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This study makes a case for the application of the numeric and analytic method of boundary states with perturbations (MBSP) to analytic problems focused on the stress-strain states (SSS) of geometrically non-linear isotropic elastic bodies. The defining relations are represented through a weakly non-linear operator equation that contains (on an additive basis) a non-linear operator decomposable into a linear combination of a sequence of linear operators. A solution is proposed for a simple case of a linearly heterogeneous uniaxial loading problem for a long half-pipe with butt ends subjected to loads. Even in this load scenario, geometrical non-linearity affects the way the body alters its shape and causes buckling. This study analyzes the SSS involved, draws conclusions, and addresses application prospects.

In the pathosystem of Dalbulus madis (DeLong & Wolcott) (Hemiptera: Cicadellidae), a vector of maize bushy stunt phytoplasma (MBSP), the interactions occurring during the passage, invasion, and multiplication of the phytoplasma inside the vector body have been generalized from other pathosystems, with a poor understanding of the specific interactions. With the aim to understand MBSP movement and potential specific interactions with its vector, D. maidis adults were dissected to obtain the intestine and salivary gland of both infected (acquisition access period = 4 d; latent period = 23 d) and noninfected individuals. The organs were processed for visualization with transmission electronic microscopy. Images of phytoplasma cells were observed in the alimentary canal, epithelium of the mesenteron, hemocele, and salivary gland of the vector, and were confirmed through observation of similar cells in maize roots with advanced disease symptoms. The study of the MBSP movement within its vector shows novel findings between the synergy of the MBSP phytoplasma and D. maidis.