On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices

Parametrization of $4\times 4$-matrices $G$ of the complex linear group $GL(4,C)$ in terms of four complex 4-vector parameters $(k,m,n,l)$ is investigated. Additional restrictions separating some subgroups of $GL(4,C)$ are given explicitly. In the given parametrization, the problem of inverting any $4\times 4$ matrix $G$ is solved. Expression for determinant of any matrix $G$ is found: $\det G = F(k,m,n,l)$. Unitarity conditions $G^{+} = G^{-1}$ have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups $G_{1}$, $G_{2}$, $G_{3}$ - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consisting of a product of a 3-parametric group isomorphic SU(2) and 1-parametric Abelian group. The Dirac basis of generators $\Lambda_{k}$, being of Gell-Mann type, substantially differs from the basis $\lambda_{i}$ used in the literature on SU(4) group, formulas relating them are found - they permit to separate SU(3) subgroup in SU(4). Special way to list 15 Dirac generators of $GL(4,C)$ can be used $\{\Lambda_k\} = \{\alpha_i\oplus\beta_j\oplus(\alpha_iV\beta_j = {\boldsymbol K} \oplus {\boldsymbol L}\oplus{\boldsymbol M})\}$, which permit to factorize SU(4) transformations according to S = e^{i\vec{a}\vec{\alpha}} e^{i\vec{b}\vec\beta}} e^{i{\boldsymbol k}{\boldsymbol K}} e^{i{\boldsymbol l}{\boldsymbol L}} e^{i\boldsymbol m}{\boldsymbol M}}, where two first factors commute with each other and are isomorphic to SU(2) group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Improved technology of frequency-selective UHF electromagnetic shields containing helical elements

An improved technology of frequency-selective electromagnetic shields has been considered. The technology has been improved by embedding classic Archimedean helical elements made from foiled materials into the bulk of the shields for the improvement of the frequency-selective performance of the shields and pinning of these elements in the bulk of the shields by means of fusion bonding. These design features provide for the main advantage of the improved technology in comparison with counterparts, i.e., lower time consumption. The technology has been improved in the following two aspects: 1) identification of helical element parameters providing for the greatest energy loss of the UHF electromagnetic radiation interacting with the helical elements; 2) identification of the optimum helical element arrangement in the shield bulk providing for the smallest transmission and reflection coefficient of the UHF electromagnetic radiation by the shields. Technology improvement in accordance with the former of the above aspects has been achieved based on analysis of publications dealing with mathematical simulation and study of the parameters of UHF electromagnetic radiation transmission by planar helical antennas. Technology improvement in accordance with the latter aspect has been achieved based on experimental data. Test shields have been fabricated with specifically arranged embedded helical elements, and comparison has been made between the UHF electromagnetic radiation transmission and reflection coefficients of the shields. Shields fabricated in accordance with the improved technology suggested herein show good promise for the electromagnetic noise protection of electronic devices

Charcoal-containing building materials for electromagnetic radiation shielding

he aim of the study presented in the current article was to experimentally substantiate the possibility of obtaining the cost effective building materials for electromagnetic radiation shielding by using powdered charcoal as a filler. Such charcoal properties as low cost and high carbon content (up to 90.0 wt.%) were the prerequisites for the study. To achieve the goal, a method for obtaining composite materials based on powdered charcoal and building gypsum was developed and experimentally substantiated by the authors. Further, the samples of charcoal-containing building materials were made according to the developed method and the electromagnetic radiation reflection and transmission coefficients values of the samples were measured in the frequency range of 0.7–17.0 GHz using scalar network analyzer. According to the measurements results, it was found that the average value of the electromagnetic radiation reflection coefficient in the specified frequency range of the materials produced in accordance with the presented method (when these materials thickness was equal to 1.0 cm) was –3.0 dB, and the average value of the electromagnetic radiation transmission coefficient was –25.0 dB. The studied materials are recommended for use in electromagnetic shielding of the rooms housing the electronic devices

Improved technology of frequency-selective UHF electromagnetic shields containing helical elements

An improved technology of frequency-selective electromagnetic shields has been considered. The technology has been improved by embedding classic Archimedean helical elements made from foiled materials into the bulk of the shields for the improvement of the frequency-selective performance of the shields and pinning of these elements in the bulk of the shields by means of fusion bonding. These design features provide for the main advantage of the improved technology in comparison with counterparts, i.e., lower time consumption. The technology has been improved in the following two aspects: 1) identification of helical element parameters providing for the greatest energy loss of the UHF electromagnetic radiation interacting with the helical elements; 2) identification of the optimum helical element arrangement in the shield bulk providing for the smallest transmission and reflection coefficient of the UHF electromagnetic radiation by the shields. Technology improvement in accordance with the former of the above aspects has been achieved based on analysis of publications dealing with mathematical simulation and study of the parameters of UHF electromagnetic radiation transmission by planar helical antennas. Technology improvement in accordance with the latter aspect has been achieved based on experimental data. Test shields have been fabricated with specifically arranged embedded helical elements, and comparison has been made between the UHF electromagnetic radiation transmission and reflection coefficients of the shields. Shields fabricated in accordance with the improved technology suggested herein show good promise for the electromagnetic noise protection of electronic devices

Recombinant Spidroin Microgel as the Base of Cell-Engineered Constructs Mediates Liver Regeneration in Rats

Aim: In this study, we seek to check if recombinant spidroin rS1/9 is applicable for cell-engineering construct development. Novel technologies of cell and tissue engineering are relevant for chronic liver failure management. Liver regeneration may represent one of the possible treatment options if a cell-engineered construct (CEC) is used. Nowadays, one can see the continuous study of various matrices to create an appropriate CEC. Materials and Methods: We have adhered allogenic liver cells and multipotent mesenchymal bone marrow stem cells (MMSC BM) to a microgel with recombinant spidroin rS1/9. Then we have studied the developed implantable CEC in a rat model (n = 80) of chronic liver failure achieved by prolonged poisoning with carbon tetrachloride. Results: Our results demonstrate that the CECs change the values of biochemical tests and morphological parameters in chronic liver failure in rats. Conclusion: We consider there to be a positive effect from the microgel-based CECs with recombinant spidroin rS1/9 in the treatment of chronic liver failure

Detyrosinated microtubules modulate mechanotransduction in heart and skeletal muscle

In striated muscle, X-ROS is the mechanotransduction pathway by which mechanical stress transduced by the microtubule network elicits reactive oxygen species. X-ROS tunes Ca(2+) signalling in healthy muscle, but in diseases such as Duchenne muscular dystrophy (DMD), microtubule alterations drive elevated X-ROS, disrupting Ca(2+) homeostasis and impairing function. Here we show that detyrosination, a post-translational modification of \u3b1-tubulin, influences X-ROS signalling, contraction speed and cytoskeletal mechanics. In the mdx mouse model of DMD, the pharmacological reduction of detyrosination in vitro ablates aberrant X-ROS and Ca(2+) signalling, and in vivo it protects against hallmarks of DMD, including workload-induced arrhythmias and contraction-induced injury in skeletal muscle. We conclude that detyrosinated microtubules increase cytoskeletal stiffness and mechanotransduction in striated muscle and that targeting this post-translational modification may have broad therapeutic potential in muscular dystrophies

Nano metal fluorides: small particles with great properties

The recently developed fluorolytic sol–gel route to metal fluorides opens a very broad range of both scientific and technical applications of the accessible high surface area metal fluorides, many of which have already been applied or tested. Specific chemical properties such as high Lewis acidity and physical properties such as high surface area, mesoporosity and nanosize as well as the possibility to apply metal fluorides on surfaces via a non-aqueous sol make the fluorolytic synthesis route a very versatile one. The scope of its scientific and technical use and the state of the art are presented.Peer Reviewe