Geometric properties of Blaschke-like maps on domains with a conic boundary

For a circle $C$ contained in the unit disk, the necessary and sufficient condition for the existence of a triangle inscribed in the unit circle and circumscribed about $C$ is known as Chapple's formula. The geometric properties of Blaschke products of degree 3 given by Daepp et al. (2002) and Frantz (2004) allow us to extend Chapple's formula to the case of ellipse in the unit disk. The main aim of this paper is to prvide a further extension of Chapple's formula. Introducing a Blaschke-like map of a domain whose boundary is a conic, we extend their results to the case that the outer curve is an ellipse or a parabola. Moreover, we also give some geometrical properties for the Blaschke-like maps of degree $d$.Comment: 18 pages, 7 figure

Reaction Behavior of a Silicide Electrode with Lithium in an Ionic-Liquid Electrolyte

Silicides are attractive novel active materials for use in the negative-electrodes of next-generation lithium-ion batteries that use certain ionic-liquid electrolytes; however, the reaction mechanism of the above combination is yet to be clarified. Possible reactions at the silicide electrode are as follows: deposition and dissolution of Li metal on the electrode, lithiation and delithiation of Si, which would result from the phase separation of the silicide, and alloying and dealloying of the silicide with Li. Herein, we examined these possibilities using various analysis methods. The results revealed that the lithiation and delithiation of silicide occurred

Unveiling the role of differential growth in 3D morphogenesis: An inference method to analyze area expansion rate distribution in biological systems

The three-dimensional (3D) morphologies of many organs in organisms, such as the curved shapes of leaves and flowers, the branching structure of lungs, and the exoskeletal shape of insects, are formed through surface growth. Although differential growth, a mode of surface growth, has been qualitatively identified as 3D morphogenesis, a quantitative understanding of the mechanical contribution of differential growth is lacking. To address this, we developed a quantitative inference method to analyze the distribution of the area expansion rate, which governs the growth of surfaces into 3D morphology. To validate the accuracy of our method, we tested it on a basic 3D morphology that allowed for the theoretical derivation of the area expansion rate distribution, and then assessed the difference between the predicted outcome and the theoretical solution. We also applied this method to complex 3D shapes and evaluated its accuracy through numerical experiments. The findings of the study revealed a linear decrease in error on a log-log scale with an increase in the number of meshes in both evaluations. This affirmed the reliability of the predictions for meshes that are sufficiently refined. Moreover, we employed our methodology to analyze the developmental process of the Japanese rhinoceros beetle Trypoxylus dichotomus, which is characterized by differential growth regulating 3D morphogenesis. The results indicated a notably high rate of area expansion on the left and right edges of the horn primordium, which is consistent with the experimental evidence of a higher rate of cell division in these regions. Hence, these findings confirm the efficacy of the proposed method in analyzing biological systems

GPU Based Software Correlators - Perspectives for VLBI2010

Caused by historical separation and driven by the requirements of the PC gaming industry, Graphics Processing Units (GPUs) have evolved to massive parallel processing systems which entered the area of non-graphic related applications. Although a single processing core on the GPU is much slower and provides less functionality than its counterpart on the CPU, the huge number of these small processing entities outperforms the classical processors when the application can be parallelized. Thus, in recent years various radio astronomical projects have started to make use of this technology either to realize the correlator on this platform or to establish the post-processing pipeline with GPUs. Therefore, the feasibility of GPUs as a choice for a VLBI correlator is being investigated, including pros and cons of this technology. Additionally, a GPU based software correlator will be reviewed with respect to energy consumption/GFlop/sec and cost/GFlop/sec

Developmental Link between Sex and Nutrition; \u3ci\u3edoublesex\u3c/i\u3e Regulates Sex-Specific Mandible Growth via Juvenile Hormone Signaling in Stag Beetles

Sexual dimorphisms in trait expression are widespread among animals and are especially pronounced in ornaments and weapons of sexual selection, which can attain exaggerated sizes. Expression of exaggerated traits is usually male-specific and nutrition sensitive. Consequently, the developmental mechanisms generating sexually dimorphic growth and nutritiondependent phenotypic plasticity are each likely to regulate the expression of extreme structures. Yet we know little about how either of these mechanisms work, much less how they might interact with each other. We investigated the developmental mechanisms of sex-specific mandible growth in the stag beetle Cyclommatus metallifer, focusing on doublesex gene function and its interaction with juvenile hormone (JH) signaling. doublesex genes encode transcription factors that orchestrate male and female specific trait development, and JH acts as a mediator between nutrition and mandible growth. We found that the Cmdsx gene regulates sex differentiation in the stag beetle. Knockdown of Cmdsx by RNA-interference in both males and females produced intersex phenotypes, indicating a role for Cmdsx in sex-specific trait growth. By combining knockdown of Cmdsx with JH treatment, we showed that female-specific splice variants of Cmdsx contribute to the insensitivity of female mandibles to JH: knockdown of Cmdsx reversed this pattern, so that mandibles in knockdown females were stimulated to grow by JH treatment. In contrast, mandibles in knockdown males retained some sensitivity to JH, though mandibles in these individuals did not attain the full sizes of wild type males. We suggest that moderate JH sensitivity of mandibular cells may be the default developmental state for both sexes, with sex-specific Dsx protein decreasing sensitivity in females, and increasing it in males. This study is the first to demonstrate a causal link between the sex determination and JH signaling pathways, which clearly interact to determine the developmental fates and final sizes of nutrition-dependent secondary-sexual characters

The Shiga toxin 2 production level in enterohemorrhagic Escherichia coli O157:H7 is correlated with the subtypes of toxin-encoding phage

Enterohemorrhagic E. coli (EHEC) causes diarrhea and hemorrhagic colitis with life-threatening complications, such as hemolytic uremic syndrome. Their major virulence factor is Shiga toxin (Stx), which is encoded by bacteriophages. Of the two types of Stx, the production of Stx2, particularly that of Stx2a (a subtype of Stx2), is a major risk factor for severe EHEC infections, but the Stx2 production level is highly variable between strains. Here, we define four major and two minor subtypes of Stx2a-encoding phages according to their replication proteins. The subtypes are correlated with Stx2a titers produced by the host O157 strains, suggesting a critical role of the phage subtype in determining the Stx2a production level. We further show that one of the two subclades in the clade 8, a proposed hyper-virulent lineage of O157, carries the Stx2 phage subtype that confers the highest Stx2 production to the host strain. The presence of this subclade may explain the proposed high virulence potential of clade 8. These results provide novel insights into the variation in virulence among O157 strains and highlight the role of phage variation in determining the production level of the virulence factors that phages encode

Cytology of malignant endocrine tumor of the pancreas : A case report

We report here a case of malignant endocrine tumor of the pancreas with lymph node metastasis in a 67-year-old woman. The cytologic preparations ex-hibited small cells having uniform round eccentrically located nuclei and large cells showing irregular-shaped nuclei with coarse chromatin and pleomorphism. The histologic, immunohistochemical and ultrastructural findings were characte-ristic of pancreatic endocrine tumor, regardless of immunophenotypic hetero-geneity. The heterogeneity observed in cytologic specimens may be important in predicting the malignant potential of this tumor group