Planar graphs with square or cube root are four-colorable

A square (cube) coloring of a graph is an assignment of colors to its points so that no two points of distance less than or equal to two (three) get the same color. We prove that planar graphs with a square or cube root are four colorable using a square (cube) coloring of their square (cube) root.     

Stabilization of the collagen structure by hydroxyproline residues

The molecular structure of collagen is now accepted to be based on a triple-stranded coiled-coil, in which the three strands are held together predominantly by hydrogen bonds. Recent experimental evidence has shown that the presence of hydroxyproline residues in the third position of the repeating tripeptide unit lends additional stability to the collagen structure. In this paper, we report a model structure, which is supported by these observations. In a model structure proposed earlier, there are two hydrogen bonds per tripeptide unit, one of which is a direct interchain hydrogen bond, while the second hydrogen bond can be formedvia a water molecule. It has now been shown that the same water molecule can also form a hydrogen bond with the oxygen of theγ-hydroxyl group of hydroxyproline in the third position in the sequence (Gly-R₂-R₃). This hydroxyl group can also take part in an inter-triple-helix hydrogen bond. Our studies thus show the role played by hydroxyproline residues in the structure and stability of collagen.     

A hybrid fuzzy neural network-expert system for a short term unit commitment problem

The major aim of this paper is to develop a hybrid model to determine the unit commitment schedule of generating units. It is proposed to produce the unit commitment schedules in two steps. In the first step, the input layer of the neural network is designed to adopt nonlinear fuzzy membership values of the load demand profile. In the second step, an adaptive expert system is used to manipulate the schedules by using rule-base and inference mechanism. To demonstrate the effectiveness of this model, extensive studies have been performed for different load profiles belonging to the power systems of Tamilnadu consisting of thermal, nuclear, hydro, wind and diesel power plants.     

Design of 2-D recursive digital filters satisfying prescribed magnitude and constant group delay response

Generation of the 2-variable very-strictly-Hurwitz polynomial (VSHP) using properties of derivatives of even or odd parts of Hurwitz polynomials and their applications in designing 2-D recursive digital filters satisfying prescribed magnitude and constant group delay response is described.     

Thermal decomposition kinetics of p-toluenesulphonamide and some of its n-halogeno and n-metal derivatives

The TG, DTG and DTA traces of p-toluene sulphonamide, chloramine-T, dichloramine-T, dibromamine-T and the Ag and Hg derivatives of p-toluene sulphonamide are given and interpreted. The kinetic parameters (energies and entropies of activation and pre-exponential factors) for the main decomposition stages have been calculated.     

Evaluation of performance criteria of the CSI-IM drive system

The stability, sensitivity, and static velocity error coefficient of an induction motor (IM) drive fed by a current-source inverter (CSI) are analyzed to obtain the necessary information for the design of a practical system. These analyses are considered useful for determining an appropriate subsystem to compensate for performance deficiencies     

Decay instability in a plasma channel

Near the critical layer, a large-amplitude laser beam creates a transverse plasma channel due to the ponderomotive force. The axis of the channel is normal to the ambient density gradient. Inside the channel, the laser beam decays into counter-propagating ion acoustic and Langmuir waves. A nonlocal theory of the process is developed for a parabolic density profile. The growth rate of the instability is significantly reduced due to the nonlocal effects