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  • Author: Li Hao, x
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Abstract

Let 𝒫 denote the set of all primes. Suppose that P 1, P 2, P 3 are three subsets of 𝒫 with d 𝒫(P 1) + d 𝒫(P 2) + d 𝒫(P 3) > 2, where d 𝒫(Pi) is the lower density of Pi relative to 𝒫. We prove that for every sufficiently large odd integer n, there exist piPi such that n = p 1 + p 2 + p 3.

Abstract

The signaling pathways that control intestinal development, regeneration and disease show a high degree of conservation between Drosophila and mammals. The gut epithelia of Drosophila provide protection against invasion of microorganisms through production of reactive oxygen species (ROS) and antimicrobial peptides (AMPs). Although Drosophila gut immunity has been extensively studied, the specific responses to Gram-positive bacteria, fungi and toxic compounds are not fully understood. To identify the physiological role of genes involved in host defense we studied Drosophila mutants in antifungal genes identified previously and tested their survival upon feeding with various pathogens and toxic compounds. The results showed that several mutants displayed decreased viability compared with wild-type flies, and the lower survival rates were attributed to morphological change and excessive cell death in mutant guts. Thus, we identified several new Drosophila genes (spen, jumeau, inv, DDB1 and shg) required for intestinal homeostasis or stress responses.

Abstract

C18H20N6O8Zn, triclinic, P1̅, a = 6.2576(6) Å, b = 6.9645(8) Å, c = 12.1262(15) Å, α = 78.536(10)°, β = 86.677(9)°, γ = 72.340(9)°, Z = 1, V = 493.52(10) Å3, R gt(F) = 0.0603, wR ref (F2) = 0.1290, T = 291(2) K.

Abstract

To improve the accuracy of an initial in-situ stress field determined by inversion, we describe a modi fied initial in-situ stress inversion method that uses partial least-squares regression based on FLAC3D. First, each stress component is regressed to improve the fitting accuracy of locally abnormal stress regions, and then the relationship between element stress and unbalanced node force is analyzed according to the computational principles of FLAC3D. The initial in-situ stresses obtained from these regression calculations are added to a numerical model, and the unbalanced node forces are recalculated. An external force equal to the recalculated unbalanced node force is then exerted on the node in the direction opposing the original unbalanced node force to satisfy the equilibrium condition. For the in-situ stresses of elements that do not satisfy the strength conditions, they are modi fied by assuming the average stress is constant and reducing the partial stress to satisfy the equilibrium and strength conditions, which also resolves the unreasonable distribution of the boundary nodal forces and results in good regression estimates. A three-dimensional hypersurface spline interpolation method is developed to calculate the in-situ stress tensor at arbitrary coordinates. Finally, we apply this method to an underground engineering project, and the results are shown to agree well with those obtained from field monitoring. Therefore, it is concluded that this modified in-situ stress inversion method could effectively improve the fitting accuracy of locally abnormal stress regions.