To determine flow curves of a material, whose plastic deformation is produced by martensitic transformation, transformation strains of a martensite plate must be characterized [1–3]. Most studies along this line adopt results obtained by the phenomenological crystallographic theory of martensitic transformation [4,5]. The theory is based on finite deformation analysis, which needs involved comp...

Using standard analysis only, we present an extension •R of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential Geometry, Analysis and Physics. On the other hand we want to show that these infinitesimals may be also useful in infinite dimensional Differential Geometry, e.g. to study space...

Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...

the purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

Let G be a reductive Lie group and O the coadjoint orbit of a hyperbolic element of g. By π is denoted the unitary irreducible representation of G associated with O by the orbit method. We give geometric interpretations in terms of concepts related to O of the constant π(g), for g ∈ Z(G). In the spirit of the orbit method we interpret geometrically the infinitesimal character of the differentia...

In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.

All the existing computers are able to do arithmetical operations only with finite numerals. Operations with infinite and infinitesimal quantities could not be realized. The paper describes a new positional system with infinite radix allowing us to write down finite, infinite, and infinitesimal numbers as particular cases of a unique framework. The new approach both gives possibilities to do ca...