Spectrum of Functions for the Dunkl Transform on R^d

Mathematics Subject Classification: 42B10

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point

Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Does money matter in inflation forecasting?

This paper provides the most fully comprehensive evidence to date on whether or not monetary aggregates are valuable for forecasting US inflation in the early to mid 2000s. We explore a wide range of different definitions of money, including different methods of aggregation and different collections of included monetary assets. In our forecasting experiment we use two nonlinear techniques, namely, recurrent neural networks and kernel recursive least squares regressiontechniques that are new to macroeconomics. Recurrent neural networks operate with potentially unbounded input memory, while the kernel regression technique is a finite memory predictor. The two methodologies compete to find the best fitting US inflation forecasting models and are then compared to forecasts from a nave random walk model. The best models were nonlinear autoregressive models based on kernel methods. Our findings do not provide much support for the usefulness of monetary aggregates in forecasting inflation. Beyond its economic findings, our study is in the tradition of physicists' long-standing interest in the interconnections among statistical mechanics, neural networks, and related nonparametric statistical methods, and suggests potential avenues of extension for such studies. © 2010 Elsevier B.V. All rights reserved.

Mitigating inconsistencies by coupling data cleaning, filtering, and contextual data validation in wireless sensor networks

With the advent of peer to peer networks, and more importantly sensor networks, the desire to extract useful information from continuous and unbounded streams of data has become more prominent. For example, in tele-health applications, sensor based data streaming systems are used to continuously and accurately monitor Alzheimer's patients and their surrounding environment. Typically, the requirements of such applications necessitate the cleaning and filtering of continuous, corrupted and incomplete data streams gathered wirelessly in dynamically varying conditions. Yet, existing data stream cleaning and filtering schemes are incapable of capturing the dynamics of the environment while simultaneously suppressing the losses and corruption introduced by uncertain environmental, hardware, and network conditions. Consequently, existing data cleaning and filtering paradigms are being challenged. This dissertation develops novel schemes for cleaning data streams received from a wireless sensor network operating under non-linear and dynamically varying conditions. The study establishes a paradigm for validating spatio-temporal associations among data sources to enhance data cleaning. To simplify the complexity of the validation process, the developed solution maps the requirements of the application on a geometrical space and identifies the potential sensor nodes of interest. Additionally, this dissertation models a wireless sensor network data reduction system by ascertaining that segregating data adaptation and prediction processes will augment the data reduction rates. The schemes presented in this study are evaluated using simulation and information theory concepts. The results demonstrate that dynamic conditions of the environment are better managed when validation is used for data cleaning. They also show that when a fast convergent adaptation process is deployed, data reduction rates are significantly improved. Targeted applications of the developed methodology include machine health monitoring, tele-health, environment and habitat monitoring, intermodal transportation and homeland security.

Spectroscopy of Electroproduced Light to Medium Mass Lambda Hypernuclei

The E01-011 experiment at Jefferson Laboratory (JLab) studied light-to-medium mass Λ hypernuclei via the AZ + e → [special characters omitted] + e' + K+ electroproduction reaction. Precise measurement of hypernuclear ground state masses and excitation energies provides information about the nature of hyperon-nucleon interactions. Until recently, hypernuclei were studied at accelerator facilities with intense π+ and K- meson beams. The poor quality of these beams limited the resolution of the hypernuclear excitation energy spectra to about 1.5 MeV (FWHM). This resolution is not sufficient for resolving the rich structure observed in the excitation spectra. By using a high quality electron beam and employing a new high resolution spectrometer system, this study aims to improve the resolution to a few hundred keV with an absolute precision of about 100 keV for excitation energies. In this work the high-resolution excitation spectra of [special characters omitted], and [special characters omitted] hypernuclei are presented. In an attempt to emphasize the presence of the core-excited states we introduced a novel likelihood approach to particle identification (PID) to serve as an alternative to the commonly used standard hard-cut PID. The new method resulted in almost identical missing mass spectra as obtained by the standard approach. An energy resolution of approximately 400–500 keV (FWHM) has been achieved, an unprecedented value in hypernuclear reaction spectroscopy. For [special characters omitted] the core-excited configuration has been clearly observed with significant statistics. The embedded Λ hyperon increases the excitation energies of the 11B nuclear core by 0.5–1 MeV. The [special characters omitted] spectrum has been observed with significant statistics for the first time. The ground state is bound deeper by roughly 400 keV than currently predicted by theory. Indication for the core-excited doublet, which is unbound in the core itself, is observed. The measurement of [special characters omitted] provides the first study of a d-shell hypernucleus with sub-MeV resolution. Discrepancies of up to 2 MeV between measured and theoretically predicted binding energies are found. Similar disagreement exists when comparing to the [special characters omitted] mirror hypernucleus. Also the core-excited structure observed between the major s-, p- and d-shell Λ orbits is not consistent with the available theoretical calculations. In conclusion, the discrepancies found in this study will provide valuable input for the further development of theoretical models.

Mitigating Inconsistencies by Coupling Data Cleaning, Filtering, and Contextual Data Validation in Wireless Sensor Networks

With the advent of peer to peer networks, and more importantly sensor networks, the desire to extract useful information from continuous and unbounded streams of data has become more prominent. For example, in tele-health applications, sensor based data streaming systems are used to continuously and accurately monitor Alzheimer's patients and their surrounding environment. Typically, the requirements of such applications necessitate the cleaning and filtering of continuous, corrupted and incomplete data streams gathered wirelessly in dynamically varying conditions. Yet, existing data stream cleaning and filtering schemes are incapable of capturing the dynamics of the environment while simultaneously suppressing the losses and corruption introduced by uncertain environmental, hardware, and network conditions. Consequently, existing data cleaning and filtering paradigms are being challenged. This dissertation develops novel schemes for cleaning data streams received from a wireless sensor network operating under non-linear and dynamically varying conditions. The study establishes a paradigm for validating spatio-temporal associations among data sources to enhance data cleaning. To simplify the complexity of the validation process, the developed solution maps the requirements of the application on a geometrical space and identifies the potential sensor nodes of interest. Additionally, this dissertation models a wireless sensor network data reduction system by ascertaining that segregating data adaptation and prediction processes will augment the data reduction rates. The schemes presented in this study are evaluated using simulation and information theory concepts. The results demonstrate that dynamic conditions of the environment are better managed when validation is used for data cleaning. They also show that when a fast convergent adaptation process is deployed, data reduction rates are significantly improved. Targeted applications of the developed methodology include machine health monitoring, tele-health, environment and habitat monitoring, intermodal transportation and homeland security.

Estabilização de órbitas periódicas instáveis utilizando controle por modos deslizantes com compensação adaptativa

The chaotic behavior has been widely observed in nature, from physical and chemical phenomena to biological systems, present in many engineering applications and found in both simple mechanical oscillators and advanced communication systems. With regard to mechanical systems, the effects of nonlinearities on the dynamic behavior of the system are often of undesirable character, which has motivated the development of compensation strategies. However, it has been recently found that there are situations in which the richness of nonlinear dynamics becomes attractive. Due to their parametric sensitivity, chaotic systems can suffer considerable changes by small variations on the value of their parameters, which is extremely favorable when we want to give greater flexibility to the controlled system. Hence, we analyze in this work the parametric sensitivity of Duffing oscillator, in particular its unstable periodic orbits and Poincar´e section due to changes in nominal value of the parameter that multiplies the cubic term. Since the amount of energy needed to stabilize Unstable Periodic Orbits is minimum, we analyze the control action needed to control and stabilize such orbits which belong to different versions of the Duffing oscillator. For that we will use a smoothed sliding mode controller with an adaptive compensation term based on Fourier series.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Spatial Articulations of Race, Desire, and Belonging in Western North Carolina

The sociocultural mythology of the South homogenizes it as a site of abjection. To counter the regionalist discourse, the dissertation intersects queer sexualities with gender and race and focuses on exploring identity and spatial formation among Black lesbian and queer women. The dissertation seeks to challenge the monolith of the South and place the region into multiple contexts and to map Black geographies through an intentional intersectional account of Black queer women. The dissertation utilizes qualitative research methods to ascertain understandings of lived experiences in the production of space. The dissertation argues that an idea of Progress has been indoctrinated as a synonym for the lgbtq civil rights movement and subsequently provides an analysis of progress discourses and queer sexualities and political campaigns of equality in the South. Analyses revealed different ways to situate progress utilizing the public contributions of three Black women interviewed for the dissertation. Moreover, the dissertation utilizes six Black queer and lesbian women to explain the multifarious nature of identities and their construction in place. Black queer and lesbian women produce spaces that deconstruct the normativity of stasis and physicality, and the dissertation explores the consequential realities of being a body in space. These consequences are particularly highlighted in the dissertation by discussions of the processes of racialization in the bounded and unbounded senses of space and place and the impacts of religious institutions, specifically Christianity. The dissertation concluded that no space is without complication. Other considerations should be made in the advancement of alleviating oppression deeply embedded in United States landscapes. Black women’s geographies offer epistemological and ontological renderings that enrich analyses of space, place, and landscape. The dissertation also concludes that Black women’s bodies represent sites for the production of geographic knowledge through narrating their spaces of material trajectories of interlocking, multiscalar lives.

The crowded magnetosphere of the post-common-envelope binary QS Virginis

We present high-speed photometry and high-resolution spectroscopy of the eclipsing post-common-envelope binary QS Virginis (QS Vir). Our Ultraviolet and Visual Echelle Spectrograph (UVES) spectra span multiple orbits over more than a year and reveal the presence of several large prominences passing in front of both the M star and its white dwarf companion, allowing us to triangulate their positions. Despite showing small variations on a time-scale of days, they persist for more than a year and may last decades. One large prominence extends almost three stellar radii from the M star. Roche tomography reveals that the M star is heavily spotted and that these spots are long-lived and in relatively fixed locations, preferentially found on the hemisphere facing the white dwarf. We also determine precise binary and physical parameters for the system. We find that the 14 220 ± 350 K white dwarf is relatively massive, 0.782 ± 0.013 M⊙, and has a radius of 0.010 68 ± 0.000 07 R⊙, consistent with evolutionary models. The tidally distorted M star has a mass of 0.382 ± 0.006 M⊙ and a radius of 0.381 ± 0.003 R⊙, also consistent with evolutionary models. We find that the magnesium absorption line from the white dwarf is broader than expected. This could be due to rotation (implying a spin period of only ˜700 s), or due to a weak (˜100 kG) magnetic field, we favour the latter interpretation. Since the M star's radius is still within its Roche lobe and there is no evidence that it is overinflated, we conclude that QS Vir is most likely a pre-cataclysmic binary just about to become semidetached.

The HARPS-N Rocky Planet Search. I. HD 219134 b: A transiting rocky planet in a multi-planet system at 6.5 pc from the Sun

We know now from radial velocity surveys and transit space missions thatplanets only a few times more massive than our Earth are frequent aroundsolar-type stars. Fundamental questions about their formation history,physical properties, internal structure, and atmosphere composition are,however, still to be solved. We present here the detection of a systemof four low-mass planets around the bright (V = 5.5) and close-by (6.5pc) star HD 219134. This is the first result of the Rocky Planet Searchprogramme with HARPS-N on the Telescopio Nazionale Galileo in La Palma.The inner planet orbits the star in 3.0935 ± 0.0003 days, on aquasi-circular orbit with a semi-major axis of 0.0382 ± 0.0003AU. Spitzer observations allowed us to detect the transit of the planetin front of the star making HD 219134 b the nearest known transitingplanet to date. From the amplitude of the radial velocity variation(2.25 ± 0.22 ms-1) and observed depth of the transit(359 ± 38 ppm), the planet mass and radius are estimated to be4.36 ± 0.44 M⊕ and 1.606 ± 0.086R⊕, leading to a mean density of 5.76 ± 1.09 gcm-3, suggesting a rocky composition. One additional planetwith minimum-mass of 2.78 ± 0.65 M⊕ moves on aclose-in, quasi-circular orbit with a period of 6.767 ± 0.004days. The third planet in the system has a period of 46.66 ± 0.08days and a minimum-mass of 8.94 ± 1.13 M⊕, at0.233 ± 0.002 AU from the star. Its eccentricity is 0.46 ±0.11. The period of this planet is close to the rotational period of thestar estimated from variations of activity indicators (42.3 ± 0.1days). The planetary origin of the signal is, however, thepreferredsolution as no indication of variation at the corresponding frequency isobserved for activity-sensitive parameters. Finally, a fourth additionallonger-period planet of mass of 71 M⊕ orbits the starin 1842 days, on an eccentric orbit (e = 0.34 ± 0.17) at adistance of 2.56 AU.The photometric time series and radial velocities used in this work areavailable in electronic form at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr(ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/584/A72