scholarly journals On the concentration of random multilinear forms and the universality of random block matrices

2014 ◽  
Vol 162 (1-2) ◽  
pp. 97-154 ◽  
Author(s):  
Hoi H. Nguyen ◽  
Sean O’Rourke
Keyword(s):  
Block Matrices ◽  
Multilinear Forms ◽  
Random Block ◽  
Random Block Matrices

𝑉-law for random block matrices under the generalized Lindeberg condition

2019 ◽  
Vol 27 (3) ◽  
pp. 177-198
Author(s):  
Vyacheslav L. Girko
Keyword(s):  
Random Matrices ◽  
Stochastic Matrix ◽  
Block Matrices ◽  
Lindeberg Condition ◽  
Random Block ◽  
Random Block Matrices

Abstract The V-law under generalized Lindeberg condition for the independent blocks of random matrices having double stochastic matrix of covariances and different expectations of their array is proven.

V-density for eigenvalues of random block matrices with independent blocks whose entries have different variances and expectations

2019 ◽  
Vol 27 (3) ◽  
pp. 161-165
Author(s):  
Vyacheslav L. Girko ◽  
L. D. Shevchuk
Keyword(s):  
Random Matrices ◽  
Block Matrices ◽  
Lindeberg Condition ◽  
Random Block ◽  
Random Block Matrices

Abstract V-density under Lindeberg condition for the independent blocks of random matrices having different variances and expectations is found.

scholarly journals Random block matrices generalizing the classical Jacobi and Laguerre ensembles

2010 ◽  
Vol 101 (8) ◽  
pp. 1884-1897
Author(s):  
Matthias Guhlich ◽  
Jan Nagel ◽  
Holger Dette
Keyword(s):  
Block Matrices ◽  
Random Block ◽  
Random Block Matrices

Largest eigenvalue of large random block matrices: A combinatorial approach

2017 ◽  
Vol 06 (02) ◽  
pp. 1750008
Author(s):  
Debapratim Banerjee ◽  
Arup Bose
Keyword(s):  
Block Structure ◽  
Extreme Points ◽  
Block Size ◽  
Relative Growth ◽  
Largest Eigenvalue ◽  
Block Matrices ◽  
Variance Formula ◽  
The Matrix ◽  
Random Block ◽  
Symmetric Block

We study the largest eigenvalue of certain block matrices where the number of blocks and the block size both increase with suitable conditions on their relative growth. In one of them, we employ a symmetric block structure with large independent Wigner blocks and in the other we have the Wigner block structure with large independent symmetric blocks. The entries are assumed to be independent and identically distributed with mean [Formula: see text] variance [Formula: see text] with an appropriate growth condition on the moments. Under our conditions the limit spectral distribution of these matrices is the standard semi-circle law. It is natural to ask if the extreme eigenvalues converge to the extreme points of its support, namely [Formula: see text]. We exhibit models where this indeed happens as well as models where the spectral norm converges to [Formula: see text]. Our proofs are based on combinatorial analysis of the behavior of the trace of large powers of the matrix.

THE IMPACT OF MINERAL FERTILIZERS ON THE BIOLOGICAL YIELD OF SUGAR BEET CROP (BETA VULGARIS L. VAR. SACCHARIFERA)

2018 ◽  
Vol 28 (4) ◽  
pp. 1281-1284
Author(s):  
Petar Petrov ◽  
Bojan Mitrovski
Keyword(s):  
Sugar Beet ◽  
Field Trials ◽  
Mineral Fertilizers ◽  
Qualitative Properties ◽  
New Production ◽  
Economic Significance ◽  
Random Block ◽  
Biological Yield ◽  
Sugar Beet Crop ◽  
The Impact

Due to the great economic significance of the sugar beet, the new production trends are aimed at improving the quantitative and qualitative properties and one of the basic agro technical measures that is directly dependent on the yield and quality of the turnip is the properly conducted plant nutrition. Exporting high quantities of nutrients from the soil, the sugar beet requires application of advanced agro-technology, primarily application of adequate and controlled nutrition and irrigation. Application of this measure, in combination with soil processing, has sustained influence over the following cultures in the crop rotation in terms of nutrients regiment and fight against weeds.In order to determine the effects of mineral fertilizers on sugar beet, field experiment was conducted on fluvisol soil. The experiment is set according to a random block system, following the standard methods of agricultural chemistry for conducting field trials. The experiment includes eight variants, as follows: 1. Control (non-fertilized), 2. NP, 3. NK, 4. PK, 5. NPK, 6. N2PK, 7. N2P2K, 8. N3PK.In the phase of technological maturity of sugar beet, collection of the vegetative material and measurement of the height of the biological yield of the turnips was carried out. Based on the survey results, it can be concluded that the variant N2P2K has achieved the highest yield of swollen roots, i.e. 69.330 kg/ha. The highest yield of leafy greens was achieved in the variant N3PK, i.e. 41.920 kg/ha, which indicates the fact that nitrogen has direct influence over the vegetation mass of sugar beet.

scholarly journals Increasing selection gain and accuracy of harvest prediction models in Jatropha through genome-wide selection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adriano dos Santos ◽  
Erina Vitório Rodrigues ◽  
Bruno Galvêas Laviola ◽  
Larissa Pereira Ribeiro Teodoro ◽  
Paulo Eduardo Teodoro ◽  
...  
Keyword(s):  
Prediction Models ◽  
Block Design ◽  
Phenotypic Selection ◽  
Breeding Population ◽  
Breeding Cycle ◽  
Selection Cycle ◽  
Genome Wide ◽  
Random Block ◽  
Random Block Design ◽  
Number Of Individuals

AbstractGenome-wide selection (GWS) has been becoming an essential tool in the genetic breeding of long-life species, as it increases the gain per time unit. This study had a hypothesis that GWS is a tool that can decrease the breeding cycle in Jatropha. Our objective was to compare GWS with phenotypic selection in terms of accuracy and efficiency over three harvests. Models were developed throughout the harvests to evaluate their applicability in predicting genetic values in later harvests. For this purpose, 386 individuals of the breeding population obtained from crossings between 42 parents were evaluated. The population was evaluated in random block design, with six replicates over three harvests. The genetic effects of markers were predicted in the population using 811 SNP's markers with call rate = 95% and minor allele frequency (MAF) > 4%. GWS enables gains of 108 to 346% over the phenotypic selection, with a 50% reduction in the selection cycle. This technique has potential for the Jatropha breeding since it allows the accurate obtaining of GEBV and higher efficiency compared to the phenotypic selection by reducing the time necessary to complete the selection cycle. In order to apply GWS in the first harvests, a large number of individuals in the breeding population are needed. In the case of few individuals in the population, it is recommended to perform a larger number of harvests.

Representations for the image-kernel (p,q)-inverses of block matrices in rings

2020 ◽  
Vol 27 (2) ◽  
pp. 297-305
Author(s):  
Dijana Mosić
Keyword(s):  
Block Matrix ◽  
Block Matrices ◽  
Schur Form

AbstractWe present the conditions for a block matrix of a ring to have the image-kernel{(p,q)}-inverse in the generalized Banachiewicz–Schur form. We give representations for the image-kernel inverses of the sum and the product of two block matrices. Some characterizations of the image-kernel{(p,q)}-inverse in a ring with involution are investigated too.

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