Journal articles: 'Median algebra'

1

Bandelt, Hans-Jürgen, and Gerasimos C. Meletiou. "The zero-completion of a median algebra." Czechoslovak Mathematical Journal 43, no. 3 (1993): 409–17. http://dx.doi.org/10.21136/cmj.1993.128419.

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Meletiou, Gerasimos C. "Median algebras acting on sets." Algebra Universalis 29, no. 4 (December 1992): 477–84. http://dx.doi.org/10.1007/bf01190774.

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Nomi, Takako, Stephen W. Raudenbush, and Jake J. Smith. "Effects of double-dose algebra on college persistence and degree attainment." Proceedings of the National Academy of Sciences 118, no. 27 (June 28, 2021): e2019030118. http://dx.doi.org/10.1073/pnas.2019030118.

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In 2003, Chicago Public Schools introduced double-dose algebra, requiring two periods of math—one period of algebra and one of algebra support—for incoming ninth graders with eighth-grade math scores below the national median. Using a regression discontinuity design, earlier studies showed promising results from the program: For median-skill students, double-dose algebra improved algebra test scores, pass rates, high school graduation rates, and college enrollment. This study follows the same students 12 y later. Our findings show that, for median-skill students in the 2003 cohort, double-dose significantly increased semesters of college attended and college degree attainment. These results were not replicated for the 2004 cohort. Importantly, the impact of the policy on median-skill students depended largely on how classes were organized. In 2003, the impacts on college persistence and degree attainment were large in schools that strongly adhered to the cut-score-based course assignment, but without grouping median-skill students with lower-skill peers. Few schools implemented the policy in such a way in 2004.

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Edwards, Michael Todd. "Promoting Understanding of Linear Equations with the Median Slope Algorithm." Mathematics Teacher 98, no. 6 (February 2005): 414–25. http://dx.doi.org/10.5951/mt.98.6.0414.

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In recent years, the influence of technology on school mathematics curricula has become increasingly pronounced. Today, for instance, calculators seem ever–present in most mathematics classrooms. In fact, a recent study of nearly 4,000 mathematics teachers and 50,000 students reports that approximately 96 percent of eighth–grade students in the United States have access to calculators for use in mathematics classrooms (IEA 2001). The computational power of handheld calculators—particularly those equipped with graphing capabilities—has significantly accelerated the introduction of numerous mathematical topics within school mathematics. For example, before the early 1990s, leastsquares regression was not found in most algebra textbooks. Because by–hand methods for calculating a least–squares regression line required students to minimize the sum of squared residuals—a technique requiring differentiation—the procedure was rarely studied before calculus. Now, however, any student with a graphing calculator can perform a leastsquares linear regression by pressing only a few buttons. Not surprisingly, linear regression is now commonly found in the school algebra curriculum.

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Cortes, Kalena E., and Joshua S. Goodman. "Ability-Tracking, Instructional Time, and Better Pedagogy: The Effect of Double-Dose Algebra on Student Achievement." American Economic Review 104, no. 5 (May 1, 2014): 400–405. http://dx.doi.org/10.1257/aer.104.5.400.

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This paper provides new evidence on tracking by studying an innovative curriculum implemented by Chicago Public Schools (CPS). In 2003, CPS enacted a double-dose algebra policy requiring 9th grade students with 8th grade math scores below the national median to take two periods of algebra instead of one. This policy led schools to sort students into algebra classes by math ability, so that tracking increased in all algebra classes. We show that double-dosed students are exposed to a much lower-skilled group of peers in their algebra classes but nonetheless benefit substantially from the additional instructional time and improved pedagogy.

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Tyson, Will, and Josipa Roksa. "Importance of Grades and Placement for Math Attainment." Educational Researcher 46, no. 3 (April 2017): 140–42. http://dx.doi.org/10.3102/0013189x17706079.

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Research on high school math course taking documents the advantages of starting high school at or beyond Algebra 1. Fewer studies examine differentiation into remedial, general, and honors Algebra 1 course types by course rigor. This study examines how course grades and course rigor are associated with math attainment among students with similar eighth-grade standardized math test scores. Students who earned an A in remedial courses had lower attainment than students with a D in general Algebra 1. Students with an A in general Algebra 1 had lower attainment than students with median grades in honors Algebra 1.

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Bandelt, Hans J�rgen. "Diagonal subalgebras and local polynomial functions of median algebras." Algebra Universalis 30, no. 1 (March 1993): 20–26. http://dx.doi.org/10.1007/bf01196547.

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8

Chamberland, Marc, and Mario Martelli. "The mean-median map." Journal of Difference Equations and Applications 13, no. 7 (July 2007): 577–83. http://dx.doi.org/10.1080/10236190701264719.

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You, Xu. "Approximation of the median of the gamma distribution." Journal of Number Theory 174 (May 2017): 487–93. http://dx.doi.org/10.1016/j.jnt.2016.11.019.

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Bandelt, Hans-J�rgen, Melvin F. Janowitz, and Gerasimos C. Meletiou. "n-median semilattices." Order 8, no. 2 (1991): 185–95. http://dx.doi.org/10.1007/bf00383403.

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Bandelt, Hans-Jürgen, and Victor Chepoi. "The algebra of metric betweenness II: Geometry and equational characterization of weakly median graphs." European Journal of Combinatorics 29, no. 3 (April 2008): 676–700. http://dx.doi.org/10.1016/j.ejc.2007.03.003.

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Kumduang, Thodsaporn. "Menger hypercompositional algebras represented by medial n-ary hyperoperations." Quasigroups and Related Systems 30, no. 2(48) (April 2023): 263–74. http://dx.doi.org/10.56415/qrs.v30.22.

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The necessary and sufficient conditions under which a Menger algebra can be isomorphically represented by medial n-ary operations are proposed. Since a Menger hypercompositional algebra can be regarded as a generalization of a Menger algebra, for this reason, the situation for medial hyperoperations is further examined and a representation theorem of Menger hypercompositional algebras by such concepts is proved.

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Abdurrazzaq, Achmad, Ismail Mohd, Ahmad Kadri Junoh, and Zainab Yahya. "Modified tropical algebra based median filter for removing salt and pepper noise in digital image." IET Image Processing 13, no. 14 (December 12, 2019): 2790–95. http://dx.doi.org/10.1049/iet-ipr.2018.6201.

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Abdul Rahim, Rini Hafzah, Aslina Baharum, and Hanafi Hijazi. "Evaluation on effectiveness of learning linear algebra using gamification." Indonesian Journal of Electrical Engineering and Computer Science 17, no. 2 (February 1, 2020): 997. http://dx.doi.org/10.11591/ijeecs.v17.i2.pp997-1004.

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This study evaluate effectiveness of learning Linear Algebra using gamification strategy. In this study, gamification with storytelling strategy is used as teaching tools to attract student to learn Linear Algebra. This study using Polytechnic Malaysia syllabus with focus group of Diploma students for semester three (Mechanical Engineering) and semester four (Electrical Engineering) for two topics; Matrix and Numerical Method. They are five methods of calculation simultaneous linear equations which is ‘Inverse’, ‘Cramer's Rule’, ‘Gauss Elimination’, ‘Lower Upper Doolittle’ and ‘Lower Upper Crout’. They are three main phases to develop this gamification; Pedagogy Phase, Design Phase and Evaluation Phase. Mixed methods approach combining quantitative (survey) and qualitative (Electroencephalogram) is used to evaluate students learning process using Linear Algebra gamification application. The findings of the five items surveyed showed that the acceptance of the prototype of the Linear Algebra Gamification Application was very encouraging from a total of 104 students. This is because all 38 questions for the five items earn a median of four and this indicates the majority of students choose “Agree” and “Strongly Agree”. The findings also show the percent “Agree” and “Strongly Agree” for all questions having a high percentage of between 61.5 and 94.2. This shows more than half satisfied and likes to use the Linear Algebra Gamification Application prototype. With the development of the Linear Algebra Gamification Application prototype, it is hoped that the use of learning based can be extended to a variety of subjects as well as topics to make the learning process more interesting and fun as well as helping to motivate students to learn

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15

Zawojewski, Judith S., and J. Michael Shaughnessy. "Take Time for Action: Mean and Median: Are They Really So Easy?" Mathematics Teaching in the Middle School 5, no. 7 (March 2000): 436–40. http://dx.doi.org/10.5951/mtms.5.7.0436.

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When are median and mean taught to students in your curriculum? Our first introduction to these terms as students was in college-level statistics courses in the mathematics department. Of course, we had learned to find arithmetic averages during elementary school as an application of long division and again in high school algebra when learning to use variables to represent relationships in equations. One of the authors taught middle school in the 1970s, and the other taught finite mathematics to college students in the 1970s. We were surprised to find these measures of central tendency in the books for middle school and equally surprised that college students had not previously seen median and mode. The procedure for finding the median is much easier than the one for finding the mean, so why not include it in the middle school curriculum? To teach the mean, all we had to say to students was that it was the same as the average that they had already learned in fifthand sixth-grade mathematics.

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Hoseana, Jonathan, and Franco Vivaldi. "On the unboundedness of the transit time of mean-median orbits." Journal of Difference Equations and Applications 26, no. 9-10 (October 2, 2020): 1398–421. http://dx.doi.org/10.1080/10236198.2020.1842385.

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17

Fioravanti, Elia. "On automorphisms and splittings of special groups." Compositio Mathematica 159, no. 2 (February 2023): 232–305. http://dx.doi.org/10.1112/s0010437x22007850.

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We initiate the study of outer automorphism groups of special groups $G$ , in the Haglund–Wise sense. We show that $\operatorname {Out}(G)$ is infinite if and only if $G$ splits over a co-abelian subgroup of a centraliser and there exists an infinite-order ‘generalised Dehn twist’. Similarly, the coarse-median preserving subgroup $\operatorname {Out}_{\rm cmp}(G)$ is infinite if and only if $G$ splits over an actual centraliser and there exists an infinite-order coarse-median-preserving generalised Dehn twist. The proof is based on constructing and analysing non-small, stable $G$ -actions on $\mathbb {R}$ -trees whose arc-stabilisers are centralisers or closely related subgroups. Interestingly, tripod-stabilisers can be arbitrary centralisers, and thus are large subgroups of $G$ . As a result of independent interest, we determine when generalised Dehn twists associated to splittings of $G$ preserve the coarse median structure.

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Tripathy, Sushreeta, and Tripti Swarnkar. "Performance observation of mammograms using an improved dynamic window based adaptive median filter." Journal of Discrete Mathematical Sciences and Cryptography 23, no. 1 (January 2, 2020): 167–75. http://dx.doi.org/10.1080/09720529.2020.1721881.

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19

Harutyunyan, David N. "ON REGULAR PARAMEDIAL DIVISION ALGEBRAS." Proceedings of the YSU A: Physical and Mathematical Sciences 56, no. 3 (259) (October 21, 2022): 107–15. http://dx.doi.org/10.46991/pysu:a/2022.56.3.107.

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In this paper $n$-ary regular division algebras are discussed, which are satisfying the hyperidentity of paramediality. It is shown that every operation in $n$-ary regular paramedial division algebra will be linearly represented over the same Abelian group. Similar results already obtained for regular medial division algebras in [1].

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20

Bossé, Michael J. "Data-Driven Mathematics Investigations on Curved Data." Mathematics Teacher 99, no. 1 (August 2005): 46–54. http://dx.doi.org/10.5951/mt.99.1.0046.

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Investigations of real–world data begin in elementary school. Students often produce scatter plots, leading to trend lines. In the middle grades, lines of best fit are often investigated through median–median lines and double–centroid lines (Shawer et al. 2002). In the secondary grades, linear regression is produced by the least squares line. While these techniques are adequate for data that is more or less linear, teachers and students often encounter data that produce a “curved” scatter plot. In these cases additional techniques are required. This article demonstrates three techniques to determine the equation of a polynomial function through two or more points that model the graph of “good fit” for a set of data. Using these techniques, students can develop functions through which they can evaluate mathematical behavior and make predictions. Secondary mathematics teachers will find these techniques particularly valuable. Each technique can be applied within various secondary mathematics courses such as algebra 2, statistics, or precalculus.

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21

Nawajah, Inad, Hassan Kanj, Yehia Kotb, Julian Hoxha, Mouhammad Alakkoumi, and Kamel Jebreen. "Bayesian Regression Analysis using Median Rank Set Sampling." European Journal of Pure and Applied Mathematics 17, no. 1 (January 31, 2024): 180–200. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.5015.

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Bayesian estimation of the linear regression parameter system is considered by deploying Median Rank Set Sampling (MRSS). The full conditional distributions and the associated posterior distribution are obtained. Therefore, based on Markov Chain Monte Carlo simulation, the Bayesian point estimates and credible intervals for the regression parameters are determined. To measure the efficiency of the obtained Bayesian estimates concerning the frequentist estimates we compute the asymptotic relative efficiency of the obtained Bayesian estimates using Markov Chain Monte Carlo simulation.

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Mäkinen, Erkki. "A Note on the Median Heuristic for Drawing Bipartite Graphs." Fundamenta Informaticae 12, no. 4 (October 1, 1989): 563–69. http://dx.doi.org/10.3233/fi-1989-12408.

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Eades and Wormald have shown that a bipartite graph drawn by the median heuristic has at most three times the number of edge crossing in the corresponding optimal drawing. In this paper we show that the bound of Eades and Wormald can be sharpened.

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Kundert, Ken. "Student-generated Data in Elementary Statistics." Mathematics Teacher 83, no. 4 (April 1990): 322–25. http://dx.doi.org/10.5951/mt.83.4.0322.

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The recent increased emphasis on the teaching of statistics in the high school classroom has focused primarily on the techniques of exploratory data analysis. Topics include stem-and-leaf plots, box plots, median-fit lines, and curve smoothing. A number ofhigh schools, however, still teach a course in statistics for the college-bound student. Included in this course are many of the classical topics of statistics generally found in an elementary statistics course taught to college students, with only intermediate algebra as a prerequisite. Although this article highlights selected topics in such a course and describes how student-generated data can be used to illustrate these topics, the basic idea can profitably be used throughout the mathematics curriculum.

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Cheng, Christine T. "A Poset-based Approach to Embedding Median Graphs in Hypercubes and Lattices." Order 29, no. 1 (March 2, 2011): 147–63. http://dx.doi.org/10.1007/s11083-011-9203-7.

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25

Denecke, K., J. Koppitz, and R. Marszałek. "Derived Varieties and Derived Equational Theories." International Journal of Algebra and Computation 08, no. 02 (April 1998): 153–69. http://dx.doi.org/10.1142/s0218196798000090.

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This paper describes a derivation process for varieties and equational theories using the theory of hypersubstitutions and M-hyperidentities. A hypersubstitution σ of type τ is a map which takes each n-ary operation symbol of the type to an n-ary term of this type. If [Formula: see text] is an algebra of type τ then the algebra [Formula: see text] is called a derived algebra of [Formula: see text]. If V is a class of algebras of type τ then one can consider the variety vσ(V) generated by the class of all derived algebras from V. In the first two sections the necessary definitions are given. In Sec. 3 the properties of derived varieties and derived equational theories are described. On the set of all derived varieties of a given variety, a quasiorder is developed which gives a derivation diagram. In the final section the derivation diagram for the largest solid variety of medial semigroups is worked out.

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Kurniadi, Edi, Ema Carnia, and Herlina Napitupulu. "The Existence of Affine Structures on the Borel Subalgebra of Dimension 6." ComTech: Computer, Mathematics and Engineering Applications 12, no. 1 (May 24, 2021): 45–52. http://dx.doi.org/10.21512/comtech.v12i1.6581.

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The notion of affine structures arises in many fields of mathematics, including convex homogeneous cones, vertex algebras, and affine manifolds. On the other hand, it is well known that Frobenius Lie algebras correspond to the research of homogeneous domains. Moreover, there are 16 isomorphism classes of 6-dimensional Frobenius Lie algebras over an algebraically closed field. The research studied the affine structures for the 6-dimensional Borel subalgebra of a simple Lie algebra. The Borel subalgebra was isomorphic to the first class of Csikós and Verhóczki’s classification of the Frobenius Lie algebras of dimension 6 over an algebraically closed field. The main purpose was to prove that the Borel subalgebra of dimension 6 was equipped with incomplete affine structures. To achieve the purpose, the axiomatic method was considered by studying some important notions corresponding to affine structures and their completeness, Borel subalgebras, and Frobenius Lie algebras. A chosen Frobenius functional of the Borel subalgebra helped to determine the affine structure formulas well. The result shows that the Borel subalgebra of dimension 6 has affine structures which are not complete. Furthermore, the research also gives explicit formulas of affine structures. For future research, another isomorphism class of 6-dimensional Frobenius Lie algebra still needs to be investigated whether it has complete affine structures or not.

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Couceiro, Miguel, Jean-Luc Marichal, and Bruno Teheux. "Conservative Median Algebras and Semilattices." Order 33, no. 1 (May 13, 2015): 121–32. http://dx.doi.org/10.1007/s11083-015-9356-x.

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28

Bandelt, Hans-Jürgen, Henry Martyn Mulder, and Elke Wilkeit. "Quasi-median graphs and algebras." Journal of Graph Theory 18, no. 7 (November 1994): 681–703. http://dx.doi.org/10.1002/jgt.3190180705.

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Jun, Young Bae, and Kyung Ho Kim. "Fuzzy convex sets in median algebras." Journal of Applied Mathematics and Computing 10, no. 1-2 (September 2002): 157–65. http://dx.doi.org/10.1007/bf02936214.

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Stanujkić, Dragiša, Darjan Karabašević, Gabrijela Popović, Predrag S. Stanimirović, Florentin Smarandache, Muzafer Saračević, Alptekin Ulutaş, and Vasilios N. Katsikis. "An Innovative Grey Approach for Group Multi-Criteria Decision Analysis Based on the Median of Ratings by Using Python." Axioms 10, no. 2 (June 19, 2021): 124. http://dx.doi.org/10.3390/axioms10020124.

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Some decision-making problems, i.e., multi-criteria decision analysis (MCDA) problems, require taking into account the attitudes of a large number of decision-makers and/or respondents. Therefore, an approach to the transformation of crisp ratings, collected from respondents, in grey interval numbers form based on the median of collected scores, i.e., ratings, is considered in this article. In this way, the simplicity of collecting respondents’ attitudes using crisp values, i.e., by applying some form of Likert scale, is combined with the advantages that can be achieved by using grey interval numbers. In this way, a grey extension of MCDA methods is obtained. The application of the proposed approach was considered in the example of evaluating the websites of tourism organizations by using several MCDA methods. Additionally, an analysis of the application of the proposed approach in the case of a large number of respondents, done in Python, is presented. The advantages of the proposed method, as well as its possible limitations, are summarized.

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Ahn, Sun-Shin, and Keum-Sook So. "ON MEDIAL Q-ALGEBRAS." Communications of the Korean Mathematical Society 25, no. 3 (July 31, 2010): 365–72. http://dx.doi.org/10.4134/ckms.2010.25.3.365.

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32

Kim, Young Hee. "ON MEDIAL B-ALGEBRAS." Journal of applied mathematics & informatics 32, no. 5_6 (September 30, 2014): 849–56. http://dx.doi.org/10.14317/jami.2014.849.

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33

KLLOGJERI, PELLUMB, and ADRIAN KLLOGJERI. "Use of GeoGebra in teaching about central tendency and spread variability." Creative Mathematics and Informatics 21, no. 1 (2012): 57–64. http://dx.doi.org/10.37193/cmi.2012.01.14.

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In data analysis are used graphs, tables, and numerical summaries to study the variation present in data under study. Graphs are effective visual tools because they present information quickly and easily. Graphs are commonly used by print and electronic media and, data can be better understood when presented by a graph than by a table because the graph can reveal a trend or comparison. Graphs display the relationship between variables or show the value spread of a given variable or phenomenon. Measuring the central tendency we identify the most representative value in a set of data. Mean, median and mode give different perspectives of a data set’s centre, but a data description is not complete until the spread variability is also known. The basic numerical description of a data set requires measures of both centre and spread. In this paper we will be concentrated on graphical representation of data collected from a population. A useful tool to get such nice visual representations is GeoGebra. GeoGebra is an interactive geometry system and, by the use of its virtual tools, we can do constructions with points, vectors, segments, lines; we can construct histogram and geometrically show the positions of the median and quartiles [4]. GeoGebra provides numerical calculations for the measures of data centre and spread. GeoGebra software is very useful and helpful for teachers and students to graphically present data and easy understand and interpret them [6]. Also, GeoGebra is dynamic mathematics software for schools that joins geometry, algebra, and calculus. Using this dynamic feature in the teaching hour of statistics, the students have a better and fuller understanding about data measures and data spread.

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Fioravanti, Elia. "Roller boundaries for median spaces and algebras." Algebraic & Geometric Topology 20, no. 3 (May 27, 2020): 1325–70. http://dx.doi.org/10.2140/agt.2020.20.1325.

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Bowditch, Brian H. "Embedding median algebras in products of trees." Geometriae Dedicata 170, no. 1 (June 6, 2013): 157–76. http://dx.doi.org/10.1007/s10711-013-9874-x.

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Couceiro, Miguel, and Gerasimos C. Meletiou. "On a special class of median algebras." Miskolc Mathematical Notes 18, no. 1 (2017): 167. http://dx.doi.org/10.18514/mmn.2017.1799.

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Couceiro, Miguel, Stephan Foldes, and Gerasimos C. Meletiou. "On homomorphisms between products of median algebras." Algebra universalis 78, no. 4 (October 20, 2017): 545–53. http://dx.doi.org/10.1007/s00012-017-0468-6.

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SALAS-RUEDA, Ricardo-adan. "USE OF FLIPPED CLASSROOM IN THE TEACHING-LEARNING PROCESS ON DESCRIPTIVE STATISTICS." Turkish Online Journal of Distance Education 23, no. 4 (October 1, 2022): 53–64. http://dx.doi.org/10.17718/tojde.1182755.

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Educational institutions seek to transform the teaching-learning conditions through the use of new pedagogical and technological models. The aim of this quantitative research is to analyze the use of flipped classroom in the teaching-learning process on descriptive statistics through data science. The participants are 49 students who took the Basic Statistics course during the 2017 school year. This study used a single group quasi-experiment to examine the research hypotheses about Flipped classroom. In the Basic Statistics course, the students have difficulties to assimilate the knowledge about mean, mode, median, range and quartiles. Therefore, this research proposes the consultation of YouTube videos before the class, use of the Mathportal application collaboratively during the class and use of the Mathportal application individually after the class. The Mathportal application is a web tool that allows checking the results of the exercises on the mean, mode, median, range and quartiles at any time. The results of machine learning (linear regression) indicate that flipped classroom positively influences the teaching-learning process on descriptive statistics. On the other hand, data science allows the identification of 3 predictive models about the consultation of the YouTube videos and use of the Mathportal application through the decision tree technique. This research recommends the use of the Mathportal application for the teaching-learning process on statistics. Even, this web application can be used in the courses of differential calculus, geometry, algebra and financial mathematics. The implications of this research are the transformation of the educational context through the use of flipped classroom and incorporation of technological tools before, during and after the face-to-face classes. Finally, flipped classroom is a pedagogical model that is transforming the organization and implementation of school activities through the use of technology inside and outside the classroom.

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Ehsani, Amir. "Characterization of regular medial algebras." ScienceAsia 40, no. 2 (2014): 175. http://dx.doi.org/10.2306/scienceasia1513-1874.2014.40.175.

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Liu, Qi, and Fu-Gui Shi. "M-fuzzifying median algebras and its induced convexities." Journal of Intelligent & Fuzzy Systems 36, no. 2 (March 16, 2019): 1927–35. http://dx.doi.org/10.3233/jifs-172271.

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Bandelt, H. J., and M. van de Vel. "Embedding Topological Median Algebras in Products of Dendrons." Proceedings of the London Mathematical Society s3-58, no. 3 (May 1989): 439–53. http://dx.doi.org/10.1112/plms/s3-58.3.439.

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Csencsits-Smith, Keri, Mary McGuire, Trinh Nguyen, and David Pascual. "What is (in)significant? The Pathway Semantics Algorithm reveals complex immune response changes over time. (58.18)." Journal of Immunology 188, no. 1_Supplement (May 1, 2012): 58.18. http://dx.doi.org/10.4049/jimmunol.188.supp.58.18.

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Abstract Results obtained from hypothesis-driven research may not represent the complex interactions between cells and cytokines required for the development of an acquired immune response. We applied a novel algorithm to measure change in immune response over time in a mouse model of anti-Factor VIII (FVIII) antibody formation in hemophilia A. Splenocytes isolated from FVIII injected mice treated with PBS or an experimental tolerogen (CFA/1) were cultured for 72 hours and cytokine concentrations determined via multiplex analysis at days 7 and 14. The concentrations of 22 individual cytokines were compared between the control and CFA/1-treated groups, and 3 cytokines statistically differentiated the two groups at day 7 and 5 cytokines at day 14. Median cytokine concentrations/group of each significance set were converted to pmol/L and Ingenuity Pathway Analysis was used to generate likely biological network pathways. Network graphs were converted to matrices and linear algebra was used to compare treatment groups. Sixteen different molecules were predicted to occur in PBS vs. CFA/1 groups at day 7. We validated the presence of two predicted outcomes - expression of TLR 4 and secretion of IL-25. At day 14, the predicted outcomes were similar between the treatment groups, despite being evoked from a larger significance set, suggesting that statistical differences in cytokine secretion do not consistently represent biologically relevant changes in immune response over time.

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Ehsani, Amir, and Yuri Movsisyan. "Linear Representation of Medial-Like Algebras." Communications in Algebra 41, no. 9 (September 2, 2013): 3429–44. http://dx.doi.org/10.1080/00927872.2012.688154.

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Algarni, Ali. "Group Acceptance Sampling Plan Based on New Compounded Three-Parameter Weibull Model." Axioms 11, no. 9 (August 29, 2022): 438. http://dx.doi.org/10.3390/axioms11090438.

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In this study, we introduce a new compounded model called the complementary Bell–Weibull model and use it to address the problem of a group acceptance sampling plan predicted on a truncated life test. The median lifespan is used as a quality index to obtain the design constraints, namely sample size and approval number, under a predefined consumerś risk and test termination period. Additionally, two real data applications are presented, and unknown parameters are estimated using the maximum likelihood approach.

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Duplij, Steven. "Graded Medial n-Ary Algebras and Polyadic Tensor Categories." Symmetry 13, no. 6 (June 9, 2021): 1038. http://dx.doi.org/10.3390/sym13061038.

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Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or ε-commutativity), we introduce almost mediality (“commutativity-to-mediality” ansatz). Higher graded twisted products and “deforming” brackets (being the medial analog of Lie brackets) are defined. Toyoda’s theorem which connects (universal) medial algebras with abelian algebras is proven for the almost medial graded algebras introduced here. In a similar way we generalize tensor categories and braided tensor categories. A polyadic (non-strict) tensor category has an n-ary tensor product as an additional multiplication with n−1 associators of the arity 2n−1 satisfying a n2+1-gon relation, which is a polyadic analog of the pentagon axiom. Polyadic monoidal categories may contain several unit objects, and it is also possible that all objects are units. A new kind of polyadic categories (called groupal) is defined: they are close to monoidal categories but may not contain units: instead the querfunctor and (natural) functorial isomorphisms, the quertors, are considered (by analogy with the querelements in n-ary groups). The arity-nonreducible n-ary braiding is introduced and the equation for it is derived, which for n=2 coincides with the Yang–Baxter equation. Then, analogously to the first part of the paper, we introduce “medialing” instead of braiding and construct “medialed” polyadic tensor categories.

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46

Al-Essa, Laila A., Mohamed S. Eliwa, Hend S. Shahen, Amal A. Khalil, Hana N. Alqifari, and Mahmoud El-Morshedy. "Bivariate Discrete Odd Generalized Exponential Generator of Distributions for Count Data: Copula Technique, Mathematical Theory, and Applications." Axioms 12, no. 6 (May 29, 2023): 534. http://dx.doi.org/10.3390/axioms12060534.

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In this article, a new family of bivariate discrete distributions is proposed based on the copula concept, in the so-called bivariate discrete odd generalized exponential-G family. Some distributional properties, including the joint probability mass function, joint survival function, joint failure rate function, median correlation coefficient, and conditional expectation, are derived. After proposing the general class, one special model of the new bivariate family is discussed in detail. The maximum likelihood approach is utilized to estimate the family parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, the importance of the new bivariate family is explained by means of two distinctive real data sets in various fields.

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Nazari, E. M. "Invertible medial algebras and a group of operations." Journal of Contemporary Mathematical Analysis 46, no. 2 (April 2011): 101–5. http://dx.doi.org/10.3103/s1068362311020051.

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48

M.Mostafa, Samy, and Reham Ghanem. "CUBIC STRUCTURES OF MEDIAL IDEAL ON BCI -ALGEBRAS." International Journal of Fuzzy Logic Systems 5, no. 2/3 (July 30, 2015): 15–32. http://dx.doi.org/10.5121/ijfls.2015.5302.

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Karamdin, Bushra, and Shaban A. Bhatti. "Decompositions of Weak BCC-Algebras." Algebra Colloquium 18, spec01 (December 2011): 889–98. http://dx.doi.org/10.1142/s1005386711000770.

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It is proved that a decomposition of a weak BCC-algebra X into branches induces on X a congruence θ such that the algebra X/θ is isomorphic to the subalgebra of X containing all initial elements of X. A decomposition of a medial weak BCC-algebra into a direct product of subalgebras generated by one element is also presented.

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50

Akhter, Zuber, Ehab M. Almetwally, and Christophe Chesneau. "On the Generalized Bilal Distribution: Some Properties and Estimation under Ranked Set Sampling." Axioms 11, no. 4 (April 13, 2022): 173. http://dx.doi.org/10.3390/axioms11040173.

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The generalized Bilal (GB) distribution can be defined as the distribution of the median of three independent random variables drawn from the Weibull distribution. Its failure rate function can be monotonic (decreasing or increasing) or upside-down bathtub-shaped. In this study, we aim to reveal some important properties of the GB distribution that have not been considered before. The findings are both theoretical and practical. From the theoretical viewpoint, we present explicit expressions for both single and product moments of order statistics from the GB distribution. The L-moments are derived as well. From the practical viewpoint, the parameter estimations are accomplished using the maximum likelihood (ML) method, which is based on two different sampling schemes: simple random sampling (SRS) and ranked set sampling (RSS) schemes. Furthermore, the asymptotic confidence intervals for the SRS and RSS estimators are discussed. For the sake of comparison and illustration, a simulation study and a real data example are presented. Concluding remarks are given at the end.

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Journal articles on the topic 'Median algebra'

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