On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures

We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface, which appears to be 2D SG fractal. The two-polymer system is modelled by two mutually crossing self-avoiding walks. By applying the Monte Carlo Renormalization Group (MCRG) method, we calculate the critical exponents $\phi$, associated with the number of contacts of the 3D SG floating polymer chain, and the 2D SG adsorbed polymer chain, for a sequence of SG fractals with $2\le b\le 40$. Besides, we propose the codimension additivity (CA) argument formula for $\phi$, and compare its predictions with our reliable set of the MCRG data. We find that $\phi$ monotonically decreases with increasing $b$, that is, with increase of the container fractal dimension. Finally, we discuss the relations between different contact exponents, and analyze their possible behaviour in the fractal-to-Euclidean crossover region $b\to\infty$.Comment: 15 pages, 3 figure

Hamiltonian walks on Sierpinski and n-simplex fractals

We study Hamiltonian walks (HWs) on Sierpinski and $n$--simplex fractals. Via numerical analysis of exact recursion relations for the number of HWs we calculate the connectivity constant $\omega$ and find the asymptotic behaviour of the number of HWs. Depending on whether or not the polymer collapse transition is possible on a studied lattice, different scaling relations for the number of HWs are obtained. These relations are in general different from the well-known form characteristic of homogeneous lattices which has thus far been assumed to hold for fractal lattices too.Comment: 22 pages, 6 figures; final versio

Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.Comment: 11 pages, REVTEX, 2 postscript figure

Clinical significance of optimal red cell mass and plasma volume estimation methods

BACKGROUND: The aim of this study was to present and compare the results of proposed methods for optimal red cell mass and plasma volume (RCM&PV) estimation, and their influence on the interpretation of obtained results. MATERIAL AND METHODS: In 120/280 patients with polycythaemia rubra vera, subjected to RCM&PV determination with autologous erythrocytes in vitro labelled with 51Cr-sodium chromate, optimal volumes were determined using: 1. traditional ml/kg of: - the real body weight method (ml/kg RBW); - the optimal body weight method (ml/kg OBW). 2. the body weight, height, and sex based method (Retzlaff's tables), 3. the method recommended by the International Council for Standardization in Haematology (ICSH), based on body surface area. RESULTS: Different interpretation of the same results of 120 RCM&PV measurements was registered in 48/120 patients (40%). The greatest disagreement existed between ml/kg RBW and ml/kg OBW methods (in 39/120 subjects, 32.5%). In underweight patients the ml/kg RBW method, and in overweight patients the ml/kg OBW method, offered better agreement with ICSH&Retzlaff's methods. The ml/kg RBW method disagreed with ICSH&Retzlaff's methods and ml/kg OBW in 25% and 19.2% of patients respectively. ICSH and Retzlaff's methods disagreed in 10/120 patients (8.3%). The ICSH method yielded significantly lower optimal volumes than Retzlaff's. CONCLUSION: Three methods for optimal RCM&PV estimation lead to different interpretations of the same results of RCM&PV measurements with 51Cr-erythrocytes in 40% of patients. Two ml/kg body weight methods show greater disagreement in comparison with ICSH and Retzlaff's methods, which differ significantly. The ICSH method yields lower optimal values compared to Retzlaff's

Development of New Liquid Chromatographic Method for Mitotane and Its Metabolites Determination in Human Plasma Employing Design of Experiments Methodology

A simple and reliable new HPLC method with UV detection has been developed and validated for simultaneous determination of mitotane and its two metabolites DDA and DDE. Method development was carried out utilizing systematical approach of the design of experiments (DoE) methodology. For estimation of factors influence on selected chromatographic responses and definition of the optimal chromatographic conditions, Box-Behnken experimental design was applied. The defined optimal separation conditions were: column Restek Ultra Aqua C-18 with pre-column Restek Ultra Aqua C-18 operating at temperature 35 degrees C; mixture of acetonitrile and 0.5% formic acid as mobile phase with 1.2mL min(-1) flow rate and detection at 230nm. As sample preparation method, liquid-liquid extraction was chosen. Method was fully validated and LOQ and LOD were experimentally determined. Finally, method was successfully applied for determination of mitotane and its metabolites in plasma samples of patients with adrenocortical carcinoma.This is peer-reviewed version of the following article: Jancic-Stojanovic, B.; Vemić, S.; Elezović, V.; Petrović, A.; Sinadinović, Z.; Ivanović, D.; Damjanović, S.; Miljković, B. Development of New Liquid Chromatographic Method for Mitotane and Its Metabolites Determination in Human Plasma Employing Design of Experiments Methodology. J. Liq. Chromatogr. Relat. Technol. 2015, 38 (14), 1371–1378. [https://doi.org/10.1080/10826076.2015.1057645

Statistical mechanics of polymer chains grafted to adsorbing boundaries of fractal lattices embedded in three-dimensional space

We study the adsorption problem of linear polymers, immersed in a good solvent, when the container of the polymer-solvent system is taken to be a member of the Sierpinski gasket (SG) family of fractals, embedded in the three-dimensional Euclidean space. Members of the SG family are enumerated by an integer b (2>lt), and it is assumed that one side of each SG fractal is impenetrable adsorbing boundary. We calculate the surface critical exponents ;11;1, and ;be which, within the self-avoiding walk model (SAW) of polymer chain, are associated with the numbers of all possible SAWs with both, one, and no ends grafted to the adsorbing surface (adsorbing boundary), respectively. By applying the exact renormalization group method, for 2>b>4, we have obtained specific values for these exponents, for various types of polymer conformations. To extend the obtained sequences of exact values for surface critical exponents, we have applied the Monte Carlo renormalization group method for fractals with 2>b≤40. The obtained results show that all studied exponents are monotonically increasing functions of the parameter b, for all possible polymer states. We discuss mutual relations between the studied critical exponents, and compare their values with those found for other types of lattices, in order to attain a unified picture of the attacked problem. © 2014 Elsevier B.V. All rights reserved