A note on life expectancy in a nonhomogeneous population

This note offers a simple mathematical model for life expectancy in a nonhomogeneous population. It is a function of life expectancy at birth and age of the population. The method is illustrated using Australian males (1961) data.     

Effective widths of rectangular slabs stiffened along two opposite edges by prestressed edge beams

The present analysis is an attempt to determine the portion of a rectangular slab that is acting with its two parallel stiffening edge beams, through which prestressing loads are applied to the entire section, in resisting load. Employing the well known theories of bending of plates and beams, the constitutive equations governing the behaviour of this type of composite system are presented. In particular, the equation of compatibility of strains between the slab edges and the stiffening edge beams at their junctions is formulated. In doing this, the biaxial nature of the bending of the edge beams, ignored in earlier formulations [1], has been incorporated. The results of the present analysis show that, under transverse loading, the portion of the slab, called the effectiv width, that can be considered effective as a part of each of the stiffening edge beams in determining stresses and deflexions is not significantly different from that obtained for an unprestressed section or a simply reinforced section. The effective width of the slab when such a section is subjected to only prestressing loads however shows a significant difference. We conclude from this that a single table of effective widths could be adopted for design purposes when considering transverse bending of this type of composite system whether the section is prestressed or not. Typical stress distributions due to (i) prestress alone, (ii) transverse loading alone and (ii) combined prestress and transverse loading are presented to demonstrate that the present formulation is versatile enough to solve problems involving prestressed edge beams in this type of composite assembly.     

On shear lag effects in orthotropic composite beams

Based upon the linearised theories of the bending and stretching of thin plates, an analysis is presented for the interaction between non-prismatic beams and an orthotropic concrete plate. It is shown that an exponential representation for the steel beam profiles provides a suitable basis for studying interaction in continuous non-prismatic beams, and for deducing suitable effective widths of slab for design purposes. The influence of “elastic” shear connection modulus is studied, as well as the effect of the varying flexural rigidity of the steel beams. The dependence of interaction on shear connection modulus in continuous beams is demonstrated through deflexion and slip characteristics, and so also is the dependence of interaction on the severity of the variation of flexural rigidity. The solution can be specialised to the limiting case of prismatic steel beams and a concrete slab and also to the solutions of rectangular plates with certain edge conditions.     

Life-expectancy in a nonhomogeneous population

Mortality differentials exist even among people of the same age and environmental risks. These differences are due to individual frailty (risks due to biological or behavioural reasons) not considered in the computation of conventional life-tables (where populations are assumed to be homogeneous). This note seeks to show empirically that life-expectancies computed from homogeneous population models are overstated for ages less than the mean, and are understated for higher ages. It is also shown that life-expectancy curves for both homogeneous and nonhomogeneous populations intersect at the mean survival age (when the most frail would have all died off) and at the maximum age lived in the population (when the last members of the cohort would have died off).     

Preparation and Characterization of Activated Carbon – nFe3O4, Activated Carbon – nSiO2 and Activated Carbon – nZnO Hybrid Materials

The preparation and physicochemical characterization of activated carbon, nano metal oxides, and activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO hybrid materials has been undertaken. The materials have been characterized by scanning and transmission electron microscopy, x‐ray diffraction, CNH analysis and Fourier transform infrared spectroscopy. Surface area and porosity, ash content, pH, and point of zero charge were also measured. The results showed that the surfaces of activated carbon, nSiO₂, activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO are suitable for the sorption of cationic complexes while the surfaces of nFe₃O₄ and nZnO are favourable to the sorption of anionic complexes of heavy metals. Results also showed that the composition of the activated carbon and nano metal oxides increased the surface and micropore areas of nano metal oxides due to the large number of micropores and crevices on the surface of the hybrid materials.     

The dependence of shear lag on partial interaction in composite beams

In this paper, the constitutive equations which relate partial interaction with shear lag are formulated and solved by series solutions for deflexion and in-plane stress in the slab to satisfy all the known boundary conditions. The results clearly demonstrate the influence of flexible shear connectors used in composite beams and also show that a more rational basis for defining effective width is from deflexion considerations. This shows that effective width increases with increasing degree of interaction, i.e. as the number of flexible shear connectors is increased. It is also established that there is a limiting degree of interaction beyond which deflexion is not sensibly influenced.     

Characterization of acid-base properties of two gibbsite samples in the context of literature results

Two different gibbsites, one commercial and one synthesized according to a frequently applied recipe, were studied in an interlaboratory attempt to gain insight into the origin of widely differing reports on gibbsite acid-base surface properties. In addition to a thorough characterization of the two solids, several methods relevant to the interfacial charging were applied to the two samples: potentiometric titrations to obtain the "apparent" proton related surface charge density, zeta-potential measurements characterizing the potential at the plane of shear, and Attenuated Total Reflection Infrared Spectroscopy (ATR-IR) to obtain information on the variation of counter-ion adsorption with pH (using nitrate as a probe). Values of the IEP at 9-10 and 11.2-11.3 were found for the commercial and synthesized sample, respectively. The experimental observations revealed huge differences in the charging behavior between the two samples. Such differences also appeared in the titration kinetics. A detailed literature review revealed similar disparity with no apparent systematic trend. While previously the waiting time between additions had been advocated to explain such differences among synthesized samples, our results do not support such a conclusion. Instead, we find that the amount of titrant added in each aliquot appears to have a significant influence on the titration curves. While we can relate a number of observations to others, a number of open questions and contradictions remain. We suggest various processes, which can explain the observed behavior.     

A study of dissolution kinetics of a Nigerian galena ore in hydrochloric acid

The results of experimental investigation on the study of dissolution kinetics of a Nigerian galena ore in hydrochloric acid solution were discussed. The influence of acid concentration, temperature, particle size, stirring speed and solid/liquid ratio on the extent of dissolution was examined. The elemental analysis by XRF showed that the galena ore is composed mainly of PbS with metals such as Sn, Fe and Zn occurring as minor elements and Mn, Rb, Sr and Nb as traces. The XRD analysis indicated galena as the dominant mineral phase, with the presence of associated minerals, such as α-quartz (SiO₂), sphalerite (ZnS), cassiterite (SnO₂), pyrite (FeS₂) and manganese oxide (MnO₂).Results of leaching studies showed that galena dissolution in HCl solution increases with increasing acid concentration and temperature; while it decreases with particle diameter and solid/liquid ratio at a fixed stirring rate of 450 rpm. The study showed that 94.8% of galena was dissolved by 8.06 M HCl at 80 °C within 120 min with initial solid/liquid ratio of 10 g/L. The corresponding activation energy, E_a was calculated to be 38.74 kJ/mol. Other parameters such as reaction order, Arrhenius constants, reaction and dissociation constants were calculated to be 0.28, 73.69 s^?1, 1.73 ± 0.13 × 10³ and 1.37 ± 0.024 × 10⁴ mol L^?1 s^?1, respectively. The mechanism of dissolution of galena was established to follow the shrinking core model for the diffusion controlled mechanism with surface chemical reaction as the rate controlling step for the dissolution process. Finally, the XRD analysis of the post-leaching residue showed the presence of elemental sulphur, lead chloride and α-quartz.     

A Co-Crystallised Cobalt(II) Cluster of Pyridinedicarboxylic Acid (PDC) as a Luminescent Material for Selective Sensing of Methanol

A luminescent Cobalt(II) co-crystal [Co₁₃(PDC)₁₆(H₂O)₂₄.7H₂O] 1 (where H₂PDC?=?2,6-pyridinedicarboxylic acid) have been prepared by oven-heating and slow evaporation of solvent. Single crystal X-ray diffraction (SCXRD) analysis revealed that 1 is a mixture of complexes that crystallizes in the triclinic space group P-1 and the geometry around the Co(II) ions is octahedral. The structure is extensively imbued with hydrogen bonding that helps in stabilizing the complex. Thermogravimetric analysis indicates that 1 is thermally stable up to 364 ^οC. The luminescence properties of 1 revealed a strong emission centered at 437 nm (λex?=?345 nm) assigned to ligand to metal charge transfer (LMCT). The luminescence sensing of 1 towards volatile organic molecules were also examined. However, 1 displayed a turn off towards methanol compared to other molecules with high quenching efficiency and low limit of detection (3.5?×?10^?4 vol%). The results show excellent selectively and high sensitivity. Powder X-ray diffraction studies revealed that the structural integrity of the complex was maintained after exposure to methanol vapour. Theoretical studies also revealed small binding energy (?413.2 au) and low energy gap (1.19) for 1-CH₃OH adduct.