An edge-colored connected graph G is properly if between every pair of distinct vertices, there exists a path such that no two adjacent edges have the same color. Fujita (2019) introduced optimal proper connection number pc opt (G) for monochromatic , to make efficiently. More precisely, ( ) smallest integer p + q when one converts given into by recoloring with colors. In this paper, we show ha...

Abstract For a given sequence $$b_k$$ b k of non-negative real numbers, the number weighted partitions positive integer n having m parts $$c_{n,m}$$ c n , m has bivariate generati...

A natural reach of montane stream (length 96 m and 7 m width) was grided into 150 cells (2 × 2 m). Density and biomass of fish (Salmo trutta L. and Cottus poecilopus Heckel) were estimated at each cell, as well as stream depth, current velocity, Froude number, bed granulation and its roughness were measured, and benthic samples from exposed bricks were collected from mid August to early October...

Submitted for the MAR10 Meeting of The American Physical Society Vortex ring refraction at large Froude numbers1 KERRY KUEHN, MATTHEW MOELLER, MICHAEL SCHULZ, DANIEL SANFELIPPO, Wisconsin Lutheran College — We have experimentally studied the impact of a planar axisymmetric vortex ring, incident at an oblique angle, upon a sharp gravity-induced interface separating two fluids of differing densit...