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applied beam bilateral test boundary coefficients components computation condition consider constant continued fraction expansion converges corresponding defined denote derivatives differential equation diffraction problem distribution domain of dependence eigenvectors elastic exact power exists follows formula Fourier transform function given Hence holds implies inequality integral inverse inverse matrix Laplace transform leading terms Lemma lim inf linear Madison Math Mathematics Research Center measurable function measure MRC Technical Summary normal obtained periodic continued fraction polynomial preliminary test Proof prove random variable regular continued fraction relation respectively Riemann matrix roots ruled surface sample size combinations satisfying scalar scalar product sequence singular solution with finite space strain Student's t-test Suppose surface symmetric t)dt Table Technical Summary Report test procedure Theorem theory unilateral uniqueness United States Army variance-covariance matrix variances vector wave zero