In this paper we introduce the growth rate of χ2 defined by modulus function and study general properties of these spaces and also establish some inclusion results and duals among them..

For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and ‘real harmonic functions’ with respect to A. We also consider certain groups which are naturally associated with a uniform algebra A. We illustrate the notions considered with several examples.

We provide necessary and sufficient conditions for the space of smooth functions with compact supports $$C^\infty _c(\Omega )$$ to be dense in Musielak–Orlicz spaces $$L^\Phi (\Omega where $$\Omega $$ is an open subset $${\mathbb {R}}^d$$ . In particular, we prove that if $$\Phi satisfies condition $$\Delta _2$$ , closure )\cap L^\Phi equal only measure singular points zero. This extends earlie...

In this work we investigate the approximation problems in the Smirnov-Orlicz spaces in terms of the fractional modulus of smoothness. We prove the direct and inverse theorems in these spaces and obtain a constructive descriptions of the Lipschitz classes of functions defined by the fractional order modulus of smoothness, in particular. 1. Preliminaries and introduction A function M (u) : R → R ...

Local electron work function, adhesive force, modulus and deformation of ferrite and austenite phases in a duplex stainless steel were analyzed by scanning force microscopy. It is demonstrated that the austenite has a higher electron work function than the ferrite, corresponding to higher modulus, smaller deformation and larger adhesive force. Relevant first-principles calculations were conduct...