Developing Structural Methods For Solving Boundary-Value Problems In Non-Smooth Boundary Domains

The paper presents the development of structural methods for solving boundary-value problems in complexshape domains to enhance calculation accuracy in the neighbourhood of angular points in the boundary-value problems solution domain. Structural methods allow building bases for solving mathematical physics boundary-value problems, which accurately account for the boundary conditions and geometric information on the domain form. These methods are based on using the mathematical tools of the theory of R-functions. They can dramatically extend the potentialities of variation methods when solving mathematical physics boundary-value problems in complexshape domains with different boundary conditions. The most common systems of R-operations used in practice are normalised; however, they are not smooth in point (0,0), and all smooth R-operations are not normalised. The paper presents the results of investigating the behaviour of smooth functions up to the domain boundary, which satisfy uniform Dirichlet and Neumann conditions, and the condition at which the function proper and its derivatives over the normal to a definite order are equal to zero. New approaches are offered to build basis functions that are smooth up to the non-smooth domain boundary and which meet the above-mentioned boundary conditions. The suggested new system of asymptotically normalised R-operations whose functions belong to the given smoothness class can be used to build smooth basis functions that satisfy certain boundary conditions. The approaches developed were tested for model problems, some of which were used for problems in modelling hydrodynamic fields in complex-shape domains

Environmental Factors Affecting the Expression of Bilateral-Symmetrical Traits in Plants

In recent years, there has been a growing interest in the problem of asymmetry of bilateral traits in plants. Three types of bilateral asymmetry are found in the leaf blade, of interest to ecologists and evolutionists. A brief review of the methods used in testing bilateral asymmetry and developmental stability discusses their role in the development of homeostasis and ontogenesis. Intra- and interspecific differences are considered on the example of woody plants under the influence of factors influencing the expression of bilaterally symmetry. The influence of stress on the manifestation of asymmetric traits is considered. Apparently, the climate and topography of the area play a more important role, determining the plastic and fluctuating variability. The relationship of plasticity, evolutionary canalization, and development stability is considered on the example of woody and cultivated plants. Plasticity and fluctuation variability are in a relationship coordinated by climatic conditions, primarily lighting and temperature. This, in turn, determines the mechanisms of gene regulatory networks. Thus, phenogenetics, which studies the patterns and mechanisms of gene expression and ontogenesis, is based on the data from field botanical studies of plant shape and asymmetry. Epigenetic and population studies of phenotypic variations play a role in standardizing and finding suitable plant species and varieties

Prompt photon hadroproduction in the k_T-factorization approach

We study the production of prompt photons at high energy in the framework of the k_T-factorization approach. The amplitude for production of a single photon associated with quark pair in the fusion of two off-shell gluons is calculated. Theoretical results are compared with the Tevatron data.Comment: 4 pages, 3 figures, to be published in the Proceedings of Workshop "Diffraction 2008", La Londe-les-Maures, France, Sept. 9-14, 200

Ultraviolet Raman Spectroscopy of Single and Multi-layer Graphene

We investigated Raman spectra of single-layer and multi-layer graphene under ultraviolet laser excitation at the wavelength of 325 nm. It was found that while the G peak of graphene remains pronounced in UV Raman spectra, the 2D band intensity undergoes severe quenching. The evolution of the ratio of the intensities of the G and 2D peaks, I(G)/I(2D), as the number of graphene layers n changes from n=1 to n=5, is different in UV Raman spectra from that in conventional visible Raman spectra excited at the 488 nm and 633 nm wavelengths. The 2D band under UV excitation shifts to larger wave numbers and is found near 2825 1/cm. The observed UV Raman features of graphene were explained by invoking the resonant scattering model. The obtained results contribute to the Raman nanometrology of graphene by providing an additional metric for determining the number of graphene layers and assessing its quality.Comment: 18 pages; 5 figures; submitted for publication on February 20, 200

Genome-wide changes in protein translation efficiency are associated with autism

We previously proposed that changes in the efficiency of protein translation are associated with autism spectrum disorders (ASDs). This hypothesis connects environmental factors and genetic factors because each can alter translation efficiency. For genetic factors, we previously tested our hypothesis using a small set of ASD-associated genes, a small set of ASD-associated variants, and a statistic to quantify by how much a single nucleotide variant (SNV) in a protein coding region changes translation speed. In this study, we confirm and extend our hypothesis using a published set of 1,800 autism quartets (parents, one affected child and one unaffected child) and genome-wide variants. Then, we extend the test statistic to combine translation efficiency with other possibly relevant variables: ribosome profiling data, presence/absence of CpG dinucleotides, and phylogenetic conservation. The inclusion of ribosome profiling abundances strengthens our results for male–male sibling pairs. The inclusion of CpG information strengthens our results for female–female pairs, giving an insight into the significant gender differences in autism incidence. By combining the single-variant test statistic for all variants in a gene, we obtain a single gene score to evaluate how well a gene distinguishes between affected and unaffected siblings. Using statistical methods, we compute gene sets that have some power to distinguish between affected and unaffected siblings by translation efficiency of gene variants. Pathway and enrichment analysis of those gene sets suggest the importance of Wnt signaling pathways, some other pathways related to cancer, ATP binding, and ATP-ase pathways in the etiology of ASDs