(n,C) such that the ring of polynomial invariants C[X1, . . . ,Xn] δn n , where An n denotes the conjugate of An with respect to...

In this paper, we give a complete description for the lexicographic world L = {(x, y) ∈ Σ × Σ : Σxy 6= ∅} = {(x, y) : y ≥ φ(x)}, where Σ = {0, 1}N, Σab = {x ∈ Σ : a ≤ σi(x) ≤ b, for all i ≥ 0}, φ : Σ→ Σ is defined by φ(a) = inf{b : Σab 6= ∅} and the order ≤ is the lexicographic order on Σ. The main result is that b = φ(a) for some a = 0x if and only if b is the Sturmian sequence b such that Orb...

We describe experiments done in using the lemon model for encoding lexicographic data we got from different sources with distinct coverages. Our focus is on delivering statements on lessons learned and on questions that still should be discussed in the lemon community, as a possible input for forthcoming versions of the model.

In this paper we present an algorithm for generating the lexicographi cally smallest representatives of all the n bead necklaces in k colors The time required is O nN k where N n k is the number of necklaces with n beads of k colors To our knowledge this is the rst algorithm for this problem which has been proved to asymptotically improve the obvious O n k approach of examining all k ary n tupl...

In this paper we consider the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements with 2 ≤ w < n ≤ 10. Computer search of lexicographic constant-weight equidistant codes is performed. Tables with bounds on the size of lexicographic constant-weight equidistant codes are presented.