Boundary Conditions of the Heliosphere

Radiative transfer equilibrium models of nearby interstellar matter (ISM) yield the boundary conditions of the heliosphere when constrained with observations of ISM inside and outside of the heliosphere. Filtration factors for interstellar neutrals crossing the heliosheath region, from charge exchange with interstellar plasma, are given for H, He, N, O, Ar, and Ne. The best models predict n(HI)~0.2 /cc, n(e)~0.1 /cc, however if the isotropic 2 kHz emission observed by Voyager (Kurth & Gurnett 2003) is formed in the surrounding ISM, an alternate model with lower electron densities is indicated. Observations of nearby ISM, the radiative transfer models, and historical 10Be records provide information on past variations in the galactic environment of the Sun

ἦ μάλα θαῦμα κύων ὅδε κεῖτ᾽ ἐνὶ κόπρῳ. The Anagnorisis of Odysseus and His Dog Argos (Hom. Od. 17, 290–327)

In the Odyssey, there is a description of Odysseus being recognized by his age-old and decrepit dog Argos, whom he had reared and trained himself before his departure for Troy. This so-called Argos episode (Od. 17.290–327) is still famous today. It has been continuously treated by generations of scholars from antiquity to our time and served as an inspiration to both the visual arts and literature. The present article deals with the function and intended effects of the Argos scene. After a brief synopsis of the position of this scene within the Odyssey as well as of its content and structure, the author discusses the role of dogs in the Iliad and the Odyssey. The focus of this article lies on the interpretations of the Argos scene, suggested by scholars so far, and on their review by means of a close reading to check their plausibility

The Implicit Takings Jurisprudence of Article 9 of the Uniform Commercial Code

Part I of this Article begins by reasserting that central to the idea of property rights is the legal entitlement to remedies that permits a person to exercise dominion over the specific asset or to exclude the exercise of dominion by others. Next, part I examines the essence of a security interest and demonstrates that it is a protected property interest. Part II sets forth a model of priorities that suggests that although property interests should ordinarily be protected by a property rule, there is something special about a security interest, implying the need for greater contingency and justifying a liability rule for their protection. Although security interests may be contingent, they should rarely be subject to an uncompensated taking. Part III surveys the development and present status of the lapsed perfection doctrine under Article 9 and suggests an alternative formulation that is intended to reflect the valid insights of the model. This part concludes that principles of compensation provide an appropriate guide for determining issues of priority. Finally, part IV briefly discusses other contexts in which application of the model might be helpful. This Article concludes that although subordination of secured claims against a variety of other claimants is inevitable, conflicts must always be resolved by a continual elaboration of the nature of the competing interests. The statutory taking of a security interest without compensation is permitted, but only when the benefits are extremely high relative to the loss of property that results

Relative polynomial closure and monadically Krull monoids of integer-valued polynomials

Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N_0,+). This implies that [f] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V). In the process, we modify the concept of polynomial closure in such a way that every subset of D has a finite polynomially dense subset. The results generalize to Int(S,V), the ring of integer-valued polynomials on a subset, provided S doesn't have isolated points in v-adic topology.Comment: 12 pages; v.2 contains corrections, in that some necessary conditions on those subsets S, for which we consider integer-valued polynomials on subsets, are impose

Extending Immersions into the Sphere

We study the problem to extend an immersed circle f in the 2-dimensional sphere to an immersion of the disc. We analyze existence and uniqueness for this problems in terms of the combinatorial structure of a word assigned to f. Our techniques are based on ideas of Blank who studied the extension problem in case of a planar target

Polynomial functions on non-commutative rings - a link between ringsets and null-ideal sets

Regarding polynomial functions on a subset $S$ of a non-commutative ring $R$, that is, functions induced by polynomials in $R[x]$ (whose variable commutes with the coefficients), we show connections between, on one hand, sets $S$ such that the integer-valued polynomials on $S$ form a ring, and, on the other hand, sets $S$ such that the set of polynomials in $R[x]$ that are zero on $S$ is an ideal of $R[x]$.Comment: 9 pages, conference paper for "advances in algebra ..." at Ton Duc Thang University, Vietnam, Dec 18-20, 201

Extended Self Similarity works for the Burgers equation and why

Extended Self-Similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier--Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the infrared and ultraviolet end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.Comment: 10 pages, 1 figure, submitted to J. Fluid Mech. (fasttrack