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In this work, the influence of amide–π interactions on stability and properties of superoxide dismutase (SOD) active centres was analysed. In the data set of 43 proteins, 5017 amide–π interactions were observed, and every active centre formed averagely about 117 interactions. Most of the interactions belonged to the backbone of proteins. The analysis of the geometry of the amide–π interactions revealed two preferred structures, parallel-displaced and T-shaped structure. The aim of this study was to investigate the energy contribution resulting the from amide–π interactions, which were in the lower range of strong hydrogen bonds. The conservation patterns in the present study indicate that more than half of the residues involved in these interactions are evolutionarily conserved. The stabilization centres for these proteins showed that all residues involved in amide–π interactions were of use in locating one or more of such centres. The results presented in this work can be very useful for the understanding of contribution of amide–π interaction to the stability of SOD active centres.

Let R be a PrUfer domain of Krull dimension one. We prove the existence of Grobner bases for finitely generated submodules of finitely generated free modules over R[X], where the term order is PoT, or, "position over term". In order to do this, we first prove that there is a Groobner basis for finitely generated ideals in R[X ], which is a special case of the main result. The proof is based on the results from [3]. In addition to this we show, in the case of valuation domains, that every Groobner basis is actually a strong Groobner basis. [ABSTRACT FROM AUTHOR]

Any square matrix over an algebraically closed field has a Jordan normal form. In this paper, we prove that every infinite upper triangular matrix over an arbitrary field has a generalized infinite Jordan normal form. [ABSTRACT FROM AUTHOR]

We present another elementary proof of the theorem of Alfred Bauer from 1952 on eigenvalue perturbation. [ABSTRACT FROM AUTHOR]

A Gröbner basis for the ideal determining mod 2 cohomology of Grassmannian G3,n, obtained in a previous paper, is used, along with the method of obstruction theory, to establish some new immersion results for these manifolds. [ABSTRACT FROM AUTHOR]

The knowledge of cohomology of a manifold has shown to be quite relevant in various investigations: the question of vector fields, immersion and embedding dimension, and recently even in topological robotics. The method of Gröbner bases is applicable when the cohomology of the manifold is a quotient of a polynomial algebra. The mod 2 cohomology of the real flag manifold F(n1, n2, ..., nr) is known to be isomorphic to a polynomial algebra modulo a certain ideal. Reduced Gröbner bases for these ideals are obtained in the case of manifolds F(1, 1, ..., 1, n) including the complete flag manifolds (n = 1). [ABSTRACT FROM AUTHOR]

Mod 2 cohomology of the Grassmann manifold G2,n is a polynomial algebra modulo a certain well-known ideal. A Groebner basis for this ideal is obtained. Using this basis, some new immersion results for Grassmannians G2,n are established. [ABSTRACT FROM AUTHOR]

Mod 2 cohomology of the Grassmann manifold G2,n is a polynomial algebra modulo a certain well-known ideal. A Groebner basis for this ideal is obtained. Using this basis, some new immersion results for Grassmannians G2,n are established. [ABSTRACT FROM AUTHOR]