65,506 research outputs found
On ℓ-adic representations for a space of noncongruence cuspforms
No full textThis paper is concerned with a compatible family of 4-dimensional ℓ-adic representations ρℓ of GQ := Gal(Q/Q) attached to the space of weight-3 cuspforms S3(Γ) on a noncongruence subgroup Γ ⊂ SL2(Z). For this representation we prove that:
1.
It is automorphic: the L-function L(s,ρℓ∨) agrees with the L-function for an automorphic form for GL4(AQ), where ρℓ∨ is the dual of ρℓ.
2.
For each prime p≥5 there is a basis hp = {hp+, hp-} of S3(Γ) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12.
The key point is that the representation ρℓ admits a quaternion multiplication structure in the sense of Atkin, Li, Liu, and Long
Letter from J. R. Eakin to Arthur G. Ringland
No full textLetter (copy) from J. R. Eakin to Arthur C. Ringland about the alignment of 40 acres near the Buggeln ranch
Letter from Arno B. Cammerer to J. R. Eakin
No full textLetter from Arno B. Cammerer to J. R. Eakin describing the procedure for purchasing Bright Angel Trail
Letter from J. R. Eakin to Carl Hayden
No full textLetter from J. R. Eakin to Carl T. Hayden concerning access to Rowe Well and the canyon
Letter from J. R. Eakin to Stephen Mather
No full textLetter from J. R. Eakin to Stephen T. Mather about expenses and reconstruction of the Kaibab Trail
Letter from Carl Hayden to J. R. Eakin
No full textLetter from Carl T. Hayden to J. R. Eakin regarding changes to the Grand Canyon National Park boundaries and the purchase of lands from William Randolph Hearst
Letter from J. R. Eakin to Stephen Mather
No full textLetter from J. R. Eaking to the National Park Service director about changes to the Grand Canyon National Park boundaries, and access to water near the Buggeln property on Desert View road
[Letter from J. R. Roberts to Sister, November 24, 1878]
No full textLetter from J. R. Roberts to sister. J. R. thanked his sister for gifts that were sent and went on to update her on what was happening in their families' lives. The letter ended with a mention that people were searching for land claims in the area and the author wanted their mother to not worry about them
Letter from J. R. Eakin, Grand Canyon National Park to Carl Hayden
No full textLetter from J. R. Eakin to Carl Hayden regarding the sale of Bass properties to the Santa Fe Railroad Company
Tuning the nanostructure and tribological properties of a non-ionic deep eutectic solvent with water addition
No full textHypothesis: The addition of water to a non-ionic N-oxide deep eutectic solvent (DES) composed of phenylacetic acid (PhAA) and N-dodecylmorpholine-N-oxide (MO-12) in a 1:1 M ratio (PhAA/MO-12) will promote interfacial nanostructure formation due to increased proton transfer and solvophobic interactions, leading to reduced friction. Experiments: The interfacial structure and friction of PhAA/MO-12 with water content up to 41.9 wt% were investigated at mica surfaces. Atomic force microscopy (AFM) was used to measure normal force-separation profiles, lateral images, and nanoscale friction. Findings: Conductivity increases over twentyfold with the addition of 23.6 wt% water. AFM force curves reveal that increasing water content in PhAA/MO-12 leads to a more pronounced interfacial structure with steps extending further into the bulk. High-resolution near-surface images show a well-defined sponge-like nanostructure at 23.6 wt% water, which is absent in the neat DES. The enhanced nanostructure is attributed to increased proton transfer from PhAA to MO-12 and segregation of polar and apolar domains driven by water strengthened solvophobic interactions. Friction reduces up to 72 % for >= 7.0 wt% water compared to the neat DES, due to a more robust boundary layer facilitated by water
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