Convexity and the difference property

We show that the class of all delta-convex selfmappings of R$\mathbb{R}$ (differences of two convex functions) enjoys the difference property in the sense of N.G. de Bruijn. The Q$\mathbb{Q}$-differentiability technique has been applied as a proof tool.     

Distribution and morphometric studies of flagellar sensilla in Emphorini bees (Hymenoptera, Apoidea)

The tribe Emphorini is a group of pollen-collecting solitary bees with a geographical distribution restricted to the western hemisphere. Most of the Emphorini bees collect Page 10 linepollen from a few specific plant families and display specialized behaviors for constructing their nests. Insect sensilla are the basic structural and functional units of cuticle receptors, serving mainly mechano- and chemo-receptor functions. The external morphology of the antennal sensilla has been well characterized in species of different families of Apoidea, however there is scarce information about this issue in solitary bees of the family Apidae. For a better understanding of the association between the external sensory system and several types of behaviors which emerged along the evolutionary history of bees, it is important to characterize the antennal receptors in several representative species of this tribe. The distribution of the antennal sensilla on the dorsal flagella of 18 taxa was studied in insects of both sexes, using light and scanning electron microscopy. There were six types of sensilla and setae on the antennae, which were identified as sensilla placodea, trichodea, basiconica, coeloconica, coelocapitular and ampullacea. The sensilla trichodea were classified into subtypes, A, B, C-D. Sensilla subtype A were the most abundant sensilla and were distributed over the entire antennae, while sensilla placodea and sensilla trichodea type B, showed a restricted distribution on specific areas of the flagella. We have recognized four patterns of spatial distribution of setae on dorsal flagella. Species having setae on the distal part of the flagellomeres tended to contain a low density of sensilla trichodea type A. Females showed a higher number of sensilla subtypes B and C-D than males; instead sensilla trichodea A were more abundant in males. No significant difference was found in the number of sensilla placodea, ampullacea, coeloconica and coelocapitular. Sensilla basiconica were found only in females. Our results showed that gustative and tactile sensilla were more abundant in female bees, as well as, olfactory receptors predominate in the antennal system of males. The possible coevolution of flagellar sensilla in males and females of solitary bees is discussed in light of previous reports. Patterns of distribution of setae determine the relative abundance of the types of sensilla in the flagellum.     

The effect of chromic sulfate concentration and immersion time on the structures and anticorrosive performance of the Cr(III) conversion coatings on aluminum alloys

The main purpose of this study is to develop trivalent chromium, Cr(III), conversion coatings on aluminum alloys. The influence of Cr(III) concentration and immersion time on structures and anticorrosive performance of the coatings has been investigated. Corrosion behaviors of the coatings were evaluated in a 0.5 M H₂SO₄ aqueous solution at room temperature using potentiodynamic polarization. The structure and valence state of the coatings were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS). The addition of Cr(III) ions to the conversion bath considerably changes structures and compositions of the coatings. The coatings with Cr oxides possess a denser and thinner structure. Moreover, the corrosion resistance of Cr(III) coatings tends to decline with increasing immersion time due to the dissolution of coatings in the dipping period. According to XPS analysis, the Cr(III) conversion coatings are composed of Cr₂O₃, Cr(OH)₃, Al₂O₃, Al(OH)₃, ZrO₂, Zr(OH)₄, AlF₃, and ZrF₄, but no hexavalent chromium component in the coatings. The result indicates that the coatings prepared in the solution with 0.01 M Cr(III) for 5 min have the smoothest and densest structure and the best anticorrosive performance among all of conversion coatings in this work.     

Stick-slip transition at the nanometer scale

We report the first observation of a stick-slip transition of surfactant solution flow through nanopores. From the experimental data, we were able to determine both the slip length and the critical wall shear stress from which slip occurs. Whereas the latter is found to increase linearly with the concentration, the former remains constant and approximately equal to 20 nm over the studied range of concentrations. We model slip to occur in the surfactant bilayer adsorbed at the nanopore wall. The stick-slip transition is then related to a reorganization of the surfactant bilayer from an entangled structure into independent layers flowing past one another, as evidenced by independent surface plasmon resonance experiments. We conclude from our analysis that surfactant solutions are always slipping in larger tubes. However, the larger the tube diameter, the smaller the relative slip contribution to the total flow.     

An external theorem on divisors of a number

Main result: Let ? be a collection of divisors of N = pe11?penn (e1 = minei for all i? {1,…, n}) such that if any two numbers in ? are coprime then their common multiple is N and maximal with respect to this condition, i.e. there is no other collection satisfying this condition which properly contains ?. We prove that ? consists of at least $\text{e}{}_1\text{П}{}^{\mathrm{n}}{}_{\mathrm{i\; =\; 2}}\text{(e}{}_{\mathrm{i}}\text{+ 1)?(e}{}_1\text{? 2)}$ elements.