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Computer simulation of the partitioning by mutually orthogonal lines
2019 IEEE 15th International Conference on the Experience of Designing and Application of CAD Systems (CADSM), 2019The partitioning problem of areas into regions along mutually orthogonal lines is considered. A mathematical model of the problem has been proposed, taking into account economic, agrotechnical and fire prevention restrictions. A method has been developed for obtaining a local-optimal partition of a given region based on the construction of two ...
Valentina Komyak +6 more
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The partitioning of an orthogonal group in six variables
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1958Abstract An orthogonal group of projectivities in six variables is partitioned into 31 disjoint sets; 17 of these constitute a subgroup, of index 2 and order 3265920, isomorphic to a group already known in great detail in another representation. The ambient space is finite, of five dimensions; its points fall into three batches of 126,
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New partitioning schemes for parallel modified Gram-Schmidt orthogonalization
Proceedings of the 1997 International Symposium on Parallel Architectures, Algorithms and Networks (I-SPAN'97), 2002In this paper we are concerned with parallel implementation of row-oriented Gram-Schmidt orthogonalization. For the data partitioning four types of columnwise partitioning schemes were considered: column (1-col), block, cyclic and block-cyclic (b-c) partitioning.
Suely Oliveira, Takako Soma
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An Orthogonal Partitioning Approach to Simplify Robust Model Predictive Control
Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005., 2005The main limitation of many robust model predictive control (MPC) algorithms is the formidable on-line computational complexity. For linear discrete-time systems with a polytopic uncertainty description, a new efficient algorithm to determine an approximate explicit state feedback solution to robust MPC is developed.
Marcin T. Cychowski +2 more
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Binary Space Partition for Orthogonal Fat Rectangles
2003We generate a binary space partition (BSP) of size O(n log8 n) and depth O(n log4 n) for n orthogonal fat rectangles in three-space, improving earlier bounds of Agarwal et al. We also give a lower bound construction showing that the size of an orthogonal BSP for these objects is Ω(n log n) in the worst case.
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A Fundamental Partition in Models with Commutative Orthogonal Block Structure
AIP Conference Proceedings, 2011Models with commutative orthogonal block structure, COBS, constitute an interesting class of models with orthogonal block structure, OBS, in which the orthogonal projection matrix on the space Ω spanned by the mean vectors commute with the known pairwise orthogonal projection matrices Q1,…, Qm that figure in the expression of the variance‐covariance ...
Francisco Carvalho +7 more
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Orthogonal and Nonorthogonal Methods for Partitioning Regression Variance
American Educational Research Journal, 1971Bottenberg and Ward's (1963) developments of the generalized exploitation of multiple linear regression and of their concept of "independent contributions" of variable sets in regression composites were based on Mood's distinction. Stimulated by these developments, two of their colleagues published a systematic application of the Bottenberg-Ward ...
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ORTHOGONAL PARTITIONS OF THE 5 × 5 LATIN SQUARES
Annals of Eugenics, 1946The articles published by the Annals of Eugenics (1925–1954) have been made available online as an historical archive intended for scholarly use. The work of eugenicists was often pervaded by prejudice against racial, ethnic and disabled groups. The online publication of this material for scholarly research purposes is not an endorsement of those views
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Orthogonality and Linear Sufficiency in Partitioned and Reduced Linear Models
Communications in Statistics - Theory and Methods, 2011The partitioned linear model ℳ12 is considered together with the reduced counterparts ℳ2 and ℳ(2), which are free from nuisance parameters present in ℳ12. The conditions are established under which the best linear unbiased estimator of parametric functions in the reduced model ℳ2(ℳ(2)) preserves its optimality in ℳ12.
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Automorphisms of orthogonal decompositions and of group algebras of groups with partitions
Sbornik: Mathematics, 1995Summary: This article is devoted to an investigation of the following conjecture. If \(\{H_i\}\) is a family of subgroups that partition a finite group \(G\), then every automorphism \(\sigma\) of the group algebra \(\mathbb{C}[G]\) that permutes the subalgebras \(\mathbb{C}[H_i]\) also permutes the lines \(\mathbb{C}\cdot g\), \(g\in G\).
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