2,740 research outputs found

    Operator-Valued Frames for the Heisenberg Group

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    A classical result of Duffin and Schaeffer gives conditions under which a discrete collection of characters on R\mathbb{R}, restricted to E=(−1/2,1/2)E = (-1/2, 1/2), forms a Hilbert-space frame for L2(E)L^2(E). For the case of characters with period one, this is just the Poisson Summation Formula. Duffin and Schaeffer show that perturbations preserve the frame condition in this case. This paper gives analogous results for the real Heisenberg group HnH_n, where frames are replaced by operator-valued frames. The Selberg Trace Formula is used to show that perturbations of the orthogonal case continue to behave as operator-valued frames. This technique enables the construction of decompositions of elements of L2(E)L^2(E) for suitable subsets EE of HnH_n in terms of representations of HnH_n

    Coordinating Complementary Waveforms for Sidelobe Suppression

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    We present a general method for constructing radar transmit pulse trains and receive filters for which the radar point-spread function in delay and Doppler, given by the cross-ambiguity function of the transmit pulse train and the pulse train used in the receive filter, is essentially free of range sidelobes inside a Doppler interval around the zero-Doppler axis. The transmit pulse train is constructed by coordinating the transmission of a pair of Golay complementary waveforms across time according to zeros and ones in a binary sequence P. The pulse train used to filter the received signal is constructed in a similar way, in terms of sequencing the Golay waveforms, but each waveform in the pulse train is weighted by an element from another sequence Q. We show that a spectrum jointly determined by P and Q sequences controls the size of the range sidelobes of the cross-ambiguity function and by properly choosing P and Q we can clear out the range sidelobes inside a Doppler interval around the zero- Doppler axis. The joint design of P and Q enables a tradeoff between the order of the spectral null for range sidelobe suppression and the signal-to-noise ratio at the receiver output. We establish this trade-off and derive a necessary and sufficient condition for the construction of P and Q sequences that produce a null of a desired order

    A fortune is near at hand: White land buyers on the Nemaha Half-Breed Tract, 1857-1860

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    Throughout the 19th century, the federal government promoted the assimilation of Native Americans as individuals within white society. Allotment of land in severalty, or the granting of land to individual Indians, was one means to achieve assimilation because it was believed that Indians would adopt the lifestyle of white farmers once they received land. Though the attempt generally failed, the government remailed undeterred in its efforts to achieve that end. In 1887, Congress passed the Dawes Severalty Act which made allotment in severalty the standard policy on most reservations throughout the United States. One clear failure of allotment in severalty occurred on the Nemaha Half-Breed Tract, a reservation established in Nebraska to benefit the mixed-bloods of several Great Plains tribes. Though Congress created the reservation by treaty in 11830, it did not begin to allot the land until 1857. Once the land became available to the mixed-bloods, most of them sold their allotments to whites. This thesis describes the major purchasers of mixed-blood land on the Half-Breed Tract, including James W. Denver, the Commissioner of Indian Affairs; Stephen F. Nuckolls, the founder of Nebraska City; a group of German immigrants who sought to establish a socialistic society at their settlement called Arago; and several prominent local land speculators

    Dismantling the Mine Act

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    Characters of the discrete Heisenberg group and of its completion

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    In this paper we describe the relationship between characters of finitely generated torsion-free nilpotent groups of class 2 and their completions. In particular we give a detailed description of this connection for the discrete Heisenberg group.Haryono Tandra and William Mora

    X-ray Emission from the Weak-lined T Tauri Binary System KH 15D

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    The unique eclipsing, weak-lined T Tauri star KH 15D has been detected as an X-ray source in a 95.7 ks exposure from the Chandra X-ray Observatory archives. A maximum X-ray luminosity of 1.5 x 10^{29} erg s−1^{-1} is derived in the 0.5--8 keV band, corresponding to L_{X}/L_bol = 7.5 x 10^{-5}. Comparison with samples of stars of similar effective temperature in NGC 2264 and in the Orion Nebula Cluster shows that this is about an order of magnitude low for a typical star of its mass and age. We argue that the relatively low luminosity cannot be attributed to absorption along the line of sight but implies a real deficiency in X-ray production. Possible causes for this are considered in the context of a recently proposed eccentric binary model for KH 15D. In particular, we note that the visible component rotates rather slowly for a weak-lined T Tauri star and has possibly been pseudosynchronized by tidal interaction with the primary near periastron
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