Branching integrals and Casselman phenomenon

Let $G$ be a real semisimple Lie group, $K$ its maximal complex subgroup, and $G_C$ its complexification. It is known that all the $K$-finite matrix elements on $G$ admit holomorphic continuation to branching functions on $G_C$ 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 $p$ be a prime and $G$ a subgroup of $GL_d(p)$. We define $G$ to be $p$-exceptional if it has order divisible by $p$, but all its orbits on vectors have size coprime to $p$. We obtain a classification of $p$-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 $p$.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