Matrix decomposition algorithms for elliptic boundary value problems: a survey

We provide an overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable elliptic boundary value problems in the unit square. An MDA is a direct method which reduces the algebraic problem to one of solving a set of independent one-dimensional problems which are generally banded, block tridiagonal, or almost block diagonal. Often, fast Fourier transforms (FFTs) can be employed in an MDA with a resulting computational cost of O(N ² logN) on an N × N uniform partition of the unit square. To formulate MDAs, we require knowledge of the eigenvalues and eigenvectors of matrices arising in corresponding two–point boundary value problems in one space dimension. In many important cases, these eigensystems are known explicitly, while in others, they must be computed. The first MDAs were formulated almost fifty years ago, for finite difference methods. Herein, we discuss more recent developments in the formulation and application of MDAs in spline collocation, finite element Galerkin and spectral methods, and the method of fundamental solutions. For ease of exposition, we focus primarily on the Dirichlet problem for Poisson’s equation in the unit square, sketch extensions to other boundary conditions and to more involved elliptic problems, including the biharmonic Dirichlet problem, and report extensions to three dimensional problems in a cube. MDAs have also been used extensively as preconditioners in iterative methods for solving linear systems arising from discretizations of non-separable boundary value problems.     

Tensor rank and stochastic entanglement catalysis for multipartite pure states

The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state |W3>=1/√3(|100> + |010> + |001>) and its N-partite generalization |W(N)>. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of |W3> have a rank of either 15 or 16, (ii) two copies of |W(N)> have a rank of 3N - 2, and (iii) n copies of |W(N)> have a rank of O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states.     

Studies of adsorption equilibria and kinetics in the systems: Aqueous solution of dyes-mesoporous carbons

Two carbonaceous materials were synthesized by using the method of impregnation of mesoporous silicas obtained by applying the Pluronic copolymers as pore-creating agents. The isotherms of adsorption of methylene blue and methyl orange from aqueous solutions were measured by the static method. The profiles of adsorbate concentration change in time were obtained from the UV-vis spectra. The adsorption isotherms and kinetic dependence were discussed in the terms of theory of adsorption on heterogeneous surfaces.     

Ma?analytische Verfahren der Invertzuckerbestimmung

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Mikrogefüge und Kolloidnatur der Kohle und Kohlengesteine

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Problem structuring in project management: an application of soft systems methodology (SSM)

Recent research suggests a major role for problem structuring methods (PSMs) in the field of project management, particularly at the front-end of projects, where objectives are often unclear and where different constituencies have conflicting aims. This paper presents a case example of soft systems methodology (SSM) at the front-end of a major project within Tesco Stores Ltd. A detailed account of the intervention is given, including the results achieved and a discussion of how the methodology was used for multiple purposes within the same intervention. Within the literature, there remains a lack of detailed examples from which people can learn more about the use of PSMs in project management. By providing a detailed example of SSM in action, this paper seeks to highlight the importance of problem structuring at the front-end of projects and the potential role an approach such as SSM can play at this crucial stage.     

Ueber Nachweis und Bestimmung der Salzs?ure im Magensaft

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