Tensor B-spline numerical method for PDEs : a high performance approach

Solutions of Partial Differential Equations (PDEs) form the basis of many mathematical models in physics and medicine. In this work, a novel Tensor B-spline methodology for numerical solutions of linear second-order PDEs is proposed. The methodology applies the B-spline signal processing framework and computational tensor algebra in order to construct high-performance numerical solvers for PDEs. The method allows high-order approximations, is mesh-free, matrix-free and computationally and memory efficient. The first chapter introduces the main ideas of the Tensor B-spline method, depicts the main contributions of the thesis and outlines the thesis structure. The second chapter provides an introduction to PDEs, reviews the numerical methods for solving PDEs, introduces splines and signal processing techniques with B-splines, and describes tensors and the computational tensor algebra. The third chapter describes the principles of the Tensor B-spline methodology. The main aspects are 1) discretization of the PDE variational formulation via B-spline representation of the solution, the coefficients, and the source term, 2) introduction to the tensor B-spline kernels, 3) application of tensors and computational tensor algebra to the discretized variational formulation of the PDE, 4) tensor-based analysis of the problem structure, 5) derivation of the efficient computational techniques, and 6) efficient boundary processing and numerical integration procedures. The fourth chapter describes 1) different computational strategies of the Tensor B-spline solver and an evaluation of their performance, 2) the application of the method to the forward problem of the Optical Diffusion Tomography and an extensive comparison with the state-of-the-art Finite Element Method on synthetic and real medical data, 3) high-performance multicore CPU- and GPU-based implementations, and 4) the solution of large-scale problems on hardware with limited memory resources

Colloidal nanoparticle inks for printing of active layers in an optoelectronic device

A method of manufacturing of an ink (100) composition comprises a biphasic ligand exchange process. A first phase liquid (10) comprising a nonpolar solvent (11) with a colloidal suspension of nanoparticles (1) that are capped with a shell of non polar ligands (2) is contacted with a second phase liquid (20) comprising a polar solvent (21) with second ligand (3). The second ligand comprises at least one surface binding head group that has an affinity for binding to the nanoparticle; and an ionically charged tail group. The second ligands displace the first ligands to form a dispersion of the nanoparticles that are capped with a shell of the second ligands in the second phase liquid. The nanoparticles can be separated from the second phase liquid. The separated nanoparticles can be (re)dispersed in a printable liquid medium, e.g. used for printing a photoactive layer

Legal principles of organic production in Ukraine: Realities and prospects

purpose of the article is to consider the prospects of Ukraine concerning attraction of foreign investments into production of organic products. Formal-legal, materialist dialectics and comparative-legal methods are used. The attention is focused on the subjects of legal relations concerning organic production, in particular, on joint ventures with attraction of foreign capital, the stages of certification regarding the production of organic products. The temporary restrictions on the possession of agricultural land in some EU countries and in Ukraine have been analyzed. A comparative analysis of land lease institutions and the right to use another's land for agricultural needs (emphyteusis) has been carried out

Legal principles of organic production in Ukraine: realities and prospects

The purpose of the article is to consider the prospects of Ukraine concerning attraction of foreign investments into production of organic products. Formal-legal, materialist dialectics and comparative-legal methods are used. The attention is focused on the subjects of legal relations concerning organic production, in particular, on joint ventures with attraction of foreign capital, the stages of certification regarding the production of organic products. The temporary restrictions on the possession of agricultural land in some EU countries and in Ukraine have been analyzed. A comparative analysis of land lease institutions and the right to use another’s land for agricultural needs (emphyteusis) has been carried out.Розглянуті перспективи України щодо залучення іноземних інвестицій у виробництво органічної продукції. Акцентовано увагу на суб’єктах правовідносин щодо органічного виробництва, зокрема, на спільних підприємствах із залученням іноземного капіталу, стадіях сертифікації щодо здійснення виробництва органічної продукції. Проаналізовані тимчасові обмеження володіння землями сільськогосподарського призначення в деяких країнах ЄС та в Україні. Здійснено порівняльний аналіз інститутів оренди землі та права користування чужою земельною ділянкою для сільськогосподарських потреб (емфітевзису).Рассмотрены перспективы Украины по привлечению иностранных инвестиций в производство органической продукции. Акцентировано внимание на субъектах правоотношений по органическому производству, в частности, на совместных предприятиях с привлечением иностранного капитала, стадиях сертификации по осуществлению производства органической продукции. Проанализированы временные ограничения владения землями сельскохозяйственного назначения в некоторых странах ЕС и в Украине. Осуществлен сравнительный анализ институтов аренды земли и права пользования чужим земельным участком для сельскохозяйственных нужд (эмфитевзис)