Hurwitz numbers count ramified genus g, degree d coverings of the projective line with fixed branch locus and fixed ramification data. Double Hurwitz numbers count such covers, where we fix two special profiles over 0 and ∞ and only simple ramification else. These objects feature interesting structural behaviour and connections to geometry. In this paper, we introduce the notion of pruned doubl...

let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

This study aimed at linear stability analysis of the stratified two-phase liquid-gas flow in a horizontal pipe. First, equations governing the linear stability of flow in each phase and boundary conditions were obtained. The governing equations were eigenvalue Orr Sommerfeld equations which are difficult and stiff problems to solve. After obtaining the velocity profiles of the gas and liquid ph...

Longitudinal clustering provides a detailed yet comprehensible description of time profiles among subjects. With several approaches that are commonly used for this purpose, it remains unclear under which conditions method is preferred over another method. We investigated the performance five methods using Monte Carlo simulations on synthetic datasets, representing various scenarios involving po...

Wheel wear has been a concern in the railway for several decades. Studying the form change of the wheel/rail contacts in particular railways consisting of sharp curves helps to identify the risk of severe or catastrophic wear to minimize maintenance costs in order to be competitive in the transportation business. In this paper, the wheel/rail contact was studied on the particular railways. The ...