Displaying similar documents to “On the twin designs with the Ionin-type parameters.”

Certain new M-matrices and their properties with applications

Ratnakaram N. Mohan, Sanpei Kageyama, Moon H. Lee, G. Yang (2008)

Discussiones Mathematicae Probability and Statistics

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The Mₙ-matrix was defined by Mohan [21] who has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [6], Ehrlich [9], Ehrlich and Zeller [10], and Wang [34]. But in this paper, while giving some resemblances of this matrix with a Hadamard matrix, and by naming it as an M-matrix, we show how to construct partially balanced incomplete block designs and some regular graphs by it. Two types of these...

Optimal chemical balance weighing designs for v + 1 objects

Bronisław Ceranka, Małgorzata Graczyk (2003)

Kybernetika

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The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for p = v objects implies the existence of an optimum chemical balance weighing design for p = v + 1 objects are given. The existence of an optimum chemical balance weighing design for p = v + 1 objects implies the existence of an optimum...

X −1 -balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

Ryszard Walkowiak (2015)

Biometrical Letters

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This paper considers block designs and row-column designs where the information matrix C has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity h−1, where h is the rank of the matrix C. It was found that for each such design there exists a diagonal positive definite matrix X such that the design is X −1-balanced.

Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Mateva, Zlatka (2008)

Serdica Journal of Computing

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Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487. The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based...

Efficiency of cropping system designs via base contrast

U. Bronowicka-Mielniczuk, J. Mielniczuk, T. Przybysz (2000)

Applicationes Mathematicae

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The present article is a continuation of previous papers by the same authors devoted to the efficiency of crop rotation experiments. We focus on plans distinguished by the cyclical pattern of the incidence matrix. For practical reasons, we slightly modify the efficiency coefficient. The relation between the resulting efficiency coefficients is examined. In addition, we provide a background material on crop rotation experiments.

Two-level Cretan matrices constructed using SBIBD

N. A. Balonin, Jennifer Seberry (2015)

Special Matrices

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Two-level Cretan matrices are orthogonal matrices with two elements, x and y. At least one element per row and column is 1 and the other element has modulus ≤ 1. These have been studied in the Russian literature for applications in image processing and compression. Cretan matrices have been found by both mathematical and computational methods but this paper concentrates on mathematical solutions for the first time. We give, for the first time, families of Cretan matrices constructed...

Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors

Bronisław Ceranka, Małgorzata Graczyk (2004)

Discussiones Mathematicae Probability and Statistics

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In this paper we study the estimation problem of individual measurements (weights) of objects in a model of chemical balance weighing design with diagonal variance - covariance matrix of errors under the restriction k₁ + k₂ < p, where k₁ and k₂ represent the number of objects placed on the right and left pans, respectively. We want all variances of estimated measurments to be equal and attaining their lower bound. We give a necessary and sufficient condition under which this lower...