The syntax of (complex) numerals in Arabic

Word order, case assignment, and agreement for gender and number are realised with remarkable complexity in the Arabic numeral system. This paper examines the internal morphological structure of simplex, compound, and complex numerals. We identify a recurrent pattern found both inside complex numerals and in the structural relations between numeral and the nouns they quantify. The structures uncovered then allow for more principled accounts of the superficial morphosyntactic complexities. The analysis suggests that DP contains a single Num head, but that Num can express both additive and multiplicative arithmetic operations.

MULTIPLICATIVE CONNECTIVITY STATUS NEIGHBORHOOD INDICES OF GRAPHS

The connectivity indices are applied to measure the chemical characteristics of compounds in Chemical Graph Theory. In this paper, we introduce the multiplicative atom bond connectivity status neighborhood index, multiplicative geometric-arithmetic status neighborhood index, multiplicative arithmetic-geometric status neighborhood index, multiplicative augmented status neighborhood index of a graph. Also we compute these newly defined indices for some standard graphs, wheel and friendship graphs.

On ranges of variants of the divisor functions that are dense

For a real number t, let st be the multiplicative arithmetic function defined by [Formula: see text] for all primes p and positive integers α. We show that the range of a function s-r is dense in the interval (0, 1] whenever r ∈ (0, 1]. We then find a constant ηA ≈ 1.9011618 and show that if r > 1, then the range of the function s-r is a dense subset of the interval [Formula: see text] if and only if r ≤ ηA. We end with an open problem.

Additive and multiplicative functions from Nottingham to Urbana-Champaign

The author remembers Heini Halberstam and views their early joint work through the lens of additive and multiplicative arithmetic functions.