In this study, we have applied the modified exp -expansion function method (MEFM) to obtain exact travelling wave solutions for (3+1) dimensional Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation and (3+1)-dimensional Jimbo-Miwa (JM) equation. Dark soliton solution, dark-bright hyperbolic solution trigonometric of KZK JM been found by using method. After that, scratched 2D 3D graphs all obtained i...

Conclusions The use of 3D-MTEE imaging, which is feasible in most patients, provides superb imaging of native MVs, which makes this modality an excellent choice for MV surgical planning and guidance of percutaneous interventions. Optimal aortic and tricuspid valve imaging will depend on further technological developments. Fast acquisition and immediate online display will facilitate wider accep...

We study the orientation preserving involutions of the orientable 3-dimensional handlebody Hg, for any genus g. A complete classification of such involutions is given in terms of their fixed points.

This paper presents a framework for shape matching and classification through scalespace decomposition of 3D models. The algorithm is based on recent developments in efficient hierarchical decomposition of a point distribution in metric space ~p,d! using its spectral properties. Through spectral decomposition, we reduce the problem of matching to that of computing a mapping and distance measure...