Renormalization: a quasi-shuffle approach

In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with values in a Rota-Baxter algebra of amplitudes. We associate in this paper to any such algebra a universal semi-group (different in nature from the Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes associated to Feynman graphs produces the expected operations: Bogoliubov's preparation map, extraction of divergences, renormalization. In this process a key role is played by commutative and noncommutative quasi-shuffle bialgebras whose universal properties are instrumental in encoding the renormalization process

Distribution and abundance of phytoplankton in Hormuzgan province, Hormuz Strait and the Persian Gulf waters

Distribution and density of different phytoplankton groups in Hormuzgan province along the Persian Gulf, from Sirik Harbor to Nayband Bay were studied during winter 2004. Sampling was carried out on board of Ferdous-1 research vessel in seven transects (21 stations) in three lines including surface layer (0-20m), middle and bottom layers (20-50m and more than 50m, respectively). We found 46 genera of diatoms (Bacillariophyceae), 19 genera of dinoflagellates, 6 genera of blue-green algae (Cyanophyceae), 1 genus of Euglenophyceae and 1 genus of Chrysophyceae. We recorded maximum and minimum phytoplankton density in different transects at 37665583 and 2433208 cells/m3 respectively. The maximum density was 62762083 cells/m3 for Bacillariophyceae group that was sampled in surface layer (0-20m) of the station 9. Also, we found that average total number of phytoplankton in three lines of seven transects was 11728973 cells/m3. One way ANOVA showed a significant difference for average number of phytoplankton for each transect (P0.05)

Time-ordering and a generalized Magnus expansion

Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including however directly a non-trivial initial condition. As a by-product we recover a variant of the time ordering operation, known as T*-ordering. Eventually, placing our results in the general context of Rota-Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations

Differentiation of embryonal carcinoma stem cells into insulin-producing cells by using pancreas extract in vitro

Introduction: Type I diabetes mellitus results from the autoimmune destruction of the β cells in pancreatic islets. Currently, extensive research is being conducted on the generation of insulin-producing cells (IPCs) from stem cells. P19 embryonal carcinoma cells are multipotent and can differentiate into cell types of all three germ layers. In this study, the differentiation of P19 cells into IPCs by using mouse pancreas extract (MPE) was investigated. Materials and Methods: Embryoid bodies (EBs) obtained from P19 cells were cultured in medium containing 3 fetal bovine serum, supplemented by concentration of 50, 100, 200,300 μg/mL MPE for 7-14 days. Dithizone (DTZ) staining was used to detect IPCs derived from EBs in vitro. Mouse monoclonal insulin-proinsulin and monoclonal insulin receptor beta antibodies were used for immunoflourescence. Insulin content from the cells and insulin secreted by differentiated cells in response to concentrations of 5.5 and 25 mM glucose were measured using ELISA kits. Results: DTZ-positive cells showed purple-red clusters. immunoflourescence indicated expression of Beta cell markers (insulin-proinsulin and insulin receptor beta) in these cells. Increasing glucose concentration, caused more insulin to be secreted by differentiated cells. Conclusions: P19 cells can in the presence of pancreas extract differentiate to cell producing and secreting insulin cells. Differentiated cells can increase insulin secretion in response to increasing glucose medium

Modeling and Control of a Smart Single-Layer Graphene Sheet

In this study, a smart single-layer graphene sheet (SLGS) is analytically modeled and its buckling is controlled using coupled polyvinylidene fluoride (PVDF) nanoplates. A voltage is applied to the PVDF nanoplate in thickness direction in order to control the critical load of the SLGS. Electric potential distribution is assumed as a combination of a half-cosine and linear variation in order to satisfy the Maxwell equation. The exact analysis is performed for the case when all four ends are simply supported and in free electrical boundary condition. The nonlocal governing equations are derived through Hamilton’s principle and energy method based on a nonlocal Mindlin plate theory. The detailed mathematical derivations are presented and numerical investigations are performed, while the emphasis is placed on investigating the effect of several parameters such as small-scale coefficient, stiffness of the internal elastic medium, graphene length, mode number, and external electric voltage on the buckling smart control of the SLGS in detail. It is explicitly shown that the imposed external voltage is an effective controlling parameter for buckling of the SLGS. Numerical results are presented to serve as benchmarks for design and smart control of nanodevices