A cut-and-paste approach using a family of structurally similar ‘growth patches’, and starting from a 24-vertex fullerene ‘seed’, allows formal construction of all fullerene isomers with up to at ...least 200 atoms.
A cut-and-paste approach using a family of structurally similar ‘growth patches’ (pairs of non-isomorphic patches with the same boundary but containing different numbers of vertices) allows formal construction from a C
24 seed of all fullerene isomers with up to at least 200 atoms. Algorithmic and chemical implications are discussed.
We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph ...\(\Lambda\) and a "code" assigned to each orbit of Aut(\(\Lambda\)), there exists a unique lobe-transitive graph \(\Gamma\) of connectivity 1 whose lobes are copies of \(\Lambda\) and is consistent with the given code at every vertex of \(\Gamma\). These results lead to necessary and sufficient conditions for a graph of connectivity \(1\) to be edge-transitive and to be arc-transitive. Countable graphs of connectivity 1 the action of whose automorphism groups is, respectively, vertex-transitive, primitive, regular, Cayley, and Frobenius had been previously characterized in the literature.
Designing a mirror that inverts in a circle Cargo, Gerald T.; Graver, Jack E.; Troutman, John L.
The Mathematical intelligencer,
12/2002, Letnik:
24, Številka:
1
Journal Article
Recenzirano
During the early part if the Industrial Revolution, engineers and mathematicians tried to design linkages to carry reflection-in-a-line transformations. Piranian et al show how to design a mirror in ...which the viewer sees the exterior of a disk as though it had been geometrically inverted into the interior of the disk.
It is shown that the automorphism group of an infinite, locally finite, planar graph acts primitively on its vertex set if and only if the graph has connectivity 1 and, for some integer
m⩾2, every ...vertex is incident with exactly
m lobes, all of which are finite. Specifically, either all of the lobes are isomorphic to
K
4 or all are circuits of length
p for some odd prime
p.
Rigidity matroids GRAVER, J. E
SIAM journal on discrete mathematics,
08/1991, Letnik:
4, Številka:
3
Journal Article
Recenzirano
This paper begins with a short discussion of the general principles of Rigidity Theory. The main interest is the combinatorial part of this subject: generic rigidity. While generic rigidity has ...several combinatorial characterizations in dimensions one and two, these characterizations have not been able to be extended to characterizations of generic rigidity in higher dimensions. In fact, no "purely combinatorial" characterization is presently known for generic rigidity in dimensions three and up. The concept of an abstract rigidity matroid is introduced and, in the context of matroid theory, the present status of the characterization problem is discussed.
Abstract only
Elevated salt sensitivity and sympathetic activity are reported to contribute to obesity/high fat diet (HFD) associated hypertension and renal injury. We have reported that feeding male ...Dahl salt‐sensitive (SS) rats a HFD (with normal salt) robustly increases blood pressure and sympathetic support of blood pressure, and also causes severe renal inflammation/injury, when compared to male Dahl SS rats fed a standard rat diet (10% kcal from fat). However, it is hard to distinguish the effects of HFD
per se
on blood pressure and renal inflammation/injury in that setting, since Dahl SS rats fed a standard diet also develop moderate hypertension and mild renal inflammation/injury. To more clearly examine the effect of the SS genotype itself, in the current study we compared the impact of HFD on blood pressure and renal inflammation/injury in male SS (SS/JrHsd) and salt‐resistant (SR/JrHsd) rats (genetic control of SS rats) (Envigo). After 24 weeks on HFD diet feeding, starting at weaning (60% kcal from fat, 0.3% NaCl), SS rats developed severe hypertension (MAP 162±5mmHg, n=6) and renal inflammation/injury as expected. But SR rats on HFD had normal blood pressure (104±8mmHg, n=8) and renal histology. Compared with SS rats, SR rats showed much smaller mean arterial pressure (MAP) responses to acute ganglion blockade (hexamethonium, 30mg/kg, ip) (−14±5mmHg vs −37±5mmHg, P<0.05) and to chronic treatment with the angiotensin converting enzyme inhibitor enalapril (250mg/kg, 7 days in drinking water) (−21±7 mmHg vs −57±8 mmHg, P<0.05). SR rats showed less HFD associated metabolic disorders as they had lower body weight and plasma levels of cholesterol and triglycerides. SR rats also had much smaller spleen weights than SS rats. Immune cell analysis by flow‐cytometry showed that the splenic CD8+ population in SR rats was higher than that found in SS rats (16.4±0.7% vs 10.3±0.4%, P<0.05), whereas the CD4+ cell population was lower than that found in SS rats (18.3±0.6% vs 21.3±0.8%, P<0.05). The ratio of splenic CD4+/CD8+ was also significantly higher in SS rats than SR rats (2.10±0.08 vs 1.13±0.05, P<0.05). There were no strain differences in NK cells and B cells. Our study indicates that in male Dahl rats on HFD, the associated hypertension, metabolic disorders and renal inflammation/injury all require a salt sensitive genotype. Our study also confirms that the mechanisms responsible for HFD induced hypertension in male Dahl SS rats include increased neurogenic support of blood pressure and increased activity of the renin‐angiotensin system. Our study further suggests that a salt sensitive genotype impacts immune system responses to HFD. The mechanisms responsible for diet associated differences in immune cell regulation in the salt sensitive genetic background remain unknown.
Support or Funding Information
NHLBI 2P01HL070687 for G.D.F, J.J.G. and H.X
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