A canonical form for positive definite matrices

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension n, but it is practical and more efficient than canonical forms based on Minkowski reduction

Effects of saline solution and simulated body fluid on ion substituted hydroxyapatites EPR spectra

Hydroxyapatite (HA, Ca10(PO4)6(OH)2), a calcium orthophosphate, due to its similarity to the inorganic part of human’s hard tissue, is among the most frequently used hard tissue regeneration biomaterial [1]. As such, the effects of HA ageing in media similar to blood plasma need to be studied, specifically after sterilization with γ-radiation, to better understand the possible structural changes it would undergo in the human body. Moreover, such changes in ion substituted HAs are particularly interesting since so called biological HA is in fact non-stoichiometric poorly crystalline, calcium deficient, Na-, Mg- and carbonate substituted HA (Dorozhkin, 2012) [2]. In this study, HA and 3 different substituted HAs were irradiated to 25 kGy with Co-60 γ-rays and their electron paramagnetic (EPR) spectra were recorded 1, 14 and 28 days after treatment with saline solution and simulated body fluid (SBF) [3]. The ion substituted HAs were doped with Mg and Si: 2% Mg; 2% Mg + 0.4% Si and 2% Mg + 1.25% Si. EPR spectra were analysed, and the most pronounced peaks assigned. The effects of ageing in the two media are presented and discussed.IX International Conference on Radiation in Various Fields of Research : RAD 2021 : book of abstracts; June 14-18, 2021; Herceg Novi, Montenegr

Automorphism groups of root systems matroids

Given a root system View the MathML source, the vector system View the MathML source is obtained by taking a representative v in each antipodal pair {v,−v}. The matroid View the MathML source is formed by all independent subsets of View the MathML source. The automorphism group of a matroid is the group of permutations preserving its independent subsets. We prove that the automorphism groups of all irreducible root system matroids View the MathML source are uniquely determined by their independent sets of size 3. As a corollary, we compute these groups explicitly, and thus complete the classification of the automorphism groups of root system matroids

The contact polytope of the Leech lattice

The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1,197,362,269,604,214,277,200 many facets in 232 orbits

Complexity and algorithms for computing Voronoi cells of lattices

In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a #P-hard problem. On the other hand we describe an algorithm for this problem which is especially suited for low dimensional (say dimensions at most 12) and for highly-symmetric lattices. We use our implementation, which drastically outperforms those of current computer algebra systems, to find the vertices of Voronoi cells and quantizer constants of some prominent lattices

A new approach to the drug release kinetics of a discrete system: SiO2 system obtained by ultrasonic dry spraying

Mesoporous silica materials have already proved to be non-toxic and biocompatible, and also to have large pore volume and very high specific surface area suitable for loading of small molecules. Having this in mind and the fact that silicon dioxide (SiO2) powders can be so designed to obtain particle structures organized at multi levels, SiO2 was chosen as a potential carrier for metronidazole, an antibiotic drug. SiO2 powder was synthesized in two stages: first silica sol was prepared by hydrothermal synthesis and second the sol was converted into powder by dry spraying with simultaneous incorporation of the antibiotic into its structure. Scanning and transmission electron microscopy study revealed very complex structure and sub-structure of SiO2 particles. Cell viability tests were used for estimation of cytotoxicity of so synthesized SiO2. The drug release data showed that the system can provide drug release for a long time. Also, the device behavior is fully predictable, according to our theoretical model of multilevel structure design, and gives many opportunities for model investigations of drug release and its kinetics. The pore sizes and their distribution were observed as a limiting factor of drug release kinetics. Therefore, as the pore sizes are given as a set of discrete values, the kinetics of drug release might also be given as a set of corresponding discrete values. (c) 2012 Elsevier B.V. All rights reserved

Calcium phosphate and calcium carbonate mineralization of bioinspired hydrogels based on β-chitin isolated from biomineral of the common cuttlefish (Sepia officinalis, L.)

Chitin, a bioactive, antibacterial and biodegradable polymer is commonly utilized by diverse marine organisms as the main scaffold material during biomineralization. Due to its properties, chitin is also of interest as a component of organo-inorganic composites for diverse biomedical applications. In this study, chitinous fibers isolated from the cuttlebone of the common cuttlefish (Sepia officinalis, L.) are characterized and evaluated for use as an integral part of mineralized hydrogels for biomedical applications. Since marine organisms use calcium carbonates (CaCO3), while vertebrates use calcium phosphates (CaP) as the main inorganic hard tissue components, and both minerals are used in hard tissue engineering, they were compared to determine which composite is potentially a better biomaterial. Hydrogel mineralization was conducted by subsequent dipping into cationic and anionic reactant solutions, resulting in the formation of a CaCO3 or CaP coating that penetrated into the hydrogel. Obtained composites were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), atomic force microscopy (AFM), scanning electron microscopy (SEM), rheology, swelling tests and simple compression. The results indicate that β-chitin can be used for the preparation of moldable hydrogels that are easily mineralized. Mineralized hydrogels have higher elasticity than non-mineralized ones while swelling is better if the extent of mineralization is lower. Further optimization of the hydrogels composition could improve their stress response and Young’s modulus, where the current hydrogel with a higher extent of CaP mineralization excels in comparison to all other investigated composites. © 2018, Springer Nature B.V.Croatian Science Foundation [IP-2013-11-5055]; Ministry of Education, Youth and Sports of the Czech Republic, Program NPU I [LO1504]; COST Action [MP1301