Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Artificial neural networks in modelling osmotic dehydration of foods

Artificial neural network (ANN) models for water loss (WL) and solid gain (SG) were evaluated as potential alternative to multiple linear regression (MLR) for osmotic dehydration of apple, banana and potato. The radial basis function (RBF) network with a Gaussian function was used in this study. The RBF employed the orthogonal least square learning method. When predictions of experimental data from MLR and ANN were compared, an agreement was found for ANN models than MLR models for SG than WL. The regression coefficient for determination (R2) for SG in MLR models was 0.31, and for ANN was 0.91. The R2 in MLR for WL was 0.89, whereas ANN was 0.84.Osmotic dehydration experiments found that the amount of WL and SG occurred in the following descending order: Golden Delicious apple > Cox apple > potato > banana. The effect of temperature and concentration of osmotic solution on WL and SG of the plant materials followed a descending order as: 55 > 40 > 32.2C and 70 > 60 > 50 > 40%, respectively.

Development and mechanical characterization of solvent-cast polymeric films as potential drug delivery systems to mucosal surfaces

Solvent-cast films from three polymers, carboxymethylcellulose (CMC), sodium alginate (SA), and xanthan gum, were prepared by drying the polymeric gels in air. Three methods, (a) passive hydration, (b) vortex hydration with heating, and (c) cold hydration, were investigated to determine the most effective means of preparing gels for each of the three polymers. Different drying conditions [relative humidity - RH (6-52%) and temperature (3-45 degrees C)] were investigated to determine the effect of drying rate on the films prepared by drying the polymeric gels. The tensile properties of the CMC films were determined by stretching dumbbell-shaped films to breaking point, using a Texture Analyser. Glycerol was used as a plasticizer, and its effects on the drying rate, physical appearance, and tensile properties of the resulting films were investigated. Vortex hydration with heating was the method of choice for preparing gels of SA and CMC, and cold hydration for xanthan gels. Drying rates increased with low glycerol content, high temperature, and low relative humidity. The residual water content of the films increased with increasing glycerol content and high relative humidity and decreased at higher temperatures. Generally, temperature affected the drying rate to a greater extent than relative humidity. Glycerol significantly affected the toughness (increased) and rigidity (decreased) of CMC films. CMC films prepared at 45 degrees C and 6% RH produced suitable films at the fastest rate while films containing equal quantities of glycerol and CMC possessed an ideal balance between flexibility and rigidity.