86,813 research outputs found

    Quadratic forms and systems of forms in many variables

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    Let F1,…,FRF_1,\dotsc,F_R be quadratic forms with integer coefficients in nn variables. When n≥9Rn\geq 9R and the variety V(F1,…,FR)V(F_1,\dotsc,F_R) is a smooth complete intersection, we prove an asymptotic formula for the number of integer points in an expanding box at which these forms simultaneously vanish, which in particular implies the Hasse principle for V(F1,…,FR)V(F_1,\dotsc,F_R). Previous work in this direction required nn to grow at least quadratically with RR. We give a similar result for RR forms of degree dd, conditional on an upper bound for the number of solutions to an auxiliary inequality. In principle this result may apply as soon as n>d2dRn> d2^dR. In the case that d≥3d\geq 3, several strategies are available to prove the necessary upper bound for the auxiliary inequality. In a forthcoming paper we use these ideas to apply the circle method to nonsingular systems of forms with real coefficients.Comment: 29 pages, in revie

    Systems of cubic forms in many variables

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    We consider a system of RR cubic forms in nn variables, with integer coefficients, which define a smooth complete intersection in projective space. Provided n≥25Rn\geq 25R, we prove an asymptotic formula for the number of integer points in an expanding box at which these forms simultaneously vanish. In particular we can handle systems of forms in O(R)O(R) variables, previous work having required that n≫R2n \gg R^2. One conjectures that n≥6R+1n \geq 6R+1 should be sufficient. We reduce the problem to an upper bound for the number of solutions to a certain auxiliary inequality. To prove this bound we adapt a method of Davenport.Comment: 23 pages, submitte

    Relationship between the atomic pair distribution function and small angle scattering: implications for modeling of nanoparticles

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    Here we show explicitly the relationship between the functions used in the atomic pair distribution function (PDF) method and those commonly used in small angle scattering (SAS) analyses. The origin of the sloping baseline, −4πrρ0-4\pi r\rho_0, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The non-linear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles.Comment: 19 pages, 0 figure

    Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices

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    We prove bounds of the form ∑_(e∈I⋂σ_d(H)) dist(e, σ_e(H)^(1/2) ≤ L^1 -norm of a perturbation, where I is a gap. Included are gaps in continuum one-dimensional periodic Schrödinger operators and finite gap Jacobi matrices, where we get a generalized Nevai conjecture about an L^(1)-condition implying a Szegő condition. One key is a general new form of the Birman-Schwinger bound in gaps

    Shifting the Burden of HIV/AIDS

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    As the economic burden of HIV/AIDS increases in sub-Saharan Africa, the allocation of the burden among levels and sectors of societies is changing. The private sector has greater scope than government, households, or NGOs to avoid the economic burden of AIDS, and a systematic shifting of the burden away from the private sector is underway. Common practices that shift the AIDS burden from businesses to households and government include pre-employment screening, reduced employee benefits, restructured employment contracts, outsourcing of less skilled jobs, selective retrenchments, and changes in production technologies. In South Africa, more than two thirds of large employers have reduced health care benefits or required larger contributions by employees. Most firms have replaced defined benefit retirement funds, which expose the firm to large annual costs but provide long-term support for families, with defined contribution funds, which eliminate firm risk but provide little to families of younger workers who die of AIDS. Contracting out of previously permanent jobs also shields firms from costs while leaving households and government to care for affected workers and their families. Many of these changes are responses to globalization and would have occurred in the absence of AIDS, but they are devastating for employees with HIV/AIDS. This paper argues that the shifting of the economic burden of AIDS is a predictable response by business to which a thoughtful public policy response is needed. Countries should make explicit decisions about each sector’s responsibilities if a socially desirable allocation is to be achieved

    Shifting the Burden of HIV/AIDS

    Full text link
    As the economic burden of HIV/AIDS increases in sub-Saharan Africa, the allocation of the burden among levels and sectors of societies is changing. The private sector has greater scope than government, households, or NGOs to avoid the economic burden of AIDS, and a systematic shifting of the burden away from the private sector is underway. Common practices that shift the AIDS burden from businesses to households and government include pre-employment screening, reduced employee benefits, restructured employment contracts, outsourcing of less skilled jobs, selective retrenchments, and changes in production technologies. In South Africa, more than two thirds of large employers have reduced health care benefits or required larger contributions by employees. Most firms have replaced defined benefit retirement funds, which expose the firm to large annual costs but provide long-term support for families, with defined contribution funds, which eliminate firm risk but provide little to families of younger workers who die of AIDS. Contracting out of previously permanent jobs also shields firms from costs while leaving households and government to care for affected workers and their families. Many of these changes are responses to globalization and would have occurred in the absence of AIDS, but they are devastating for employees with HIV/AIDS. This paper argues that the shifting of the economic burden of AIDS is a predictable response by business to which a thoughtful public policy response is needed. Countries should make explicit decisions about each sector’s responsibilities if a socially desirable allocation is to be achieved
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