5,676 research outputs found

    Alien Registration- Judd, John N. (Baldwin, Cumberland County)

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    https://digitalmaine.com/alien_docs/32989/thumbnail.jp

    Implications of non-feasible transformations among icosahedral hh orbitals

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    The symmetric group S6S_6 that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group II. Owing to the correspondence hdh\leftrightarrow d, the calculation of the Coulomb energies for the icosahedral configurations hNh^N based on the sequence O(5)S6S5IO(5) \supset S_6 \supset S_5 \supset I can be brought to bear on Racah's classic theory for the atomic d shell based on SO(5)SOL(3)ISO(5) \supset SO_L(3) \supset I. Among the elements of S6S_6 is the kaleidoscope operator K{\cal K} that rotates the weight space of SO(5) by π/2\pi/2. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figur

    More on coupling coefficients for the most degenerate representations of SO(n)

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    We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for the most degenerate representation of SO(n), is discussed in detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and Discussion, References adde

    An extension of Green's theorem with application

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    The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on September 5, 2008)Thesis (M.S.) University of Missouri-Columbia 2008.The main result of this thesis is a generalization of Green's Theorem. Green' s Theorem states: If Omega is an open subset of R[logical and]2 containing a compact subset K with smooth boundary. Let P and Q be two real valued functions on Omega which are differentiable with continuous partial derivatives. Then the integral over the boundary of K of Pdx [plus] Qdy is equal to the double integral over K of a package of partial derivatives (namely the partial derivative of Q with respect to x minus the partial derivative of P with respect to y). In this thesis we prove that the conditions on P and Q can be weakened. In fact, we prove that the conclusion of Green's Theorem holds if P and Q are only differentiable on a neighborhood of K and the package of partial derivatives is continuous on K. After proving the main result we can conclude two further results, a generalization of the Divergence Theorem in R[logical and]2 and a generalization of Cauchy's Integral Formula.Includes bibliographical reference

    The Sensitivity of First Generation Epoch of Reionization Observatories and Their Potential for Differentiating Theoretical Power Spectra

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    Statistical observations of the epoch of reionization (EOR) power spectrum provide a rich data set for understanding the transition from the cosmic "dark ages" to the ionized universe we see today. EOR observations have become an active area of experimental cosmology, and three first generation observatories--MWA, PAST, and LOFAR--are currently under development. In this paper we provide the first quantitative calculation of the three dimensional power spectrum sensitivity, incorporating the design parameters of a planned array. This calculation is then used to explore the constraints these first generation observations can place on the EOR power spectrum. The results demonstrate the potential of upcoming power spectrum observations to constrain theories of structure formation and reionization.Comment: 7 pages with 5 figures. Submitted to Ap

    Detecting periodicity in experimental data using linear modeling techniques

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    Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

    Toward Empirical Constraints on the Global Redshifted 21 cm Brightness Temperature During the Epoch of Reionization

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    Preliminary results are presented from a simple, single-antenna experiment designed to measure the all-sky radio spectrum between 100 and 200 MHz. The system used an internal comparison-switching scheme to reduce non-smooth instrumental contaminants in the measured spectrum to 75 mK. From the observations, we place an initial upper limit of 450 mK on the relative brightness temperature of the redshifted 21 cm contribution to the spectrum due to neutral hydrogen in the intergalactic medium (IGM) during the epoch of reionization, assuming a rapid transition to a fully ionized IGM at a redshift of 8. With refinement, this technique should be able to distinguish between slow and fast reionization scenarios. To constrain the duration of reionization to dz > 2, the systematic residuals in the measured spectrum must be reduced to 3 mK.Comment: Submitted to ApJ. 9 pages including 6 figure
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