Graph colorings and acyclic orientations

This paper presents new combinatorial proofs of two identities due to R. Stanley relating the chromatic polynomial and acyclic orientations of a graph. In addition, using elementary means, explicit formulae for the generating functions of the chromatic numbers and the number of color compatible acyclic orientations are derived. These formulae immediately show a reciprocity law concerning the generating functions.     

The interaction of foils activated by thermal neutrons

The interaction of foils lying in a plane during their activation by thermal neutrons has been calculated. Numerical values of functions are listed, which can be used in calculations, especially for graphite. The interaction was measured in the graphite column of the VVR-S reactor.

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, , . , , . VVR-S.

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We thank J. Frytacký, T. Kania and V. ervenka for their help in the numerical calculations and measurements.     

An analogue of Hartshorne and Serre problems for 1-convex surfaces

Let C be an elliptic curve and let L∈Pic(C). If c₁(L)<0, a well known result of Grauert tells us that L is rigid. On the other hand, Arnold provided a criterion for the rigidity of L when c₁(L)=0. However, a concrete example of such a bundle is hard to come by. In this paper, we construct explicitly such an L which turns out to be the line bundle associated to some toroidal group , viewed as topologically trivial -bundle over C. This example turns out to be the counterexample to the following analogue of a problem of Serre for 1-convex surfaces:Let X be a compactifiable surface such that - for all p?0 and q?1. Is X always 1-convex?Also a cohomological characterization of toroidal groups of finite type is established, as well as an analogue of a problem of Hartshorne for 1-convex surfaces will be discussed.     

A multi-heuristic approach for solving the pre-marshalling problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the pre-marshalling problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method. The improvement is twofold, both in the quality of found solutions, and in the computational effort.     

Magnetically active Ag–Zn nanoferrites synthesized by solution combustion route: physical chemical studies and density functional theory analysis

Nanoparticles with mixed compositions, particularly spinel ferrites with magnetic activity, have arisen as contrast agents for magnetic resonance imaging, magnetic hyperthermia. For such applications, it is desirable to possess specific particle size and physicochemical properties, i.e., magnetic response, porosity, crystallinity, and so on. It is well known that controlling specific variables in the synthetic process has a dramatic effect on final product properties and behavior. Amid preparation techniques reported in the literature, low-temperature solution combustion method has shown the ability to control and direct synthesis simply and efficiently. We are presenting a study about controlling and tuning the magnetic properties and the effect of particle size modified in Ag–Zn nanoferrites with different amounts of Co and Ni as doping metals. Different combinations of Co and Ni within Ag–Zn (Ag_0.25Zn_0.5-xM_xFe_2.25O₄) nanoferrites have been synthesized using the low-temperature solution combustion technique, and this method proved to be efficient and reliable for developing homogenous, fine structured materials. X-ray diffraction confirmed that the atomic structure of prepared nanoferrites is pure and cubic, whereas electron microscopy confirmed a semispherical and monodisperse morphology with particle diameter around 20 nm. The magnetic behavior of bred materials has been explained by analyzing magnetic factors such as saturation magnetization, coercivity, and retentivity, and all experimental findings are matched with theoretical density functional theory (DFT) studies to understand the effect of each material within A and B sites in ferrite crystal cell. The observed magnetic properties highlight the superparamagnetic behavior and the effect of doping metals which is an asset in developing new materials for diagnostic and therapeutic applications. DFT modeling was achieved in an attempt to understand the effect of metal substitution in cubic ferrite cells.     

Development and Validation of a Bioanalytical LC-MS/MS Method for Simultaneous Determination of Sirolimus in Porcine Whole Blood and Lung Tissue and Pharmacokinetic Application with Coronary Stents

Sirolimus is a hydrophobic macrolide compound that has been used for long-term immunosuppressive therapy, prevention of restenosis, and treatment of lymphangioleiomyomatosis. In this study, a simple and sensitive liquid chromatography-tandem mass spectrometry (LC-MS/MS) was developed and validated for the simultaneous determination of sirolimus in both porcine whole blood and lung tissue. Blood and lung tissue homogenates were deproteinized with acetonitrile and injected into the LC-MS/MS system for analysis using the positive electrospray ionization mode. The drug was separated on a C18 reversed phase column with a gradient mobile phase (ammonium formate buffer (5 mM) with 0.1% formic acid and acetonitrile) at 0.2 mL/min. The selected reaction monitoring transitions of m/z 931.5 → 864.4 and m/z 809.5 → 756.5 were applied for sirolimus and ascomycin (the internal standard, IS), respectively. The method was selective and linear over a concentration range of 0.5–50 ng/mL. The method was validated for sensitivity, accuracy, precision, extraction recovery, matrix effect, and stability in porcine whole blood and lung tissue homogenates, and all values were within acceptable ranges. The method was applied to a pharmacokinetic study to quantitate sirolimus levels in porcine blood and its distribution in lung tissue following the application of stents in the porcine coronary arteries. It enabled the quantification of sirolimus concentration until 2 and 14 days in blood and in lung tissue, respectively. This method would be appropriate for both routine porcine pharmacokinetic and bio-distribution studies of sirolimus formulations.