Quadrature by two expansions: Evaluating Laplace layer potentials using complex polynomial and plane wave expansions
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Abstract We use administrative data from the Internal Revenue Service to examine long-term impacts of childhood Medicaid eligibility expansions on outcomes in adulthood at each age from 19 to 28. Greater Medicaid eligibility increases college enrolment and decreases fertility, especially through age 21. Starting at age 23, females have higher contemporaneous wage income, although male increases are imprecise. Together, both genders have lower mortality. These adults collect less from the earned income tax credit and pay more in taxes. Cumulatively from ages 19 to 28, at a 3% discount rate, the federal government recoups 58 cents of each dollar of its “investment” in childhood Medicaid.more » « less
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Todorov, M D (Ed.)Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions — resembling trigonometric sines and cosines, as well as the so-called “beam” functions. These functions intrinsically satisfy boundary conditions (BCs) of relevance to thin-film flows, since they are the solutions of a self-adjoint sixth-order Sturm–Liouville BVP with the same BCs. Next, we propose a Galerkin spectral approach for sixth-order problems; namely the sought function as well as all its derivatives and terms appearing in the differential equation are expanded into an infinite series with respect to the derived complete orthonormal (CON) set of eigenfunctions. The unknown coefficients in the series expansion are determined by solving the algebraic system derived by taking successive inner products with each member of the CON set of eigenfunctions. The proposed method and its convergence are demonstrated by solving two model sixth-order BVPs.more » « less