As p—► » we get the space E„ with the distance function max,-=i,... ,m | x< — as/ |. Let, furthermore, lp stand for the space of real sequences with the series of pth powers of the absolute values convergent. Similarly let Lp denote the space of real measurable functions in the interval (0, 1) which are oummable to the ^»th power, while C shall mean the space of real continuous functions in the...

We introduce a problem that is a common generalization of the uncapacitated facility location and minimum latency (ML) problems, where facilities need to be opened to serve clients and also need to be sequentially activated before they can provide service. Formally, we are given a set F of n facilities with facility-opening costs fi, a set D of m clients, connection costs cij specifying the cos...

A long standing conjecture says that the integrality ratio of the subtour LP for metric TSP is 4/3. A well known family of graphic TSP instances achieves this lower bound asymptotically. For Euclidean TSP the best known lower bound on the integrality ratio was 8/7. We improve this value by presenting a family of Euclidean TSP instances for which the integrality ratio of the subtour LP converges...

We prove that the first reduced cohomology with values in a mixing Lp-representation, 1 < p < ∞, vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. ...

In this paper, we establish Lp norm bounds for spectral clusters on compact manifolds, under the assumption that the metric is C1,1. Precisely, we show that the Lp estimates proven by Sogge [12] in the case of smooth metrics hold under this limited regularity assumption. It is known by examples of Smith-Sogge [11] that such estimates fail for C1,α metrics if α < 1.

q-ary lattices are obtained from linear q-ary codes via the so-called Construction A. We study these lattices in the lp norm in R and the associated q-ary codes in the induced p-Lee metric in Zq . This induced metric extends to 1 ≤ p < ∞ the well-known Lee metric when p = 1. A previous result on lattice decoding in the Lee metric is generalized for p > 1 and the existence of perfect codes in su...

This paper proposes a mathematical model as the bi-objective capacitated multi-vehicle allocation of customers to distribution centers. An evolutionary algorithm named non-dominated sorting ant colony optimization (NSACO) is used as the optimization tool for solving this problem. The proposed methodology is based on a new variant of ant colony optimization (ACO) specialized in multi-objective o...

In this paper, it is proved that the weak convergence of Lp Gaussian surface area measures implies corresponding convex bodies in Hausdorff metric for p ≥ 1. Moreover, continuity solution to Minkowski problem with respect obtained.

In this paper, we give a characterization of compact sets in Lp-spaces on metric measure spaces, which is generalization the Kolmogorov-Riesz theorem. Using criterion, investigate topological type space consisting Lipschitz maps with bounded supports.