Temperature structure and emergent flux of the Jovian planets

Long path, low temperature, moderate resolution spectra of methane and ammonia, broadened by hydrogen and helium, are used to calculate non-gray model atmospheres for the four Jovian planets. The fundamental and first overtone of hydrogen contributes enough absorption to create a thermal inversion for each of the planets. The suite of emergent spectral fluxes and representative limb darkenings and brightenings are calculated for comparison with the Voyager infrared spectra. The temperature differences between Jovian belts and zones corresponds to a difference in the ammonia cirrus particle radii (1 to 3 micron in zones; 10 micron in belts). The Jovian tropopause is approximately at the 0.1 bar level. A thin ammonia cirrus haze should be distributed throughout the Saturnian troposphere; and NH3 gas must be slightly supersaturated or ammonia ice particles are carried upwards convectively in the upper troposphere of Saturn. Substantial methane clouds exist on both Uranus and Neptune. There is some evidence for almost isothermal structures in the deep atmospheres of these two planets

On ultraviolet light and the origin of ribosomes

Function of UV light in evolution of contemporary ribosome

On principal hook length partitions and durfee sizes in skew characters

In this paper we construct for a given arbitrary skew diagram A all partitions nu with maximal principal hook lengths among all partitions with the character [nu] appearing in the skew character [A]. Furthermore we show that these are also partitions with minimal Durfee size. This we use to give the maximal Durfee size for [nu] appearing in [A] for the cases when A decays into two partitions and for some special cases of A. Also this gives conditions for two skew diagrams to represent the same skew character.Comment: 13 pages, minor changes from v1 to v2 as suggested by the referee, to appear in Annals. Com

Equality of multiplicity free skew characters

In this paper we show that two skew diagrams lambda/mu and alpha/beta can represent the same multiplicity free skew character [lambda/mu]=[alpha/beta] only in the the trivial cases when lambda/mu and alpha/beta are the same up to translation or rotation or if lambda=alpha is a staircase partition lambda=(l,l-1,...,2,1) and lambda/mu and alpha/beta are conjugate of each other.Comment: 16 pages, changes from v1 to v2: corrected the proof of Theorem 3.5 and some typos, changes from v2 to v3: minor layout change, enumeration changed, to appear in J. Algebraic Combi

Permutation patterns and statistics

Let S_n denote the symmetric group of all permutations of the set {1, 2, ...,n} and let S = \cup_{n\ge0} S_n. If Pi is a set of permutations, then we let Av_n(Pi) be the set of permutations in S_n which avoid every permutation of Pi in the sense of pattern avoidance. One of the celebrated notions in pattern theory is that of Wilf-equivalence, where Pi and Pi' are Wilf equivalent if #Av_n(Pi)=#Av_n(Pi') for all n\ge0. In a recent paper, Sagan and Savage proposed studying a q-analogue of this concept defined as follows. Suppose st:S->N is a permutation statistic where N represents the nonnegative integers. Consider the corresponding generating function, F_n^{st}(Pi;q) = sum_{sigma in Av_n(Pi)} q^{st sigma}, and call Pi,Pi' st-Wilf equivalent if F_n^{st}(Pi;q)=F_n^{st}(Pi';q) for all n\ge0. We present the first in-depth study of this concept for the inv and maj statistics. In particular, we determine all inv- and maj-Wilf equivalences for any Pi containd in S_3. This leads us to consider various q-analogues of the Catalan numbers, Fibonacci numbers, triangular numbers, and powers of two. Our proof techniques use lattice paths, integer partitions, and Foata's fundamental bijection. We also answer a question about Mahonian pairs raised in the Sagan-Savage article.Comment: 28 pages, 5 figures, tightened up the exposition, noted that some of the conjectures have been prove

Terrestrial production vs. extraterrestrial delivery of prebiotic organics to the early Earth

A comprehensive treatment of comet/asteroid interaction with the atmosphere, ensuring surface impact, and resulting organic pyrolysis is required to determine whether more than a negligible fraction of the organics in incident comets and asteroids actually survived collision with Earth. Results of such an investigation, using a smoothed particle hydrodynamic simulation of cometary and asteroidal impacts into both oceans and rock, demonstrate that organics will not survive impacts at velocities approx. greater than 10 km s(exp -1), and that even comets and asteroids as small as 100m in radius cannot be aerobraked to below this velocity in 1 bar atmospheres. However, for plausible dense (10 bar CO2) early atmospheres, there will be sufficient aerobraking during atmospheric passage for some organics to survive the ensuing impact. Combining these results with analytical fits to the lunar impact record shows that 4.5 Gyr ago Earth was accreting at least approx. 10(exp 6) kg yr(exp 1) of intact cometary organics, a flux which thereafter declined with a approx. 100 Myr half-life. The extent to which this influx was augmented by asteroid impacts, as well as the effect of more careful modelling of a variety of conservative approximations, is currently being quantified. These results may be placed in context by comparison with in situ organic production from a variety of terrestrial energy sources, as well as organic delivery by interplanetary dust. Which source dominated the early terrestrial prebiotic inventory is found to depend on the nature of the early terrestrial atmosphere. However, there is an intriguing symmetry: it is exactly those dense CO2 atmospheres where in situ atmospheric production of organic molecules should be the most difficult, in which intact cometary organics would be delivered in large amounts

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

Measurement and Compensation of Horizontal Crabbing at the Cornell Electron Storage Ring Test Accelerator

In storage rings, horizontal dispersion in the rf cavities introduces horizontal-longitudinal (xz) coupling, contributing to beam tilt in the xz plane. This coupling can be characterized by a "crabbing" dispersion term {\zeta}a that appears in the normal mode decomposition of the 1-turn transfer matrix. {\zeta}a is proportional to the rf cavity voltage and the horizontal dispersion in the cavity. We report experiments at the Cornell Electron Storage Ring Test Accelerator (CesrTA) where xz coupling was explored using three lattices with distinct crabbing properties. We characterize the xz coupling for each case by measuring the horizontal projection of the beam with a beam size monitor. The three lattice configurations correspond to a) 16 mrad xz tilt at the beam size monitor source point, b) compensation of the {\zeta}a introduced by one of two pairs of RF cavities with the second, and c) zero dispersion in RF cavities, eliminating {\zeta}a entirely. Additionally, intrabeam scattering (IBS) is evident in our measurements of beam size vs. rf voltage.Comment: 5 figures, 10 page

Mars climate engineering using orbiting solar reflectors

The manned mission is seen as a first step towards a Mars surface exploration base-station and, later, establishing permanent settlement. The location and use of Mars's natural resources is vital to enable cost-effective long-duration human exploration and exploitation missions as well as subsequent human colonization. Planet resources include various crust-lodged materials, a low-pressure natural atmosphere, assorted forms of utilizable energy, lower gravity than Earth's, and ground placement advantages relative to human operability and living standards. Power resources may include using solar and wind energy, importation of nuclear reactors and the harvesting of geothermal potential. In fact, a new branch of human civilization could be established permanently on Mars in the next century. But, meantime, an inventory and proper social assessment of Mars's prospective energy and material resources is required. This book investigates the possibilities and limitations of various systems supplying manned bases on Mars with energy and other vital resources. The book collects together recent proposals and innovative options and solutions. It is a useful source of condensed information for specialists involved in current and impending Mars-related activities and a good starting point for young researchers