On Certain Divisibility Property of Polynomials

We review the definition of D-rings introduced by H. Gunji & D. L. MacQuillan. We provide an alternative characterization for such rings that allows us to give an elementary proof of that a ring of algebraic integers is a D-ring. Moreover, we give a characterization for D-rings that are also unique factorization domains to determine divisibility of polynomials using polynomial evaluations

Understanding the relative importance of vertical and horizontal flow in ice-wedge polygons

Ice-wedge polygons are common Arctic landforms. The future of these landforms in a warming climate depends on the bidirectional feedback between the rate of ice-wedge degradation and changes in hydrological characteristics. This work aims to better understand the relative roles of vertical and horizontal water fluxes in the subsurface of polygonal landscapes, providing new insights and data to test and calibrate hydrological models. Field-scale investigations were conducted at an intensively instrumented location on the Barrow Environmental Observatory (BEO) near Utqiagvik, AK, USA. Using a conservative tracer, we examined controls of microtopography and the frost table on subsurface flow and transport within a low-centered and a high-centered polygon. Bromide tracer was applied at both polygons in July 2015 and transport was monitored through two thaw seasons. Sampler arrays placed in polygon centers, rims, and troughs were used to monitor tracer concentrations. In both polygons, the tracer first infiltrated vertically until encountering the frost table and was then transported horizontally. Horizontal flow occurred in more locations and at higher velocities in the low-centered polygon than in the high-centered polygon. Preferential flow, influenced by frost table topography, was significant between polygon centers and troughs. Estimates of horizontal hydraulic conductivity were within the range of previous estimates of vertical conductivity, highlighting the importance of horizontal flow in these systems. This work forms a basis for understanding complexity of flow in polygonal landscapes