Letter from David S. Jordan to John Muir, 1901 Dec 20.

Stanford,Dec. 20 - 1901.My dear Muir:Please accept my sincere thanks for your very kind remembrance. I shall read the book as I read everything of yours with the pleasure one gets from the real thing in literature or science. I have long meant to visit you at Martinez - long meant to insist on your visiting me03182 here. Can you not come soon? I won\u27t ask you to lecture.Cordially yours,David S. Jorda

Letter from David S. Jordan to Warren Olney, 1896 Dec 9.

COPY Washington, D. C. Dec. 9. 1896.Mr. Warren Glncy,101 Sansome St., San Francisco, Cal.Dear Sir:-I have taken the first available afternoon since coming here to talk over the Sierra Reservation with Secretary Francis and Commissioner Lamereaux, and I find them strongly in favor not only of shutting out interlopers from the Tallac region, but of preserving the entire crest of the Sierras. Secretary Francis has directed Mr. Arnold Hagua of the Geological Survey to look into the matter. He is a member with Professor Sargent of the subcommittee on Forestry Reservations. I have arranged with Mr. Hague to have Mr. Lundgren of the Geological Survey, who charted the Tallac region, draw up a provisional outline of the region to be reserved. It is understood that if Senator Perkins will push the matter when he arrives, Mr. Francis will have set aside the forest reservation in question.There seems to bo no difficulty in getting what is wanted, if it is clearly known what that is. The only trouble I anticipate will be the difficulty of mapping the high Sierras so as to exclude the invasions of meadow land and mountain pastures . I went over the map as closely as I could with Mr. Lundgren and left your letter to Mr. Lamereaux with \u27him. Mr. Lamereaux will withhold the entries.Very truly yours,(signed) David S. Jordan.0618

Continuous phase amplification with a Sagnac interferometer

We describe a weak value inspired phase amplification technique in a Sagnac interferometer. We monitor the relative phase between two paths of a slightly misaligned interferometer by measuring the average position of a split-Gaussian mode in the dark port. Although we monitor only the dark port, we show that the signal varies linearly with phase and that we can obtain similar sensitivity to balanced homodyne detection. We derive the source of the amplification both with classical wave optics and as an inverse weak value.Comment: 5 pages, 4 figures, previously submitted for publicatio

Fractal Weyl law behavior in an open, chaotic Hamiltonian system

We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relatively far away from the classical limit. The complex resonance wave functions are found to be localized on the fractal classical repeller.Comment: 4 pages, 3 figures. to appear in Phys Rev

A Modified SIR Model Equivalent to a Generalized Logistic Model, with Standard Logistic Approximations

https://knowledgeconnection.mainehealth.org/lambrew-retreat-2021/1000/thumbnail.jp

Heights on stacks and a generalized Batyrev-Manin-Malle conjecture

We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties. We explain how to compute this height for various stacks of interest (for instance: classifying stacks of finite groups, symmetric products of varieties, moduli stacks of abelian varieties, weighted projective spaces). In many cases our uniform definition reproduces ways already in use for measuring the complexity of rational points, while in others it is something new. Finally, we formulate a conjecture about the number of rational points of bounded height (in our sense) on a stack X, which specializes to the Baytev-Manin conjecture when X is a scheme and to Malle's conjecture when X is the classifying stack of a finite group.Comment: 61 pages; comments very welcom

The effects of degassing on magmatic gas waves and long period eruptive precursors at silicic volcanoes

Author Posting. © American Geophysical Union, 2020. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Solid Earth 125 (10), (2020): e2020JB019755, https://doi.org/10.1029/2020JB019755Cyclical ground deformation, associated seismicity, and elevated degassing are important precursors to explosive eruptions at silicic volcanoes. Regular intervals for elevated activity (6–30 hr) have been observed at volcanoes such as Mount Pinatubo in the Philippines and Soufrière Hills in Montserrat. Here, we explore a hypothesis originally proposed by Michaut et al. (2013, https://doi.org/10.1038/ngeo1928) where porosity waves containing magmatic gas are responsible for the observed periodic behavior. We use two‐phase theory to construct a model where volatile‐rich, bubbly, viscous magma rises and decompresses. We conduct numerical experiments where magma gas waves with various frequencies are imposed at the base of the model volcanic conduit. We numerically verify the results of Michaut et al. (2013, https://doi.org/10.1038/ngeo1928) and then expand on the model by allowing magma viscosity to vary as a function of dissolved water and crystal content. Numerical experiments show that gas exsolution tends to damp the growth of porosity waves during decompression. The instability and resultant growth or decay of gas wave amplitude depends strongly on the gas density gradient and the ratio of the characteristic magma extraction rate to the characteristic magma degassing rate (Damköhler number, Da). We find that slow degassing can lead to a previously unrecognized filtering effect, where low‐frequency gas waves may grow in amplitude. These waves may set the periodicity of the eruptive precursors, such as those observed at Soufrière Hills Volcano. We demonstrate that degassed, crystal‐rich magma is susceptible to the growth of gas waves which may result in the periodic behavior.J. S. J. and D. B. were supported by NSF grant EAR‐1645057. C. M. has received financial support of the IDEXLyon Project of the University of Lyon in the frame of the Programme Investissements dAvenir (ANR‐16‐IDEX‐0005)

Reversible skew laurent polynomial rings and deformations of poisson automorphisms

A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1). We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent polynomial rings, namely a localization of the enveloping algebra of the two-dimensional non-abelian solvable Lie algebra and the coordinate ring of the quantum torus, both of which are deformations of Poisson algebras over the base field F. Their reversing automorphisms are deformations of Poisson automorphisms of those Poisson algebras. In each case, the ring of invariants of the Poisson automorphism is the coordinate ring B of a surface in F-3 and the ring of invariants S-theta of the reversing automorphism is a deformation of B and is a factor of a deformation of F[x(1), x(2), x(3)] for a Poisson bracket determined by the appropriate surface