Let f be an arithmetic function satisfying some simple conditions. The aim of this paper is to establish asymptotical formula for the quantitySf(x):=∑n⩽xf([xn]) x→∞, where [t] integral part real number t. This generalises recent results Bordellès, Dai, Heyman, Pan & Shparlinski and Zhai (f=φ=the Euler function), Zhao Wu (f=σ=the sum-of-divisors function).

Polyacrylonitril (PAN)-supported chitosan (CS) nanocomposite membranes were prepared by cross-linking the CS with 3-aminopropyl-triethoxysilane (APTEOS) via sol-gel method. Pervaporative performances of the CS-SiO2/PAN membrane for dehydration of aqueous alcohol solutions were investigated. From SEM cross-sectional images of the membrane, the spongy pores and the finger-like pores we...

The acquisition of relational concepts plays an integral role and is assumed to be a prerequisite for analogical reasoning. Language and token-trained apes (e.g. Premack, 1976; Thompson, Oden, and Boysen, 1997) are the only nonhuman animals to succeed in solving and completing analogies, thus implicating language as the mechanism enabling the phenomenon. In the present study, I examine the role...

Elongation is a commonly found feature in artefacts made and used by humans and other animals and can be analysed in comparative study. Whether made for use in hand or beak, the artefacts have some common properties of length, breadth, thickness and balance point, and elongation can be studied as a factor relating to construction or use of a long axis. In human artefacts, elongation can be trac...

Introducing a new method to visualize large stretches of genomic DNA (see Appendix S1) the article reports that most GA-sequences [1] shared chains of tetra-GA-motifs and contained upstream poly(A)-segments. Although not integral parts of them, Alu-elements were found immediately upstream of all human and chimpanzee GA-sequences with an upstream poly(A)-segment. The article hypothesizes that ge...

1 Vail, A. L., Manica, A., & Bshary, R. (2014). Fish choose appropriately when and with whom to collaborate. Current Biology, 24, R791-R793. Notes: Collaborative abilities are integral to human society [1] and their evolutionary origins are of great interest. Chimpanzees are capable of determining appropriately when and with whom to collaborate in a rope-pull experiment [2] the only non-human s...