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  • 1
    Electronic Resource
    Electronic Resource
    Multiresolution properties of the wavelet Galerkin operator (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1440-1443 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529300
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  • 2
    Electronic Resource
    Electronic Resource
    Tight frames of compactly supported affine wavelets (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1898-1901 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528688
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  • 3
    Electronic Resource
    Electronic Resource
    Necessary and sufficient conditions for constructing orthonormal wavelet bases (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 57-61 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529093
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  • 4
    Electronic Resource
    Electronic Resource
    Model of a nonlinear directional coupler in gallium arsenide (1987)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 51 (1987), S. 403-405 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.98403
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  • 5
    Electronic Resource
    Electronic Resource
    High-power Nd:glass laser transmission through optical fibers and its use in acceleration of thin foil targets (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 3297-3301 
    Details
    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).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.345364
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  • 6
    Electronic Resource
    Electronic Resource
    Self-capacitance of a Thomas–Fermi nanosphere (2000)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 77 (2000), S. 3797-3799 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1331349
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  • 7
    Electronic Resource
    Electronic Resource
    Optically generated liquid crystal gratings (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 65 (1994), S. 2542-2544 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Optically controlled planar orientation of liquid crystal molecules with polarized light is used to make phase gratings in liquid crystal media. The electro-optical properties of liquid crystal linear and chirped gratings are discussed. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.112629
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