Fix a prime number l. In this paper we prove a conjecture [16, p. 300], which Ihara attributes to Deligne, about the action of the absolute Galois group on the pro-l completion of the fundamental group of the thrice punctured projective line. It is stated below. Similar techniques are also used to prove part of a conjecture of Goncharov [11, Conj. 2.1], also about the action of the absolute Gal...

| Jobs arriving over time must be nonpreemptively processed on one of m parallel machines, each of which running at its own speed, so as to minimize a weighted sum of the job completion times. In this on-line environment, the processing requirement and weight of a job are not known before the job arrives. The Weighted Shortest Processing Requirement (WSPR) on-line heuristic is a simple extensio...

We consider the problem of permutation reconstruction, which is a variant of graph reconstruction. Given a permutation p of length n, we delete k of its entries in each possible way to obtain (n k ) subsequences. We renumber the sequences from 1 to n−k preserving the relative size of the elements to form (n−k)-minors. These minors form a multiset Mk(p) with an underlying set M ′ k(p). We study ...

Erdős and Lovász conjectured in 1968 that for every graph G with χ(G) > ω(G) and any two integers s, t ≥ 2 with s+ t = χ(G)+1, there is a partition (S, T ) of the vertex set V (G) such that χ(G[S]) ≥ s and χ(G[T ]) ≥ t. Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for line graphs of multigraphs.

nowadays project management is a key component in introductory operations management. the educators and the researchers in these areas advocate representing a project as a network and applying the solution approaches for network models to them to assist project managers to monitor their completion. in this paper, we evaluated project’s completion time utilizing the q-learning algorithm. so the ...

Nowadays project management is a key component in introductory operations management. The educators and the researchers in these areas advocate representing a project as a network and applying the solution approaches for network models to them to assist project managers to monitor their completion. In this paper, we evaluated project’s completion time utilizing the Q-learning algorithm. So the ...

Depth completion aims to generate a dense depth map from the sparse and aligned RGB image. However, current methods use extremely expensive 64-line LiDAR(about $100,000) obtain maps, which will limit their application scenarios. Compared with LiDAR, single-line LiDAR is much less more robust. Therefore, we propose method tackle problem of completion, in aim info A dataset proposed based on exis...

Probabilistic Packet Marking (PPM ) is one of the most promising schemes for performing IP Traceback. PPM reconstructs the attack graph in order to trace back to the attackers. Finding the Completion Condition Number (i.e. precise number of packets required to complete the traceback) is very important. Without a proper completion-condition, we might reconstruct a wrong attack-graph and attacker...