On elliptic curves with an isogeny of degree 7

We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\mathbf{Q}(\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the exceptions are exactly the curves with complex multiplication. As a by-product of one of the key steps in our proof, we determine exactly when there exist elliptic curves over an arbitrary field $k$ of characteristic not 7 with a $k$-rational isogeny of degree 7 and a specified Galois action on the kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in Version 1. Version 3 will appear in the American Journal of Mathematic

The optimization air separation plants for combined cycle MHD-power plant applications

Some of the design approaches being employed during a current supported study directed at developing an improved air separation process for the production of oxygen enriched air for magnetohydrodynamics (MHD) combustion are outlined. The ultimate objective is to arrive at conceptual designs of air separation plants, optimized for minimum specific power consumption and capital investment costs, for integration with MHD combined cycle power plants

Variational Principle in the Algebra of Asymptotic Fields

This paper proposes a variational principle for the solutions of quantum field theories in which the ``trial functions'' are chosen from the algebra of asymptotic fields, and illustrates this variational principle in simple cases.Comment: 15 pages, Latex, no figure

High-order optical nonlinearity at low light levels

We observe a nonlinear optical process in a gas of cold atoms that simultaneously displays the largest reported fifth-order nonlinear susceptibility \chi^(5) = 1.9x10^{-12} (m/V)^4 and high transparency. The nonlinearity results from the simultaneous cooling and crystallization of the gas, and gives rise to efficient Bragg scattering in the form of six-wave-mixing at low-light-levels. For large atom-photon coupling strengths, the back-action of the scattered fields influences the light-matter dynamics. This system may have important applications in many-body physics, quantum information processing, and multidimensional soliton formation.Comment: 5 pages, 3 figure

Tidal Heating of Extra-Solar Planets

Extra-solar planets close to their host stars have likely undergone significant tidal evolution since the time of their formation. Tides probably dominated their orbital evolution once the dust and gas had cleared away, and as the orbits evolved there was substantial tidal heating within the planets. The tidal heating history of each planet may have contributed significantly to the thermal budget that governed the planet's physical properties, including its radius, which in many cases may be measured by observing transit events. Typically, tidal heating increases as a planet moves inward toward its star and then decreases as its orbit circularizes. Here we compute the plausible heating histories for several planets with measured radii, using the same tidal parameters for the star and planet that had been shown to reconcile the eccentricity distribution of close-in planets with other extra-solar planets. Several planets are discussed, including for example HD 209458 b, which may have undergone substantial tidal heating during the past billion years, perhaps enough to explain its large measured radius. Our models also show that GJ 876 d may have experienced tremendous heating and is probably not a solid, rocky planet. Theoretical models should include the role of tidal heating, which is large, but time-varying.Comment: Accepted for publication to Ap

Query Expansion of Zero-Hit Subject Searches: Using a Thesaurus in Conjunction with NLP Techniques

The focus of our study is zero-hit queries in keyword subject searches and the effort of increasing recall in these cases by reformulating and, then, expanding the initial queries using an external source of knowledge, namely a thesaurus. To this end, the objectives of this study are twofold. First, we perform the mapping of query terms to the thesaurus terms. Second, we use the matched terms to expand the user’s initial query by taking advantage of the thesaurus relations and implementing natural language processing (NLP) techniques. We report on the overall procedure and elaborate on key points and considerations of each step of the process

Superfield Realizations of Lorentz and CPT Violation

Superfield realizations of Lorentz-violating extensions of the Wess-Zumino model are presented. These models retain supersymmetry but include terms that explicitly break the Lorentz symmetry. The models can be understood as arising from superspace transformations that are modifications of the familiar one in the Lorentz-symmetric case.Comment: 10 page

Hanbury-Brown and Twiss Intensity Correlations of Parabosons

This paper shows that in intensity correlation measurements there will be clear and unambiguous signals that new-physics particles are, or aren't, parabosons. For a parabosonic field in a dominant single-mode, there is a diagonal P-representation in the "even and odd coherent states" basis. It is used to analyze zero-time-interval intensity correlations of parabosons in a maximum-entropic state. As the mean number of parabosons decreases, there is a monotonic reduction to (2/p) of the constant bosonic ``factor of two'' proportionality of the second-order versus the squared first-order intensity correlation function.Comment: 16 pages; version 4 to add simple p-independent recursion relatio

Locating regions in a sequence under density constraints

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to appear in SIAM Journal on Computin