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Journal articles on the topic 'Melodic analysis Mathematical models'

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Published: 10 December 2022

Last updated: 29 January 2023

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1

Carrozza, Sylvain, and Sabine Harribey. "Melonic Large N Limit of 5-Index Irreducible Random Tensors." Communications in Mathematical Physics 390, no. 3 (January 18, 2022): 1219–70. http://dx.doi.org/10.1007/s00220-021-04299-1.

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AbstractWe demonstrate that random tensors transforming under rank-5 irreducible representations of $$\mathrm {O}(N)$$ O ( N ) can support melonic large N expansions. Our construction is based on models with sextic (5-simplex) interaction, which generalize previously studied rank-3 models with quartic (tetrahedral) interaction (Benedetti et al. in Commun Math Phys 371:55, 2019. arXiv:1712.00249; Carrozza in JHEP 06:039, 2018. arXiv:1803.02496). Beyond the irreducible character of the representations, our proof relies on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs. Our results provide further evidence that the melonic limit is a universal feature of irreducible tensor models in arbitrary rank.

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2

Temperley, David. "Probabilistic Models of Melodic Interval." Music Perception 32, no. 1 (September 1, 2014): 85–99. http://dx.doi.org/10.1525/mp.2014.32.1.85.

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Two probabilistic models of melodic interval are compared. In the Markov model, the “interval probability” of a note is defined by the corpus frequency of its melodic interval (the interval to the previous note), conditioned on the previous one or two intervals; in the Gaussian model, the interval probability is a simple mathematical function of the size of the note’s melodic interval and its position in relation to the range of the melody. In both models, this interval probability is then multiplied by the probability of the note’s scale degree to yield its actual probability. The two models were tested on four corpora of tonal melodies using cross-entropy. The Markov model yielded a somewhat lower (better) cross-entropy than the Gaussian model, but is also much more complex, requiring far more parameters. The models were also tested on melodic expectation data, and on their ability to predict the distribution of intervals in a corpus. Possible ways of improving the models are discussed, as well as their broader implications for music cognition.

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Buchok, Lianna. "V. Telychko’s “Children’s Album” as an example of the modern tonal image of the world: peculiarities of the musical vocabulary and melodic ideas." Problems of Interaction Between Arts, Pedagogy and the Theory and Practice of Education 49, no. 49 (September 15, 2018): 70–84. http://dx.doi.org/10.34064/khnum1-49.05.

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Background. The beginning of the development of musical art in Transcarpathia dates back to the end of the nineteenth century and lasts during the first third of the twentieth century. First of all, it was an interest in the genre of choral music (a synthetic genre based on the merging of the Word and Music), which fully corresponded to the enlightened spirit of life of the Transcarpathians under the political conditions of that time. And only in the second half of the twentieth century intensive blossoming of the varieties of instrumental (kind of «pure») music with its conceptually most complex types of creative thinking and adaptation to the methods of style transformation takes place. The piano music, one of the most abstract forms of the creative process, has revealed its peculiarities in this process. However, the researchers virtually never paid attention to piano pieces for children, which are naturally inferior by their practically necessary and didactically appropriate visual simplicity of musical vocabulary to the works of the so-called large genre. In addition, historically, the creative work of Transcarpathian composers has been considered only as a product of a purely regional significance. Therefore, it is important that the piano works of Transcarpathian composers for children should also be considered in the context of such integrity as the Intentional period of the music history, which has been defined as non-classical and at the same time permeated with the idea of global cultural synthesis Objectives. The essence of the tasks and the purpose is to present the "Child Album" by V. Telychko (the first in Transcarpathia sample of the genre of children’s musical album, 2016) as an example of the creation of the modern intonational image of the world - in its associative diversity and intentionality. Methods. A selection of research methods, namely, analytical (analysis and synthesis, induction and deduction, systematization, classification and generalization), comparative, systemic, phenomenological, functional, has been used in view of the holistic approach – in the spirit of spiritual development of the world. In this regard, the interpretive potential of the concepts of the intonational model and the modal nature of musical themes as types of thinking by sound images is considered methodologically appropriate: both purposefully focus attention of the recipient on the sound «body» and the intonational "soul" of the musical matter in the integrity of the creative idea of the work, and also is didactically productive in terms of comprehension of the architectonics of the world of music as a world of musical ideas. Results. V. Telichko’s "Children’s Album" is a cyclic structure of the linear/plot type, where step-by-step compositional and dramaturgical organization of the whole ensures the principle of successive naming of new, but equal in figurative semantic content pieces. At the same time, it will be superfluous to reflect on the fact that the structure of cycles such as "album" is rarely evaluated as such that it is actually "filled in" (for example, with memorable photos or pictures), and only since then its "white" (from alba) of the blank/empty sheets is filled in with the semantics and the logic of placement of fixed events, phenomena, impressions, etc in a certain order. Against the background of such reflection the memory recalls such "albums" of romantics: all of them are based on the logic of the course of a day lived by a child (for example, P. I. Tchaikovsky). V. Telichko’s principle of collecting pieces "into the album" has such a life-justifiable logic – the gradual flow of events of the day, embodied in a child’s only perception of the world and itself. The semantic code of the composer’s plan is referenced in his dedication: "I devote my love to grandchildren Angelina and Anna" - expressing love for grandchildren, admiring their fantasy and energy, caring for the formation of their worldview on a certain system of values (family, native land, diversity of traditions of the countries of the world , historical memory): the pieces "Morning", "My Mother", "Our Grandmother" represent an idea of an ingenuous and happy feeling of a child in the family; "Anna’s Teddy-Bear", "Angelina’s Hobbyhorse" and "Angelina’s Waltz " represent a lively imagination of children, each of them having a favorite game "theme"; the plays "About Transcarpathia", "Kolomyika", "Tropotyanka", "Long road" and "It’s raining" are outlined by the situation of instructive stories of grandfather about the regionally formed traditions of the Transcarpathians, their spirit and uneasy destiny; while the pieces "On Scotland", "On Slovakia" and "On Japan" outline the interests of somewhat different cognitive significance - the intention to comprehend a certain national "otherness", which has its own color of its culture; in the end, "A Lullaby for Anna" creates, so to say, a backlash against the grand finale-prologue, consisting of the pieces "On Austria" (the cultural center of the European musical classicism) and "On Romania" (regionally closest to Transcarpathia country). Another signifying circumstance of the idea and plan of the cycle refers to the types of performances and personification of images, both as members of the family circle and as a certain social unity: in addition to the versions of solo performance, in a considerable number of plays there is ensemble performance in four and six hands; at the same time, each of the parts is composed as a certain texture layer, which in aggregate (duo, terzetto) gives the effect of an "orchestral" score. However, the most important thing is that for the instrumentalist performer, and for the listener or analyst (who is also a "listener"), the "Children’s Album" by V. Telichko is a test of the ability to perceive musical vocabulary in the form of a certain sound form/idea with which it is necessary to have a relationship according to the algorithm of personal identification. On the one hand, in the musical text there is an opportunity to recognize the classical models of musical vocabulary (cantilena, recitation, motility, general forms of motion, signaling, sound illustration); and on the other - due to the constructive interference of the classical techniques of the creation of musical matter (emancipated dissonance, the non-systemic character of the tonality, etc.) the meanings are accumulated. Another important component of the composer’s plan is to introduce a purely methodical (level of methodical reception) task of developing the technology of the game on the piano into the original sound form/idea, which first of all requires a skillful usage of all the fingers. Conclusions. As a research material the "Children’s Album" by a contemporary composer from Transcarpathia, V. Telichko provides several important and mutually perceptible scientific tasks directly related to musicology and pedagogical practice: testing of the theoretically updated analytical apparatus for tracking the intonational field of music and its thoughts and comprehension of the didactically expedient implementation of its results in the educational sphere; in particular, in terms of the prospective guideline for the development of musicality (a high measure of the ability to self-identification with the musical image) and the piano skills of a child musician.

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4

Arthur, Claire. "Taking Harmony Into Account." Music Perception 34, no. 4 (April 1, 2017): 405–23. http://dx.doi.org/10.1525/mp.2017.34.4.405.

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Probabilistic models have proved remarkably successful in modeling melodic organization (e.g., Huron, 2006a; Pearce, 2005; Temperley, 2008). However, the majority of these models rely on pitch information taken from melody alone. Given the prevalence of homophonic music in Western culture, however, surprisingly little attention has been directed at exploring the predictive power of harmonic accompaniment in models of melodic organization. The research presented here uses a combination of the three main approaches to empirical musicology—exploratory analysis, modeling, and hypothesis testing—to investigate the influence of harmony on melodic behavior. In this study a comparison is made between models that use only melodic information and models that consider the melodic information along with the underlying harmonic accompaniment to predict melodic continuations. A test of overall performance shows a significant improvement using a melodic-harmonic model. When individual scale degrees are examined, the major diatonic scale degrees are shown to have unique probability distributions for each of their most common harmonic settings. That is, the results suggest a robust effect of harmony on melodic organization. Perceptual implications and directions for future research are discussed.

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Schmuckler, Mark A. "Testing Models of Melodic Contour Similarity." Music Perception 16, no. 3 (1999): 295–326. http://dx.doi.org/10.2307/40285795.

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In two experiments, descriptions of melodic contour structure and predictions of perceived similarity relations between pairs of contours produced by a number of different models are examined. Two of these models, based on the music- theoretic approaches of Friedmann (1985) and Marvin and Laprade (1987), characterize contours in terms of interval content or contour subset information. The remaining two approaches quantify the global shape of the contours, through the presence of cyclical information (assessed via Fourier analysis) and the amount of oscillation (e. g., reversals in direction, pitch deviations) in the contours. Theoretical predictions for contour similarity generated by these models were examined for 20th century, nontonal melodies (Experiment 1) and simplistic, tonal patterns (Experiment 2). These experiments demonstrated that similarity based on Fourier analysis procedures and oscillation measures predicted a derived measure of perceived similarity, with both variables contributing relatively independently; the music- theoretic models were inconsistent in their predictive power. These results suggest that listeners are sensitive to the presence of global shape information in melodic contour, with such information underlying the perception of contour structure and contour similarity.

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6

Bod, Rens. "Memory-Based Models of Melodic Analysis: Challenging the Gestalt Principles." Journal of New Music Research 31, no. 1 (March 1, 2002): 27–36. http://dx.doi.org/10.1076/jnmr.31.1.27.8106.

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7

Schmuckler, Mark A. "Melodic Contour Similarity Using Folk Melodies." Music Perception 28, no. 2 (December 1, 2010): 169–94. http://dx.doi.org/10.1525/mp.2010.28.2.169.

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Melodic contour, or the pattern of rises and falls in pitch, is a critical component of melodic structure, and has an important impact on listeners' perceptions of, and memory for, music. Despite its centrality, few formal models of contour structure exist. One recent exception involves characterizing contour by the relative degrees of strength of its cyclic information, quantified via a Fourier analysis of the pitch code of the contour. Three experiments explored the applicability of this approach, demonstrating that listeners' similarity ratings for pairs of melodies were predictable from Fourier analysis quantifications of rhythmically complex (Experiment 1) and rhythmically simple (Experiment 2) melodies, as well as for derived similarity measures based on melodic complexity judgments (Experiment 3). These findings indicate that Fourier analysis is an effective model of melodic contour, and that it can predict perceived melodic similarity.

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8

Eerola, Tuomas. "Expectancy-Violation and Information-Theoretic Models of Melodic Complexity." Empirical Musicology Review 11, no. 1 (July 8, 2016): 2. http://dx.doi.org/10.18061/emr.v11i1.4836.

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The present study assesses two types of models for melodic complexity: one based on expectancy violations and the other one related to an information-theoretic account of redundancy in music. Seven different datasets spanning artificial sequences, folk and pop songs were used to refine and assess the models. The refinement eliminated unnecessary components from both types of models. The final analysis pitted three variants of the two model types against each other and could explain from 46-74% of the variance in the ratings across the datasets. The most parsimonious models were identified with an information-theoretic criterion. This suggested that the simplified expectancy-violation models were the most efficient for these sets of data. However, the differences between all optimised models were subtle in terms both of performance and simplicity.

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9

Ray, W. D., and F. Y. M. Wan. "Mathematical Models and Their Analysis." Journal of the Operational Research Society 41, no. 12 (December 1990): 1173. http://dx.doi.org/10.2307/2583116.

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10

Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.2307/30141966.

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11

Chen, Zhangxin, and Richard Ewing. "Mathematical Analysis for Reservoir Models." SIAM Journal on Mathematical Analysis 30, no. 2 (January 1999): 431–53. http://dx.doi.org/10.1137/s0036141097319152.

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12

Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.1086/647503.

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13

Ray, W. D. "Mathematical Models and Their Analysis." Journal of the Operational Research Society 41, no. 12 (December 1990): 1173. http://dx.doi.org/10.1057/jors.1990.186.

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14

Thompson, William Forde, and Murray Stainton. "Expectancy in Bohemian Folk Song Melodies: Evaluation of Implicative Principles for Implicative and Closural Intervals." Music Perception 15, no. 3 (1998): 231–52. http://dx.doi.org/10.2307/40285766.

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Principles of melodic implication were evaluated in an analysis of folk song melodies. Implicative and closural intervals were identified in 513 Bohemian melodies, and the note following each interval (the continuation note) was analyzed. Multinomial log-linear analysis was conducted to assess the extent to which Narmour's (1990) implicative principles could predict continuation notes. Support was found for five principles, with slightly greater support for strongly implicative intervals than for closural intervals, and for large intervals than for small intervals. Alternative models of melodic implication are discussed.

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15

Li, Xiong, Hao Wang, Zheng Zhang, and Alan Hastings. "Mathematical analysis of coral reef models." Journal of Mathematical Analysis and Applications 416, no. 1 (August 2014): 352–73. http://dx.doi.org/10.1016/j.jmaa.2014.02.053.

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16

Belsole, Robert J., Don R. Hilbelink, J. Anthony Llewellyn, Stephen Stenzler, Thomas L. Greene, and Mark Dale. "Mathematical analysis of computed carpal models." Journal of Orthopaedic Research 6, no. 1 (January 1988): 116–22. http://dx.doi.org/10.1002/jor.1100060115.

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17

Jones, Don A. "Mathematical Analysis of Geophysical Balance Models." Journal of Differential Equations 179, no. 1 (February 2002): 1–26. http://dx.doi.org/10.1006/jdeq.2001.4024.

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18

Buikis, A., J. Cepitis, H. Kalis, A. Reinfelds, A. Ancitis, and A. Salminš. "Mathematical Models of Papermaking." Nonlinear Analysis: Modelling and Control 6, no. 1 (April 1, 2001): 9–19. http://dx.doi.org/10.15388/na.2001.6.1.15221.

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The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations.

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19

McAdams, Stephen. "Musical Forces and Melodic Expectations: Comparing Computer Models and Experimental Results." Music Perception 21, no. 4 (June 1, 2004): 457–98. http://dx.doi.org/10.1525/mp.2004.21.4.457.

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Recent work on "musical forces" asserts that experienced listeners of tonal music not only talk about music in terms used to describe physical motion, but actually experience musical motion as if it were shaped by quantifiable analogues of physical gravity, magnetism, and inertia. This article presents a theory of melodic expectation based on that assertion, describes two computer models of aspects of that theory, and finds strong support for that theory in comparisons of the behavior of those models with the behavior of participants in several experiments. The following summary statement of the theory is explained and illustrated in the article: Experienced listeners of tonal music expect completions in which the musical forces of gravity, magnetism, and inertia control operations on alphabets in hierarchies of embellishment whose stepwise displacements of auralized traces create simple closed shapes. A "single-level" computer program models the operation of these musical forces on a single level of musical structure. Given a melodic beginning in a certain key, the model not only produces almost the same responses as experimental participants, but it also rates them in a similar way; the computer model gives higher ratings to responses that participants sing more often. In fact, the completions generated by this model match note-for-note the entire completions sung by participants in several psychological studies as often as the completions of any one of those participants matches those of the other participants. A "multilevel" computer program models the operation of these musical forces on multiple hierarchical levels. When the multilevel model is given a melodic beginning and a hierarchical description of its embellishment structure (i.e., a Schenkerian analysis of it), the model produces responses that reflect the operation of musical forces on all the levels of that hierarchical structure. Statistical analyses of the results of a number of experiments test hypotheses arising from the computer models' algorithm (S. Larson, 1993a) for the interaction of musical forces as well as from F. Lerdahl's similar (1996) algorithm. Further statistical analysis contrasts the explanatory power of the theory of musical forces with that of E. Narmour's (1990, 1992) implication-realization model. The striking agreement between computer-generated responses and experimental results suggests that the theory captures some important aspects of melodic expectation. Furthermore, the fact that these data can be modeled well by the interaction of constantly acting but contextually determined musical forces gives support to the idea that we experience musical motions metaphorically in terms of our experience of physical motions.

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SHEINA, G., and S. SKRYPNYK. "Analysis of mathematical models of transmission lines." Journal of Electrical and power engineering, no. 1 (2019): 14–17. http://dx.doi.org/10.31474/2074-2630-2019-1-14-17.

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SHEINA, G. "Analysis of mathematical models of transmission lines." Journal of Electrical and power engineering 23, no. 2 (December 23, 2020): 16–19. http://dx.doi.org/10.31474/2074-2630-2020-2-16-19.

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This paper investigates a mathematical model of one elements of the power supply system - power transmission lines. The type of models depends on the initial simplifications, which in turn are determined by the complexity of the physics of processes. The task of improving the accuracy of modeling of emergency processes in the power system is due to the significant complexity of modern power systems and their equipment, high-speed relay protection, automation of emergency management and the introduction of higher-speed switching equipment. One of the reasons for a significant number of serious emergencies in the system is the lack of complete and reliable information for modeling modes in the design and operation of power systems. The development of a mathematical model of a three-phase power line, which provides adequate reflection of both normal and emergency processes, is relevant. The advanced mathematical model of power transmission lines allows to investigate various operational modes of electric networks. The improved mathematical model of the power transmission line reflects all the features of physical processes at state modes and transient process and provides sufficient accuracy of the results. The type of mathematical model of power transmission lines depends on the accepted simplifications, depending on the task of research. The purpose of this work is to analyze the mathematical model of the power transmission line to study the modes of operation of the power supply system, with the possibility of its application to take into account all the design features of overhead and cable power lines. The mathematical model of the power line for the study of the modes of operation of the power supply system is analyzed. It is used to take into account the design features of overhead and cable power lines, skin effect.

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22

Qin, Xuan Hua, and Li Li Zheng. "Mathematical Models for Analysis of Water Pollution." Applied Mechanics and Materials 209-211 (October 2012): 1941–47. http://dx.doi.org/10.4028/www.scientific.net/amm.209-211.1941.

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The water qualityr was considered by multiple regression analysis. The linear relationship between integrated pollution index and weight pollution index were obtained, the 5 day biochemical oxygen demanded and total nitrogen were the most important pollution factor by the relationship. And then, the two main components influencing water quality were given based on the principal component analysis affecting data..

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23

Falces, J. R., A. M. Trigueros, L. G. Useros, I. R. Carreno, and J. N. Irujo. "A mathematical analysis of SFAP convolutional models." IEEE Transactions on Biomedical Engineering 52, no. 5 (May 2005): 769–83. http://dx.doi.org/10.1109/tbme.2005.845045.

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24

KRASUCKI, FRANCOISE, ARNAUD MÜNCH, and YVES OUSSET. "MATHEMATICAL ANALYSIS OF NONLINEAR BONDED JOINT MODELS." Mathematical Models and Methods in Applied Sciences 14, no. 04 (April 2004): 535–56. http://dx.doi.org/10.1142/s0218202504003349.

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Within the framework of nonlinear elasticity, we consider the problem of two adherents joined along their common surface by a thin soft adhesive. Two stored energy functions are considered: the stored energy function of Saint Venant–Kirchhoff and the stored energy function of Ciarlet–Geymonat. Using the asymptotic expansion method, the limit energy associated to each of these stored energy functions is obtained. The aim of this paper is to give a rigorous mathematical analysis of the formally derived limit problem. We show that the limit problem associated to the Saint Venant–Kirchhoff case admits at least one solution and the limit problem associated to the Ciarlet–Geymonat case admits exactly one solution. An analytical comparison in the one-dimensional case and a three-dimensional numerical application are also presented.

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25

Blischke, W. R. "Mathematical models for analysis of warranty policies." Mathematical and Computer Modelling 13, no. 7 (1990): 1–16. http://dx.doi.org/10.1016/0895-7177(90)90124-6.

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Abdallah, N. Ben, S. Mas-Gallic, and P. A. Raviart. "A Mathematical analysis of electric probe models." Transport Theory and Statistical Physics 25, no. 3-5 (April 1996): 263–81. http://dx.doi.org/10.1080/00411459608220701.

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Fernández-Calvín, Begoña, Juan Orellana, and Domenico Pignone. "Genome Analysis of Triploids Using Mathematical Models." Hereditas 122, no. 1 (May 28, 2004): 41–45. http://dx.doi.org/10.1111/j.1601-5223.1995.00041.x.

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Raichenko, A. I. "Comparative analysis of one-particle mathematical models in materials science and oncology. I. Mathematical models." Powder Metallurgy and Metal Ceramics 44, no. 11-12 (November 2005): 578–82. http://dx.doi.org/10.1007/s11106-006-0028-7.

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Ospanova, Aiman, Meruyert Berdiyeva, and Tamara Zhukbaeva. "Mathematical Models Of Polimerization Processes." Applied Mathematics & Information Sciences 7, no. 4 (July 1, 2013): 1533–37. http://dx.doi.org/10.12785/amis/070437.

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Chaskalovic, J. "New mathematical models for media exposure." Journal of Interdisciplinary Mathematics 12, no. 3 (June 2009): 395–408. http://dx.doi.org/10.1080/09720502.2009.10700632.

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Meirmanov, Anvarbek, and Irina Nekrasova. "Mathematical models of a hydraulic shock." Journal of Mathematical Analysis and Applications 408, no. 1 (December 2013): 76–90. http://dx.doi.org/10.1016/j.jmaa.2013.05.024.

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Sentis, Rémi. "Mathematical models for laser-plasma interaction." ESAIM: Mathematical Modelling and Numerical Analysis 39, no. 2 (March 2005): 275–318. http://dx.doi.org/10.1051/m2an:2005014.

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Neetu Rani, Kiran Bamel, Abhinav Shukla, and Nandini Singh. "Analysis of Five Mathematical Models for Crop Yield Prediction." South Asian Journal of Experimental Biology 12, no. 1 (February 27, 2022): 46–54. http://dx.doi.org/10.38150/sajeb.12(1).p46-54.

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A review of mathematical models used for the prediction of crop yield has been presented. Though there are many other non-mathematical techniques also available for the purpose, but mathematical modeling used for any real world problem opens many perspectives and provides many possible solu-tions of the problem for the betterment of human race. Five mathematical models (remote sensing followed by mathematical modeling, fuzzy logic based model, multiple linear regression mechanistic model, linear algebra based descriptive model and growth model based on TOMGRO mechanistic model) have been extracted and analyzed critically. These models are based on different mathematical concepts and techniques (non-linear optimization, fuzzy logic, linear predictor functions, linear algebra and differential calculus) covering a wide range of mathematical modeling. The general forms of these models have been derived. Average accuracy of presented models was found to be in the range 90% - 99% that strongly favors the optimum usage of mathematical modeling for crop yield forecasting processes. The section giving gaps and future research prospects presents the comparative analysis of the models. Development of new and moderated mathematical models for more precision and better accuracy has also been suggested using new mathematical techniques and hybridization or modifying the existing models.

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Mazur, James E. "MATHEMATICAL MODELS AND THE EXPERIMENTAL ANALYSIS OF BEHAVIOR." Journal of the Experimental Analysis of Behavior 85, no. 2 (March 2006): 275–91. http://dx.doi.org/10.1901/jeab.2006.65-05.

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Ojimadu, U. H., A. O. Oluwole, A. O. Olasupo, M. A. Usman, T. J. Odule, O. O. Olubanwo, O. Oyewole, and M. A. Ayodele. "MATHEMATICAL ANALYSIS OF ELECTROPHYSIOLOGICAL CARDIAC TISSUE MEMBRANE MODELS." FUDMA JOURNAL OF SCIENCES 6, no. 2 (May 11, 2022): 138–43. http://dx.doi.org/10.33003/fjs-2022-0602-931.

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This paper presents some cardiac electrophysiological models. Proper mathematical analysis was done on the proposed models. In the cause of the analysis, several assumptions were made which helped in providing a parallel platform for making qualitative solutions so as to reduce any form of bias. Graphical analysis was adopted in solving the cardiac electrophysiological models using conservation and dispersions equations. The results obtained were derived from computer simulation by observing ring lengths on a valid restitution curve. The restitution curves helps us to subject three different turns of ring lengths and certain observations were made on the behavior of the three ring lengths. An increase in ring length will cause a corresponding increase in blood circulation and vice versa. It was suggested that 2D or 3D computer simulation should be adopted for better performance and yield of the models

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Dela, An, Blerta Shtylla, and Lisette de Pillis. "Multi-method global sensitivity analysis of mathematical models." Journal of Theoretical Biology 546 (August 2022): 111159. http://dx.doi.org/10.1016/j.jtbi.2022.111159.

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Mayank, Rahul, Amrita Ranjan, and Vijayanand S. Moholkar. "Mathematical models of ABE fermentation: review and analysis." Critical Reviews in Biotechnology 33, no. 4 (October 16, 2012): 419–47. http://dx.doi.org/10.3109/07388551.2012.726208.

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Іvchenko, P. O. "Analysis of mathematical models of the oxygen sensor." Electronics and Communications 17, no. 3 (September 24, 2012): 29–33. http://dx.doi.org/10.20535/2312-1807.2012.17.3.219578.

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WILLINGER, R., L. TALEB, and C.-M. KOPP. "Modal and Temporal Analysis of Head Mathematical Models." Journal of Neurotrauma 12, no. 4 (August 1995): 743–54. http://dx.doi.org/10.1089/neu.1995.12.743.

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Glen, J. J. "Mathematical programming models for piecewise-linear discriminant analysis." Journal of the Operational Research Society 56, no. 3 (March 2005): 331–41. http://dx.doi.org/10.1057/palgrave.jors.2601818.

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Spreen, Thomas H. "Price Endogenous Mathematical Programming Models and Trade Analysis." Journal of Agricultural and Applied Economics 38, no. 2 (August 2006): 249–53. http://dx.doi.org/10.1017/s1074070800022276.

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Abstract:

Takayama and Judge introduced the price endogenous mathematical programming model as an alternative to the traditional econometric approach to sector-level policy analysis. McCarl and Spreen provided a review of price endogenous mathematical programming models. In that paper, they showed how price endogeneity can be introduced into a standard firm-level linear programming model. The introduction of price endogeneity allows expansion of the firm-level specification to a market-level analysis. At the time of publication of McCarl and Spreen, however, the application of price endogenous mathematical programming models was limited by the availability of software packages that could directly solve such models. The typical application used linear supply and/or demand relationships, which resulted in a quadratic programming (QP) specification. The advent of MINOS in the 1980s and then its incorporation into GAMS has lifted the computation constraint. In the present day, numerous price endogenous models have been developed. I can lay claim to six such models.

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Savula, Y. H., I. I. Dyyak, and V. V. Krevs. "Heterogeneous mathematical models in numerical analysis of structures." Computers & Mathematics with Applications 42, no. 8-9 (October 2001): 1201–16. http://dx.doi.org/10.1016/s0898-1221(01)00233-4.

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Harbi, H., and N. U. Ahmed. "Mathematical Analysis of Dynamic Models of Suspension Bridges." SIAM Journal on Applied Mathematics 58, no. 3 (June 1998): 853–74. http://dx.doi.org/10.1137/s0036139996308698.

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Zumsande, Martin, Dirk Stiefs, Stefan Siegmund, and Thilo Gross. "General analysis of mathematical models for bone remodeling." Bone 48, no. 4 (April 2011): 910–17. http://dx.doi.org/10.1016/j.bone.2010.12.010.

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Emvudu, Yves, Danhrée Bongor, and Rodoumta Koïna. "Mathematical analysis of HIV/AIDS stochastic dynamic models." Applied Mathematical Modelling 40, no. 21-22 (November 2016): 9131–51. http://dx.doi.org/10.1016/j.apm.2016.05.007.

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Il'inskii, A. S., and Yu G. Smirnov. "Analysis of mathematical models of microstrip transmission lines." Computational Mathematics and Modeling 1, no. 2 (1990): 218–34. http://dx.doi.org/10.1007/bf01129065.

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Phanawadee, Phungphai, Monrudee Phongaksorn, Nalinee Chaimongkol, Attasak Jaree, and Jumras Limtrakul. "Mathematical analysis of TAP models for porous catalysts." Chemical Engineering Journal 115, no. 1-2 (December 2005): 51–62. http://dx.doi.org/10.1016/j.cej.2005.09.010.

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Koehler, Gary J. "Considerations for mathematical programming models in discriminant analysis." Managerial and Decision Economics 11, no. 4 (1990): 227–34. http://dx.doi.org/10.1002/mde.4090110404.

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Lipovetsky, Stan. "Mathematical Modeling: Models, Analysis and Applications, 2nd Edition." Technometrics 64, no. 4 (October 2, 2022): 580–81. http://dx.doi.org/10.1080/00401706.2022.2126659.

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Blyumin, S. L., A. V. Galkin, and A. S. Sysoev. "ON SENSITIVITY ANALYSIS BY FACTORS OF MATHEMATICAL MODELS." Mathematical Methods in Technologies and Technics, no. 10 (2022): 39–43. http://dx.doi.org/10.52348/2712-8873_mmtt_2022_10_39.

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