Bouvaist Cubic of a Triangle in an Isotropic Plane

KoG ◽

10.31896/k.23.4 ◽

2019 ◽

pp. 37-39

Author(s):

Ružica Kolar-Šuper

Keyword(s):

Steiner Point ◽

Isotropic Plane

The cubic in an isotropic plane which passes through the intersections of the sides of an orthic triangle with the sides of a complementary triangle of a given triangle, and through the point which is complementary to the Steiner point of triangle is studied in this paper. It is proved that its non-isotropic asymptote is parallel to Lemoine line of a given triangle.

Download Full-text

A new methodology to obtain the exact solutions of isotropic plane beam subjected to arbitrary loads

Mechanics Research Communications ◽

10.1016/j.mechrescom.2010.05.006 ◽

2010 ◽

Vol 37 (5) ◽

pp. 476-483 ◽

Cited By ~ 1

Author(s):

Lang Zhang ◽

Puyun Gao ◽

Dongxu Li ◽

Xue Wang

Keyword(s):

Exact Solutions ◽

Isotropic Plane

Download Full-text

A Tight Lower Bound for the Steiner Point Removal Problem on Trees

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - Lecture Notes in Computer Science ◽

10.1007/11830924_9 ◽

2006 ◽

pp. 70-81 ◽

Cited By ~ 1

Author(s):

T. -H. Hubert Chan ◽

Donglin Xia ◽

Goran Konjevod ◽

Andrea Richa

Keyword(s):

Lower Bound ◽

Steiner Point

Download Full-text

Bound state in a model of electromagnetic field interacting with a material plan

Modern Physics Letters A ◽

10.1142/s0217732320501709 ◽

2020 ◽

Vol 35 (21) ◽

pp. 2050170

Author(s):

Yu. M. Pismak ◽

D. Shukhobodskaia

Keyword(s):

Electromagnetic Field ◽

Maxwell Equations ◽

Singular Potential ◽

Bound State ◽

Material Object ◽

Two Dimensional ◽

Isotropic Plane ◽

Chern Simons ◽

Material Plane ◽

State Of Field

In the model with Chern-Simons potential describing the coupling of electromagnetic field with a two-dimensional material, the possibility of the appearance of bound field states, vanishing at sufficiently large distances from interacting with its macro-objects, is considered. As an example of such two-dimensional material object we consider a homogeneous isotropic plane. Its interaction with electromagnetic field is described by a modified Maxwell equation with singular potential. The analysis of their solution shows that the bound state of field cannot arise without external charges and currents. In the model with currents and charges the Chern-Simons potential in the modified Maxwell equations creates bound state in the form of the electromagnetic wave propagating along the material plane with exponentially decreasing amplitude in the orthogonal to its direction.

Download Full-text