Entire functions of restricted hyper-order sharing a set of two small functions IM with their linear c-shift operators

PurposeThe paper aims to build the relationship between an entire function of restricted hyper-order with its linear c-shift operator.Design/methodology/approachStandard methodology for papers in difference and shift operators and value distribution theory have been used.FindingsThe relation between an entire function of restricted hyper-order with its linear c-shift operator was found under the periphery of sharing a set of two small functions IM (ignoring multiplicities) when exponent of convergence of zeros is strictly less than its order. This research work is an improvement and extension of two previous papers.Originality/valueThis is an original research work.

A Topology on a Hyper BCI-algebra Generated by a Hyper-order

In this paper, we introduce an operator on a hyper BCI-algebra via application of aleft hyper-order. The family consisting of the images of subsets under the operator turns out to be a base for some topology on the hyper BCI-algebra. We investigate some important properties of the induced topology on certain hyper BCI-algebras. In particular, we show that the generated topology on a non-trivial hyper subalgebra of an ordered hyper BCI-algebra coincides with the relative topology on this hyper subalgebra.

A note on power of meromorphic function and its shift operator of certain hyper-order sharing one small function and a value

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing a small function together with a value which improve and complement some earlier results. In particular, more or less we have improved and extended two results of Qi-Yang [Meromorphic functions that share values with their shifts or their $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling the superfluous conclusions in them.

The Modern State and the Society of Hyper-Order to 1939

For the past 200 years the defining feature of most domestic contests between Western governments and armed opponents has tended to be their lopsided asymmetry. Since the later nineteenth century a recurrent phenomenon of Western societies have been hopeless micro-insurrections mounted against stable societies: the armed utopianism of the violently delusional. Time and again, it is only society’s dreamers and deranged who have dared to mount any kind of sustained violent challenge to the state. This chapter traces the emergence of such dominant state power from the late eighteenth century up until the eve of the Second World War.

The Modern State and the Society of Hyper-Order from 1939

This chapter serves as a companion to its predecessor. It surveys the temporary dislocation of state power across much of Europe during the Second World War: before turning to its reinforcement and enhancement in the decades that followed. It examines the unfolding consequences of the 1968 crisis of legitimacy across Western societies: before noting the apparently unassailable position of the Western State against all violent challengers in the post-Cold War Brave New World of the early 1990s. Finally, it introduces the strikingly open-ended juncture of the early twenty-first century, setting up a more in-depth discussion in Chapter Three.