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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1440-1443 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper extends recent results by the author [J. Math. Phys. 31, 1898 (1990), J. Math. Phys. 32, 57 (1991)] that show a scaling parameter sequence h yields an orthonormal wavelet basis for L2(R) if and only if an associated operator Sh has eigenvalue 1 with multiplicity 1. The operator transforms a sequence a by Sh(a)(k)=2Σm,n∼(h(m))h(n)a(2k+m−n). A correspondence is derived between Sh and Galerkin projection operators related to the multiresolution analysis defined by the orthonormal wavelet basis. The spectrum of Sh is characterized in terms of the Fourier modulus of the (unique) scaling function φ that satisfies φ(x)=2Σnh(n)φ(2x−n). This characterization yields several results including a direct, alternate proof that the eigenvalue 1 of Sh has multiplicity 1.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1898-1901 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by Daubechies [Commun. Pure Appl. Math. 41, 909 (1988)]. For each integer N≥1, a family of wavelet functions ψ having support [0,2N−1] is constructed such that {ψjk(x)=2j/2ψ(2jx−k) kj,k∈Z} is a tight frame of L2(R), i.e., for every f∈L2(R), f=c∑jk 〈ψjk||f〉ψjk for some c〉0. This family is parametrized by an algebraic subset VN of R4N. Furthermore, for N≥2, a proper algebraic subset WN of VN is specified such that all points in VN outside of WN yield orthonormal bases. The relationship between these tight frames and the theory of group representations and coherent states is discussed.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 57-61 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper proves a previous conjecture of the author characterizing sequences h∈l2(Z) that yield orthonormal wavelet bases of L2(R) in terms of the multiplicity of the eigenvalue 1 of an operator associated to h. The proof utilizes a result of Cohen characterizing these sequences in terms of the real zeros of their Fourier transforms. The mapping from sequences to wavelets is shown to define a continuous mapping from a subset of l2(Z) into L2(R). Related conjectures are discussed.
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  • 4
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 208 (1965), S. 1203-1203 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The complexes are readily generated by mixing rigorously purified solutions of the donor and acceptor. Special care must be taken to remove thiols, which are the major impurities in disulphides, since these react with TCNE. Table 1 lists some representative spectral data; several sulphides are ...
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  • 5
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 423 (2003), S. 397-397 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] We have compared the sequences of mitochondrial DNA extracted from museum skins of white-footed mice caught in the Chicago area since 1855 and from modern mice trapped alive in the same locations. We found a consistently similar directional change of mouse genotype over this period at each of ...
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  • 6
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 419 (2002), S. 679-680 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] How can tumours develop when the immune system should instead attack and destroy them? Especially difficult to understand is the situation in which tumour cells display surface molecules that should identify them as abnormal, and so should specifically activate immune cells. This makes little sense ...
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  • 7
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] We measured the detection threshold for a brief tone presented before, during or after two different masking noises in eight children diagnosed with specific language impairment, and in eight control children with normal language skills who matched the others in age and non-verbal intelligence ...
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  • 8
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 51 (1987), S. 403-405 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We have calculated the response of a nonlinear directional coupler fabricated in an AlGaAs/GaAs structure using a realistic model for the optical nonlinearities. The model takes into account carrier-density-dependent index of refraction and absorption, and lateral carrier diffusion in each of the two coupled channel waveguides. Our results differ considerably from those obtained using a Kerr model for the optical nonlinearities.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 3297-3301 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Measurements on commercially available fused silica fibers and fiber tapers have shown that Nd:glass laser pulses of irradiance 〉3.5 GW cm−2 can be transmitted without bulk or surface damage. Optical energy at the fiber output can be used for efficient acceleration of thin metal foils. For 0.025-mm-thick aluminum coupled to a 0.2-mm-diam fiber, target foil velocities up to 2.3 km s−1 have been achieved with very modest laser energies (〈25 mJ).
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  • 10
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 77 (2000), S. 3797-3799 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We calculate the self-capacitance and charging energy of a spherical nanoparticle in the Thomas–Fermi approximation. The result is CTF=C0[1−p−1 tanh p]/[1−(1−cursive-epsilon−1)p−1 tanh p], with CTF≥C0. Here C0=4πcursive-epsilon0R is the classical geometrical value, p=R/l is the ratio of the particle radius R to the Thomas–Fermi screening length l, and cursive-epsilon is the material dielectric constant. The addition of surface localized states drives C toward C0. These results should be relevant to tunneling spectroscopy studies of giant carbon onions and "large" semiconductor nanocrystals that do not require a full quantum treatment. © 2000 American Institute of Physics.
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