On Graphical Studies of PEN-IM Sets of Boolean Functions and their Minimizations. Part I†

The graphs of the sets of all penultimate implicants of certain types of Boolean functions are obtained in this part of the paper. Identification of different C.H. Boolean functions with their graphs are then made and terms are coined to designate these functions for the easy pattern recognition of their graphs. Finally formulae are deduced which give the number of prime implicants that must be present in any minimal cover of these functions.     

Identification of large scale distributed parameter systems—some simplifications in the multidimensional Poisson moment functional (MDPMF) approach

This paper is concerned with two practically important aspects of identification of large scale distributed parameter systems by the multidimensional Poisson moment functional (MDPMF) method (Saha and Prasada Rao 1980). The existing methods of (i) development and diagrammatic representations of the relations among the MDPMFs of partial derivative terms and those of the original multivariable function, and (ii) elimination of the effects of boundary functions and their partial derivatives from the identification equations, become extremely unwieldy as the order and dimensions of the model increase. This paper suggests alternative techniques in these two situations, leading to a simplification of the algorithm and an enormous reduction of the related analytical and computational burden. In the former situation, the suggested alternative uses the concept of separated variables. In the latter, the boundary function effects are estimated and then inserted into the algorithm to simplify it.     

Generalized probability model for estimating the proportion of the female population at different levels of fertility based on census sampling from a mixed population

The present exercise is an attempt to generalize a probability model referring to the waiting time distribution for conception in a mixed group of fecund females with two varying levels of fecundity, based on a census sample truncated at time T =t from the date of resumption of fecundity following an earlier conception (Biswas, 1975, Sankhya, Series B, 37, Part III). The generalization is made in two aspects, viz. instead of fixed conception rates, time-dependent rates decreasing with the age of the woman have been used. Additionally, unlike the model of Biswas (1975) consisting of two different fecund groups, three different levels of fecundity have been taken into consideration in this paper. Estimates of the proportion of fecund females over time, viz. π_i(t) (i = 1, 2, 3) are attempted by the method of maximum likelihood on the basis of a census sample truncated at time T = t under the generalized set up.     

Separately balanced realization of two-dimensional separable-denominator transfer functions†

In this paper a method is developed for the computation of a separately balanced state-space model for a given two-dimensional transfer function with separable denominator. The procedure relies on the eigenvalue/eigenvector decomposition (or singular-value decomposition) of two real symmetric matrices determined directly from the given transfer function.     

Retardation of Cs+ and Cl− Diffusion Using Blended Cement Admixtures

Diffusion of cesium chloride through thin plates of hardened cement pastes was studied. Blast-furnace slag and condensed silica fume were used as blending admixtures in an attempt to retard the diffusion of cesium and chloride ions. The curing and diffusion temperatures were varied from 27° to 60°C, and the water/solid ratio was varied from 0.30 to 0.40. Results indicate that the cesium ion diffuses more slowly than the chloride ion in hardened cement paste systems. Blending admixtures caused a further reduction in diffusivity for both ions, which is important for preventing corrosion or restricting radionuclide transport.     

Mechanical and morphological investigation of virgin polyethylene and silver nanoparticle-loaded nanocomposites film: comprehensive analysis of kinetic models for non-isothermal crystallization

This research was accomplished to examine the mechanical, morphological and crystallization kinetics study of polyethylene/silver nanoparticles (Ag-NPs) nanocomposite films. In this research, low-density polyethylene (LDPE) nanocomposite films were prepared containing Ag-NPs using maleic-anhydride-grafted low-density polyethylene (LDPE-g-MAH) as a compatibilizer by the melt mixing process. From mechanical property evaluation, it is revealed that the LDPE/LDPE-g-MAH/Ag-NPs nanocomposite films showed decreased tensile strength as compared with virgin LDPE matrix. Thermal characteristics of the prepared virgin LDPE and its nanocomposite films were studied by differential scanning calorimetry (DSC). Comprehensive analysis of different kinetic models such as the Avrami and Mo model on non-isothermal crystallization kinetics was performed in order to correlate the rate of crystallization and its various kinetic parameters. Further, the macrokinetic equation as proposed by Malkin has been applied to describe the kinetics of crystallization in the light of the Avrami equation. Concerning virgin LDPE and Ag-NP-reinforced LDPE, the former shows primary crystallization, whereas the later exhibits both primary and secondary crystallization with varying Avrami exponents. Kinetic parameters are recognized, and confirm the influence of Ag-NPs on crystallization kinetics. X-ray diffraction spectroscopy and transmission electron microscopic analysis of the nanocomposite films were conducted to verify the dispersion of inorganic filler particles in the resulting hybrids.