38,955 research outputs found

    Optimal Focusing for Monochromatic Scalar and Electromagnetic Waves

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    For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation, the electric field maximizing the value at the origin follows longitude lines on the sphere at infinity. In dimension d=3d=3 the highest electric field for Maxwell's equation is smaller by a factor 2/3 than the highest corresponding scalar waves. The highest electric field densities on the balls BR(0)B_R(0) occur as R→0R\to 0. The density dips to half max at RR approximately equal to one third the wavelength. The extremizing fields are identical to those that attain the maximum field intensity at the origin.Comment: 30 pages, 7 figure

    Adolf Reinach: An Intellectual Biography

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    The essay provides an account of the development of Reinach’s philosophy of “Sachverhalte” (states of affairs) and on problems in the philosophy of law, leading up to his discovery of the theory of speech acts in 1913. Reinach’s relations to Edmund Husserl and to the Munich phenomenologists are also dealt with

    On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

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    We consider domains D⊆RnD\subseteq\mathbb R^n with C1C^1 -smooth boundary and study the following question: when the Fourier transform 1D^\hat{1_D} of the characteristic function 1D1_D belongs to Lp(Rn)L^p(\mathbb R^n)?Comment: added two references; added footnotes on pages 6 and 1

    OPE analysis of the nucleon scattering tensor including weak interaction and finite mass effects

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    We perform a systematic operator product expansion of the most general form of the nucleon scattering tensor WμνW_{\mu \nu} including electro-magnetic and weak interaction processes. Finite quark masses are taken into account and a number of higher-twist corrections are included. In this way we derive relations between the lowest moments of all 14 structure functions and matrix elements of local operators. Besides reproducing well-known results, new sum rules for parity-violating polarized structure functions and new mass correction terms are obtained.Comment: 50 pages, additional references adde

    LDEF fiber-composite materials characterization

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    Degradation of a number of fiber/polymer composites located on the leading and trailing surfaces of LDEF where the atomic oxygen (AO) fluences ranged from 10(exp 22) to 10(exp 4) atoms/cm(sup 2), respectively, was observed and compared. While matrices of the composites on the leading edge generally exhibited considerable degradation and erosion-induced fragmentation, this 'asking' process was confined to the near surface regions because these degraded structures acted as a 'protective blanket' for deeper-lying regions. This finding leads to the conclusion that simple surface coatings can significantly retard AO and other combinations of degrading phenomena in low-Earth orbit. Micrometeoroid and debris particle impacts were not a prominent feature on the fiber composites studied and apparently do not contribute in a significant way to their degradation or alteration in low-Earth orbit
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