Heterochromatic paths in edge colored graphs without small cycles and heterochromatic-triangle-free graphs

Conditions for the existence of heterochromatic Hamiltonian paths and cycles in edge colored graphs are well investigated in literature. A related problem in this domain is to obtain good lower bounds for the length of a maximum heterochromatic path in an edge colored graph G. This problem is also well explored by now and the lower bounds are often specified as functions of the minimum color degree of G - the minimum number of distinct colors occurring at edges incident to any vertex of G - denoted by v(G). Initially, it was conjectured that the lower bound for the length of a maximum heterochromatic path for an edge colored graph G would be 2v(G)/3]. Chen and Li (2005) showed that the length of a maximum heterochromatic path in an edge colored graph G is at least v(G) - 1, if 1 <= v(G) <= 7, and at least 3v(G)/5] + 1 if v(G) >= 8. They conjectured that the tight lower bound would be v(G) - 1 and demonstrated some examples which achieve this bound. An unpublished manuscript from the same authors (Chen, Li) reported to show that if v(G) >= 8, then G contains a heterochromatic path of length at least 120 + 1. In this paper, we give lower bounds for the length of a maximum heterochromatic path in edge colored graphs without small cycles. We show that if G has no four cycles, then it contains a heterochromatic path of length at least v(G) - o(v(G)) and if the girth of G is at least 4 log(2)(v(G)) + 2, then it contains a heterochromatic path of length at least v(G) - 2, which is only one less than the bound conjectured by Chen and Li (2005). Other special cases considered include lower bounds for the length of a maximum heterochromatic path in edge colored bipartite graphs and triangle-free graphs: for triangle-free graphs we obtain a lower bound of 5v(G)/6] and for bipartite graphs we obtain a lower bound of 6v(G)-3/7]. In this paper, it is also shown that if the coloring is such that G has no heterochromatic triangles, then G contains a heterochromatic path of length at least 13v(G)/17)]. This improves the previously known 3v(G)/4] bound obtained by Chen and Li (2011). We also give a relatively shorter and simpler proof showing that any edge colored graph G contains a heterochromatic path of length at least (C) 2015 Elsevier Ltd. All rights reserved.

How important are shock waves to single-bubble sonoluminescence?

By solving numerically the full set of hydrodynamic equations governing the pulsation of a bubble,we show that shock waves are often absent in a stable sonoluminescing bubble. Nevertheless, for a wide range of physical parameters, a continuous compressional wave emerges and heats up the bubble, and the resulting black-body radiations have pulse heights and widths that agree with experimental data. Shock waves, being much less robust, are not essential for stable single-bubble sonoluminescence.

On dilatational plastic constitutive equation of ductile materials and plastic loading paths at bifurcation

The dilatational plastic constitutive equation presented in this paper is proved to be in a form of generality. Based on this equation, the constitutive behaviour of materials at the moment of bifurcation is demonstrated to follow a loading path with the response as "soft" as possible.

Second-best tax policy in a growing economy with externalities

This paper investigates the exploitation of environmental resources in a growing economy within a second-best scal policy framework. Agents derive utility from two types of consumption goods one which relies on an environmental input and one which does not as well as from leisure and from environmental amenity values. Property rights for the environmental resource are potentially incomplete. We connect second best policy to essential components of utility by considering the elasticity of substitution among each of the four utility arguments. The results illustrate potentially important relationships between environmental amentity values and leisure. When amenity values are complementary with leisure, for instance when environmental amenities are used for recreation, taxes on extractive goods generally increase over time. On the other hand, optimal taxes on extractive goods generally decrease over time when leisure and environmental amenity values are substitutes. Unders some parameterizations, complex dynamics leading to nonmonotonic time paths for the state variables can emerge.

Explosive Hyperinflation, Inflation Tax Laffer Curve and Modelling the use of Money

This paper analyzes the existence of an inflation tax Laffer curve (ITLC) in the context of two standard optimizing monetary models: a cash-in-advance model and a money in the utility function model. Agents’ preferences are characterized in the two models by a constant relative risk aversion utility function. Explosive hyperinflation rules out the presence of an ITLC. In the context of a cash-in-advance economy, this paper shows that explosive hyperinflation is feasible and thus an ITLC is ruled out whenever the relative risk aversion parameter is greater than one. In the context of an optimizing model with money in the utility function, this paper firstly shows that an ITLC is ruled out. Moreover, it is shown that explosive hyperinflations are more likely when the transactions role of money is more important. However, hyperinflationary paths are not feasible in this context unless certain restrictions are imposed.

Commercially Important Crabs, Shrimps and Lobsters of the North Pacific Ocean

Table of Contents [pdf, 1 Kb] Summary [pdf, 85 Kb] Introduction [pdf, 0.8 Mb] Major Species and Stocks of Crabs in the PICES Region [pdf, 1.23 Mb] Major Species and Stocks of Shrimps in the PICES Region [pdf, 0.5 Mb] Oceanography [pdf, 0.4 Mb] Sampling and Data Analysis [pdf, 0.38 Mb] Acknowledgements [pdf, 0.27 Mb] References [pdf, 0.33 Mb] Appendices [pdf, 0.3 Mb] Plates 1-5 [pdf, 0.95 Mb] (Document contains 83 pages)

A Drift Card Study in Monterey Bay, California, September 1971 to April 1973: Annual Report, Part 4, 1973

Drift cards were released in Monterey Bay, California, to detect seasonal variations in the California Current system, and seasonal and diurnal wind variations in the immediate vicinity of the bay. About 23% of the cards were recovered, although the recovery rate varied from about 5% in the winter to about 60% in the late summer. Drift card speeds ranged from 1 to 8 km/day, in the winter and summer months respectively. Good agreement was observed between geostrophic current, wind, drogue, and drift card data, although drift cards were observed to be primarily wind driven. A weekend bias in drift card recoveries was observed for the entire period of study; however, it was less pronounced for those cards released during the summer months. Two bogus releases were used to estimate the discovery lag time, reported position accuracy, and longshore drift currents. Diurnal winds were observed during a 24-hour study, and indicated daily variations in the wind field may be as important as seasonal changes in moving surface water. The drift card speed was observed to be about 3% of the wind velocity, and 1 m/sec was estimated as the minimum effective wind. The wind factor, ranging from 2.2% to 4.0%, was used to estimate the actual paths of drift cards and to examine the role of diurnal winds in affecting surface water movement. (PDF contains 79 pages)

Embedding ORCID Across Researcher Career Paths

Northumbria University final Jisc-ARMA ORCID pilot summary

Self-recruiting species (SRS) from farmer managed aquatic systems: are they important to the livelihoods of rural communities?

Why are SRS important? The answer is to be found in this well-structured survey under: SRS as food source; SRS as additional source of cash income; Role of SRS in social capital. An analysis of the threats to SRS and the potential management options for farmer managed aquatic systems are also available in this survey along with the following definition of SRS: SRS are defined as aquatic animals that can be harvested from farmer managed aquatic systems without regular stocking. (PDF contains 4 pages)