For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

The goal of this paper is to introduce the reader distinction between intensional and extensional as a different approaches meaning. We will argue that despite common belief, aspects mathematical notions can be, in fact have been successfully described mathematics. One for us particularly interesting notion deduction depicted general proof theory. Our considerations result defending a) importan...

In this paper, we propose a novel mesh repairing method for voids from several meshes to ensure desired topological correctness. The input our is closed and manifold without labels. basic idea of the search repair based on multi-labeled data structure graph theory. We judgment rules between void specified model priorities. It consists three steps: (a) converting into mesh; (b) searching quasi-v...

The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first pa...

SUMMARY A METHOD for assembling and managing global terrain data is presented, the Geodesic Elevation Model. Derived from concepts in geometry, geography , geodesy, applied mathematics and computer science, GEM is designed to digitally archive and access measurements of points given in latitude, longitude and elevation from any source, by embedding them in a regular, polyhedral data structure. ...

Article history: Received 7 August 2015 Received in revised form 21 January 2016 Accepted 22 January 2016 Available online 23 January 2016 In order to better understand the activity of the Akşehir normal fault in SW Turkey and the associated seismic hazard, we investigated the tectonic geomorphology of a 60-km stretch of the 100-km-long Akşehir fault block. The fault can be separated into seven...

Abstract To identify all desired shape parameters of granular particles with less computational cost, this study proposes a three‐dimensional convolutional neural network (3D‐CNN) based model. Datasets are made 100 ballast and Fujian sand particles, the (i.e., aspect ratio, roundness, sphericity, convexity) obtained by conventional methods used to label particles. For model training, feeding sl...

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