in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

SUMMARY Herein, we present CONSRANK, a web tool for analyzing, comparing and ranking protein-protein and protein-nucleic acid docking models, based on the conservation of inter-residue contacts and its visualization in 2D and 3D interactive contact maps. AVAILABILITY AND IMPLEMENTATION CONSRANK is accessible as a public web tool at https://www.molnac.unisa.it/BioTools/consrank/. CONTACT rom...

The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical bundle of moving frames and the complete system of symplectic invariants, called curvature maps, for parametr...

The geometric structures of proteins are vital to the understanding of biochemical interactions. However, there is much yet to be understood about the spatial arrangements of the chains of amino acids making up any given protein. In particular, while conventional analysis tools like the Ramachandran plot supply some insight into the local relative orientation of pairs of amino acid residues, th...

We show that for any periodic mapping class, there is some power which maps a nonseparating, simple closed curve to distinct, disjoint nonseparating curve. As an application of this result, we introduce the notion stable specific torsion length group element and Dehn twist bounded above by six.

Abstract Taking the hint from usual parametrization of circle and hyperbola, inspired by pathwork initiated Cayley Dixon for “Fermat” elliptic curve $$x^3+y^3=1$$ x 3 + y = 1 , we...

Quantum mechanical semiempirical comparative binding energy analysis calculations have been carried out for a series of protein kinase B (PKB) inhibitors derived from fragment- and structure-based drug design. These protein-ligand complexes were selected because they represent a consistent set of experimental data that includes both crystal structures and affinities. Seven scoring functions wer...

A contact map is a 2D derivative of the 3D structure of proteins, containing various residue-residue (RR) contacts within the structure. Contact maps can be used for the reconstruction of structure with high accuracy and can be predicted from the amino acid sequence. Therefore understanding the various properties of contact maps is an important step in protein structure prediction. For investig...

The toric residue is a map depending on n + 1 divisors on a complete toric variety of dimension n . It appears in a variety of contexts such as sparse polynomial systems, mirror symmetry, and GKZ hypergeometric functions. In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated po...

In the accompanying paper, it was necessary to align partial denaturation maps of linear but circularly permuted DNA molecules in order to determine the relative positions of the ends. As mentioned in Materials and Methods, this was accomplished by visual alignment of maps plotted on paper strips, a tedious process of possibly questionable objectivity. This Appendix describes a technique for th...