Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galilean particle interacting with an external electric field.Comment: 23 pages, 2 table

Statistical analysis of excitation functions for elastic and inelastic scattering of α\alpha-particles on Mg and Si nuclei

The excitation functions for inelastic $\alpha$-scattering leading to the low lying excited states in $^{24}$Mg and $^{28}$Si were measured at $\Theta_{LAB}$ = 170°, 175° and 179° in the LAB energy range 22.75–28.40 MeV. Statistical analysis of these excitation functions and those previously measured for elastic scattering was performed. The direct interaction contribution $\mathit{y}_{D}$ to the reaction studied was obtained from probability distributions of cross sections and from correlation coefficients. Cross correlation coefficients between different reaction channels were calculated

On the electrodynamics of moving bodies at low velocities

We discuss the seminal article in which Le Bellac and Levy-Leblond have identified two Galilean limits of electromagnetism, and its modern implications. We use their results to point out some confusion in the literature and in the teaching of special relativity and electromagnetism. For instance, it is not widely recognized that there exist two well defined non-relativistic limits, so that researchers and teachers are likely to utilize an incoherent mixture of both. Recent works have shed a new light on the choice of gauge conditions in classical electromagnetism. We retrieve Le Bellac-Levy-Leblond's results by examining orders of magnitudes, and then with a Lorentz-like manifestly covariant approach to Galilean covariance based on a 5-dimensional Minkowski manifold. We emphasize the Riemann-Lorenz approach based on the vector and scalar potentials as opposed to the Heaviside-Hertz formulation in terms of electromagnetic fields. We discuss various applications and experiments, such as in magnetohydrodynamics and electrohydrodynamics, quantum mechanics, superconductivity, continuous media, etc. Much of the current technology where waves are not taken into account, is actually based on Galilean electromagnetism

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Effects of intravitreal ranibizumab on the untreated eye and systemic gene expression profile in age-related macular degeneration

Katarzyna Michalska-Małecka,1,2 Adam Kabiesz,2 Malgorzata W Kimsa,3 Barbara Strzałka-Mrozik,3 Maria Formińska-Kapuścik,2,4 Malgorzata Nita,5 Urszula Mazurek31Clinical Department of Ophthalmology, Medical University of Silesia, Katowice, Poland; 2University Center for Ophthalmology and Oncology, Independent Public Clinical Hospital, Medical University of Silesia, Katowice, Poland; 3Department of Molecular Biology, School of Pharmacy with the Division of Laboratory Medicine in Sosnowiec, Medical University of Silesia, Katowice, Poland; 4Clinical Department of Children Ophthalmology, Medical University of Silesia, Katowice, Poland; 5Domestic and Specialized Medicine Centre &ldquo;Dilmed&rdquo;, Katowice, PolandAbstract: The purpose of this study was to evaluate the systemic effects of intravitreal ranibizumab (Lucentis) treatment in patients with neovascular age-related macular degeneration (AMD). The impact of intravitreal ranibizumab injections on central retinal thickness (CRT) of treated and contralateral untreated eyes, and differences in gene expression patterns in the peripheral blood mononuclear cells were analyzed. The study included 29 patients aged 50&nbsp;years old and over with diagnosed neovascular AMD. The treatment was defined as 0.5 mg of ranibizumab injected intravitreally in the form of one injection every month during the period of 3 months. CRT was measured by optical coherence tomography. The gene expression profile was assigned using oligonucleotide microarrays of Affymetrix HG-U133A. Studies have shown that there was a change of CRT between treated and untreated eyes, and there were differences in CRT at baseline and after 1, 2, and 3 months of ranibizumab treatment. Three months after intravitreal injection, mean CRT was reduced in the treated eyes from 331.97&plusmn;123.62 to 254.31&plusmn;58.75 &micro;m, while mean CRT in the untreated fellow eyes reduced from 251.07&plusmn;40.29 to 235.45&plusmn;36.21 &micro;m at the same time. Furthermore, the research has shown that among all transcripts, 3,097 expresses change after the ranibizumab treatment in relation to controls. Among these transcripts, 1,339 were up-regulated, whereas 1,758 were down-regulated. Our results show the potential systemic effects of anti-VEGF therapy for AMD. Moreover, our study indicated different gene expression in peripheral blood mononuclear cells before and after intravitreal ranibizumab treatment. Keywords: ranibizumab, contralateral eye, central retinal thickness, oligonucleotide microarrayCorrigendum for this paper has been published.&nbsp

Recent developments in therapeutic applications of Cyanobacteria

The cyanobacteria (blue-green algae) are photosynthetic prokaryotes having applications in human health with numerous biological activities and as a dietary supplement. It is used as a food supplement because of its richness in nutrients and digestibility. Many cyanobacteria (Microcystis sp, Anabaena sp, Nostoc sp, Oscillatoria sp., etc.) produce a great variety of secondary metabolites with potent biological activities. Cyanobacteria produce biologically active and chemically diverse compounds belonging to cyclic peptides, lipopeptides, fatty acid amides, alkaloids and saccharides. More than 50% of the marine cyanobacteria are potentially exploitable for extracting bioactive substances which are effective in killing cancer cells by inducing apoptotic death. Their role as anti-viral, anti-tumor, antimicrobial, anti-HIV and a food additive have also been well established. However, such products are at different stages of clinical trials and only a few compounds have reached to the market