Indecomposable modules and Gelfand rings

It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. Commutative rings for which each indecomposable module has a local endomorphism ring are studied. These rings are clean and elementary divisor rings

MV3: A new word based stream cipher using rapid mixing and revolving buffers

MV3 is a new word based stream cipher for encrypting long streams of data. A direct adaptation of a byte based cipher such as RC4 into a 32- or 64-bit word version will obviously need vast amounts of memory. This scaling issue necessitates a look for new components and principles, as well as mathematical analysis to justify their use. Our approach, like RC4's, is based on rapidly mixing random walks on directed graphs (that is, walks which reach a random state quickly, from any starting point). We begin with some well understood walks, and then introduce nonlinearity in their steps in order to improve security and show long term statistical correlations are negligible. To minimize the short term correlations, as well as to deter attacks using equations involving successive outputs, we provide a method for sequencing the outputs derived from the walk using three revolving buffers. The cipher is fast -- it runs at a speed of less than 5 cycles per byte on a Pentium IV processor. A word based cipher needs to output more bits per step, which exposes more correlations for attacks. Moreover we seek simplicity of construction and transparent analysis. To meet these requirements, we use a larger state and claim security corresponding to only a fraction of it. Our design is for an adequately secure word-based cipher; our very preliminary estimate puts the security close to exhaustive search for keys of size < 256 bits.Comment: 27 pages, shortened version will appear in "Topics in Cryptology - CT-RSA 2007

A classification of smooth embeddings of 3-manifolds in 6-space

We work in the smooth category. If there are knotted embeddings S^n\to R^m, which often happens for 2m<3n+4, then no concrete complete description of embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint unions of spheres. Let N be a closed connected orientable 3-manifold. Our main result is the following description of the set Emb^6(N) of embeddings N\to R^6 up to isotopy. The Whitney invariant W : Emb^6(N) \to H_1(N;Z) is surjective. For each u \in H_1(N;Z) the Kreck invariant \eta_u : W^{-1}u \to Z_{d(u)} is bijective, where d(u) is the divisibility of the projection of u to the free part of H_1(N;Z). The group Emb^6(S^3) is isomorphic to Z (Haefliger). This group acts on Emb^6(N) by embedded connected sum. It was proved that the orbit space of this action maps under W bijectively to H_1(N;Z) (by Vrabec and Haefliger's smoothing theory). The new part of our classification result is determination of the orbits of the action. E. g. for N=RP^3 the action is free, while for N=S^1\times S^2 we construct explicitly an embedding f : N \to R^6 such that for each knot l:S^3\to R^6 the embedding f#l is isotopic to f. Our proof uses new approaches involving the Kreck modified surgery theory or the Boechat-Haefliger formula for smoothing obstruction.Comment: 32 pages, a link to http://www.springerlink.com added, to appear in Math. Zei

Ozone Photochemistry in an oil and natural gas extraction region during winter: simulations of a snow-free season in the Uintah Basin, Utah

The Uintah Basin in northeastern Utah, a region of intense oil and gas extraction, experienced ozone (O3) concentrations above levels harmful to human health for multiple days during the winters of 2009–2010 and 2010–2011. These wintertime O3 pollution episodes occur during cold, stable periods when the ground is snow-covered, and have been linked to emissions from the oil and gas extraction process. The Uintah Basin Winter Ozone Study (UBWOS) was a field intensive in early 2012, whose goal was to address current uncertainties in the chemical and physical processes that drive wintertime O3 production in regions of oil and gas development. Although elevated O3 concentrations were not observed during the winter of 2011–2012, the comprehensive set of observations tests our understanding of O3 photochemistry in this unusual emissions environment. A box model, constrained to the observations and using the near-explicit Master Chemical Mechanism (MCM) v3.2 chemistry scheme, has been used to investigate the sensitivities of O3 production during UBWOS 2012. Simulations identify the O3 production photochemistry to be highly radical limited (with a radical production rate significantly smaller than the NOx emission rate). Production of OH from O3 photolysis (through reaction of O(1D) with water vapor) contributed only 170 pptv day−1, 8% of the total primary radical source on average (primary radicals being those produced from non-radical precursors). Other radical sources, including the photolysis of formaldehyde (HCHO, 52%), nitrous acid (HONO, 26%), and nitryl chloride (ClNO2, 13%) were larger. O3 production was also found to be highly sensitive to aromatic volatile organic compound (VOC) concentrations, due to radical amplification reactions in the oxidation scheme of these species. Radical production was shown to be small in comparison to the emissions of nitrogen oxides (NOx), such that NOx acted as the primary radical sink. Consequently, the system was highly VOC sensitive, despite the much larger mixing ratio of total non-methane hydrocarbons (230 ppbv (2080 ppbC), 6 week average) relative to NOx (5.6 ppbv average). However, the importance of radical sources which are themselves derived from NOx emissions and chemistry, such as ClNO2 and HONO, make the response of the system to changes in NOx emissions uncertain. Model simulations attempting to reproduce conditions expected during snow-covered cold-pool conditions show a significant increase in O3 production, although calculated concentrations do not achieve the highest seen during the 2010–2011 O3 pollution events in the Uintah Basin. These box model simulations provide useful insight into the chemistry controlling winter O3 production in regions of oil and gas extraction