Optimal investment strategies with a reallocation constraint

We study a Merton type optimization problem under a reallocation constraint. Under this restriction, the stock holdings can not be liquidated faster than a certain rate. This is a common restriction in certain type of investment firms. Our main objective is to study the large time optimal growth rate of the expected value of the utility from wealth. We also consider a discounted infinite horizon problem as a step towards understanding the first problem. A numerical study is done by solving the dynamic programming equations. Under the assumption of a power utility function, an appropriate dimension reduction argument is used to reduce the original problem to a two dimensional one in a bounded domain with convenient boundary conditions. Computation of the optimal growth rate introduces additional numerical difficulties as the straightforward approach is unstable. In this direction, new analytical results characterizing the growth rate as the limit of a sequence of finite horizon problems with continuously derived utility are proved.     

Element Fractionation Analysis for Milk in Its Real Matrix by Inductively Coupled Plasma Optical Emission Spectrometry

Fractionation of elements in food is essential for understanding and prediction of its bioavailability, effects, and toxicity. In the present study, an analytical fractionation scheme for milk samples was developed for the common elements, such as Fe, Cu, Zn, Mn, Mg, Ca, Cr, Ni, Mo, Al, Pb, Sn, V, Ba, Co, and Cd. For this purpose, applying a sequential separation procedure, the protein, lipid, and serum fractions were obtained separately. The recovery percentages were in the range of 96.3–104.0 for the separation of fractions in the synthetic milk. The results achieved in the paper were compared with reported literature data. Additionally, the fractionation pattern for each metal studied was different relating to the origin of milk. Although there were some exceptions, it was seen that Fe, Cu, and Al preferred to be in protein fraction; however, Zn, Mn, Mg, Ca, Cr, Ni, and Mo preferred to be in serum fraction.     

Solid phase extraction and preconcentration of some metal ions using Schiff base immobilised silica gel followed by ICP-OES

ABSTRACT

In this study, a simple and efficient solid phase extraction procedure was developed for simultaneous separation and preconcentration of Ba, Cd, Co, Cu, Mn and Ni. The methodology was based on preconcentration of the target analytes on N,N’-bis(4-methoxysalicylidene)-1,3-propanediamine modified silica gel prior to inductively coupled plasma optic emission spectrometry detection. The experimental conditions were as follows: pH of sample 5.00; sample and eluent flow rates 3 mL min^?1; sample volume 25 mL; eluent 0.5 mol L^?1 HNO₃; eluent volume 3.0 mL. Preconcentration factor was achieved as 33.3 for Ba, Co, Mn; 83.3 for Cd, Ni; 166.7 for Cu. Limits of detection were found as 0.33, 0.26, 0.27, 0.36, 0.27 and 0.19 µg L^?1 for Ba, Cd, Co, Cu, Mn and Ni, respectively. The relative standard deviations of 2.6–3.8% were obtained via nine parallel analyses. The suggested procedure was successfully validated by the analysis of TMDA-53.3 Lake Ontario water and ERM-CA022a soft drinking water certified reference materials and applied to various natural water samples.     

Novel and Validated Spectrophotometric Matrix Matching Method for Simple and Rapid Determination of Chromium in Oily Media

N,N’-bis(4-methoxysalicylidene) ethylenediamine is proposed as analytical reagent for the direct determination of chromium in original matrix of liquid oils. The method is based on the complexation of N,N’-bis(4-methoxysalicylidene) ethylenediamine and chromium in n-hexane∶acetone (1∶4) medium and spectrophotometric determination at 355 nm against reagent blank. Complexation of MSE and chromium is completed in 20 seconds at molar ratio 1∶1. The molar absorptivity and the formation constant of the complex are determined as 9 740 L·mol-1·cm-1 and 3.6(±0.1)×105, respectively. Beer’s law is obeyed in range 0.02～1.50 mg·L-1 chromium concentration. Limits of detection and quantification of the suggested method were 7.5 and 25.1 μg·kg-1, respectively. The accuracy and precision of the method was checked by finding mean recovery and relative standard deviation by oil-based chromium standard analysis as 96.4%±1.4% and 1.5%, respectively. The practical applicability of elaborate method was tested using oil-based chromium standard spiked and unspiked corn, sunflower, soybean, olive and canola oils.     

Kuhn–Tucker Conditions for a Convex Programming Problem in Banach Spaces Partially Ordered by Cone with Empty Interior

The existence of saddle point of the Lagrange function for a convex programming problem in Banach spaces ordered by a cone with empty interior is established under a strong simultaneity condition. As a consequence, the Kuhn–Tucker conditions are derived. It is shown that the Slater and the strong simultaneity condition are equivalent if the cone determining the partial order has an interior.