Generalized Colorings of Graphs

A graph coloring is an assignment of labels called “colors” to certain elements of a graph subject to certain constraints. The proper vertex coloring is the most common type of graph coloring, where each vertex of a graph is assigned one color such that no two adjacent vertices share the same color, with the objective of minimizing the number of colors used. One can obtain various generalizations of the proper vertex coloring problem, by strengthening or relaxing the constraints or changing the objective. We study several types of such generalizations in this thesis. Series-parallel graphs are multigraphs that have no K4-minor. We provide bounds on their fractional and circular chromatic numbers and the defective version of these pa-rameters. In particular we show that the fractional chromatic number of any series-parallel graph of odd girth k is exactly 2k/(k − 1), confirming a conjecture by Wang and Yu. We introduce a generalization of defective coloring: each vertex of a graph is assigned a fraction of each color, with the total amount of colors at each vertex summing to 1. We define the fractional defect of a vertex v to be the sum of the overlaps with each neighbor of v, and the fractional defect of the graph to be the maximum of the defects over all vertices. We provide results on the minimum fractional defect of 2-colorings of some graphs. We also propose some open questions and conjectures. Given a (not necessarily proper) vertex coloring of a graph, a subgraph is called rainbow if all its vertices receive different colors, and monochromatic if all its vertices receive the same color. We consider several types of coloring here: a no-rainbow-F coloring of G is a coloring of the vertices of G without rainbow subgraph isomorphic to F ; an F -WORM coloring of G is a coloring of the vertices of G without rainbow or monochromatic subgraph isomorphic to F ; an (M, R)-WORM coloring of G is a coloring of the vertices of G with neither a monochromatic subgraph isomorphic to M nor a rainbow subgraph isomorphic to R. We present some results on these concepts especially with regards to the existence of colorings, complexity, and optimization within certain graph classes. Our focus is on the case that F , M or R is a path, cycle, star, or clique

Chemical Fractionation Of Cu And Zn And Their Impacts On Microbial Properties In Slightly Contaminated Soils

Chemical fractionation of Cu and Zn in bulk soil and its effects on soil microbial properties were determined in Cu and Zn contaminated soils (Cu: 35.57~46.37 mg·kg-1, Zn: 74.33~127.20 mg·kg-1) sampled from an agricultural field in outskirts of Zibo, China during the month of September, 2011. A sequential extraction technique (SET) was used for metals chemical fractionation analysis in soils and a correlation analysis was applied to determinate the effects of metal on soil microbial properties. Chemical speciation showed that Cu and Zn were mostly present in the residual fraction and their concentrations in the most labile fraction (acid soluble fraction) were the lowest in the investigated soils. However, the correlation analysis indicated that the labile forms of Cu/Zn, such as its acid soluble, reducible or oxidizable fractions, were usually significantly negatively correlated with the tested microbial activities at 0.05 or 0.01 probability levels. These results indicate that the metal labile fractions could exert an inhibitory effect on the soil microbial parameters even in the minor contaminated soils. Int. J. Agril. Res. Innov. & Tech. 3 (1): 20-25, June, 2013 DOI: http://dx.doi.org/10.3329/ijarit.v3i1.1604

The graph distance game

In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this note, we examine the distance game for various graphs, and provide general bounds, exact results for special graphs, and an algorithm for trees. Computer calculations suggest interesting conjectures for grids

EQUILIBRIUM MOISTURE CONTENT UNDER VACUUM CONDITIONS

The equilibrium moisture content (EMC) of three species was measured under vacuum conditions. Temperature, RH, and ambient pressure in a chamber were controlled during the experiments to obtain accurate EMC measurement under vacuum. Based on the experimental results and on the Hailwood–Horrobin model for EMC, the desorption isotherms of wood under vacuum were analyzed.EMC charts and a database under vacuum conditions were also built. Results showed that the desorption isotherms of wood under vacuum conditions also presented a typical sigmoid shape similar to the one at atmospheric conditions. The effect of ambient pressure on EMC was small at high RH ranges and became obvious with decreasing RH. Also, the EMC of ambient pressure from 53.3 to 101.3 kPa was not obvious because the difference in EMC was only 0.1-0.4%. Conversely, the effect of pressure became greater from 53.3 to 13.3 kPa and the difference in EMC was 1.2-1.9%. EMC corresponding to temperature, RH, and ambient pressure at vacuum conditions was built with the chart and equations based on experimental results from the real-time MC measurement for vacuum drying and serves as an aid in wood research and drying control under vacuum conditions

Advances in Single Nucleotide Polymorphisms of Vitamin D Metabolic Pathway Genes and Respiratory Diseases

Vitamin D is a fat-soluble vitamin. It is an essential vitamin for human body. It has a classical effect on regulating calcium and phosphorus metabolism. Participate in cellular and humoral immune processes by regulating the growth, differentiation and metabolism of immune cells. A large number of studies in recent years have shown that vitamin D deficiency increases the incidence of respiratory diseases. Respiratory diseases mainly include bronchial asthma, chronic obstructive pulmonary disease, tuberculosis, acute upper respiratory tract infection and pneumonia. Vitamin D metabolic pathway genes play a very important regulatory role in the transformation of vitamin D into active vitamin D, including CYP2R1,,CYP27B1, CYP24A1, VDBP, VDR five genes. Genetic polymorphism of genes is the molecular basis of individual differences and disease development. Therefore, this paper summarizes the research on single nucleotide polymorphism of vitamin D metabolic pathway gene and respiratory diseases. In order to provide a new idea for future treatment