We consider the travelling salesman problem on metrics which can be viewed as the shortest path metric of an undirected graph with unit edge-lengths. Finding a TSP tour in such a metric is then equivalent to finding a connected Eulerian subgraph in the underlying graph. Since the length of the tour is the number of edges in this Eulerian subgraph our problem can equivalently be stated as follow...

Let X be a linear space. A p-norm on X is a real-valued function on X with 0 < p ≤ 1, satisfying the following conditions: (i) ‖x‖p ≥ 0 and ‖x‖p = 0⇔ x = 0, (ii) ‖αx‖p = |α|p‖x‖p, (iii) ‖x+ y‖p ≤ ‖x‖p +‖y‖p, for all x, y ∈ X and all scalars α. The pair (X ,‖ · ‖p) is called a p-normed space. It is a metric linear space with a translation invariant metric dp defined by dp(x, y)= ‖x− y‖p for all ...

We study noncommutative maximal inequalities and ergodic theorems for group actions on von Neumann algebras. Consider a locally compact G of polynomial growth with symmetric subset V. Let ? be continuous action algebra M by trace-preserving automorphisms. then show that the operators defined Anx=1m(Vn)?Vn?gxdm(g),x?Lp(M),n?N,1?p??, are weak type (1,1) strong (p,p) 1<p<?. Consequently, sequence ...

risk management is one of the nine project management processes, which provides positive results and minimizes the probability and consequences of adverse effects in the project.  in this article a zero-one linear programming model with multiple objectives is used to characterize the potential risks. the proposed model has two main objectives. the first objective is the minimization of the expe...

Lipoprotein(a) levels in plasma are considered an independent risk factor for atherosclerosis at different sites. Although Lp(a) measurements have recently gained interest in clinical laboratories, several problems are still unresolved. A potential source of pre-analytical variability lies in the treatment of the specimens, since it has been reported that values of several lipid quantities are ...

it is called nontrivial if {0} 6= J 6= X. This notion was introduced by Alfsen and Effros [1] and has proved useful in Banach space geometry, approximation theory and harmonic analysis; see [12] for a detailed account. A number of authors have studied the M -ideal structure in L(X), the space of bounded linear operators on a Banach space X, with special emphasis on the question whether K(X), th...

Sagittal trunk motion is accomplished through a coordination of pelvic rotation and lumbar spine flexion/extension. As trunk range of motion in healthy subjects is not fundamentally different to persons with lowback pain (LBP), other means of discriminating the two populations must be used. Research suggests that lumbar-pelvic (LP) coordination could be a potential diagnostic metric for LBP. Th...

Enhancing the speed and competition in an exhibition of services and products motivated the companies to provide high-quality products to the customers. One of the effective strategies to reach these goals is to create working groups. These groups can help the companies to improve the quality and exposure of their services along with reducing the costs. This approach is applicable in the health...