In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.

This paper presents the construction and verification of a new better semi-analytical, statistically derived universal model than that modified from Huet and Blasingame equation for estimating absolute permeability from mercury injection capillary pressure data. The foundation of my new model is the petrophysical relation between absolute permeability and capillary-pressure/wetting phase saturation properties. I also incorporate characteristics of capillary pressure behavior using the classic Brooks-Corey power-law model. The final form of my new proposed model allowed us to predict absolute permeability as a function of effective porosity, irreducible wetting phase saturation, displacement or threshold pressure corresponding pore throat radius, and basic pore size characteristics. I built my model using 189 sets of mercury—injection (Hg-air) capillary pressure data and measured permeability-including core samples from several reservoirs both carbonate and sandstone lithologies. I identified this correlation by quantifying its accuracy and precision based on regression analysis. I compared permeability estimates obtained from Huet and Blasingame mercury-injection capillary-pressure-based model and my new universal predicted permeability model to a set of laboratory measured permeability of my studied core sample and previously published data results respectively, where I quantified the method’s accuracy and precision based on error analysis. The measured permeability samples range is from 0.003 mD to 5341 mD. I review current employed models that are classified as belonging to Poiseuille model.

Aim: The aim of this study was to survey the root canal morphology of mandibular incisor teeth in a Palestinian population using radiographic approach. Materials and Methods: Five hundred and twenty two extracted mandibular incisor teeth were randomly collected from Palestinian population. The teeth were radiographed from a mesiodistal direction and examined for the presence of a second canal and for the type of canal configuration. Results: All teeth had single root. Three hundred and sixty nine teeth (70.7%) had one canal (type I Vertucci classification). The rest (29.3%) had a second canal (type II and III). Conclusion: Mandibular central and lateral teeth were mostly found to have one root and Type I canal system.