599 research outputs found
Bounding sup-norms of cusp forms of large level
Let f be an -normalized weight zero Hecke-Maass cusp form of square-free
level N, character and Laplacian eigenvalue . It is
shown that , from which the hybrid
bound (for some
) is derived. The first bound holds also for where F
is a holomorphic cusp form of weight k with the implied constant now depending
on k.Comment: version 3: substantially revised versio
Non-vanishing of -functions associated to cusp forms of half-integral weight
In this article, we prove non-vanishing results for -functions associated
to holomorphic cusp forms of half-integral weight on average (over an
orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to
forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings
(Springer
Pinwheel patterns and powder diffraction
Pinwheel patterns and their higher dimensional generalisations display
continuous circular or spherical symmetries in spite of being perfectly
ordered. The same symmetries show up in the corresponding diffraction images.
Interestingly, they also arise from amorphous systems, and also from regular
crystals when investigated by powder diffraction. We present first steps and
results towards a general frame to investigate such systems, with emphasis on
statistical properties that are helpful to understand and compare the
diffraction images. We concentrate on properties that are accessible via an
alternative substitution rule for the pinwheel tiling, based on two different
prototiles. Due to striking similarities, we compare our results with the toy
model for the powder diffraction of the square lattice.Comment: 7 pages, 4 figure
The third moment of quadratic Dirichlet L-functions
We study the third moment of quadratic Dirichlet L-functions, obtaining an
error term of size .Comment: 27 pages. v2: modified a remark on p.
Pilot Study: Unique Response of Bone Tissue During an Investigation of Radio-Adaptive Effects in Mice
PURPOSE: We obtained bone tissue to evaluate the collateral effects of experiments designed to investigate molecular mechanisms of radio-adaptation in a mouse model. Radio-adaptation describes a process by which the prior exposure to low dose radiation can protect against the toxic effect of a subsequent high dose exposure. In the radio-adaptation experiments, C57Bl/6 mice were exposed to either a Sham or a priming Low Dose (5 cGy) of Cs-137 gamma rays before being exposed to either a Sham or High Dose (6 Gy) 24 hours later. ANALYSIS: Bone tissue were obtained from two experiments where mice were sacrificed at 3 days (n=3/group, 12 total) and at 14 days (n=6/group, 24 total) following high dose exposure. Tissues were analyzed to 1) evaluate a radio-adaptive response in bone tissue and 2) describe cellular and microstructural effects for two skeletal sites with different rates of bone turnover. One tibia and one lumbar vertebrae (LV2), collected at the 3-day time-point, were analyzed by bone histomorphometry and micro-CT to evaluate the cellular response and any evidence of microarchitectural impact. Likewise, tibia and LV2, collected at the 14-day time-point, were analyzed by micro-CT alone to evaluate resulting changes to bone structure and microarchitecture. The data were analyzed by 2-way ANOVA to evaluate the effects of the priming low dose radiation, of the high dose radiation, and of any interaction between the priming low and high doses of radiation. Bone histomorphometry was performed in the cancellous bone (aka trabecular bone) compartments of the proximal tibial metaphysis and of LV2. RESULTS: Cellular Response @ 3 Days The priming Low Dose radiation decreased osteoblast-covered bone perimeter in the proximal tibia and the total cell density in the bone marrow in the LV2. High Dose radiation, regardless of prior exposure to priming dose, dramatically reduced total cell density in bone marrow of both the long bone and vertebra. However, in the proximal tibia, High Dose radiation increased the osteoclast-covered bone perimeters, the density of adipocytes in bone marrow, and the area of bone marrow occupied by fat cells -- while in the LV2, adipocytes were rare and not stimulated by High Dose radiation. In an unexpected response, High Dose radiation dramatically increased (10-fold) osteoblast-covered bone perimeter in the LV2
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