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The mechanical properties of bed bug (Cimex lectularius L.) tarsi and pretarsi were investigated in order to evaluate their vulnerability to piercing by plant trichomes (sharp microscopic hairs). Nanoindentation was used to measure the force required to insert a sharp probe into the cuticle of these different regions, as well as to determine creep and reduced elastic moduli for the cuticle. Scanning electron microscopy was used to visualize the indents that had been generated by nanoindentation. The force required to insert a cube corner nanoindenter probe into the cuticle was determined for a range of displacements (1 to 9 μm) and strain rates (0.003 to 0.5 s-1). Greater force was required to insert this sharp probe at greater depth or at faster strain rates. A specific region of the pretarsus (membrane with microtrichia) more frequently pierced by trichomes during bed bug locomotion required approximately 20-30% less force, exhibited more creep, and had a lower reduced elastic modulus for the first micron of indentation compared to the other regions; although this pattern was not consistent for greater displacements. These mechanical attributes, which will facilitate the initial stage of puncture in addition to the presence of natural infoldings in the cuticle of this area, may make that area of the pretarsus particularly vulnerable to piercing. This information will help inform development of physical methods for control of insect pests such as bed bugs.

We present upper and lower estimates of the error of approximation of periodic functions by Fejér means in the Lebesgue spaces L2πp{L}_{2{\pi }}^{p}. The estimates are given in terms of a K-functional for 1≤p≤∞1\le p\le \infty and in terms of the first modulus of continuity in the case 1

Insect antennae are important mechanosensory and chemosensory organs. Insect appendages, such as antennae, are encased in a cuticular exoskeleton and are thought to bend only between segments or subsegments where the cuticle is thinner, more flexible, or bent into a fold. There is a growing appreciation of the dominating influence of folds in the mechanical behavior of a structure, and the bending of cricket antennae was considered in this context. Antennae will bend or deflect in response to forces, and the resulting bending behavior will affect the sensory input of the antennae. In some cricket antennae, such as in those of Acheta domesticus, there are a large number (>100) of subsegments (flagellomeres) that vary in their length. We evaluated whether these antennae bend only at the joints between flagellomeres, which has always been assumed but not tested. In addition we questioned whether an antenna undergoes a length change as it bends, which would result from some patterns of joint deformation. Measurements using light microscopy and SEM were conducted on both male and female adult crickets (Acheta domesticus) with bending in four different directions: dorsal, ventral, medial, and lateral. Bending occurred only at the joints between flagellomeres, and antennae shortened a comparable amount during bending, regardless of sex or bending direction. The cuticular folds separating antennal flagellomeres are not very deep, and therefore as an antenna bends, the convex side (in tension) does not have a lot of slack cuticle to "unfold" and does not lengthen during bending. Simultaneously on the other side of the antenna, on the concave side in compression, there is an increasing overlap in the folded cuticle of the joints during bending. Antennal shortening during bending would prevent stretching of antennal nerves and may promote hemolymph exchange between the antenna and head.

Insect antennae are important mechanosensory and chemosensory organs. Insect appendages, such as antennae, are encased in a cuticular exoskeleton and are thought to bend only between segments or subsegments where the cuticle is thinner, more flexible, or bent into a fold. There is a growing appreciation of the dominating influence of folds in the mechanical behavior of a structure, and the bending of cricket antennae was considered in this context. Antennae will bend or deflect in response to forces, and the resulting bending behavior will affect the sensory input of the antennae. In some cricket antennae, such as in those of Acheta domesticus, there are a large number (>100) of subsegments (flagellomeres) that vary in their length. We evaluated whether these antennae bend only at the joints between flagellomeres, which has always been assumed but not tested. In addition we questioned whether an antenna undergoes a length change as it bends, which would result from some patterns of joint deformation. Measurements using light microscopy and SEM were conducted on both male and female adult crickets (Acheta domesticus) with bending in four different directions: dorsal, ventral, medial, and lateral. Bending occurred only at the joints between flagellomeres, and antennae shortened a comparable amount during bending, regardless of sex or bending direction. The cuticular folds separating antennal flagellomeres are not very deep, and therefore as an antenna bends, the convex side (in tension) does not have a lot of slack cuticle to unfold and does not lengthen during bending. Simultaneously on the other side of the antenna, on the concave side in compression, there is an increasing overlap in the folded cuticle of the joints during bending. Antennal shortening during bending would prevent stretching of antennal nerves and may promote hemolymph exchange between the antenna and head.