10,106 research outputs found
Branching integrals and Casselman phenomenon
Let be a real semisimple Lie group, its maximal complex subgroup, and
its complexification.
It is known that all the -finite matrix elements on admit holomorphic
continuation to branching functions on having singularities at the a
prescribed divisor. We propose a geometric explanation of this phenomenon. The
note also contsins a general survey of holomorphic continuations of
infinite-dimensional representations.Comment: 13pp, an addendum is adde
Arithmetic results on orbits of linear groups
Let be a prime and a subgroup of . We define to be
-exceptional if it has order divisible by , but all its orbits on vectors
have size coprime to . We obtain a classification of -exceptional linear
groups. This has consequences for a well known conjecture in representation
theory, and also for a longstanding question concerning 1/2-transitive linear
groups (i.e. those having all orbits on nonzero vectors of equal length),
classifying those of order divisible by .Comment: slight revisions after referee's comment
When the going gets rough – studying the effect of surface roughness on the adhesive abilities of tree frogs
Tree frogs need to adhere to surfaces of various roughnesses in their natural habitats; these include bark, leaves and rocks. Rough
surfaces can alter the effectiveness of their toe pads, due to factors such as a change of real contact area and abrasion of the pad
epithelium. Here, we tested the effect of surface roughness on the attachment abilities of the tree frog Litoria caerulea. This was
done by testing shear and adhesive forces on artificial surfaces with controlled roughness, both on single toe pads and whole animal
scales. It was shown that frogs can stick 2–3 times better on small scale roughnesses (3–6 µm asperities), producing higher adhesive
and frictional forces, but relatively poorly on the larger scale roughnesses tested (58.5–562.5 µm asperities). Our experiments
suggested that, on such surfaces, the pads secrete insufficient fluid to fill the space under the pad, leaving air pockets that would
significantly reduce the Laplace pressure component of capillarity. Therefore, we measured how well the adhesive toe pad would
conform to spherical asperities of known sizes using interference reflection microscopy. Based on experiments where the conformation
of the pad to individual asperities was examined microscopically, our calculations indicate that the pad epithelium has a low
elastic modulus, making it highly deformable
Non-minimal Einstein-Yang-Mills-Higgs theory: Associated, color and color-acoustic metrics for the Wu-Yang monopole model
We discuss a non-minimal Einstein-Yang-Mills-Higgs model with uniaxial
anisotropy in the group space associated with the Higgs field. We apply this
theory to the problem of propagation of color and color-acoustic waves in the
gravitational background related to the non-minimal regular Wu-Yang monopole.Comment: 14 pages, no figure
Maximum allowable values of the heavy metals in recycled water for household laundry
Household laundry as a new end use of recycled water in dual reticulation systems has a great potential as the significant amount of potable water from urban households can be saved. However, there is still no sufficient evidence and supporting recycled water quality guidelines for this particular use. A key gap in knowledge is the impact of heavy metals in recycled water on clothes and washing machines. Thus, this study aims to determine the maximum allowable values (MAVs) of the heavy metals iron (Fe), lead (Pb), zinc (Zn), copper (Cu), and manganese (Mn) in recycled water for washing clothes in washing machines. Six different concentrations of each targeted metals were prepared in tap water for the washing machine experiments. The tearing/tensile strength tests were used for the assessment of cloth durability. MINITAB 16 as a statistical tool was used and ANOVA one way test was applied for the significance analysis (Turkey's test p. <. 0.05). The results show that the MAVs of the heavy metals Fe, Pb, Zn, Cu and Mn were found to be 1. mg/l, 1. mg/l, 10. mg/l, 5. mg/l and 1. mg/l respectively in terms of cloth durability. © 2013 Elsevier B.V
Ultrahigh sensitivity of slow-light gyroscope
Slow light generated by Electromagnetically Induced Transparency is extremely
susceptible with respect to Doppler detuning. Consequently, slow-light
gyroscopes should have ultrahigh sensitivity
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