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Journal articles on the topic 'Generation of Latin squares'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

M., I. Garcia-Planas, and Roca-Borrego D. "Cyclic-union Operation to Obtain Latin Squares." British Journal of Mathematics & Computer Science 22, no. 5 (2017): 1–8. https://doi.org/10.9734/BJMCS/2017/33945.

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With the power that has taken the information technologies, one has developed the study and research about cryptography, and cryptanalysis, in which Latin squares are ideal candidates for being used in cryptographic systems because the Cayley tables of the nite groups are Latin squares. This fact has awakened a new interest in the study of Latin squares by applying them to the study of code theory and error correcting codes. They also play a significant role in the statistical theory of experimental design. In this work, we develop an algorithm for the generation of Latin squares based on the

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2

Fontana, Roberto. "Random Latin squares and Sudoku designs generation." Electronic Journal of Statistics 8, no. 1 (2014): 883–93. http://dx.doi.org/10.1214/14-ejs913.

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3

Kim, Beob G., and Hans H. Stein. "A spreadsheet program for making a balanced Latin Square design." Revista Colombiana de Ciencias Pecuarias 22, no. 4 (2009): 6. http://dx.doi.org/10.17533/udea.rccp.324493.

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Summary Latin square designs are often employed in animal experiments to minimize the number of animals required to detect statistical differences. Generally, potential carryover effects are not balanced out by randomization. Systemic methods are available for equalizing the residual effects. We have developed an Excel® spreadsheet-based program, the Balanced Latin Square Designer (BLSD), to facilitate the generation of Latin squares balanced for carryover effects. The program allows a user to input the number of treatments that is equal to the number of animals and periods in a square. A user

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Zolfaghari, Behrouz, Khodakhast Bibak, and Takeshi Koshiba. "From Random Numbers to Random Objects." Entropy 24, no. 7 (2022): 928. http://dx.doi.org/10.3390/e24070928.

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Many security-related scenarios including cryptography depend on the random generation of passwords, permutations, Latin squares, CAPTCHAs and other types of non-numerical entities. Random generation of each entity type is a different problem with different solutions. This study is an attempt at a unified solution for all of the mentioned problems. This paper is the first of its kind to pose, formulate, analyze and solve the problem of random object generation as the general problem of generating random non-numerical entities. We examine solving the problem via connecting it to the well-studie

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5

Strube, Michael J. "A BASIC program for the generation of Latin squares." Behavior Research Methods, Instruments, & Computers 20, no. 5 (1988): 508–9. http://dx.doi.org/10.3758/bf03202706.

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Johnson, Laura M., and Stephanie Perkins. "A Discussion of a Cryptographical Scheme Based in F-Critical Sets of a Latin Square." Mathematics 9, no. 3 (2021): 285. http://dx.doi.org/10.3390/math9030285.

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This communication provides a discussion of a scheme originally proposed by Falcón in a paper entitled “Latin squares associated to principal autotopisms of long cycles. Applications in cryptography”. Falcón outlines the protocol for a cryptographical scheme that uses the F-critical sets associated with a particular Latin square to generate access levels for participants of the scheme. Accompanying the scheme is an example, which applies the protocol to a particular Latin square of order six. Exploration of the example itself, revealed some interesting observations about both the structure of

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7

Jacobson, Mark T., and Peter Matthews. "Generating uniformly distributed random latin squares." Journal of Combinatorial Designs 4, no. 6 (1996): 405–37. http://dx.doi.org/10.1002/(sici)1520-6610(1996)4:6<405::aid-jcd3>3.0.co;2-j.

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Selvi, D., G. Velammal, and Thevasahayam Arockiadoss. "Modified Method of Generating Randomized Latin Squares." IOSR Journal of Computer Engineering 16, no. 1 (2014): 76–80. http://dx.doi.org/10.9790/0661-16187680.

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Saka, J. A., and O. O. Oyadare. "A general construction of mutually orthogonal latin squares of prime order." International Journal of Algebra and Statistics 7, no. 1-2 (2018): 77–93. http://dx.doi.org/10.20454/ijas.2018.1451.

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This paper presents a general method of constructing a complete set of Mutually Orthogonal Latin Squares (MOLS) of the order of any prime, via the use of generating functions dened on the nite eld of this order. Apart from using the generating function to get a complete set of Mutually Orthogonal Latin Squares, the studies of the generating functions opens up the possibility of getting at the deep structural properties of MOLS. Copious examples were given for detailed illustrations.

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10

SEBERRY, JENNIFER, and DONGVU TONIEN. "SOME CONSTRUCTIONS OF MUTUALLY ORTHOGONAL LATIN SQUARES AND SUPERIMPOSED CODES." Discrete Mathematics, Algorithms and Applications 04, no. 03 (2012): 1250022. http://dx.doi.org/10.1142/s179383091250022x.

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Superimposed codes is a special combinatorial structure that has many applications in information theory, data communication and cryptography. On the other hand, mutually orthogonal latin squares is a beautiful combinatorial object that has deep connection with design theory. In this paper, we draw a connection between these two structures. We give explicit construction of mutually orthogonal latin squares and we show a method of generating new larger superimposed codes from an existing one by using mutually orthogonal latin squares. If n denotes the number of codewords in the existing code th

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11

Yadav, Kaushal Kumar, Sukanta Dash, Baidya Nath Mandal, and Rajender Parsad. "Construction of Partially Balanced Semi-Latin Rectangles in Block Size Three." INTERNATIONAL JOURNAL OF AGRICULTURAL AND STATISTICAL SCIENCES 21, no. 01 (2025): 167. https://doi.org/10.59467/ijass.2025.21.167.

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Semi-Latin rectangles (SLR) are row-column designs, where each intersection contains the same number of experimental units, denoted as k > 1. Moreover, each treatment appears an equal number of times in each row (nr, say ) and in each column (nc, say ) (nr > 1 and nc > 1 may or may not be equal). Balanced Semi-Latin rectangles (BSLR) form a subset of SLR, extending the concepts of Latin squares and Semi-Latin squares (SLS). These designs are applicable in various agricultural and industrial experiments, particularly in scenarios where one effect is considered a column effect and the o

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Yadav, Kaushal Kumar, Sukanta Dash, Rajender Parsad, Baidya Nath Mandal, Anil Kumar, and Mukesh Kumar. "Construction of Partially Balanced Semi-Latin Rectangles with Block Size 4." Journal of the Indian Society of Agricultural Statistics 78, no. 2 (2024): 115–23. http://dx.doi.org/10.56093/jisas.v78i2.5.

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Semi-Latin rectangles represent row-column designs where each row-column intersection contains the same number of experimental units, denoted as k >1. Additionally, each treatment appears an equal number of times in each row ( r n , say) and in each column ( c n , say) ( 1 r n ≥ and 1 c n ≥ may or may not be same). Partially Balanced Semi-Latin rectangles (PBSLR) constitute a subset of Semi-Latin rectangles (SLR), serving as generalizations of Latin squares and Semi-Latin squares (SLS). These designs find utility in various agricultural and industrial experiments, particularly situations wh

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13

Kim, Beob Gyun, and Taemin Kim. "A program for making completely balanced Latin Square designs employing a systemic method." Revista Colombiana de Ciencias Pecuarias 23, no. 3 (2010): 277–82. http://dx.doi.org/10.17533/udea.rccp.324588.

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SummaryAnimal scientists employ Latin square designs to reduce the required number of animals for detecting statistical differences in animal experiments. Randomization procedures do not balance residual effects that possibly exist in Latin square experiments. A spreadsheet-based program is available for making Latin square designs balanced for the first-order residual effects. The balance of remote residual effects may also be very important to consider when a relatively long latent period exists after a treatment. We have developed a spreadsheet-based program, the Completely Balanced Latin S

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Bhagat, Sumit A., and Prashant M. Kakade. "Efficient Route Optimization using Distance Matrices for Generation of Latin Square." IJARCCE 6, no. 1 (2017): 380–82. http://dx.doi.org/10.17148/ijarcce.2017.6176.

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15

Galve-Górriz, Carmen, and Alejandro Hernández-Trasobares. "Institutional framework, concentration of ownership and results of large family corporations in Latin America and Spain." Corporate Governance 15, no. 4 (2015): 409–26. http://dx.doi.org/10.1108/cg-12-2014-0144.

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Purpose – This paper aims to clarify the relationship between institutional framework, concentration of ownership in family firms and results. Design/methodology/approach – Data comprises two samples of family firms from eight Latin American countries and Spain in the year 2010. The first sample contains the largest 20 corporations from each country. The second comprises the 20 largest listed family corporations in each country. To test the hypothesis, the study uses ordinary least squares. Findings – First, firms located in countries with a higher than average quality of the institutional and

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16

Zhang, Xuncai, Tao Wu, Yanfeng Wang, Liying Jiang, and Ying Niu. "A Novel Chaotic Image Encryption Algorithm Based on Latin Square and Random Shift." Computational Intelligence and Neuroscience 2021 (September 6, 2021): 1–13. http://dx.doi.org/10.1155/2021/2091053.

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To realize the safe transmission of images, a chaotic image encryption algorithm based on Latin square and random shift is proposed. The algorithm consists of four parts: key generation, pixel scrambling, pixel replacement, and bit scrambling. Firstly, the key is generated from the plain image to improve the sensitivity of the encryption method. Secondly, each pixel in each row of the image matrix is moved cyclically to the right, in turn, to change the position of the image pixel and realize pixel position scrambling. Then, a 256-order Latin square matrix composed of a chaotic sequence is use

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17

An, Ran, Xueyuan Ge, and Miaohui Wang. "Vascular Stents with Controllable Negative Poisson’s Ratio Based on Energy Homogenization Method." Journal of Physics: Conference Series 2566, no. 1 (2023): 012120. http://dx.doi.org/10.1088/1742-6596/2566/1/012120.

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Abstract Based on the energy uniformization method and topology optimization method, a negative Poisson’s ratio generating model was designed. Using the generated cells, a novel negative Poisson’s ratio vascular stent was designed. A finite element model of the expansion process, including the vessel, stent, and balloon, was established. The analysis results showed an obvious tensile deformation pattern. Based on this expansion model, 23 sample points were sampled using the Latin hypercube method. Material parameters were used as variables, and cell equivalent Poisson’s ratio was used as a res

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Romaní, Gianni, Karla Soria-Barreto, Guillermo Honores-Marín, Rafael Ruiz Escorcia, and Javier Rueda. "Not Like My Parents! The Intention to Become a Successor of Latin American Students with Entrepreneur Parents." Sustainability 14, no. 3 (2022): 1193. http://dx.doi.org/10.3390/su14031193.

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The article presents an extension of the theory of planned behaviour (TPB) to identify, in a Latin American university, the students who are children of entrepreneurial parents and the determinants of their willingness to succeed them. The TPB is used as a basis to analyse the intention to be a successor, and three constructs are added: affective commitment, normative commitment and parental role model. The analysis is carried out using structural equations via the partial least squares (PLS) method, which allows for the study of multiple relationships between construct-type variables. The sam

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Isaev, Alexander, Tatiana Dobroserdova, Alexander Danilov, and Sergey Simakov. "Physically Informed Deep Learning Technique for Estimating Blood Flow Parameters in Four-Vessel Junction after the Fontan Procedure." Computation 12, no. 3 (2024): 41. http://dx.doi.org/10.3390/computation12030041.

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This study introduces an innovative approach leveraging physics-informed neural networks (PINNs) for the efficient computation of blood flows at the boundaries of a four-vessel junction formed by a Fontan procedure. The methodology incorporates a 3D mesh generation technique based on the parameterization of the junction’s geometry, coupled with an advanced physically regularized neural network architecture. Synthetic datasets are generated through stationary 3D Navier–Stokes simulations within immobile boundaries, offering a precise alternative to resource-intensive computations. A comparative

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Cherrez-Ojeda, Ivan, Valeria L. Mata, Emanuel Vanegas, et al. "Influence of Generational Cohorts on the Preferences for Information and Communication Technologies in Latin American Patients with Obstructive Lung Diseases." International Journal of Telemedicine and Applications 2020 (January 23, 2020): 1–7. http://dx.doi.org/10.1155/2020/2489890.

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Background. Advances in information and communication technologies (ICTs) represent a growing platform for the expansion of healthcare related services, but there is little information on how generational differences might account for distinct patterns of use and interest for ICTs. Our study aims to achieve a better understanding on how generational cohorts might influence the use and preferences for ICTs among patients with obstructive lung diseases in Latin America. Materials and Methods. We conducted an anonymous cross-sectional survey-based study, involving 968 patients with obstructive lu

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Birney, Damian P., David B. Bowman, Jens F. Beckmann, and Yuan Zhi Seah. "Assessment of Processing Capacity." European Journal of Psychological Assessment 28, no. 3 (2012): 216–26. http://dx.doi.org/10.1027/1015-5759/a000146.

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Research over the last 10 years on Latin square tasks (LST) suggests a significant potential for their use in assessing fluid cognition. In the current work, we outline the LST and the more complex Greco-Latin square task (GLST). The objectives were (1) to validate the appropriateness of LST as measures of fluid cognition in business managers and (2) to demonstrate the separation of the LST into working memory and deductive reasoning components. Participants were 264 midlevel managers from four large international companies. Consistent with expectations, SEM analyses indicated that the GLST an

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22

Mangone, Carlos A. "Argentina." International Psychogeriatrics 8, S3 (1997): 473–78. http://dx.doi.org/10.1017/s1041610297003888.

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Argentina covers an area of 3 million square kilometers, with almost one third of the population living in the capital district of Buenos Aires and the greater Buenos Aires area (the neighborhoods surrounding the capital district). Like other Latin American countries, Argentina is populated by a mixture of different ethnic cultures; however, unlike other Latin American countries, most Argentinians are of central and west European descent. People older than age 50 are mainly European immigrants or first- or second-generation Europeans. The mestizos—a fusion of Europeans and native Argentinians—

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23

Belli, Simone, and Cristian López Raventós. "Collective subjects and political mobilization in the public space: Towards a multitude capable of generating transformative practices." Human Affairs 31, no. 1 (2020): 59–72. http://dx.doi.org/10.1515/humaff-2021-0006.

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Abstract During the last twenty years in Latin America, there has been a rise in governments drawn from self-defining progressive political currents. Consequently a revitalization is underway of the debate on the viability, pertinence, and characteristics of the welfare state in the twenty-first century. In this context, the present article explores emerging social practices that redefine the various senses of the public space; practices that go beyond nation states, situated in a global territoriality, articulating languages and eliciting emotions capable of producing new socialities. The mul

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Liu, Xinghua, Xiang Li, Jiaqiang Tian, Yubo Wang, Gaoxi Xiao, and Peng Wang. "Day-Ahead Economic Dispatch of Renewable Energy System considering Wind and Photovoltaic Predicted Output." International Transactions on Electrical Energy Systems 2022 (June 1, 2022): 1–14. http://dx.doi.org/10.1155/2022/6082642.

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To alleviate the issues of global warming and energy crisis, countries are vigorously developing renewable energy technology. The integration of large-scale renewable energy, including wind energy, hydropower, and photovoltaic (PV), has a great impact on system operation scheduling and economic dispatch. This paper presents an economic dispatching method of wind-PV-CSP-hydro-battery system with wind and photovoltaic power generation as the main energy sources. The long short-term memory (LSTM) neural network is applied to predict wind and PV power, besides, the Latin Hypercube Sampling (LHS) m

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Le Bras, Ronan, Carla Gomes, and Bart Selman. "From Streamlined Combinatorial Search to Efficient Constructive Procedures." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (2021): 499–506. http://dx.doi.org/10.1609/aaai.v26i1.8147.

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In recent years, significant progress in the area of search, constraint satisfaction, and automated reasoning has been driven in part by the study of challenge problems from combinatorics and finite algebra. This work has led to the discovery of interesting discrete structures with intricate mathematical properties. While some of those results have resolved open questions and conjectures, a shortcoming is that they generally do not provide further mathematical insights, from which one could derive more general observations. We propose an approach that integrates specialized combinatorial searc

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Mangi, Ghulam Shabir, Zahoor Ahmed Soomro, Wajid Ali Jatoi, Qamar-Ur-Din Chachar, and Shah Nawaz Mari. "BREEDING FOR HIGHER FIBRE QUALITY TRAITS IN UPLAND COTTON THROUGH LINE × TESTER ANALYSIS." Pakistan Journal of Biotechnology 21, no. 1 (2024): 101–13. http://dx.doi.org/10.34016/pjbt.2024.21.01.875.

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The experiment was conducted using a randomized complete block design with three replications at Shah Abdul Latif Experimental Farm, Sindh Agriculture University, Tandojam. Employing a line × tester mating design in upland cotton (Gossypium hirutum L.), twenty-one cross combinations were obtained from seven females and three males. F1 and F2 generations, along with their parents, were sown in a randomized complete block design with three replications during 2012-13 and 2013-14. Studied traits included lint yield (g) per plant, G.O.T (%), staple length (mm), fiber fineness (mic.value), and fibe

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Yu, Changle, Lin Yang, Penglong Qi, Jia Wan, Yuanda Zhu, and Qingqing Zhang. "Research on dynamic energy optimization strategy of park smart energy system with complementary multi-energy." Journal of Physics: Conference Series 2401, no. 1 (2022): 012008. http://dx.doi.org/10.1088/1742-6596/2401/1/012008.

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Abstract The only way to develop a smart grid is to build a smart energy system in the park with coordinated optimization of source, network and load, and flexible interaction. In order to achieve the best operation of the multi-energy complementation of cooling, heating, and electricity in the smart energy system of the park when the output of renewable energy is uncertain, the Latin hyper square sampling method and the synchronous back generation method are used to analyze and model the uncertainty of renewable energy in the system. A model for the optimal operation of the integrated energy

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28

Bagchi, Bhaskar. "Latin squares." Resonance 17, no. 9 (2012): 895–902. http://dx.doi.org/10.1007/s12045-012-0098-4.

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29

Fearn, Tom. "Latin Squares." NIR news 17, no. 1 (2006): 15. http://dx.doi.org/10.1255/nirn.875.

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30

Ahmed, Mun, and Koji Shimada. "The Effect of Renewable Energy Consumption on Sustainable Economic Development: Evidence from Emerging and Developing Economies." Energies 12, no. 15 (2019): 2954. http://dx.doi.org/10.3390/en12152954.

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The objective of the paper is to figure out the nexus between renewable energy consumption and sustainable economic development for emerging and developing countries. In this paper, a panel of 30 emerging and developing countries is selected using the World Development Indicators (WDI) of the World Bank, Renewable Energy Country Attractiveness Index (RECAI) by Ernst and Young, and a random selection method based on the current trend of renewable energy consumption for five different regions of the world i.e., Asia, South-Asia, Latin America, Africa and the Caribbean. To achieve the objective,

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31

Yu, Glebsky L., and Carlos J. Rubio. "Latin Squares, Partial Latin Squares and Their Generalized Quotients." Graphs and Combinatorics 21, no. 3 (2005): 365–75. http://dx.doi.org/10.1007/s00373-005-0614-3.

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32

Emanouilidis, Emanuel. "Latin and cross Latin squares." International Journal of Mathematical Education in Science and Technology 39, no. 5 (2008): 697–700. http://dx.doi.org/10.1080/00207390801935921.

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33

Bailey, R. A. "Semi-Latin squares." Journal of Statistical Planning and Inference 18, no. 3 (1988): 299–312. http://dx.doi.org/10.1016/0378-3758(88)90107-3.

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34

Cavenagh, Nicholas, Carlo Hämäläinen, James G. Lefevre, and Douglas S. Stones. "Multi-latin squares." Discrete Mathematics 311, no. 13 (2011): 1164–71. http://dx.doi.org/10.1016/j.disc.2010.06.026.

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Danziger, Peter, Ian M. Wanless, and Bridget S. Webb. "Monogamous latin squares." Journal of Combinatorial Theory, Series A 118, no. 3 (2011): 796–807. http://dx.doi.org/10.1016/j.jcta.2010.11.011.

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Heinrich, Katherine, Kichul Kim, and V. K. Prasanna Kumar. "Perfect latin squares." Discrete Applied Mathematics 37-38 (July 1992): 281–86. http://dx.doi.org/10.1016/0166-218x(92)90139-2.

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37

Chaves, Brunele Weber, Gustavo Argenta Figueira Valles, Rudolf Brand Scheibler, Jorge Schafhauser Junior, and Jose Laerte Nornberg. "Milk yield of cows submitted to different levels of olive pomace in the diet." Acta Scientiarum. Animal Sciences 43 (November 6, 2020): e51158. http://dx.doi.org/10.4025/actascianimsci.v43i1.51158.

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The cultivation of olive trees is expanding in Brazil, mainly in Rio Grande do Sul in order to meet the demand for olive oil, the main product of the industrialization of olives. However, from the extraction, there is a significant generation of waste. This residue has high moisture and an appropriate destination is necessary given its environmental and economic importance. The chemical composition of the residue is similar to other products used in animal feed, such as corn silage or sorghum, in relation to DM, CP and NDF, the differential being high levels of EE and ADL. In order to evaluate

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Sharma, Mona, Smita Pareek, and Kulwant Singh. "Comparative Review and Performance Evaluation of Various Solar PV System Reconfigurations." Asian Journal of Water, Environment and Pollution 19, no. 5 (2022): 31–36. http://dx.doi.org/10.3233/ajw220068.

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In the current context, the most challenging and demanding research is to obtain maximum power from solar photovoltaic (SPV) power systems. Partial shadowing (PS) is a prominent cause of solar photovoltaic panels output power loss. The output decreases proportionally to the shaded area, the placement of shaded panels within the array, panel interconnections, shade pattern, etc. Numerous static and dynamic approaches for reducing the PS effect have been reported in the literature. Of these, the most common is the reconfiguration technique based on the static method, which distributes shaded pan

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Madhanmohan, Vishnu P., Abdul Saleem, and Nandakumar Madathil Kovilakam. "Improved performance of partially shaded photovoltaic array with reformed-total cross tied configuration." Energy Harvesting and Systems 7, no. 2 (2020): 63–75. http://dx.doi.org/10.1515/ehs-2021-0010.

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Abstract Renewable energy sources are receiving wide popularity due to the shortage of fossil fuels and environmental problems caused by conventional energy sources. Solar photovoltaic energy is a widely used sustainable energy source. The power developed by a solar cell is greatly influenced by the insolation level. Partial shading occurs when one or more photovoltaic (PV) cells receive lesser radiation as compared to other cells, which in turn affects the overall electrical performance of PV cells including reduced generated power. This paper proposes a newly developed configuration known as

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40

Kuhl, Jaromy Scott, and Tristan Denley. "On avoiding odd partial Latin squares and r-multi Latin squares." Discrete Mathematics 306, no. 22 (2006): 2968–75. http://dx.doi.org/10.1016/j.disc.2006.05.028.

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Wang, Wei, Yanjun Liu, Fagang Bai, and Gang Xue. "Capture Power Prediction of the Frustum of a Cone Shaped Floating Body Based on BP Neural Network." Journal of Marine Science and Engineering 9, no. 6 (2021): 656. http://dx.doi.org/10.3390/jmse9060656.

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How to improve the power generation of wave energy converters (WEC) has become one of the main research objectives in wave energy field. This paper illustrates a framework on the use of back propagation (BP) neural network in predicting capture power of the frustum of a cone shaped floating body. Mathematical model of single floating body is derived, and radius, semi-vertical angle, mass, submergence depth, power take-off (PTO) damping coefficient, and stiffness coefficient are identified as key variables. Commercial software ANSYS-AQWA is used for numerical simulations to obtain hydrodynamic

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Weitzel, Alexander, Claudia Samol, Peter J. Oefner, and Wolfram Gronwald. "Robust Metabolite Quantification from J-Compensated 2D 1H-13C-HSQC Experiments." Metabolites 10, no. 11 (2020): 449. http://dx.doi.org/10.3390/metabo10110449.

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The spectral resolution of 2D 1H-13C heteronuclear single quantum coherence (1H-13C-HSQC) nuclear magnetic resonance (NMR) spectra facilitates both metabolite identification and quantification in nuclear magnetic resonance-based metabolomics. However, quantification is complicated by variations in magnetization transfer, which among others originate mainly from scalar coupling differences. Methods that compensate for variation in scalar coupling include the generation of calibration factors for individual signals or the use of additional pulse sequence schemes such as quantitative HSQC (Q-HSQC

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43

Okedoyin, Deborah O., Joel O. Alabi, Chika C. Anotaenwere, et al. "Metabolomic Profiling, Volatile Fatty Acids, and Greenhouse Gas Emissions of Beef Cattle Infused with Different Essential Oil Blends." Ruminants 4, no. 3 (2024): 329–51. http://dx.doi.org/10.3390/ruminants4030024.

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Essential oils are natural feed additives that improve animal health and enhance their performance. This study investigated the effects of the rumen infusion of five essential oil blends (EOBs) on greenhouse gas (GHG) emissions, rumen fermentation parameters, and rumen metabolome and metabolic pathways in Black Angus cows. Using a 6 × 6 Latin Square experimental design, a 90-day study was conducted with six cattle. A daily dosage of 4 mL of EOBs was administered during each infusion. Volcano plot analyses between the control (CON) and each of the EOBs (EOB1, EOB2, EOB3, EOB4, and EOB5) reveale

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44

Behforooz, Hossein. "91.49 Mirror magic squares from Latin Squares." Mathematical Gazette 91, no. 521 (2007): 316–21. http://dx.doi.org/10.1017/s0025557200181793.

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Faruqi, Shahab, S. A. Katre, and Manisha Garg. "Pseudo orthogonal Latin squares." Discrete Mathematics and Applications 31, no. 1 (2021): 5–17. http://dx.doi.org/10.1515/dma-2021-0002.

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Abstract Two Latin squares A, B of order n are called pseudo orthogonal if for any 1 ≤ i, j ≤ n there exists a k, 1 ≤ k ≤ n, such that A(i, k) = B(j, k). We prove that the existence of a family of m mutually pseudo orthogonal Latin squares of order n is equivalent to the existence of a family of m mutually orthogonal Latin squares of order n. We also obtain exact values of clique partition numbers of several classes of complete multipartite graphs and of the tensor product of complete graphs.

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Galatenko, A. V., V. A. Nosov, and A. E. Pankratiev. "Latin Squares over Quasigroups." Lobachevskii Journal of Mathematics 41, no. 2 (2020): 194–203. http://dx.doi.org/10.1134/s1995080220020079.

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Emanouilidis, Emanuel. "Latin and magic squares." International Journal of Mathematical Education in Science and Technology 36, no. 5 (2005): 546–49. http://dx.doi.org/10.1080/00207390412331336201.

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Pittenger, Arthur O. "Mappings of latin squares." Linear Algebra and its Applications 261, no. 1-3 (1997): 251–68. http://dx.doi.org/10.1016/s0024-3795(96)00408-9.

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Hilton, A. J. W., M. Mays, C. A. Rodger, and C. St J. A. Nash-Williams. "Hamiltonian double latin squares." Journal of Combinatorial Theory, Series B 87, no. 1 (2003): 81–129. http://dx.doi.org/10.1016/s0095-8956(02)00029-1.

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50

Easton, T., and R. Gary Parker. "On completing latin squares." Discrete Applied Mathematics 113, no. 2-3 (2001): 167–81. http://dx.doi.org/10.1016/s0166-218x(00)00282-1.

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