84,568 research outputs found
Differential Equations of Some Classes of Special Functions via the Factorization Method
No full textLet {P n(x)} n=0∞ be a sequence of polynomials of degree n. We define two sequences of differential operators Φ n and ψ n satisfying the following properties Φ n(P n(x))=P n-1(x), Ψ n(Pn(x)) = P n+1(x). By constructing these two operators for some classes of special functions, we determine their differential equations via the factorization method introduced in [3]. We illustrate our method by including classical orthogonal polynomials, d-orthogonal polynomials, confluent hypergeometric functions and hypergeometric functions as the applications. Copyright 2004 Eudoxus Press, LLC
A 2 h periodic variation in the low-mass X-ray binary Ser X-1
No full textSpectroscopy of the low-mass X-ray binary Ser X-1 using the Gran Telescopio Canarias have revealed a ?2 h periodic variability that is present in the three strongest emission lines. We tentatively interpret this variability as due to orbital motion, making it the first indication of the orbital period of Ser X-1. Together with the fact that the emission lines are remarkably narrow, but still resolved, we show that a main-sequence K dwarf together with a canonical 1.4 M? neutron star gives a good description of the system. In this scenario, the most likely place for the emission lines to arise is the accretion disc, instead of a localized region in the binary (such as the irradiated surface or the stream-impact point), and their narrowness is due instead to the low inclination (?10°) of Ser X-1
On Taylor’s Formula for the Resolvent of a Complex Matrix
No full textThe resolvent Rλ(A) of a complex r×r matrix A is an analytic function in any domain with empty intersection with the spectrum ΣA of A. The well known Taylor expansion of Rλ(A) in a neighborhood of any given λ0∉ΣA is modified taking into account that only the first powers of Rλ0(A) are linearly independent. The main tool in this framework is given by the multivariable polynomials depending on the invariants v1,v2,…,vr of Rλ(A) (m denotes the degree of the minimal polynomial). These functions are used in order to represent the coefficients of the subsequent powers of Rλ0(A) as a linear combination of the first m of them
TOPS Imaging with TerraSAR-X: Mode Design and Performance Analysis
No full textThis paper reports about the performed investigations for the implementation of the wide swath TOPS imaging mode with TerraSAR-X. The TOPS mode overcomes the limitations imposed by the ScanSAR mode by steering the antenna along-track during the acquisition of a burst. In this way, a uniform signal to noise ratio (SNR) is achieved, and consequently, scalloping and an azimuth-dependent distributed target ambiguity ratio (DTAR) are avoided. However, the use of electronically steered antennas leads to a quantization of the steering law and a non-ideal pattern for squinted angles (grating lobes and main lobe reduction). The former provokes spurious peaks, while the latter introduces a slight scalloping and DTAR deterioration. These effects are analyzed and quantified for TerraSAR-X and a TOPS system design approach is presented. Next, the requirements concerning interferometry are investigated. Finally, several results are shown with TerraSAR-X data, including a comparison between the TOPS and ScanSAR modes and the reporting of first TOPS interferometric results
Synchrotron X-ray topographic analysis of the impact of processing steps on the fabrication of AlGaAs/InGaAs p-HEMT's
No full textSynchrotron X-Ray Topography (SXRT) has been uniquely applied to nondestructively reveal and evaluate the damage throughout the depth of the wafer, caused by the deposition of source/gate/drain metallization and of so-called “passivation” dielectric layers on power Al ₀.₂₂Ga₀.₇₈As/In₀.₂₁Ga₀.₇₉As pseudomorphic HEMT's. Device metallization is visible due to the stress imposed on the underlying substrate and is detected as a strain field by SXRT. Experimental results are in good agreement with simulation. The quality and detail of the initial control topographs disappear when the Si₃N₄ dielectric layer is deposited. This is believed due to the passivating layer introducing such strain into the crystal that it overwhelms the metallization strain, in addition to producing a significant amount of stress-induced defect and dislocation generatio
Operando X-ray absorption spectroscopy investigations on NaxNi1/3Fe1/3Mn1/3O2 positive electrode materials for sodium and sodium ion batteries
No full textNaxMn1/3Fe1/3Ni1/3O2 (x = 2/3 and 1) layered oxides are synthesized and applied as positive electrode materials for sodium batteries. The crystal structure of the material changes from the O3 single phase to P2/O3 mixed phases as the Na content decreases from 1 to 2/3. The mixed-phases Na2/3Mn1/3Fe1/3Ni1/3O2 shows superior cycling performance compared to the single-phase NaMn1/3Fe1/3Ni1/3O2 due to different redox process and structural change that are demonstrated by operando X-ray absorption spectroscopy (XAS). The Na2/3Mn1/3Fe1/3Ni1/3O2 experiences redox reactions of Ni3+|Ni4+ and Fe3+|Fe4+ with inactive Mn ions during the charge/discharge processes, while the NaMn1/3Fe1/3Ni1/3O2 undergoes deeper redox reactions from Ni2+|Ni3+|Ni4+ and Fe3+|Fe4+ that Mn ions are irreversibly oxidized to Mn4+ in the 1st charge process. In addition, the mixed-phases material has smaller changes in the transition metal oxygen bond lengths during cycling, corresponding to less distortions of TMO6 units in the crystal structure. The better reversibility of the redox reactions and the occurrence of less structural changes are both responsible for the enhanced cycling performance obtained from the mixed-phases material compared to the single-phase material. These results strengthen the understanding of interactions of transition metals in the layered cathode and provide guidelines for designing positive electrode materials for sodium batteries
Relativistic Jacobi Polynomials
No full textA new polynomials set, of generalized hypergeometric type, is defined. These polynomials, called relativistic Jacobi polynomials (RJP) and denoted by
represent an extension of the classical Jacobi orthogonal polynomials in the sense that they reduce to the latter in the non-relativistic limit (N→ ∞). Some basic properties of these polynomials, as well as for the RHP (see [6] and [7]) and the RLP (see [2] and [3]), are derived
Fore and Aft Channel Reconstruction in the TerraSAR-X Dual Receive Antenna Mode
No full textThe TerraSAR-X satellite is a high resolution synthetic aperture radar (SAR) system launched in June 2007 which provides the option to split the antenna in along-track direction and sample two physical channels separately. Modern SARs are equipped with active phased array antennas and multiple channels. In order to keep costs low TerraSAR-X uses the redundant receiver unit for the second channel such that fore and aft channel signals are combined by a hybrid coupler to form sum and difference channel data. The dual receive antenna mode can either be used to acquire along-track interferometric data or to acquire signals with different polarizations at the same time (Quad pol). Fore and aft channel reconstruction is necessary if ground moving target indication algorithms such as the displaced phase center antenna technique or along-track interferometry shall be applied, and in order to separate the horizontally and vertically polarized received signal components. The proposed approach uses internal calibration pulses from different calibration beams in order to estimate and compensate the hardware impact. The theoretical framework together with the results from the experimental data evaluation for the fore and aft channel reconstruction of the TerraSAR-X dual receive antenna mode are presented. The impact of the receive hardware transformation matrix estimation accuracy on errors in the reconstructed fore and aft channel image data is studied, and
first examples on the ground moving target indication capability of the TerraSAR-X dual receive antenna mode are given
Retinitis Pigmentosa GTPase Regulator (RPGR) protein isoforms in mammalian retina:insights into X-linked Retinitis Pigmentosa and associated ciliopathies
No full textMutations in the cilia-centrosomal protein Retinitis Pigmentosa GTPase Regulator (RPGR) are a frequent cause of retinal degeneration. The RPGR gene undergoes complex alternative splicing and encodes multiple protein isoforms. To elucidate the function of major RPGR isoforms (RPGR 1-19 and RPGR ORF15), we have generated isoform-specific antibodies and examined their expression and localization in the retina. Using sucrose-gradient centrifugation, immunofluorescence and co-immunoprecipitation methods, we show that RPGR isoforms localize to distinct sub-cellular compartments in mammalian photoreceptors and associate with a number of cilia-centrosomal proteins. The RCC1-like domain of RPGR, which is present in all major RPGR isoforms, is sufficient to target it to the cilia and centrosomes in cultured cells. Our findings indicate that multiple isotypes of RPGR may perform overlapping yet somewhat distinct transport-related functions in photoreceptors
Solution of the Dirichlet problem for the Laplace equation in general cylinder.
No full textWe consider the Dirichlet problem for the Laplace equation in a bounded cylindrical domain C:=D , where D is a starlike domain of the (x,y)-plane. We show how to construct the solution by using the Fourier series method. We derive some numerical results defining by means of the so called “superformula” introduced by J.Gielis. By using a computer algebra system we find a quite rapid convergence of the approximate solutions to the real one, with only possible exceptions corresponding to singular points in which oscillations recalling Gibbs’ phenomenon appear. Our findings are in agreement with the theoretical results on Fourier series due to L.Carleson
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