We show that if a locally compact group G acts properly on a locally compact σ-compact space X, then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is, furthermore, metrizable, then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

This note is motivated by the similarity between multiobjective programming (MOP) and bargaining theory. It uses the known MOP concepts to establish two new bargaining results: (1) the efficiency of KalaiSmorodinsky (KS) and Nash (NA) solutions for large classes of bargaining problems can be refined to the sharper concept of proper efficiency; (2) the independence of irrelevant alternatives (II...

introduction: the human resources are considered the main asset of any society. if used properly and effectively, it will create other sources and above all the added value. the quality of the life is usually dependent on the quality of human professional life including factors such as job security, services and welfare pensions, health services, income, and job quality. the purpose of this stu...

We would like to arrive at a single coherent pair of credences in X and X. Perhaps we wish to use these to set our own credences; or perhaps we wish to publish them in a report of the WHO as the collective view of expert epidemiologists; or perhaps we wish to use them in a decision-making process to determine how medical research funding should be allocated in 2018. Given their expertise, we wo...

An injective map from the vertex set of a graph G—its order may not be finite—to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is c...

Analgesic drugs are the first line of pain relief in cancer, but they should not be the only treatment offered. If nerve blocks and other destructive procedures are to be used they should be used early with conviction and persistence. They might not be being used because there are not enough doctors who can use them properly.

Background and Purpose The use of three methods of measuring carotid stenosis, which produce different values on the same angiograms, has caused confusion and reduced the generalizability of the results of research. If the results of future studies are to be properly applied to clinical practice, and if noninvasive methods of imaging are to be properly validated against angiography, a single, s...

Let G(V,E) be a k-uniform hypergraph. A hyperedge e ∈ E is said to be properly (r, p) colored by an r-coloring of vertices in V if e contains vertices of at least p distinct colors in the rcoloring. An r-coloring of vertices in V is called a strong (r, p) coloring if every hyperedge e∈E is properly (r, p) colored by the r-coloring. We study the maximum number of hyperedges that can be properly ...