This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical

In this article, finite difference method (FDM) is used to study the size-dependent free vibration characteristics of rectangular nanoplates considering the surface stress effects. To include the surface effects in the equations, Gurtin-Murdoch continuum elasticity approach has been employed. The effects of surface properties including the surface elasticity, surface residual stress and surface...

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versio...

We present a brief exposition of Teichmüller’s theorem. Introduction An orientation preserving homeomorphism f from a Riemann surface X onto a Riemann surface Y is given. Teichmüller’s problem is to find a quasiconformal homeomorhism in the homotopy class of f with minimal maximal dilatation, that is, to find a homeomorphism f0 whose maximal dilatation K(f0) is as small as possible in its homot...

ÐIn this paper, we develop integrated techniques that unify physics-based modeling with geometric subdivision methodology and present a scheme for dynamic manipulation of the smooth limit surface generated by the (modified) butterfly scheme using physics-based aforceo tools. This procedure-based surface model obtained through butterfly subdivision does not have a closed-form analytic formulatio...

Abstract. A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Möbius graphs. The contribution of each graph is an invariant of the topological type of the surface on which the graph is drawn. As an example, we calculate the inte...

It is shown that the space of finite-to-finite holomorphic correspondences on an OT-manifold is discrete. When the OT-manifold has no proper infinite complex-analytic subsets, it then follows by known model-theoretic results that its cartesian powers have no interesting complex-analytic families of subvarieties. The methods of proof, which are similar to [Moosa, Moraru, and Toma “An essentially...

Austenite is a semi-stable phase in most stainless steels that deforms to martensite under Md30 and forms martensitetype ά and ε due to the deformation in the steels. Since the distribution of strain induced martensite plays animportant role in achieving desired properties, the main objective of the present work is to model martensitedistribution of ά during cold rolling using...

In this paper‎, ‎the static bending‎, ‎free vibration‎, ‎and dynamic response of functionally graded‎ ‎piezoelectric beams have been carried out by finite element method‎‎under different sets of mechanical‎, ‎thermal‎, ‎and electrical‎ ‎loadings‎. ‎The beam with functionally graded piezoelectric material‎ ‎(FGPM) is assumed to be graded across the thickness with a simple‎ ‎power law distributio...