Algebraic {qq}-Integration and Fourier Theory on Quantum and Braided Spaces

We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson $q$-integral as indefinite integration on the braided group of functions in one variable $x$. Here $x$ is treated with braid statistics $q$ rather than the usual bosonic or Grassmann ones. We show that the definite integral $\int x$ can also be evaluated algebraically as multiples of the integral of a $q$-Gaussian, with $x$ remaining as a bosonic scaling variable associated with the $q$-deformation. Further composing our algebraic integration with a representation then leads to ordinary numbers for the integral. We also use our integration to develop a full theory of $q$-Fourier transformation $F$. We use the braided addition $\Delta x=x\otimes 1+1\otimes x$ and braided-antipode $S$ to define a convolution product, and prove a convolution theorem. We prove also that $F^2=S$. We prove the analogous results on any braided group, including integration and Fourier transformation on quantum planes associated to general R-matrices, including $q$-Euclidean and $q$-Minkowski spaces.Comment: 50 pages. Minor changes, added 3 reference

Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces

In this work, the scattering of surface plasmons by a finite periodic array of one-dimensional grooves is theoretically analyzed by means of a modal expansion technique. We have found that the geometrical parameters of the array can be properly tuned to achieve optimal performance of the structure either as a Bragg reflector or as a converter of surface plasmons into light. In this last case, the emitted light is collimated within a few degrees cone. Importantly, we also show that a small number of indentations in the array are sufficient to fully achieve its functional capabilities.Comment: 5 pages, 5 figures; changed sign convention in some definition

Higgs boson production with one bottom quark including higher-order soft-gluon corrections

A Higgs boson produced in association with one or more bottom quarks is of great theoretical and experimental interest to the high-energy community. A precise prediction of its total and differential cross-section can have a great impact on the discovery of a Higgs boson with large bottom-quark Yukawa coupling, like the scalar (h^0 and H^0) and pseudoscalar (A^0) Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) in the region of large \tan\beta. In this paper we apply the threshold resummation formalism to determine both differential and total cross-sections for b g \to b\Phi (where \Phi = h^0, H^0), including up to next-to-next-to-next-to-leading order (NNNLO) soft plus virtual QCD corrections at next-to-leading logarithmic (NLL) accuracy. We present results for both the Fermilab Tevatron and the CERN Large Hadron Collider (LHC).Comment: revtex4, 13 pages, 11 figures; new references and additional comment

Structural concepts and experimental considerations for a versatile high-speed research airplane

Future aircraft may be hydrogen fueled and fly at hypersonic speeds. The resulting environments will require new structural concepts to satisfy performance goals. Large representative structures will have to be flight tested prior to commitment to a costly vehicle fleet. To perform flight tests, a versatile, economical, high-speed research airplane is defined. Results of this study including experimental considerations for a hypersonic research airplane are reported

Aircraft and satellite measurement of ocean wave directional spectra using scanning-beam microwave radars

A microwave radar technique for remotely measuring the vector wave number spectrum of the ocean surface is described. The technique, which employs short-pulse, noncoherent radars in a conical scan mode near vertical incidence, is shown to be suitable for both aircraft and satellite application, the technique was validated at 10 km aircraft altitude, where we have found excellent agreement between buoy and radar-inferred absolute wave height spectra

Lax matrices for Yang-Baxter maps

It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations on quad-graphs has been recently discovered by A. Bobenko and one of the authors, and by F. Nijhoff

Decanal work: Using role theory and the sociology of time to study the executive behavior of college of education deans

The purpose of this study was: (1) to generate an understanding of the daily administrative processes (activities) of the college of education dean; and (2) to generate a theory based on the delineated roles of the dean as it relates to the executive behavior of the position during the work day. Upon the collection of data determining the dean\u27s executive behavior a comparative analysis using role theory between the dean\u27s executive roles and executive roles found by Mintzberg (1973) was provided. The roles were then aggregated to form the executive behavior of academic deans;Qualitative and quantitative methodologies were both employed in this research. A field study methodology borrowed from the discipline of anthropology was used to collect structured (quantitative) and unstructured observation (qualitative) data on four college of education deans. The specific methods emphasized are structured observations, and unstructured observations. The structured data was collected in one area: chronology records. The chronology record was designed to provide basic data on the design of the work day and to provide a reference to the field notes (unstructured data);After undertaking the data analysis of each kind of activity for this study Mintzberg\u27s roles were reaffirmed; however, additional roles were added and categorized in order to accommodate academic deans. To support the academic executive behavioral theory presented, it was necessary to describe rigorously the activities of academic deans. The primary focus was to recount the activities the deans were observed performing, and secondarily offer suggestions on why these activities occurred. To provide a theoretical grounding to guide the analysis of the data, the sociology of time was employed. The overarching findings from both sets of data demonstrate that academic deans adhere closely to Mintzberg\u27s executive behavioral theory

Multipole expansion at the level of the action

Sources of long wavelength radiation are naturally described by an effective field theory (EFT) which takes the form of a multipole expansion. Its action is given by a derivative expansion where higher order terms are suppressed by powers of the ratio of the size of the source over the wavelength. In order to determine the Wilson coefficients of the EFT, i.e. the multipole moments, one needs the mapping between a linear source term action and the multipole expansion form of the action of the EFT. In this paper we perform the multipole expansion to all orders by Taylor expanding the field in the source term and then decomposing the action into symmetric trace free tensors which form irreducible representations of the rotation group. We work at the level of the action, and we obtain the action to all orders in the multipole expansion and the exact expressions for the multipole moments for a scalar field, electromagnetism and linearized gravity. Our results for the latter two cases are manifestly gauge invariant. We also give expressions for the energy flux and the (gauge dependent) radiation field to all orders in the multipole expansion. The results for linearized gravity are a component of the EFT framework NRGR and will greatly simplify future calculations of gravitational wave observables in the radiation sector of NRGR.Comment: 39 pages, some typos corrected, published versio

Integration of remote sensing and surface geophysics in the detection of faults

Remote sensing was included in a comprehensive investigation of the use of geophysical techniques to aid in underground mine placement. The primary objective was to detect faults and slumping, features which, due to structural weakness and excess water, cause construction difficulties and safety hazards in mine construction. Preliminary geologic reconnaissance was performed on a potential site for an underground oil shale mine in the Piceance Creek Basin of Colorado. LANDSAT data, black and white aerial photography and 3 cm radar imagery were obtained. LANDSAT data were primarily used in optical imagery and digital tape forms, both of which were analyzed and enhanced by computer techniques. The aerial photography and radar data offered supplemental information. Surface linears in the test area were located and mapped principally from LANDSAT data. A specific, relatively wide, linear pointed directly toward the test site, but did not extend into it. Density slicing, ratioing, and edge enhancement of the LANDSAT data all indicated the existence of this linear. Radar imagery marginally confirmed the linear, while aerial photography did not confirm it