4,079 research outputs found
The Nullity of Bicyclic Signed Graphs
Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of
\Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the
spectrum of A(\Gamma). In this paper we characterize the signed graphs of order
n with nullity n-2 or n-3, and introduce a graph transformation which preserves
the nullity. As an application we determine the unbalanced bicyclic signed
graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs
(including simple bicyclic graphs) of order n with nullity n-5
The earliest herbivorous marine reptile and its remarkable jaw apparatus
Newly discovered fossils of the Middle Triassic reptile Atopodentatus unicus call for a radical reassessment of its feeding behavior. The skull displays a pronounced hammerhead shape that was hitherto unknown. The long, straight anterior edges of both upper and lower jaws were lined with batteries of chisel-shaped teeth, whereas the remaining parts of the jaw rami supported densely packed needle-shaped teeth forming a mesh. The evidence indicates a novel feeding mechanism wherein the chisel-shaped teeth were used to scrape algae off the substrate, and the plant matter that was loosened was filtered from the water column through the more posteriorly positioned tooth mesh. This is the oldest record of herbivory within marine reptiles
Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges
An -by- () weighted shift matrix is one of the form
[{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & &
0{array}], where the 's, called the weights of , are complex numbers.
Assume that all 's are nonzero and is an -by- weighted shift
matrix with weights . We show that is unitarily equivalent to
if and only if and, for some fixed , , () for all . Next, we show that
is reducible if and only if has periodic weights, that is, for some
fixed , , is divisible by , and
for all . Finally, we prove that and
have the same numerical range if and only if and
for all , where 's are the circularly symmetric functions.Comment: 27 page
3-Hydroxyadamantane-1-acetic acid
The crystal structure of the title adamantane derivative, C12H18O3, has been determined by X-ray diffraction. The structure is stabilized by intermolecular O—H⋯O hydrogen bonds, forming a chain
Interaction of XRCC1
Background. To explore the correlation between the Arg399Gln polymorphism and susceptibility to esophageal cancer in Korean and Han Chinese individuals in Harbin, China, and its potential interaction with alcohol consumption. Methods. This prospective study included 203 patients with esophageal squamous cell carcinoma; 88 were of Korean descent and 115 were of Han Chinese descent. A group of healthy controls included 105 participants of Korean descent and 105 of Han Chinese descent. Genotyping of the Arg399Gln locus of XRCC1 was performed by PCR-RFLP. Results. The allelic and genotypic frequencies were not significantly different between individuals with esophageal cancer and controls or between individuals of Korean and Han Chinese descent (P>0.05). However, when individuals with the wild-type Arg/Arg genotype also consumed alcohol, the risk of esophageal cancer was lower (OR = 3.539; 95% CI = 2.039–6.142; P<0.05). Conclusions. The XRCC1 Arg399Gln polymorphism does not appear to be associated with esophageal cancer in individuals of Korean or Han Chinese descent in Harbin, China. However, alcohol consumption may decrease the risk of esophageal cancer in persons with the wild-type genotype
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