We consider two types of folding applied to equilateral plane graph linkages. First, under continuous folding motions, we show how to reconfigure any linear equilateral tree (lying on a line) into a canonical configuration. By contrast, such reconfiguration is known to be impossible for linear (nonequilateral) trees and for (nonlinear) equilateral trees. Second, under instantaneous folding moti...

The genetic code is a mapping of 64 codons to 22 actions, including polypeptide chain initiation, termination, and incorporation of the twenty amino acids. The standard tabular representation is useful for looking up which amino acid is encoded by a particular codon, but says little about functional relationships in the code. The possibility of making sense of the code rather than simply enumer...

This paper shows how to obtain accurate and efficient trajectory calculations for spherical geodesic grids in Cartesian space. Determination of the departure points is essential to characteristic-based methods that trace the value of a function to the foot of the characteristics and then either integrate or interpolate at this location. In this paper, the departure points are all computed in re...

An elementary geometric construction, known as Napoleon’s theorem, produces an equilateral triangle, obtained from equilateral triangles erected on the sides of any initial triangle: The centers of the three equilateral triangles erected on the sides of the arbitrarily given original triangle, all outward or all inward, are the vertices of the new equilateral triangle. In this note, we observe ...

Abstract We suggest triangular aperture modeling for the computation of speckle size using point spread function (PSF) concept. The fast Fourier transform (FFT) algorithm indicates three models apertures in computation. calculated first time average from full width at half maximum (FWHM) PSF. results are compared with sizes obtained autocorrelation images corresponding to considered showed an a...

Abstract Nuclear deformations are fundamentally important in nuclear physics. We recently developed a multidimensionally constrained relativistic Hartree–Bogoliubov (MDCRHB) model, which all multipole respecting the V 4 symmetry can be considered self-consistently. In this work we extend model by incorporating angular momentum projection and parity to restore rotational symmetries broken mean-f...