15 citations · 38 across the 29 of their papers we have counts for
10 papers · 1 filter
Hyperplane families creating envelopes
Takashi Nishimura
A simple geometric mechanism: "the locus of intersections of perpendicular bisectors and normal lines", often arises in many guises in Nonlinear Sciences. In this paper, a new appl…
Spherical orthotomic curve-germs
Xihe Liu, Takashi Nishimura
In this paper, it is shown that for an -dimensional spherical unit speed curve , a given point and a point of the open interval , the spherical…
Simultaneous smoothness and simultaneous stability of a strictly convex integrand and its dual
Erica Boizan Batista, Huhe Han, Takashi Nishimura
In this paper, we investigate simultaneous properties of a convex integrand and its dual . The main results are the following three. (1) For a convex integrand $γ…
Preservation of immersed or injective properties by composing generic generalized distance-squared mappings
Shunsuke Ichiki, Takashi Nishimura
Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalize…
Simultaneous stability of convex integrands and their duals
Erica Boizan Batista, Huhe Han, Takashi Nishimura
In this paper, the following three are shown. (1) For a convex integrand , its dual convex integrand is of class $C^\inf…
Stability of convex integrands
Erica Boizan Batista, Huhe Han, Takashi Nishimura
In this paper, it is shown that the set consisting of stable convex integrands is open and dense in the set consisting of convex integrands with re…