Chains on a Grating in Euclidean Space

Birefringence Properties and Surface Relief Grating Formation on Methylacrylate Polymers with Photochromic Side Chains

We have studied light-induced birefringence (LIB) and surface relief grating (SRG) formation in the series of methylacrylate polymers. The effect of material structure such as length of photochromic side chain, glass transition temperature and molecular structure of azo units on LIB and SRG are studied. The optical formation of self-induced SRG on films of these materials is also presented.

On the Quaternionic Curves in the Semi-Euclidean Space E_4_2

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

Tangent Bundle of the Hypersurfaces in a Euclidean Space

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

تبیین الگوی نااقلیدسی در برنامه ریزی شهری

With domination of Kant's epistemology and instrumental reason in social science and human geography, interpretation of  space have been based on neo physics that often it is equivalent with intuitive and physical  experience and the place of capital and it's reproduction. Therefore we firstly have represented of ontological transform of space concept and by the way we enumerate the c...

On images of continuous functions from a compact manifold to Euclidean space

Parallel Transport Frame in 4 -dimensional Euclidean Space

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...