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Analysis of multivariate repeated measures data using a MANOVA model and principal components

. Lancaster P., Tismenetsky M. (1985): The Theory of Matrices, Second Edition: With Applications. Academic Press, Orlando. Mathew T. (1989): MANOVA in the multivariate components of variance model. Journal of Multivariate Analysis 29: 30-38. Naik D. N., Rao S. (2001): Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix. J. Appl. Statist. 28: 91-105. Ortega J. M. (1987): Matrix Theory: A Second Course. Plenum Press, New York. Reinsel G. (1982): Multivariate

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On Controllability of Fuzzy Dynamical Matrix Lyapunov Systems

References [1] Alexander Graham, Kronecker products and matrix calculus with applications, Ellis Horwood Ltd., England, 1981 [2] R.J.Aumann, Integrals of set-valued functions, Journal of Mathematical Analysis and Applications, 12, (1965), 1-12 [3] J.B.Conway, A course in functional analysis, Springer-Verlag, New York, 1990 [4] G.Debreu, Integration of correspondence, in: Proc. Fifth Berkeley Symp. Math. Statist. Probab. Part 1(Univ. California Press, Berkeley, CA), 2, (1967), 351

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Union of Distance Magic Graphs

.K. Jha, S. Klažar and B. Zmazek, Isomorphic components of Kronecker product of bipartite graphs , Preprint Ser. Univ. Ljubljana 32 (1994) no. 452. [19] R.H. Lamprey and B.H. Barnes, Product graphs and their applications , in: Proc. Fifth Annual Pittsburgh Conference, Instrument Society of America, Pittsburgh, PA, 1974, Modelling and Simulation 5 (1974) 1119–1123. [20] M.K. Shafiq, G. Ali and R. Simanjuntak, Distance magic labelings of a union of graphs , AKCE Int. J. Graphs. Combin. 6 (2009) 191–200. [21] M. Miller, C. Rodger and R

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Use of α-resolvable designs in the construction of two-factor experiments of split-plot type


We consider an incomplete split-plot design (ISPD) with two factors generated by the semi-Kronecker product of two α-resolvable designs. We use an α-resolvable design for the whole plot treatments and an affine α-resolvable design for the subplot treatments. We characterize the ISPDs with respect to the general balance property, and we give the stratum efficiency factors for the ISPDs.

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Incomplete split-block designs constructed by affine α-resolvable designs


We construct an incomplete split-block design (ISBD) by the semi- Kronecker product of two affine α-resolvable designs for row and column treatments. We characterize such ISBDs with respect to the general balance property and we give the stratum efficiency factors for the ISBDs.

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Covariance regularization for metabolomic data on the drought resistance of barley

International Conference on Acoustics, Speech and Signal Processing III, Honolulu, 3: 1021–1024. Cui X., Li X., Zhao J., Zeng L., Zhang D., Pan J. (2016): Covariance structure regularization via Frobenius norm discrepancy. Linear Algebra Appl. 510: 124–145. Dey D.K., Srinivasan C. (1985): Estimation of a covariance matrix under Stein’s loss. Ann. Statist. 13(4): 1581–1591. Filipiak K., Klein D. (2018a): Approximation with Kronecker product structure with one component as compound symmetry or autoregression. Linear Algebra and Its Applications 559: 11

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Maximum Independent Sets in Direct Products of Cycles or Trees with Arbitrary Graphs

the Carte- sian product of caterpillars, Ars Combin. 60 (2001) 73-84. [16] T. Sitthiwirattham, Independent and vertex covering number on Kronecker product of Pn, Int. J. Pure Appl. Math. 73 (2011) 227-234. [17] T. Sitthiwirattham and J. Soontharanon, Independent and vertex covering number on Kronecker product of Cn, Int. J. Pure Appl. Math. 71 (2011) 149-157. [18] S. Špacapan, The k-independence number of direct products of graphs and Hedet- niemi’s conjecture, European J. Combin. 32 (2011) 1377-1383. doi:10.1016/j

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All intra-regular generalized hypersubstitutions of type (2)

Verlag, (2000), 135–145 [8] W. D. Neumann, Mal’cev Conditions, Spectra and Kronecker Product, J. Austral. Math. Soc.(A) , 25 (1987), 103–117. [9] M. Petrich, N. R. Reilly, Completely Regular Semigroups, John Wiley and Sons,Inc., New York, (1999). [10] W. Puninagool, S. Leeratanavalee, The Monoid of Generalized Hypersubstitutions of type τ = (n), Discussiones Mathematicae General Algebra and Applications , 30 (2010), 173–191. [11] Sl. Shtrakov, Essential Variables and Positions in Terms, Algebra Universalis , 61 (3-4) (2009), 381

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The Super-Connectivity of Kneser Graphs

Theory 8 (1984) 487-499. doi: 10.1002/jgt.3190080406 [5] G. Boruzanlı Ekinci and J.B. Gauci, On the reliability of generalized Petersen graphs, Discrete Appl. Math., in press. doi: 10.1016/j.dam.2017.02.002 [6] G. Boruzanlı Ekinci and A. Kırlangi¸c, Super connectivity of Kronecker product of complete bipartite graphs and complete graphs, Discrete Math. 339 (2016) 1950-1953. doi: 10.1016/j.disc.2015.10.036 [7] B.-L. Chen and K.-W. Lih, Hamiltonian uniform subset graphs, J. Combin. Theory, Ser. B 42 (1987) 257-263. doi: 10

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On The Ψ – Asymptotic Stability Of Nonlinear Lyapunov Matrix Differential Equations

. Massera and J. J. Sch¨affer, Linear differential equations and functional analysis, I, Ann. of math. 67, (1958), 517 - 573. [8] M. S. N. Murty and B. V. Apparao, On two point boundary value problems for ˙X = AX + XB, Ultra Science, 16(2)M, (2004), 223 - 227. [9] M. S. N. Murty and B. V. Apparao, Two point boundary value problems for matrix differential equations, Journal of the Indian Math. Soc., Vol. 73, Nos. 1-2, (2006), 1-7. [10] M. S. N. Murty and B. V. Apparao, Kronecker product boundary value problems - existence and

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