24 research outputs found
On some notions of good reduction for endomorphisms of the projective line
Let be an endomorphism of \SR(\bar{\Q}), the projective line over
the algebraic closure of \Q, of degree defined over a number field
. Let be a non-archimedean valuation of . We say that has
critically good reduction at if any pair of distinct ramification points of
do not collide under reduction modulo and the same holds for any
pair of branch points. We say that has simple good reduction at if
the map , the reduction of modulo , has the same degree of
. We prove that if has critically good reduction at and the
reduction map is separable, then has simple good reduction at
.Comment: 15 page
Studio del risalto ondulare in corrispondenza di un salto di fondo in alveo di canale a sezione trapezia
Limiting and sill-controlled adverse-slope hydraulic jump
This note analyzes, from a theoretical and experimental point of view, hydraulic jumps on adverse slopes in rectangular prismatic channels. The analysis is carried out for the classical adverse-slope hydraulic jump and the jump forced by the presence of a sill. Data collected in two series of experiments involving different equipment were added to available results to obtain a general relationship for the sequent depth ratio as a function of the upstream Froude number and adverse-slope angle. The presence of a sill stabilizes the jump