The Relaxed Game Chromatic Index of \u3cem\u3ek\u3c/em\u3e-Degenerate Graphs

The (r, d)-relaxed coloring game is a two-player game played on the vertex set of a graph G. We consider a natural analogue to this game on the edge set of G called the (r, d)-relaxed edge-coloring game. We consider this game on trees and more generally, on k-degenerate graphs. We show that if G is k-degenerate with ∆(G) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆+k−1 and d≥2k2 + 4k

Complete Multipartite Graphs and the Relaxed Coloring Game

Let k be a positive integer, d be a nonnegative integer, and G be a finite graph. Two players, Alice and Bob, play a game on G by coloring the uncolored vertices with colors from a set X of k colors. At all times, the subgraph induced by a color class must have maximum degree at most d. Alice wins the game if all vertices are eventually colored; otherwise, Bob wins. The least k such that Alice has a winning strategy is called the d-relaxed game chromatic number of G, denoted χ gd (G). It is known that there exist graphs such that χ g0 (G) = 3, but χ g1 (G) \u3e 3. We will show that for all positive integers m, there exists a complete multipartite graph G such that m ≤ χ g0 (G) \u3c χ g1 (G)

The Relaxed Edge-Coloring Game and \u3cem\u3ek\u3c/em\u3e-Degenerate Graphs

The (r, d)-relaxed edge-coloring game is a two-player game using r colors played on the edge set of a graph G. We consider this game on forests and more generally, on k-degenerate graphs. If F is a forest with ∆(F) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆ − j and d ≥ 2j + 2 for 0 ≤ j ≤ ∆ − 1. This both improves and generalizes the result for trees in [10]. More broadly, we generalize the main result in [10] by showing that if G is k-degenerate with ∆(G) = ∆ and j ∈ [∆ + k − 1], then there exists a function h(k, j) such that Alice has a winning strategy for this game with r = ∆ + k − j and d ≥ h(k, j)

Declines and conservation of Himalayan Galliformes

PhD ThesisThe Greater Himalaya has been identified as a key conservation region that supports high levels of biodiversity but has exceptionally high proportions of threatened species. One taxonomic group that is thought to be of particular concern is the bird order Galliformes. The Greater Himalaya is home to 24 species of resident Galliformes with a variety of ecological characteristics, geographical distribution patterns and abundance levels. Our current knowledge of South Asian Galliformes and Himalayan species in particular, contains many gaps. For example, it is suspected that many Himalayan Galliformes have undergone marked population declines but as to what extent they have declined and even the current status of some species is not fully known. There is a similar paucity of knowledge regarding both the distributions of the rarest of Himalayan Galliformes species and how well the current protected area network represents such distributions. Here I provide new insights into the distribution of the rarest Himalayan Galliform, the Critically Endangered Himalayan Quail (Orphrysia superciliosa) by using two proxy species with similar habitat preferences to create an environmental niche model. I show that by calculating an estimate of extinction likelihood, we have good reason to believe that the Himalayan quail to be extant and that recent searches in Nepal would be better targeted in North East India. Moving from single species to multiple species, I then examine long-term population changes across all Himalayan Galliformes by using changes in geographic range size as a proxy. I show that population changes for this suite of species both within and outside the Himalaya can help us to set conservation priorities and baselines. In addition, it can help us to identify species that have undergone large population changes that are not reflected in contemporary IUCN Red List statues. Species with small geographic ranges are currently top priorities for conservation efforts because they are thought to be at a greater risk of extinction. However, because it is also easier to track long term population changes over smaller spatial scales, concern exists that we may have underestimated the declines and therefore the extinction risk of more i widespread species. I show that across the entire Galliformes taxon, geographic range size does not predict the rate of geographic range decline. Finally, I move from population declines across all Galliformes to distributions of Himalayan Galliformes and assess how well the current protected area network represents such species. Using a combination of species distribution modelling and spatial prioritisation software, I show that the current protected area network in the greater Himalayas could be improved to offer better coverage for Himalayan Galliformes. I conclude by discussing the generality of my results and how they can be applied to other taxa and localities. Finally I make a series of recommendations for future Galliformes research and conservation within the Himalaya

A Study of signature analysis regarding a Rzeppa type constant velocity joint

The objective for the CV Joint Test Stand Thesis is to design and develop a test stand that will allow the ability to test a constant velocity (CV) joint with a computer interface for data collection. This thesis concentrates on two separate sections, one is the specification of equipment and computer program for data collection, and the second is a moderate outlook on signature analysis of the system. The APRA (Automotive Parts Rebuilders Association) along with the National Center for Remanufacturing and Resource Recovery (NCRRR) are dedicated to the quality and the need for better remanufacturing techniques. The specification of the equipment includes instruments such as an infrared thermocouple, accelerometer, microphone, and a magnetic particle brake. The infrared (IR) thermocouple will be used to check the temperature of the CV Joint. This type of thermocouple was chosen since it does not need to be permanently mounted on the object it is reading. An accelerometer is used to provide vibration analysis information for the system. The magnetic particle brake will be needed to provide a torque to simulate road like-conditions and to accurately investigate the system. The computer interface will utilize Labview to control and monitor the system during operation. Programming will be done in Labview to complete these tasks. Data files can then be exported to Matlab for further analysis. Finally, a conservative look at the signature analysis of the system will be done to try and correlate CV joint ball wear with noise. No attempt will be made to correlate CV joint wear with temperature and/or vibration at this time. However, this instrumentation can be used for future research