In 2009, Shapiro posed the following question: “What is the asymptotic proportion of Dyck paths having an even number of hills?” In this paper, we answer Shapiro’s question, as well as a generalization of the question to ternary paths. We find that the probability that a randomly chosen ternary path has an even number of hills approaches 125/169 as the length of the path approaches infinity. Ou...

a Rubenstein School of Environment and Natural Resources, University of Vermont, Utah State University, 5215 Old Main Hill, Logan, UT 84322, USA b Department of Environment and Society and the Ecology Center, Utah State University, 5215 Old Main Hill, Logan, UT 84322, USA c Rubenstein School of Environment and Natural Resources, University of Vermont, 218 Hills Building, 81 Carrigan Drive, Burl...

of two cases, which proved fatal at the dispensary since I have had medical charge of the G-aro Hills district. I would premise that the disease occurs most frequently in the lower hills bordering on the plains, and on low marshy localities. It usually begins as an ordinary paroxysmal fever, tending, however, to the remittent type. The symptoms in the beginning are rarely violent, but from bein...

An approach to extract watersheds and watercourses, as well as their corresponding valleys and hills, from grid DTMs and digital images with subpixel accuracy is proposed. The critical points of the terrain, which are essential as the starting points for the construction of these separatrices, are extracted efficiently with subpixel accuracy by a linear-filter-based approach. The separatrices a...

Ankur Khare 1,†, Piyush Kumar Shukla 2,*, Murtaza Abbas Rizvi 3,† and Shalini Stalin 4,† 1 Regional Institute of Education (RIE), Shyamla Hills, Bhopal 462001, India; [email protected] 2 Department of Computer Science and Engineering, University Institute of Technology, RGPV, Bhopal 462033, India 3 National Institute of Technical Teachers’ and Research, Shyamla Hills, Bhopal 462001, India;...

Two species of soricids are present in the Chadronian Medicine Pole Hills Local Fauna, Domnina cf. D. thompsoni and a new species of Domnina described herein. The new species is the third Chadronian species of Domnina and differs from other species in being larger and in having the M2 nearly the same size as the M1. The most similar described material is from the Uintan Swift Current Local Faun...