Extremal Values of the Interval Number of a Graph

The interval number $i( G )$ of a simple graph $G$ is the smallest number $t$ such that to each vertex in $G$ there can be assigned a collection of at most $t$ finite closed intervals on the real line so that there is an edge between vertices $v$ and $w$ in $G$ if and only if some interval for $v$ intersects some interval for $w$. The well known interval graphs are precisely those graphs $G$ with $i ( G )\leqq 1$. We prove here that for any graph $G$ with maximum degree $d, i ( G )\leqq \lceil \frac{1}{2} ( d + 1 ) \rceil$. This bound is attained by every regular graph of degree $d$ with no triangles, so is best possible. The degree bound is applied to show that $i ( G )\leqq \lceil \frac{1}{3}n \rceil$ for graphs on $n$ vertices and $i ( G )\leqq \lfloor \sqrt{e} \rfloor$ for graphs with $e$ edges

AGRICULTURE AND RURAL DEVELOPMENT: LESSONS FOR CHRISTIAN GROUPS COMBATING PERSISTENT POVERTY

Persistent poverty is one of the core challenges faced by Christians and by development scholars and practitioners alike. There is no question that Jesus was concerned about the poor - both materially and spiritually. From his first public address in the Synagogue in Nazareth, His home town, where He concluded by saying that He had come to "preach good news to the poor" (Luke 4:18), Jesus lived the gospel in word and deed. We, as Christian men and women, whether researchers or practitioners, are called to do no less. When Jesus made His parting remarks to His disciples, He said (John 20:21) "As the Father has sent me, I am sending you." emphasizing that we are to do likewise. This concern permeates the Old and New Testament, another example being the words of the prophet Micah (6:8): "He has showed you, O man, what is good. And what does the LORD require of you? To act justly and to love mercy and to walk humbly with your God." We are here to think through together some of the implications of this mandate for ourselves as researchers and practitioners. More specifically, to consider how the work we do as researchers can inform our work in the field as practitioners in such a way as to more effectively help those who are materially poor.Community/Rural/Urban Development, O1, Q12, Q18,

Anomalous Creation of Branes

In certain circumstances when two branes pass through each other a third brane is produced stretching between them. We explain this phenomenon by the use of chains of dualities and the inflow of charge that is required for the absence of chiral gauge anomalies when pairs of D-branes intersect.Comment: 7 pages, two figure

Notes on a new mealybug (Hemiptera: Coccoidea: Pseudococcidae) pest in Florida and the Caribbean : the papaya mealybug, Paracoccus marginatus Williams and Granara de Willink

Paracoccus marginatus Williams and Granara de Willink, here called the papaya mealybug, was first detected in the United States in Hollywood, Florida in 1998. By the end of 1998 it was found in four localities in the state and has since spread to nine localities in five counties. This mealybug appears to have moved through the Caribbean area since its 1994 detection in the Dominican Republic. The pest is reported to cause serious damage to tropical fruit, especially papaya, and has been detected most frequently, in Florida, on hibiscus. It is now known from Antigua, Belize, the British Virgin Islands, Costa Rica, Guatemala, Mexico, Nevis, Puerto Rico, St. Barthelemy, St. Kitts, St. Martin, and the US Virgin Islands. Hosts include: Acacia sp.(Luguminosae), Acalypha sp.(Euphorbiaceae), Ambrosia cumanensis (Compositae), Annona squamosa (Annonaceae), Carica papaya (Caricaceae), Guazuma ulmifolia (Sterculiaccea), Hibiscus rosa-sinensis (Euphorbiaceae), Hibiscus sp. (Euphorbiaceae), Ipomoea sp. (Convolvulaceae), Manihot chloristica (Euphorbiaceae), Manihot esculenta (Euphorbiaceae), Mimosa pigra (Lugiminosae), Parthenium hysterophorus (Compositae), Persea americana (Lauraceae), Plumeria sp. (Apocynaceae), Sida sp. (Malvaceae), Solanum melongena (Solanaceae). The species is believed to be native to Mexico andlor Central America

A three-state model with loop entropy for the over-stretching transition of DNA

We introduce a three-state model for a single DNA chain under tension that distinguishes between B-DNA, S-DNA and M (molten or denatured) segments and at the same time correctly accounts for the entropy of molten loops, characterized by the exponent c in the asymptotic expression S ~ - c ln n for the entropy of a loop of length n. Force extension curves are derived exactly employing a generalized Poland-Scheraga approach and compared to experimental data. Simultaneous fitting to force-extension data at room temperature and to the denaturation phase transition at zero force is possible and allows to establish a global phase diagram in the force-temperature plane. Under a stretching force, the effects of the stacking energy, entering as a domain-wall energy between paired and unpaired bases, and the loop entropy are separated. Therefore we can estimate the loop exponent c independently from the precise value of the stacking energy. The fitted value for c is small, suggesting that nicks dominate the experimental force extension traces of natural DNA.Comment: 12 pages, 5 figures + Supplementary informatio