Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

Intron Dynamics in Ribosomal Protein Genes

The role of spliceosomal introns in eukaryotic genomes remains obscure. A large scale analysis of intron presence/absence patterns in many gene families and species is a necessary step to clarify the role of these introns. In this analysis, we used a maximum likelihood method to reconstruct the evolution of 2,961 introns in a dataset of 76 ribosomal protein genes from 22 eukaryotes and validated the results by a maximum parsimony method. Our results show that the trends of intron gain and loss differed across species in a given kingdom but appeared to be consistent within subphyla. Most subphyla in the dataset diverged around 1 billion years ago, when the “Big Bang” radiation occurred. We speculate that spliceosomal introns may play a role in the explosion of many eukaryotes at the Big Bang radiation

Loss of Ribosomal Protein L11 Affects Zebrafish Embryonic Development through a p53-Dependent Apoptotic Response

Ribosome is responsible for protein synthesis in all organisms and ribosomal proteins (RPs) play important roles in the formation of a functional ribosome. L11 was recently shown to regulate p53 activity through a direct binding with MDM2 and abrogating the MDM2-induced p53 degradation in response to ribosomal stress. However, the studies were performed in cell lines and the significance of this tumor suppressor function of L11 has yet to be explored in animal models. To investigate the effects of the deletion of L11 and its physiological relevance to p53 activity, we knocked down the rpl11 gene in zebrafish and analyzed the p53 response. Contrary to the cell line-based results, our data indicate that an L11 deficiency in a model organism activates the p53 pathway. The L11-deficient embryos (morphants) displayed developmental abnormalities primarily in the brain, leading to embryonic lethality within 6–7 days post fertilization. Extensive apoptosis was observed in the head region of the morphants, thus correlating the morphological defects with apparent cell death. A decrease in total abundance of genes involved in neural patterning of the brain was observed in the morphants, suggesting a reduction in neural progenitor cells. Upregulation of the genes involved in the p53 pathway were observed in the morphants. Simultaneous knockdown of the p53 gene rescued the developmental defects and apoptosis in the morphants. These results suggest that ribosomal dysfunction due to the loss of L11 activates a p53-dependent checkpoint response to prevent improper embryonic development

Ion cyclotron resonance heating system in the RT-1 magnetospheric plasma

We have developed an ion cyclotron resonance frequency (ICRF) heating system for the Ring Trap 1 (RT-1) magnetospheric device. We excite slow waves from the polar region of the dipole magnetic field. The target helium plasma is produced by electron cyclotron heating. The electrons comprise high-temperature (>10 keV) and low-temperature (<100 eV) components with both typically exhibiting densities of the same order of magnitude. The ICRF heating causes an increase in the ion temperatures and toroidal flow velocities in the core plasma region. We observe appreciable temperature differences between the different ion species (main He+ and impurity C2+), suggesting a strong influence of the charge-exchange loss, which caused the bulk ions to remain relatively cold (~20 eV) compared to the impurity ions (~40 eV). By developing an electro-optical measurement system, we have measured the local wave electric field in the plasma

On a Penrose-Fife Model with Zero Interfacial Energy Leading to a Phase-field System of Relaxed Stefan Type

In this paper we study an initial-boundary value Stefan-type problem with phase relaxation where the heat flux is proportional to the gradient of the inverse absolute temperature. This problem arises naturally as limiting case of the Penrose-Fife model for diffusive phase transitions with non-conserved order parameter if the coefficient of the interfacial energy is taken as zero. It is shown that the relaxed Stefan problem admits a weak solution which is obtained as limit of solutions to the Penrose-Fife phase-field equations. For a special boundary condition involving the heat exchange with the surrounding medium, also uniqueness of the solution is proved

On the Language of Standard Discrete Planes and Surfaces

International audienceA standard discrete plane is a subset of Z^3 verifying the double Diophantine inequality mu =< ax+by+cz < mu + omega, with (a,b,c) != (0,0,0). In the present paper we introduce a generalization of this notion, namely the (1,1,1)-discrete surfaces. We first study a combinatorial representation of discrete surfaces as two-dimensional sequences over a three-letter alphabet and show how to use this combinatorial point of view for the recognition problem for these discrete surfaces. We then apply this combinatorial representation to the standard discrete planes and give a first attempt of to generalize the study of the dual space of parameters for the latter [VC00]