Journal articles: 'Modelling math'

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Jain, Sonal, and Youssef El-Khatib. "Modelling chaotic dynamical attractor with fractal-fractional differential operators." AIMS Mathematics 6, no. 12 (2021): 13689–725. http://dx.doi.org/10.3934/math.2021795.

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<abstract>Differential operators based on convolution have been recognized as powerful mathematical operators able to depict and capture chaotic behaviors, especially those that are not able to be depicted using classical differential and integral operators. While these differential operators have being applied with great success in many fields of science, especially in the case of dynamical system, we have to confess that they were not able depict some chaotic behaviors, especially those with additionally similar patterns. To solve this issue new class of differential and integral operators were proposed and applied in few problems. In this paper, we aim to depict chaotic behavior using the newly defined differential and integral operators with fractional order and fractal dimension. Additionally we introduced a new chaotic operators with strange attractors. Several simulations have been conducted and illustrations of the results are provided to show the efficiency of the models.</abstract>

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Mohammed, Heba S., Zubair Ahmad, Alanazi Talal Abdulrahman, Saima K. Khosa, E. H. Hafez, M. M. Abd El-Raouf, and Marwa M. Mohie El-Din. "Statistical modelling for Bladder cancer disease using the NLT-W distribution." AIMS Mathematics 6, no. 9 (2021): 9262–76. http://dx.doi.org/10.3934/math.2021538.

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Lee, Deokro, Amit Koul, Nikhat Lubna, Sean A. McKenna, and Stéphanie Portet. "Mathematical modelling of OAS2 activation by dsRNA and effects of dsRNA lengths." AIMS Mathematics 6, no. 6 (2021): 5924–41. http://dx.doi.org/10.3934/math.2021351.

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Cahyono, Adi Nur, Yohanes Leonardus Sukestiyarno, Mohammad Asikin, Miftahudin Miftahudin, Muhammadi Ghozian Kafi Ahsan, and Matthias Ludwig. "LEARNING MATHEMATICAL MODELLING WITH AUGMENTED REALITY MOBILE MATH TRAILS PROGRAM: HOW CAN IT WORK?" Journal on Mathematics Education 11, no. 2 (March 3, 2020): 181–92. http://dx.doi.org/10.22342/jme.11.2.10729.181-192.

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The aim of this study is to investigate how an augmented reality mobile math trails program can provide opportunities for students to engage in meaningful mathematical modelling activities. An explorative research design was conducted involving two mathematics teachers and 30 eight grades in Semarang, Indonesia. An Augmented Reality Mobile Math Trails App was created, and several math trail tasks were designed, then students run the activity. Data were gathered by means of participatory observation, interviews, questionnaires, tests, and worksheets. Data analysis began with the organisation, annotation, description of the data and statistic tests. The findings indicate that an educational program was successfully designed, which offered students a meaningful mathematical experience. A mobile app was also developed to support this program. The mobile app with augmented reality features is helpful for students as a tool that bridges the gap between real-world situations and mathematical concepts in problem-solving following the mathematical modelling cycle. The program thus contributes to a higher ability in mathematical modelling. The study identified a link between instrumented techniques in programs and mathematical modelling, as built during the instrumentation process. Further studies are essential for project development and implementation in other cities with different situations and aspects of study.

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Gyorfi, Z. "The Bolyai lamp, a new math manipulative modelling the hyperbolic plane." Teaching Mathematics and its Applications 26, no. 4 (October 15, 2007): 225. http://dx.doi.org/10.1093/teamat/hrm002.

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HYDE, B., D. BARBIER, J. HUBNER, J. M. JOUANNO, A. KEVORKIAN, and A. LUPASCU. "Waveguide amplifiers in rare-earth doped glasses : fabrication, characterisation [MATH] modelling." Le Journal de Physique IV 04, no. C4 (April 1994): C4–277—C4–280. http://dx.doi.org/10.1051/jp4:1994468.

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Clampitt, David. "The Math Behind the Music." Journal of Mathematics and Music 3, no. 1 (March 2009): 59–61. http://dx.doi.org/10.1080/17459730902907148.

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Garcke, Harald, and Kei Fong Lam. "Global weak solutions and asymptotic limits of a Cahn–Hilliard–Darcy system modelling tumour growth." AIMS Mathematics 1, no. 3 (2016): 318–60. http://dx.doi.org/10.3934/math.2016.3.318.

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Ji, Bing, Jiawei Bai, Luis A J Mur, Mengjia Zou, Jiwan Han, Rui Gao, and Qing Yang. "Mathematical modelling of Her2 (ErbB2) PI3K/AKT signalling pathways during breast carcinogenesis to include PTPD2." AIMS Mathematics 5, no. 5 (2020): 4946–58. http://dx.doi.org/10.3934/math.2020316.

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Sanabria, Rafael. "Inelastic Boltzmann equation driven by a particle thermal bath." Kinetic & Related Models 14, no. 4 (2021): 639. http://dx.doi.org/10.3934/krm.2021018.

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We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient <inline-formula><tex-math id="M1">\begin{document}$ \alpha\in(0,1) $\end{document}</tex-math></inline-formula>, under the thermalization induced by a host medium with fixed <inline-formula><tex-math id="M2">\begin{document}$ e\in(0,1] $\end{document}</tex-math></inline-formula> and a fixed Maxwellian distribution. When the restitution coefficient <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> is close to 1 we prove existence and uniqueness of global solutions considering the close-to-equilibrium regime. We also study the long-time behaviour of these solutions and prove a convergence to equilibrium with an exponential rate.

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Callan, Torrington, and Stephen Woodcock. "Stochastic modelling of chlamydial infections." ANZIAM Journal 61 (July 6, 2020): C89—C103. http://dx.doi.org/10.21914/anziamj.v61i0.15159.

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Chlamydia trachomatis is a bacterial pathogen that can cause serious reproductive harm. We describe a class of stochastic branching processes and their application in modelling the growth of an infection by Chlamydia. Using simulations we show that the model can reproduce biological phenomena of interest, and we show the variability in outcomes of infections under the same parameter conditions. We further speculate how this model might be used to explain long-term adverse reproductive sequelae. References Y. M. AbdelRahman and R. J. Belland. The chlamydial developmental cycle. FEMS Microbio. Rev., 29(5):949–959, 2005. doi:10.1016/j.femsre.2005.03.002. T. E. Harris. Branching processes. Ann. Math. Stat., 19(4):474–494, 12 1948. doi:10.1214/aoms/1177730146. C. Jacob. Branching processes: Their role in epidemiology. Int. J. Env. Res. Public Health, 7(3):1186–1204, 2019. doi:10.3390/ijerph7031204. N. Low, M. Egger, J. A. C. Sterne, R. M. Harbord, F. Ibrahim, B. Lindblom, and B. Herrmann. Incidence of severe reproductive tract complications associated with diagnosed genital chlamydial infection: The Uppsala women's cohort study. Sexually Trans. Infect., 82(3):212–218, 2006. doi:10.1136/sti.2005.017186. D. Mallet, M. Bagher-Oskouei, A. Farr, D. Simpson, and K. Sutton. A mathematical model of chlamydial infection incorporating movement of chlamydial particles. Bull. Math. Bio., 75:2257–2270, 10 2013. doi:10.1007/s11538-013-9891-9. H. K. Maxion, W. Liu, M.-H. Chang, and K. A. Kelly. The infecting dose of chlamydia muridarum modulates the innate immune response and ascending infection. Infect. Immun., 72(11):6330–6340, 2004. doi:10.1128/IAI.72.11.6330-6340.2004. S. Menon, P. Timms, J. A. Allan, K. Alexander, L. Rombauts, P. Horner, M. Keltz, J. Hocking, and W. M. Huston. Human and pathogen factors associated with chlamydia trachomatis-related infertility in women. Clinic. Microbio. Rev., 28(4):969–985, 2015. doi:10.1128/CMR.00035-15. D. P. Wilson. Mathematical modelling of chlamydia. In J. Crawford and A. J. Roberts, editors, Proc. of 11th Computational Techniques and Applications Conference CTAC-2003, ANZIAM J., volume 45, pages C201–C214, 2004. doi:10.21914/anziamj.v45i0.883. D. P. Wilson and D. L. S. McElwain. A model of neutralization of chlamydia trachomatis based on antibody and host cell aggregation on the elementary body surface. J. Theor. Bio., 226(3):321–330, 2004. doi:10.1016/j.jtbi.2003.09.010. D. P. Wilson, P. Timms, and D. L. S. McElwain. A mathematical model for the investigation of the Th1 immune response to chlamydia trachomatis. Math. Biosci., 182(1):27–44, 2003. doi:10.1016/S0025-5564(02)00180-3.

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Jódar, Lucas, Elena de la Poza, Juan Carlos Cortés, and Luis Acedo. "Corrigendum to “Preface: The challenge of modelling aggregated human behaviour” [Math. Comput. Modelling 57 (2013) 1617–1618]." Mathematical and Computer Modelling 57, no. 9-10 (May 2013): 2580. http://dx.doi.org/10.1016/j.mcm.2013.03.001.

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Raphel, Fabien, Muriel Boulakia, Nejib Zemzemi, Philippe Zitoun, and Jean-Frédéric Gerbeau. "From Field Potential Waves to Ionic Current Knowledge by Leveraging Math Modelling." Journal of Pharmacological and Toxicological Methods 88 (November 2017): 197. http://dx.doi.org/10.1016/j.vascn.2017.09.094.

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Asl, Hadi Adibi, Roydon A. Fraser, and John McPhee. "Math-based spark ignition engine modelling including emission prediction for control applications." International Journal of Vehicle Systems Modelling and Testing 10, no. 2 (2015): 148. http://dx.doi.org/10.1504/ijvsmt.2015.068977.

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Yi, Pilnam, and In-soo Shin. "MULTILEVEL RELATIONS BETWEEN EXTERNAL ACCOUNTABILITY, INTERNAL ACCOUNTABILITY, AND MATH ACHIEVEMENT: A CROSS-COUNTRY ANALYSIS." Problems of Education in the 21st Century 76, no. 3 (June 15, 2018): 318–32. http://dx.doi.org/10.33225/pec/18.76.318.

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External accountability policies have spread fast across various educational systems over the past decades. This research examines the relations of internal and external accountability with students’ math achievement drawing on PISA 2012. With a sample of 44 educational systems, of which external accountability policies were identified, the research conducted three-level hierarchical linear modelling (HLM) analyses. This research found that some internal accountability factors had tighter relations with math achievement, while the relations of external accountability policies with student performance were rather tenuous. However, equity of student math achievement was better ensured under strong accountability systems. The results suggest that policy makers of each country should consider strengths and weaknesses of external accountability in their own educational contexts. Keywords: external accountability, educational equity, internal accountability, math achievement, PISA.

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Galerkin, Y., A. Drozdov, and A. Rekstin. "Centrifugal compressor impeller loading factor analysis." E3S Web of Conferences 124 (2019): 01005. http://dx.doi.org/10.1051/e3sconf/201912401005.

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The loading factor performance modelling is an important part of centrifugal compressor performance calculation. The presented information on model stages’ test data confirms the fact that the loading factor versus flow coefficient at an impeller exit is a linear function independent of Mach number (subsonic flow). The test data and the design characteristics of the series of 10 model stages are compared with the calculation of an inviscid flow and with calculations done using the NUMECA software. Math models offered by the authors, and inviscid calculations solve the problem of a primary design. The CFD-calculation for final solution is non-satisfactory. If the loading factor is calculated by total temperature difference and flow coefficient is calculated by a continuity equation, the performance is not quite linear and lies much higher. For the considered stages CFD-calculation inaccuracy is + (0,06 … 0,12). CFD-calculated flow coefficient is inside 0,96 … 0,98 of the measured and of the calculated by the Math model.

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Li, Huiping, and Song Li. "Phase retrieval from Fourier measurements with masks." Inverse Problems & Imaging 15, no. 5 (2021): 1051. http://dx.doi.org/10.3934/ipi.2021028.

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This paper concerns the problem of phase retrieval from Fourier measurements with random masks. Here we focus on researching two kinds of random masks. Firstly, we utilize the Fourier measurements with real masks to estimate a general signal <inline-formula><tex-math id="M1">\begin{document}$ \mathit{\boldsymbol{x}}_0\in \mathbb{R}^d $\end{document}</tex-math></inline-formula> in noiseless case when <inline-formula><tex-math id="M2">\begin{document}$ d $\end{document}</tex-math></inline-formula> is even. It is demonstrated that <inline-formula><tex-math id="M3">\begin{document}$ O(\log^2d) $\end{document}</tex-math></inline-formula> real random masks are able to ensure accurate recovery of <inline-formula><tex-math id="M4">\begin{document}$ \mathit{\boldsymbol{x}}_0 $\end{document}</tex-math></inline-formula>. Then we find that such real masks are not adaptable to reconstruct complex signals of even dimension. Subsequently, we prove that <inline-formula><tex-math id="M5">\begin{document}$ O(\log^4d) $\end{document}</tex-math></inline-formula> complex masks are enough to stably estimate a general signal <inline-formula><tex-math id="M6">\begin{document}$ \mathit{\boldsymbol{x}}_0\in \mathbb{C}^d $\end{document}</tex-math></inline-formula> under bounded noise interference, which extends E. Candès et al.'s work. Meanwhile, we establish tighter error estimations for real signals of even dimensions or complex signals of odd dimensions by using <inline-formula><tex-math id="M7">\begin{document}$ O(\log^2d) $\end{document}</tex-math></inline-formula> real masks. Finally, we intend to tackle with the noisy phase problem about an <inline-formula><tex-math id="M8">\begin{document}$ s $\end{document}</tex-math></inline-formula>-sparse signal by a robust and efficient approach, namely, two-stage algorithm. Based on the stable guarantees for general signals, we show that the <inline-formula><tex-math id="M9">\begin{document}$ s $\end{document}</tex-math></inline-formula>-sparse signal <inline-formula><tex-math id="M10">\begin{document}$ \mathit{\boldsymbol{x}}_0 $\end{document}</tex-math></inline-formula> can be stably recovered from composite measurements under near-optimal sample complexity up to a <inline-formula><tex-math id="M11">\begin{document}$ \log $\end{document}</tex-math></inline-formula> factor, namely, <inline-formula><tex-math id="M12">\begin{document}$ O(s\log(\frac{ed}{s})\log^4(s\log(\frac{ed}{s}))) $\end{document}</tex-math></inline-formula>

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Kolodinskaya, V. I., and V. Yu Nefyodova. "THE EXPERIENCE OF TEACHING THE THEME “MODELLING” BASED ON SOLVING APPLIED MILITARY CASES." Informatics in school, no. 9 (December 18, 2019): 7–15. http://dx.doi.org/10.32517/2221-1993-2019-18-9-7-15.

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The article is dealing with the theme “Modeling” basing it on applied military case studies. The universal educational actions were formulated, as well as educational outcomes. Math modeling tasks are reviewed using the available aerial photographs, and the modelling task for armed military confrontation is given.

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Kale, Mustafa. "Examining school variables affecting PISA 2012 math achievement in Turkey and Shanghai-China." Contemporary Educational Researches Journal 6, no. 4 (February 8, 2017): 167–74. http://dx.doi.org/10.18844/cerj.v6i4.586.

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The main purpose of the research is to examine school variables that have effect on Programme for International Student Assessment (PISA) 2012 math achievement in Turkey and Shanghai-China. The research was designed in casual comparison model. Research population was constituted by student in age group of 15 in Turkey and Shanghai-China in 2012.The sample consists of 4848 students and 170 schools in Turkey and 5177 students and 155 schools in Shanghai-China that participated in PISA 2012. Two-leveled Hierarchical Linear Modelling (HLM) was used to analyze data because the data collected in PISA 2012 had a hierarchical data structure. As a result of analysis, variability in math scores, 63% in Turkey and 47% in Shanghai-China, was found due to the difference between the mean math scores of schools. It was determined that MACTIV, SCMATEDU and TCMORALE in Turkey and MACTIV, in Shanghai-China statistically affect on math achievement. Keywords: PISA, school administration, school variables, HLM

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MANÁSEVICH, RAÚL, QUOC HUNG PHAN, and PHILIPPE SOUPLET. "Global existence of solutions for a chemotaxis-type system arising in crime modelling." European Journal of Applied Mathematics 24, no. 2 (November 27, 2012): 273–96. http://dx.doi.org/10.1017/s095679251200040x.

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We consider a nonlinear, strongly coupled, parabolic system arising in the modelling of burglary in residential areas. This model appeared in Pitcher (Eur. J. Appl. Math., 2010, Vol. 21, pp. 401–419), as a more realistic version of the Short et al. (Math. Models Methods Appl. Sci., 2008, Vol. 18, pp. 1249–1267) model. The system under consideration is of chemotaxis-type and involves a logarithmic sensitivity function and specific interaction and relaxation terms. Under suitable assumptions on the data of the problem, we give a rigorous proof of the existence of a global and bounded, classical solution, thereby solving a problem left open in previous work on this model. Our proofs are based on the construction of approximate entropies and on the use of various functional inequalities. We also provide explicit numerical conditions for global existence when the domain is a square, including concrete cases involving values of the parameters which are expected to be physically relevant.

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Kaltenbacher, Barbara, and William Rundell. "On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements." Inverse Problems & Imaging 15, no. 5 (2021): 865. http://dx.doi.org/10.3934/ipi.2021020.

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We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomography. In particular, we investigate the recovery of the nonlinearity coefficient commonly labeled as <inline-formula><tex-math id="M1">\begin{document}$ B/A $\end{document}</tex-math></inline-formula> in the literature which is part of a space dependent coefficient <inline-formula><tex-math id="M2">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> in the Westervelt equation governing nonlinear acoustics. Corresponding to the typical measurement setup, the overposed data consists of time trace measurements on some zero or one dimensional set <inline-formula><tex-math id="M3">\begin{document}$ \Sigma $\end{document}</tex-math></inline-formula> representing the receiving transducer array. After an analysis of the map from <inline-formula><tex-math id="M4">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> to the overposed data, we show injectivity of its linearisation and use this as motivation for several iterative schemes to recover <inline-formula><tex-math id="M5">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula>. Numerical simulations will also be shown to illustrate the efficiency of the methods.

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Fagioli, Simone, and Yahya Jaafra. "Multiple patterns formation for an aggregation/diffusion predator-prey system." Networks & Heterogeneous Media 16, no. 3 (2021): 377. http://dx.doi.org/10.3934/nhm.2021010.

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We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually proportional by a negative constant <inline-formula><tex-math id="M1">\begin{document}$ -\alpha $\end{document}</tex-math></inline-formula>, with <inline-formula><tex-math id="M2">\begin{document}$ \alpha>0 $\end{document}</tex-math></inline-formula>. Each species is also subject to non-local self-attraction forces together with quadratic diffusion effects. The competition between the aforementioned mechanisms produce a rich asymptotic behavior, namely the formation of steady states that are composed of multiple bumps, i.e. sums of Barenblatt-type profiles. The existence of such stationary states, under some conditions on the positions of the bumps and the proportionality constant <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>, is showed for small diffusion, by using the functional version of the Implicit Function Theorem. We complement our results with some numerical simulations, that suggest a large variety in the possible strategies the two species use in order to interact each other.

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Le Sauteur-Robitaille, Justin, Zhe Si Yu, and Morgan Craig. "Impact of estrogen population pharmacokinetics on a QSP model of mammary stem cell differentiation into myoepithelial cells." AIMS Mathematics 6, no. 10 (2021): 10861–80. http://dx.doi.org/10.3934/math.2021631.

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<abstract> Stem cell differentiation cascades are critical components of healthy tissue maintenance. Dysregulation in these systems can lead to serious diseases, including cancer. Myoepithelial mammary cells are produced from differentiated mammary stem cells in processes regulated, in part, by estrogen signalling and concentrations. To quantify and predict the production of mammary myoepithelial cell production by estrogen, we developed a mechanistic, quantitative systems pharmacology (QSP) model that includes the explicit characterization of free and unbound estrogen concentrations in circulation. Linking this model to a previously developed population pharmacokinetics model for ethinyl estradiol, a synthetic form of estrogen included in oral contraceptives, we predicted the effects of estrogen on myoepithelial cell development. Interestingly, pharmacokinetic intraindividual variability alone did not significantly impact on our modelos predictions, suggesting that combinations of physiological and pharmacokinetic variability drive heterogeneity in mechanistic QSP models. Our model is one component of an improved understanding of mammary myoepithelial cell production and development, and our results support the call for mechanistically constructed systems models for disease and pharmaceutical modelling. </abstract>

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Asl, Hadi Adibi, Nasser Lashgarian Azad, and John McPhee. "Math-based torque converter modelling to evaluate damping characteristics and reverse flow mode operation." International Journal of Vehicle Systems Modelling and Testing 9, no. 1 (2014): 36. http://dx.doi.org/10.1504/ijvsmt.2014.059155.

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Eroglu, A. "Optimal lot sizing with regular maintenance interruptions [Appl. Math. Modelling 21 (1997) 85–90]." Applied Mathematical Modelling 29, no. 2 (February 2005): 211–12. http://dx.doi.org/10.1016/j.apm.2004.09.001.

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Beirão da Veiga, L., F. Brezzi, L. D. Marini, and A. Russo. "Virtual Element Method for general second-order elliptic problems on polygonal meshes." Mathematical Models and Methods in Applied Sciences 26, no. 04 (February 16, 2016): 729–50. http://dx.doi.org/10.1142/s0218202516500160.

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We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [A. H. Schatz, An observation concerning Ritz–Galerkin methods with indefinite bilinear forms, Math. Comput. 28 (1974) 959–962] the problem is supposed to have a unique solution, but the associated bilinear form is not supposed to be coercive. Contrary to what was previously done for Virtual Element Methods (as for instance in [L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013) 199–214]), we use here, in a systematic way, the [Formula: see text]-projection operators as designed in [B. Ahmad, A. Alsaedi, F. Brezzi, L. D. Marini and A. Russo, Equivalent projectors for virtual element methods, Comput. Math. Appl. 66 (2013) 376–391]. In particular, the present method does not reduce to the original Virtual Element Method of [L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013) 199–214] for simpler problems as the classical Laplace operator (apart from the lowest-order cases). Numerical experiments show the accuracy and the robustness of the method, and they show as well that a simple-minded extension of the method in [L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013) 199–214] to the case of variable coefficients produces, in general, sub-optimal results.

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Buffa, Annalisa, and Carlotta Giannelli. "Remarks on Poincaré and interpolation estimates for Truncated Hierarchical B-splines." Mathematical Models and Methods in Applied Sciences 31, no. 03 (March 2021): 525–35. http://dx.doi.org/10.1142/s0218202521500111.

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This paper should be considered as an addendum to [A. Buffa and C. Giannelli, Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence, Math. Models Methods Appl. Sci. 26 (2016) 1–25] and [A. Buffa and C. Giannelli, Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates, Math. Models Methods Appl. Sci. 27 (2017) 2781–2802] where Poincaré and approximation estimates are used as theoretical tools to study properties of adaptive numerical methods based on hierarchical B-splines. After noting that the support of truncated hierarchical B-splines may be disconnected (and thus no Poincaré estimate can hold), we study minimal extensions of their support on suitable mesh configurations such that (i) Poincaré estimates can be established on them and (ii) their overlaps stay independent of the number of levels. The Poincaré estimates proposed in this note should replace the ones used in the proofs of Theorem 11 and Lemma 7 in [A. Buffa and C. Giannelli, Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence, Math. Models Methods Appl. Sci. 26 (2016) 1–25] and [A. Buffa and C. Giannelli, Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates, Math. Models Methods Appl. Sci. 27 (2017) 2781–2802], respectively, in order to include the most general meshes, i.e. the cases when the support of truncated basis functions can be disconnected.

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Brenner, Susanne C., and Li-Yeng Sung. "Virtual element methods on meshes with small edges or faces." Mathematical Models and Methods in Applied Sciences 28, no. 07 (June 19, 2018): 1291–336. http://dx.doi.org/10.1142/s0218202518500355.

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We consider a model Poisson problem in [Formula: see text] ([Formula: see text]) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ([Formula: see text]) or small faces ([Formula: see text]). Our results extend the ones in [L. Beirão da Veiga, C. Lovadina and A. Russo, Stability analysis for the virtual element method, Math. Models Methods Appl. Sci. 27 (2017) 2557–2594] for the original two-dimensional virtual element method from [L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013) 199–214] to the version of the virtual element method in [B. Ahmad, A. Alsaedi, F. Brezzi, L. D. Marini and A. Russo, Equivalent projectors for virtual element methods, Comput. Math. Appl. 66 (2013) 376–391] that can also be applied to problems in three dimensions.

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Neubauer, Andreas. "On Tikhonov-type regularization with approximated penalty terms." Inverse Problems & Imaging 15, no. 5 (2021): 1035. http://dx.doi.org/10.3934/ipi.2021027.

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In this paper, we deal with (nonlinear) ill-posed problems that are regularized by minimizing Tikhonov-type functionals. If the minimization is tedious for some penalty term <inline-formula><tex-math id="M1">\begin{document}$ P_0 $\end{document}</tex-math></inline-formula>, we approximate it by a family of penalty terms <inline-formula><tex-math id="M2">\begin{document}$ ({P_\beta}) $\end{document}</tex-math></inline-formula> having nicer properties and analyze what happens as <inline-formula><tex-math id="M3">\begin{document}$ \beta\to 0 $\end{document}</tex-math></inline-formula>.We investigate the discrepancy principle for the choice of the regularization parameter and apply all results to linear problems with sparsity constraints. Numerical results show that the proposed method yields good results.

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Kurima, Shunsuke. "Time discretization of an initial value problem for a simultaneous abstract evolution equation applying to parabolic-hyperbolic phase-field systems." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 3 (April 22, 2020): 977–1002. http://dx.doi.org/10.1051/m2an/2019086.

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This article deals with a simultaneous abstract evolution equation. This includes a parabolic-hyperbolic phase-field system as an example which consists of a parabolic equation for the relative temperature coupled with a semilinear damped wave equation for the order parameter (see e.g., Grasselli and Pata [Adv. Math. Sci. Appl. 13 (2003) 443–459, Comm. Pure Appl. Anal. 3 (2004) 849–881], Grasselli et al. [Comm. Pure Appl. Anal. 5 (2006) 827–838], Wu et al. [Math. Models Methods Appl. Sci. 17 (2007) 125–153, J. Math. Anal. Appl. 329 (2007) 948–976]). On the other hand, a time discretization of an initial value problem for an abstract evolution equation has been studied (see e.g., Colli and Favini [Int. J. Math. Math. Sci. 19 (1996) 481–494]) and Schimperna [J. Differ. Equ. 164 (2000) 395–430] has established existence of solutions to an abstract problem applying to a nonlinear phase-field system of Caginalp type on a bounded domain by employing a time discretization scheme. In this paper we focus on a time discretization of a simultaneous abstract evolution equation applying to parabolic-hyperbolic phase-field systems. Moreover, we can establish an error estimate for the difference between continuous and discrete solutions.

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Brezavšček, Alenka, Janja Jerebic, Gregor Rus, and Anja Žnidaršič. "Factors Influencing Mathematics Achievement of University Students of Social Sciences." Mathematics 8, no. 12 (December 1, 2020): 2134. http://dx.doi.org/10.3390/math8122134.

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The paper aims to investigate the main factors influencing the mathematics achievement of social sciences university students in Slovenia. A conceptual model was derived where three categories of variables were taken into account: attitude towards mathematics and math anxiety, engagement in learning activities, and attitude towards involving technology in learning mathematics. Data were collected for seven consecutive academic years and analysed using Structural Equation Modelling (SEM). The results showed a very high coefficient of determination for mathematics achievement (0.801), indicating that variables “Perceived Level of Math Anxiety”, “Self-Engagement in Mathematics Course at University”, and “Perceived Usefulness of Technology in Learning Mathematics”, together, explain 80.1% of the total variance. Based on our findings, we can conclude that teaching in secondary school is a crucial determinant for success in mathematics at university. It is essential to identify the best methods for secondary school math teachers which will help them give future students better entry-level knowledge for universities. These methods will, hopefully, also improve the level of mathematics self-confidence, as well as lower the level of math anxiety, which all considerably affect the performance of students in university mathematics.

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Li, Jin, Jianlin Luo, and Zaihong Wang. "RETRACTION NOTICE TO “PERIODIC SOLUTIONS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS AT RESONANCE VIA VARIATIONAL APPROACH” [MATH. MODEL. ANAL. 19(5):664–675, 2014]." Mathematical Modelling and Analysis 20, no. 2 (March 30, 2015): 289. http://dx.doi.org/10.3846/13926292.2015.1024973.

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Merkin, J. H., Y. Y. Lok, and I. Pop. "A note on non-symmetric flow: surface shrinking in mutually orthogonal directions." Meccanica 56, no. 7 (April 8, 2021): 1727–37. http://dx.doi.org/10.1007/s11012-020-01294-z.

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AbstractIn this note, we extend the problem treated in (Lok, Math Modelling Anal 24:617–634 (2019)) to the case of permeable surface which is shrinking in mutually orthogonal directions. Both numerical and asymptotic solutions are obtained for two important governing parameters, $$\gamma $$ γ the shrinking rate and S characterizing the fluid transfer through the boundary. In this problem, a restriction on S is required for a solution to exist. This contrasts with the problem in (Lok, Math Modelling Anal 24:617–634 (2019)) where no restriction on S is needed. Numerical solutions show that for a fixed value of S, two critical points $$\gamma _c$$ γ c are observed for $$S > 2$$ S > 2 . Conversely, two critical points $$S_c$$ S c are found for a given value of $$\gamma $$ γ when $$S > 2$$ S > 2 . A discussion on the nonexistence of solution for $$S = 2$$ S = 2 is given and asymptotic solutions for S large and $$(S-2)$$ ( S - 2 ) small are also presented.

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34

Hamilton, Sarah J., David Isaacson, Ville Kolehmainen, Peter A. Muller, Jussi Toivainen, and Patrick F. Bray. "3D Electrical Impedance Tomography reconstructions from simulated electrode data using direct inversion $ \mathbf{t}^{\rm{{\textbf{exp}}}} $ and Calderón methods." Inverse Problems & Imaging 15, no. 5 (2021): 1135. http://dx.doi.org/10.3934/ipi.2021032.

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The first numerical implementation of a <inline-formula><tex-math id="M2">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> method in 3D using simulated electrode data is presented. Results are compared to Calderón's method as well as more common TV and smoothness regularization-based methods. The <inline-formula><tex-math id="M3">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> method for EIT is based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. In 2D, <inline-formula><tex-math id="M4">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> methods have shown great promise for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D <inline-formula><tex-math id="M5">\begin{document}$ \mathbf{t}^{\rm{{\textbf{exp}}}} $\end{document}</tex-math></inline-formula> and Calderón methods are demonstrated to provide comparable quality to their 2D counterparts and hold promise for real-time reconstructions due to their fast, non-optimized, computational cost.

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Manuel, Paul, Sandi Klavžar, Antony Xavier, Andrew Arokiaraj, and Elizabeth Thomas. "Strong edge geodetic problem in networks." Open Mathematics 15, no. 1 (October 3, 2017): 1225–35. http://dx.doi.org/10.1515/math-2017-0101.

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Abstract Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [Math. Comput. Modelling, 1993, 17, 89-95]. Here we introduce a variation of the geodetic problem and call it strong edge geodetic problem. We illustrate how this problem is evolved from social transport networks. It is shown that the strong edge geodetic problem is NP-complete. We derive lower and upper bounds for the strong edge geodetic number and demonstrate that these bounds are sharp. We produce exact solutions for trees, block graphs, silicate networks and glued binary trees without randomization.

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36

Wen, Chun, Ting-Zhu Huang, Xian-Ming Gu, Zhao-Li Shen, Hong-Fan Zhang, and Chen Liu. "Multipreconditioned GMRES for simulating stochastic automata networks." Open Mathematics 16, no. 1 (August 24, 2018): 986–98. http://dx.doi.org/10.1515/math-2018-0083.

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AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

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Ibort, Alberto, and Alberto López-Yela. "Quantum tomography and the quantum Radon transform." Inverse Problems & Imaging 15, no. 5 (2021): 893. http://dx.doi.org/10.3934/ipi.2021021.

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A general framework for the tomographical description of states, that includes, among other tomographical schemes, the classical Radon transform, quantum state tomography and group quantum tomography, in the setting of <inline-formula><tex-math id="M1">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebras is presented. Given a <inline-formula><tex-math id="M2">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebra, the main ingredients for a tomographical description of its states are identified: A generalized sampling theory and a positive transform. A generalization of the notion of dual tomographic pair provides the background for a sampling theory on <inline-formula><tex-math id="M3">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebras and, an extension of Bochner's theorem for functions of positive type, the positive transform.The abstract theory is realized by using dynamical systems, that is, groups represented on <inline-formula><tex-math id="M4">\begin{document}$ C^* $\end{document}</tex-math></inline-formula>-algebra. Using a fiducial state and the corresponding GNS construction, explicit expressions for tomograms associated with states defined by density operators on the corresponding Hilbert spade are obtained. In particular a general quantum version of the classical definition of the Radon transform is presented. The theory is completed by proving that if the representation of the group is square integrable, the representation itself defines a dual tomographic map and explicit reconstruction formulas are obtained by making a judiciously use of the theory of frames. A few significant examples are discussed that illustrates the use and scope of the theory.

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Henríquez, Fernando, and Carlos Jerez-Hanckes. "Multiple traces formulation and semi-implicit scheme for modelling biological cells under electrical stimulation." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 2 (March 2018): 659–703. http://dx.doi.org/10.1051/m2an/2018019.

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We model the electrical behavior of several biological cells under external stimuli by extending and computationally improving the multiple traces formulation introduced in Henríquez et al. [Numer. Math. 136 (2016) 101–145]. Therein, the electric potential and current for a single cell are retrieved through the coupling of boundary integral operators and non-linear ordinary differential systems of equations. Yet, the low-order discretization scheme presented becomes impractical when accounting for interactions among multiple cells. In this note, we consider multi-cellular systems and show existence and uniqueness of the resulting non-linear evolution problem in finite time. Our main tools are analytic semigroup theory along with mapping properties of boundary integral operators in Sobolev spaces. Thanks to the smoothness of cellular shapes, solutions are highly regular at a given time. Hence, spectral spatial discretization can be employed, thereby largely reducing the number of unknowns. Time-space coupling is achieved via a semi-implicit time-stepping scheme shown to be stable and second order convergent. Numerical results in two dimensions validate our claims and match observed biological behavior for the Hodgkin–Huxley dynamical model.

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Zhou, Changcheng, Chuanbo Ren, Xueyi Zhang, and Jie Meng. "Math model for throttle slice thickness analytical design of telescopic shock absorber." International Journal of Vehicle Systems Modelling and Testing 4, no. 3 (2009): 133. http://dx.doi.org/10.1504/ijvsmt.2009.029386.

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Sezer, Sefa Anil, and Ibrahim Canak. "TAUBERIAN REMAINDER THEOREMS FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY." Mathematical Modelling and Analysis 19, no. 2 (April 15, 2014): 275–80. http://dx.doi.org/10.3846/13926292.2014.910280.

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Using the weighted general control modulo, we prove several Tauberian remainder theorems for the weighted mean method of summability. Our results generalize the results proved by Meronen and Tammeraid [Math. Model. Anal. 18 (1) 2013, 97–102].

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41

Hu, Jun, and Shangyou Zhang. "Finite element approximations of symmetric tensors on simplicial grids in ℝn: The lower order case." Mathematical Models and Methods in Applied Sciences 26, no. 09 (July 26, 2016): 1649–69. http://dx.doi.org/10.1142/s0218202516500408.

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In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric tensor finite element spaces of order [Formula: see text] from [Finite element approximations of symmetric tensors on simplicial grids in [Formula: see text]: The higher order case, J. Comput. Math. 33 (2015) 283–296], enriched, for each [Formula: see text]-dimensional simplex, by [Formula: see text] face bubble functions in the symmetric tensor finite element space of order [Formula: see text] from [Finite element approximations of symmetric tensors on simplicial grids in [Formula: see text]: The higher order case, J. Comput. Math. 33 (2015) 283–296] when [Formula: see text], and by [Formula: see text] face bubble functions in the symmetric tensor finite element space of order [Formula: see text] from [Finite element approximations of symmetric tensors on simplicial grids in [Formula: see text]: The higher order case, J. Comput. Math. 33 (2015) 283–296] when [Formula: see text]. These spaces can be used to approximate the symmetric matrix field in a mixed formulation problem where the other variable is approximated by discontinuous piecewise [Formula: see text] polynomials. This in particular leads to first-order mixed elements on simplicial grids with total degrees of freedom per element [Formula: see text] plus [Formula: see text] in 2D, 48 plus 6 in 3D. The previous record of the degrees of freedom of first-order mixed elements is, 21 plus 3 in 2D, and 156 plus 6 in 3D, on simplicial grids. We also derive, in a unified way which is completely different from those used in [D. Arnold, G. Awanou and R. Winther, Finite elements for symmetric tensors in three dimensions, Math. Comput. 77 (2008) 1229–1251; D. N. Arnold and R. Winther, Mixed finite element for elasticity, Number Math. 92 (2002) 401–419], a family of Arnold–Winther mixed finite elements in any space dimension. One example in this family is the Raviart–Thomas elements in one dimension, the second example is the mixed finite elements for linear elasticity in two dimensions due to Arnold and Winther, the third example is the mixed finite elements for linear elasticity in three dimensions due to Arnold, Awanou and Winther.

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42

Pivovarchik, V. "Corrigendum: Characteristic functions under series and parallel connection of quantum graphs (2015J. Math. Phys. A: Math. Theor.48365201)." Journal of Physics A: Mathematical and Theoretical 49, no. 19 (April 4, 2016): 199501. http://dx.doi.org/10.1088/1751-8113/49/19/199501.

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43

Xia, Fu Yi, Li Ming Xu, and De Jin Hu. "Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid." Key Engineering Materials 693 (May 2016): 837–42. http://dx.doi.org/10.4028/www.scientific.net/kem.693.837.

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A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

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Almuthaybiri, Saleh S., and Christopher C. Tisdell. "Sharper existence and uniqueness results for solutions to fourth-order boundary value problems and elastic beam analysis." Open Mathematics 18, no. 1 (September 28, 2020): 1006–24. http://dx.doi.org/10.1515/math-2020-0056.

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Abstract We examine the existence and uniqueness of solutions to two-point boundary value problems involving fourth-order, ordinary differential equations. Such problems have interesting applications to modelling the deflections of beams. We sharpen traditional results by showing that a larger class of problems admit a unique solution. We achieve this by drawing on fixed-point theory in an interesting and alternative way via an application of Rus’s contraction mapping theorem. The idea is to utilize two metrics on a metric space, where one pair is complete. Our theoretical results are applied to the area of elastic beam deflections when the beam is subjected to a loading force and the ends of the beam are either both clamped or one end is clamped and the other end is free. The existence and uniqueness of solutions to the models are guaranteed for certain classes of linear and nonlinear loading forces.

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Kouche, Mahiéddine, Bilal Boulfoul, and Bedr’Eddine Ainseba. "Mathematical analysis of an HIV infection model including quiescent cells and periodic antiviral therapy." International Journal of Biomathematics 10, no. 05 (May 9, 2017): 1750065. http://dx.doi.org/10.1142/s1793524517500656.

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In this paper, we revisit the model by Guedj et al. [J. Guedj, R. Thibaut and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics 63 (2007) 198–206; J. Guedj, R. Thibaut and D. Commenges, Practical identifiability of HIV dynamics models, Bull. Math. Biol. 69 (2007) 2493–2513] which describes the effect of treatment with reverse transcriptase (RT) inhibitors and incorporates the class of quiescent cells. We prove that there is a threshold value [Formula: see text] of drug efficiency [Formula: see text] such that if [Formula: see text], the basic reproduction number [Formula: see text] and the infection is cleared and if [Formula: see text], the infectious equilibrium is globally asymptotically stable. When the drug efficiency function [Formula: see text] is periodic and of the bang–bang type we establish a threshold, in terms of spectral radius of some matrix, between the clearance and the persistence of the disease. As stated in related works [L. Rong, Z. Feng and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol. 69 (2007) 2027–2060; P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bull. Math. Biol. 71 (2009) 189–210.], we prove that the increase of the drug efficiency or the active duration of drug must clear the infection more quickly. We illustrate our results by some numerical simulations.

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Cocea, Mihaela, and George D. Magoulas. "Design and Evaluation of a Case-Based System for Modelling Exploratory Learning Behavior of Math Generalization." IEEE Transactions on Learning Technologies 10, no. 4 (October 1, 2017): 436–49. http://dx.doi.org/10.1109/tlt.2017.2661310.

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Gervais, Pierre. "A spectral study of the linearized Boltzmann operator in $ L^2 $-spaces with polynomial and Gaussian weights." Kinetic & Related Models 14, no. 4 (2021): 725. http://dx.doi.org/10.3934/krm.2021022.

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The spectrum structure of the linearized Boltzmann operator has been a subject of interest for over fifty years and has been inspected in the space <inline-formula><tex-math id="M2">\begin{document}$ L^2\left( {\mathbb R}^d, \exp(|v|^2/4)\right) $\end{document}</tex-math></inline-formula> by B. Nicolaenko [<xref ref-type="bibr" rid="b27">27</xref>] in the case of hard spheres, then generalized to hard and Maxwellian potentials by R. Ellis and M. Pinsky [<xref ref-type="bibr" rid="b13">13</xref>], and S. Ukai proved the existence of a spectral gap for large frequencies [<xref ref-type="bibr" rid="b33">33</xref>]. The aim of this paper is to extend to the spaces <inline-formula><tex-math id="M3">\begin{document}$ L^2\left( {\mathbb R}^d, (1+|v|)^{k}\right) $\end{document}</tex-math></inline-formula> the spectral studies from [<xref ref-type="bibr" rid="b13">13</xref>,<xref ref-type="bibr" rid="b33">33</xref>]. More precisely, we look at the Fourier transform in the space variable of the inhomogeneous operator and consider the dual Fourier variable as a fixed parameter. We then perform a precise study of this operator for small frequencies (by seeing it as a perturbation of the homogeneous one) and also for large frequencies from spectral and semigroup point of views. Our approach is based on Kato's perturbation theory for linear operators [<xref ref-type="bibr" rid="b22">22</xref>] as well as enlargement arguments from [<xref ref-type="bibr" rid="b25">25</xref>,<xref ref-type="bibr" rid="b19">19</xref>].

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Totur, Umit, and Muhammet Ali Okur. "SOME TAUBERIAN REMAINDER THEOREMS FOR HOLDER SUMMABILITY." Mathematical Modelling and Analysis 20, no. 2 (March 30, 2015): 139–47. http://dx.doi.org/10.3846/13926292.2015.1011719.

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In this paper, we prove some Tauberian remainder theorems that generalize the results given by Meronen and Tammeraid [Math. Model. Anal., 18(1):97– 102, 2013] for Holder summability method using the notion of the general control modulo of the oscillatory behaviour of nonnegative integer order.

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Griffin-Pickering, Megan, and Mikaela Iacobelli. "Global strong solutions in $ {\mathbb{R}}^3 $ for ionic Vlasov-Poisson systems." Kinetic & Related Models 14, no. 4 (2021): 571. http://dx.doi.org/10.3934/krm.2021016.

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Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-posedness theory for Vlasov-Poisson systems is well established, the well-posedness theory for ion models has been investigated more recently. In this article, we prove global well-posedness for two Vlasov-Poisson systems for ions, posed on the whole three-dimensional Euclidean space <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^3 $\end{document}</tex-math></inline-formula>, under minimal assumptions on the initial data and the confining potential.

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Santos, M. Lian Kamyl P., Rene R. Belecina, and Rosemarievic V. Diaz. "Mathematical Modeling: Effects on Problem Solving Performance and Math Anxiety of Students." International Letters of Social and Humanistic Sciences 65 (December 2015): 103–15. http://dx.doi.org/10.18052/www.scipress.com/ilshs.65.103.

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This study determined the effects of the integration of mathematical modeling on the problem solving performance and math anxiety level of Grade 9 students. Two groups of students were exposed to different strategies: the control group was taught using guided practice while the experimental group was taught using the integration of mathematical modelling. Pretests and Posttests were given to measure the performance of both groups in terms of their problem solving skills and their math anxiety level. T-test of independent and dependent were used to determine whether there exists significant difference between the performance of the two groups in terms of their pretest and posttest scores. Questionnaire and Interview Method were implemented were used to elicit students’ reactions on the integration of mathematical modeling in the classroom.Findings showed that there is a significant difference between the pretest and posttest mean scores of both groups in terms of their problem solving performance test and their mathematics anxiety test. However, when their posttest mean scores were compared, the experimental group made a large improvement in terms of their problem solving performance and a reduction in terms of their mathematics anxiety level, thus, the integration of mathematical modeling was effective in improving the problem solving performance and reducing the math anxiety level of students

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Journal articles on the topic 'Modelling math'

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