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Journal articles on the topic 'Mathematical models. Calculus'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Mehta, U., R. Prasad, and K. Kothari. "VARIOUS ANALYTICAL MODELS FOR SUPERCAPACITORS: A MATHEMATICAL STUDY." Resource-Efficient Technologies, no. 1 (May 9, 2020): 1–15. http://dx.doi.org/10.18799/24056537/2020/1/218.

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Supercapacitors (SCs) are used extensively in high-power potential energy applications like renewable energy systems, electric vehicles, power electronics, and many other industrial applications. This is due to SCs containing high-power density and the ability to respond spontaneously with fast charging and discharging demands. Advancements in material and fabrication techniques have induced a scope for research to improve the application of SCs. Many researchers have studied various SC properties and their effects on energy storage and management performance. In this paper, various fractional

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2

Barroso, Norman Cuello. "Mathematical Models in Predicting Retention of STEM Students in Pre-Calculus." International Journal of Pedagogical Development and Lifelong Learning 1, no. 1 (2020): ep2004. http://dx.doi.org/10.30935/ijpdll/8342.

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3

Long, Chun-Ying, Yang Zhao, and Hossein Jafari. "Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/782393.

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The forest new gap models via local fractional calculus are investigated. The JABOWA and FORSKA models are extended to deal with the growth of individual trees defined on Cantor sets. The local fractional growth equations with local fractional derivative and difference are discussed. Our results are first attempted to show the key roles for the nondifferentiable growth of individual trees.

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Rchid Sidi Ammi, Moulay, and Mostafa Tahiri. "Analysis of the spread of COVID-19 in Morocco based on a SEIR epidemic model." General Letters in Mathematics 10, no. 2 (2021): 72–78. http://dx.doi.org/10.31559/glm2021.10.2.8.

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Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. In order to illustrate the efficiency of this non-integer order calculus, we employ SEIR models to model the dynamics, with and without memory, of the spread of Covid-19 in Morocco country.

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5

Roche, Ph. "Ocneanu cell calculus and integrable lattice models." Communications in Mathematical Physics 127, no. 2 (1990): 395–424. http://dx.doi.org/10.1007/bf02096764.

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6

Sutulo, Serge, and C. Guedes Soares. "ON APPLICABILITY OF MATHEMATICAL MODELS BASED ON FRACTIONAL CALCULUS TO SHIP DYNAMICS." IFAC Proceedings Volumes 43, no. 20 (2010): 190–95. http://dx.doi.org/10.3182/20100915-3-de-3008.00038.

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7

PYKACZ, JAROSŁAW, and BART D'HOOGHE. "BELL-TYPE INEQUALITIES IN FUZZY PROBABILITY CALCULUS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 02 (2001): 263–75. http://dx.doi.org/10.1142/s021848850100079x.

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Bell-type inequalities, used in mathematical physics as a criterion to check whether a physical situation allows description in terms of classical (Kolmogorovian) or quantum probability calculus are applied to various fuzzy probability models. It occurs that the standard set of Bell-type inequalities does not allow to distinguish Kolmogorovian probabilities from fuzzy probabilities based on the most frequently used Zadeh intersection or probabilistic intersection, but it allows to distinguish all these models from fuzzy probability models based on Giles (Łukasiewicz) intersection. It is proved

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8

Story, Troy L. "Exterior Calculus: Thermodynamics and Navier-Stokes Dynamics." Advanced Materials Research 747 (August 2013): 761–64. http://dx.doi.org/10.4028/www.scientific.net/amr.747.761.

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Mathematical models of dynamics employing exterior calculus are shown to be mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus to a set of differential equations and a characteristic tangent vector which define transformations of the system [1-4]. This principle, whose origin is V. I. Arnolds use of exterior calculus to describe Hamiltonian mechanics and geometric optics, is applied to irreversible thermodynami

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Bainy, Eduarda, Ervin Lenzi, Marcos Corazza, and Marcelo Lenzi. "Mathematical modeling of fish burger baking using fractional calculus." Thermal Science 21, no. 1 Part A (2017): 41–50. http://dx.doi.org/10.2298/tsci160422241b.

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Tilapia (Oreochromis sp.) is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electr

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Tarasov, Vasily. "On History of Mathematical Economics: Application of Fractional Calculus." Mathematics 7, no. 6 (2019): 509. http://dx.doi.org/10.3390/math7060509.

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Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe economic phenomena, effects, and processes. At the present moment the new revolution, which can be called “Memory revolution”, is actually taking place in modern economics. This revolution is intended to “cure amnesia” of modern economic theory, which is caused by the use of differential and integral operators of integer orders. In economics, the des

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11

Daumont, Isabelle, Thierry Dombre, and Jean-Louis Gilson. "Instanton calculus in shell models of turbulence." Physical Review E 62, no. 3 (2000): 3592–610. http://dx.doi.org/10.1103/physreve.62.3592.

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12

Patrascioiu, A., та J. L. Richard. "Itô calculus for σ-models and Yang-Mills theories". Letters in Mathematical Physics 9, № 3 (1985): 191–94. http://dx.doi.org/10.1007/bf00402828.

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13

Dulf, Eva-H., Dan C. Vodnar, Alex Danku, Cristina-I. Muresan, and Ovidiu Crisan. "Fractional-Order Models for Biochemical Processes." Fractal and Fractional 4, no. 2 (2020): 12. http://dx.doi.org/10.3390/fractalfract4020012.

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Biochemical processes present complex mechanisms and can be described by various computational models. Complex systems present a variety of problems, especially the loss of intuitive understanding. The present work uses fractional-order calculus to obtain mathematical models for erythritol and mannitol synthesis. The obtained models are useful for both prediction and process optimization. The models present the complex behavior of the process due to the fractional order, without losing the physical meaning of gain and time constants. To validate each obtained model, the simulation results were

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14

Tabunshchikov, Yuri, and Marianna Brodach. "OPTIMIZATION PROBLEMS OF MATHEMATICAL MODELLING OF A BUILDING AS A UNIFIED HEAT AND POWER SYSTEM." International Journal for Computational Civil and Structural Engineering 16, no. 1 (2020): 156–61. http://dx.doi.org/10.22337/2587-9618-2020-16-1-156-161.

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The mathematical model of a building as a single heat energy system by the decomposition method is represented by three interconnected mathematical models: the first is a mathematical model of the energy interaction of a building’s shell with an outdoor climate; the second is a mathematical model of energy flows through the shell of a building; the third is a mathematical model of optimal control of energy consumption to ensure the required microclimate. Optimization problems for three mathematical models with objective functions are formulated. Methods for solving these problems are determine

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Brown, Jennifer L., Glennelle Halpin, and Gerald Halpin. "Relationship between High School Mathematical Achievement and Quantitative GPA." Higher Education Studies 5, no. 6 (2015): 1. http://dx.doi.org/10.5539/hes.v5n6p1.

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<p>The demand for STEM graduates has increased, but the number of incoming freshmen who declare a STEM major has remained stagnant. High school courses, such as calculus, can open or close the gate for students interested in careers in STEM. The purpose of this study was to determine if high school mathematics preparation was a significant prerequisite for success in the pre-engineering curriculum at the post-secondary level. The College Freshman Survey was administered to a sample of 2,328 incoming freshman students, then their survey responses were matched with the grades and standardi

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Abbas, Marat M., та Vladimir A. Zakharov. "Even Simple Processes of π-calculus are Hard for Analysis". Modeling and Analysis of Information Systems 25, № 6 (2018): 589–606. http://dx.doi.org/10.18255/1818-1015-2018-6-589-606.

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Mathematical models of distributed computations, based on the calculus of mobile processes (π-calculus) are widely used for checking the information security properties of cryptographic protocols. Since π-calculus is Turing-complete, this problem is undecidable in general case. Therefore, the study is carried out only for some special classes of π-calculus processes with restricted computational capabilities, for example, for non-recursive processes, in which all runs have a bounded length, for processes with a bounded number of parallel components, etc. However, even in these cases, the propo

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17

DEZANI-CIANCAGLINI, MARIANGIOLA, GIUSEPPE LONGO, and JONATHAN P. SELDIN. "Preface." Mathematical Structures in Computer Science 9, no. 4 (1999): 321. http://dx.doi.org/10.1017/s0960129598009682.

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This special double issue of Mathematical Structures in Computer Science is in honour of Roger Hindley and is devoted to the topic of lambda-calculus and logic.It is a great pleasure for us to greet Roger Hindley on the occasion of his retirement from the University of Wales, Swansea, and his 60th birthday. We have known Roger for many years and we have had the chance to collaborate with him and appreciate his intellectual standard, his remarkable mathematical rigor, and his inexhaustible sense of humour. This has enabled Roger to step back critically even in the face of a difficult mathematic

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18

Stamova, Ivanka M., and Gani Tr Stamov. "On the Mittag–Leffler Stability of Impulsive Fractional Solow-Type Models." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 5 (2017): 315–25. http://dx.doi.org/10.1515/ijnsns-2016-0027.

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AbstractIn this article, we introduce fractional-order Solow-type models as a new tool for modeling and analysis in mathematical finance. Sufficient conditions for the Mittag–Leffler stability of their states are derived. The main advantages of the proposed approach are using of fractional-order derivatives, whose nonlocal property makes the fractional calculus a suitable tool for modeling actual financial systems as well as using of impulsive perturbations which give an opportunity to control the dynamic behavior of the model. The modeling approach proposed in this article can be applied to i

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Yang, Xiao-Jun, Feng Gao, and Hong-Wen Jing. "New mathematical models in anomalous viscoelasticity from the derivative with respect to another function view point." Thermal Science 23, no. 3 Part A (2019): 1555–61. http://dx.doi.org/10.2298/tsci190220277y.

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In this article, we address the mathematical models in anomalous viscoelasticity containing the derivatives with respect to another function for the first time. The Newton-like, Maxwell-like, Kelvin-Voigt-like, Burgers-like, and Zener-like models via the new derivatives with respect to another functions are discussed in detail. The results for the calculus with respect to another function are as a new perspective proposed to present the better accuracy and efficiency in the descriptions of the complex behaviors of the materials.

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20

Luft, Miroslaw, Zbigniew Lukasik, and Daniel Pietruszczak. "Mathematical Models of a Pneumatic Cascade and Pneumatic Membrane Actuator Described with a Fractional Calculus." TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation 14, no. 3 (2020): 643–48. http://dx.doi.org/10.12716/1001.14.03.16.

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21

Valentim, Carlos A., José A. Rabi, and Sergio A. David. "Fractional Mathematical Oncology: On the potential of non-integer order calculus applied to interdisciplinary models." Biosystems 204 (June 2021): 104377. http://dx.doi.org/10.1016/j.biosystems.2021.104377.

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22

Usher, David C., Tobin A. Driscoll, Prasad Dhurjati, et al. "A Transformative Model for Undergraduate Quantitative Biology Education." CBE—Life Sciences Education 9, no. 3 (2010): 181–88. http://dx.doi.org/10.1187/cbe.10-03-0029.

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The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised it

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23

LOPEZ, C. "VARIATIONAL CALCULUS, SYMMETRIES AND REDUCTION." International Journal of Geometric Methods in Modern Physics 03, no. 03 (2006): 577–90. http://dx.doi.org/10.1142/s0219887806001260.

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Variational Principles and Symmetries are both fundamental ingredients of the most relevant (either classical or modern) physical theories, and of many interesting models in Pure and Applied Mathematics. While the variational principle determines the law (differential and sometimes algebraic equations) of the dynamics, the symmetries give way to reduction. Noether's theorem connects some symmetries with constants of the motion in the framework of Lagrangian (point symmetries) or Hamiltonian (canonical symmetries) systems, becoming a powerful tool in the reduction process. This entanglement bet

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24

Pečeliūnas, Robertas, Olegas Prentkovskis, Giedrius Garbinčius, Saulius Nagurnas, and Saugirdas Pukalskas. "EXPERIMENTAL RESEARCH INTO MOTOR VEHICLE OSCILLATIONS IN THE CASE OF CHANGEABLE DECELERATION." TRANSPORT 20, no. 5 (2005): 171–75. http://dx.doi.org/10.3846/16484142.2005.9638016.

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In this paper processes of oscillation of flexible mounted and inflexible mounted masses are analysed. The tangential effect of the wheel contact with bearing surface is given, thus enabling more precise calculus of vehicle braking parameters. The methodology of research includes the development of mathematical algorithms and theoretical calculus of the analysed processes as well as the presentation of the influence of various factors on vehicle oscillations during braking. Analytical methods and those in figures have been applied for the research. Experimental investigations were carried out

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25

Kiryakova, Virginia. "A Guide to Special Functions in Fractional Calculus." Mathematics 9, no. 1 (2021): 106. http://dx.doi.org/10.3390/math9010106.

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Dedicated to the memory of Professor Richard Askey (1933–2019) and to pay tribute to the Bateman Project. Harry Bateman planned his “shoe-boxes” project (accomplished after his death as Higher Transcendental Functions, Vols. 1–3, 1953–1955, under the editorship by A. Erdélyi) as a “Guide to the Functions”. This inspired the author to use the modified title of the present survey. Most of the standard (classical) Special Functions are representable in terms of the Meijer G-function and, specially, of the generalized hypergeometric functions pFq. These appeared as solutions of differential equati

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de Angelis, Fabio. "On the Relation between Two Constitutive Models Frequently Adopted in Viscoplasticity." Applied Mechanics and Materials 256-259 (December 2012): 995–1003. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.995.

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The constitutive models of plasticity and viscoplasticity are formulated in a unified framework by taking advantage of the appropriate mathematical tools of convex analysis and subdifferential calculus. Two viscoplastic constitutive models frequently adopted in viscoplasticity are analyzed, the Duvaut and Lions viscoplastic constitutive model and the Perzyna viscoplastic constitutive model. In literature these two models are frequently adopted as alternatives. In the present paper it is discussed on the relation between the two models and it is shown that, under certain conditions and assumpti

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27

Jia, Zirui, and Chongxin Liu. "Fractional-Order Modeling and Simulation of Magnetic Coupled Boost Converter in Continuous Conduction Mode." International Journal of Bifurcation and Chaos 28, no. 05 (2018): 1850061. http://dx.doi.org/10.1142/s021812741850061x.

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By using fractional-order calculus theory and considering the condition that capacitor and inductor are naturally fractional, we construct the fractional mathematical model of the magnetic coupled boost converter with tapped-inductor in the operation of continuous conduction mode (CCM). The fractional state average model of the magnetic coupled boost converter in CCM operation is built by exploiting state average modeling method. In these models, the effects of coupling factor, which is viewed as one generally, are directly pointed out. The DC component, the AC component, the transfer function

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Xu, Dong, Gang Zhu, and De Zhen Xu. "Towards Checking Bigraphical Context-Aware Models." Applied Mechanics and Materials 411-414 (September 2013): 545–48. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.545.

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Context-aware computing is an important aspect of Pervasive Computing, Cyber-physical Systems (CPS), Cloud computing, etc. Recently, few works have been reported on formal approaches for this area. Bigraph was proposed as a mathematical structure that is consist of two graphs, a place graph and a link graph, intended for modeling distributed, mobile systems, etc. Bigraphs and its corresponding Bigraphical Reactive Systems (BRSs) present a modern, graphical structure, algebra calculus for the description of the syntax and semantics of systems in accordance with the orthogonal notions of connect

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Pomini, Mario. "ECONOMIC DYNAMICS AND THE CALCULUS OF VARIATIONS IN THE INTERWAR PERIOD." Journal of the History of Economic Thought 40, no. 1 (2018): 57–79. http://dx.doi.org/10.1017/s1053837217000116.

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Analogies with rational mechanics played a pivotal role in the search for formal models in economics. In the period between the two world wars, a small group of mathematical economists tried to extend this view from statics to dynamics. The main result was the extensive application of calculus of variations to obtain a dynamic representation of economic variables. This approach began with the contributions put forward by Griffith C. Evans, a mathematician who, in the first phase of his scientific career, published widely in economics. Evans’s research was further developed by his student Charl

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Pietruszczak, Daniel, and Artur Nowocień. "Description of selected pneumatic elements and systems using fractional calculus." Journal of Automation, Electronics and Electrical Engineering 1, no. 1 (2019): 43–49. http://dx.doi.org/10.24136/jaeee.2019.006.

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The paper presents the application of fractional calculus to describe the dynamics of selected pneumatic elements and systems. In the construction of mathematical models of the analysed dynamic systems, the Riemann-Liouville definition of differintegral of non- integer order was used. For the analysed model, transfer function of integer and non-integer order was determined. Functions describing characteristics in frequency domains were determined, whereas the characteristics of the elements and systems were obtained by means of computer simulation. MATLAB programme were used for the simulation

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31

Robeva, Raina, Robin Davies, Terrell Hodge, and Alexander Enyedi. "Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics." CBE—Life Sciences Education 9, no. 3 (2010): 227–40. http://dx.doi.org/10.1187/cbe.10-03-0019.

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We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebrai

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Tenreiro Machado, J. A., António M. Lopes, and Rui de Camposinhos. "Fractional-order modelling of epoxy resin." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (2020): 20190292. http://dx.doi.org/10.1098/rsta.2019.0292.

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This paper describes epoxy resins by means of electrical impedance spectroscopy (EIS) and the mathematical tool of fractional calculus (FC). Two stages are considered: first, the EIS is used for testing the samples and, second, the measured data are approximated using integer and fractional order models. The FC-based modelling describes the epoxy resins using a small number of parameters that reflect their main characteristics. The EIS data gathered for the epoxies samples are compared with those of different adhesives and sealants by means of a hierarchical clustering algorithm that unravels

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33

Aniszewska, Dorota. "New Discrete Chaotic Multiplicative Maps Based on the Logistic Map." International Journal of Bifurcation and Chaos 28, no. 09 (2018): 1850118. http://dx.doi.org/10.1142/s0218127418501183.

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Chaos is a phenomenon which cannot be predicted if it manifests itself in a nonlinear system. Simple deterministic models, such as the logistic map [Formula: see text], are constructed to capture the essence of processes observed in nature. They are interesting also from a mathematical point of view: nonlinear models can behave in chaotic and complicated ways. The logistic map is the simplest mathematical model exhibiting chaotic behavior. Therefore, its dynamical properties, stable points and stable cycles are well known and widely described. In this paper, the properties of multiplicative ca

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Li, Jian, and Yongmei Liu. "Automatic Verification of Liveness Properties in the Situation Calculus." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 03 (2020): 2886–92. http://dx.doi.org/10.1609/aaai.v34i03.5679.

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In dynamic systems, liveness properties concern whether something good will eventually happen. Examples of liveness properties are termination of programs and goal achievability. In this paper, we consider the following theorem-proving problem: given an action theory and a goal, check whether the goal is achievable in every model of the action theory. We make the assumption that there are finitely many non-number objects. We propose to use mathematical induction to address this problem: we identify a natural number feature and prove by mathematical induction that for any values of the feature,

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COLLINSON, MATTHEW, and DAVID PYM. "Algebra and logic for resource-based systems modelling." Mathematical Structures in Computer Science 19, no. 5 (2009): 959–1027. http://dx.doi.org/10.1017/s0960129509990077.

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Mathematical modelling is one of the fundamental tools of science and engineering. Very often, models are required to be executable, as a simulation, on a computer. In this paper, we present some contributions to the process-theoretic and logical foundations of discrete-event modelling with resources and processes. We present a process calculus with an explicit representation of resources in which processes and resources co-evolve. The calculus is closely connected to a logic that may be used as a specification language for properties of models. The logic is strong enough to allow requirements

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Pearl, Judea. "TRYGVE HAAVELMO AND THE EMERGENCE OF CAUSAL CALCULUS." Econometric Theory 31, no. 1 (2014): 152–79. http://dx.doi.org/10.1017/s0266466614000231.

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Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had (and still have) to overcome and lays out a logical framework that has evolved from Haavelmo’s insight and matured into a coherent and comprehensive account of the relationships between theory, data, and policy questions. The mathematical tools that emerge from this framework now enable investigators to answer complex policy and counterfactual questions using simple routines, some by mere inspection of the model’s structure. Several suc

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Roşca, Vâlcu, and Cosmin Mihai Miriţoiu. "Fnk Model of Cracking Rate Calculus for a Variable Asymmetry Coefficient." ACTA Universitatis Cibiniensis 69, no. 1 (2017): 72–81. http://dx.doi.org/10.1515/aucts-2017-0010.

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Abstract In the process of materials fracture, a very important parameter to study is the cracking rate growth da/dN. This paper proposes an analysis of the cracking rate, in a comparative way, by using four mathematical models:1 - polynomial method, by using successive iterations according to the ASTM E647 standard; 2 - model that uses the Paris formula; 3 - Walker formula method; 4 - NASGRO model or Forman - Newman - Konig equation, abbreviated as FNK model. This model is used in the NASA programs studies. For the tests, CT type specimens were made from stainless steel, V2A class, 10TiNiCr17

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Bârsan, Ghiţă, Silviu Mihai Petrişor, and Luminiţa Giurgiu. "Validation of the Mathematical and Numerical Models for Artillery Barrels Autofrettage Based on Hydrostatic Procedure." Applied Mechanics and Materials 186 (June 2012): 58–69. http://dx.doi.org/10.4028/www.scientific.net/amm.186.58.

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The research of advanced gun barrels focuses on materials or the combination between advanced materials and new innovative processes that enable the increase of the life cycle and performances of all calibers cannons. In addition to the investigation of new materials, considerable efforts were made for developing new techniques. The paper describes a theoretical framework validated with the experimental tests for increasing mechanical properties of thick-walled tubes subjected to high interior pressure loads. The theoretical model established a mathematical model of calculus for non-linear env

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Luft, Mirosław, Artur Nowocień, and Daniel Pietruszczak. "Mathematical models of the pneumatic cascade and a mem-brane pneumatic actuator described by the fractional calculus." AUTOBUSY – Technika, Eksploatacja, Systemy Transportowe 19, no. 12 (2018): 526–31. http://dx.doi.org/10.24136/atest.2018.444.

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The paper presents the analysis of dynamic properties of pneumatic systems such aa pneumatic cascade and a membrane pneumatic actuator using differential equations of integer orders and differential equations with derivatives of non-integer orders. The analyzed systems were described in the domain of time by means of step characteristics and in terms of frequency with the help of Bode characteristics, i.e. logarithmic amplitude and phase characteristics. Each characteristic was determined on the basis of a differential equation with derivatives of non-integer order. To determine the characteri

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Lai, Jinxing, Sheng Mao, Junling Qiu, et al. "Investigation Progresses and Applications of Fractional Derivative Model in Geotechnical Engineering." Mathematical Problems in Engineering 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/9183296.

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Over the past couple of decades, as a new mathematical tool for addressing a number of tough problems, fractional calculus has been gaining a continually increasing interest in diverse scientific fields, including geotechnical engineering due primarily to geotechnical rheology phenomenon. Unlike the classical constitutive models in which simulation analysis gradually fails to meet the reasonable accuracy of requirement, the fractional derivative models have shown the merits of hereditary phenomena with long memory. Additionally, it is traced that the fractional derivative model is one of the m

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Ionescu, C. M., I. R. Birs, D. Copot, C. I. Muresan, and R. Caponetto. "Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (2020): 20190284. http://dx.doi.org/10.1098/rsta.2019.0284.

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The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from

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ALI, ZEESHAN, FARANAK RABIEI, KAMAL SHAH, and ZANARIAH ABDUL MAJID. "DYNAMICS OF SIR MATHEMATICAL MODEL FOR COVID-19 OUTBREAK IN PAKISTAN UNDER FRACTAL-FRACTIONAL DERIVATIVE." Fractals 29, no. 05 (2021): 2150120. http://dx.doi.org/10.1142/s0218348x21501206.

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There are still mathematical predictions in the fight against epidemics. Speedy expansion, ways and procedures for the pandemic control require early understanding when solutions with better computer-based mathematical modeling and prognosis are developed. Despite high uncertainty in each of these models, one of the important tools for public health management system is epidemiology models. The fractional order is shown to be more effective in modeling epidemic diseases, in relation to the memory effects. Notably, recently founded calculus tools, called fractal-fractional calculus, having a fr

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Aristika, Ayu, Darhim, Dadang Juandi, and Kusnandi. "The Effectiveness of Hybrid Learning in Improving of Teacher-Student Relationship in Terms of Learning Motivation." Emerging Science Journal 5, no. 4 (2021): 443–56. http://dx.doi.org/10.28991/esj-2021-01288.

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The Advanced Mathematical Thinking (AMT) ability is one of the prioritized mathematical abilities needed to be developed in learning mathematics during tertiary education. The present study sought to test the effectiveness of hybrid learning in improving students' advanced mathematical thinking. The research used a quasi-experimental design with a non-equivalent control group design. The subject of this study was students of a mathematics education study program at a university in Bandung who attended lecture for the multi-variable in a calculus course. The sampling technique used was purposiv

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Dimakis, Aristophanes, and Folkert Müller-Hoissen. "Integrable discretizations of chiral models via deformation of the differential calculus." Journal of Physics A: Mathematical and General 29, no. 16 (1996): 5007–18. http://dx.doi.org/10.1088/0305-4470/29/16/022.

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Alshammari, Nawa A. "Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures." Advances in Mathematical Physics 2020 (August 30, 2020): 1–7. http://dx.doi.org/10.1155/2020/2394037.

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Boron nitride (BN) nanomaterials such as boron nitride graphenes, boron nitride nanotubes, and boron nitride nanocones are attracting attention among the most promising nanomaterials due to their physical, chemical, and electronic properties when compared to other nanomaterials. BN nanomaterials suggest many exciting potential applications in various fields. Joining between BN nanostructures gives new enhanced structures with outstanding properties and potential applications for design of probes for scanning tunnelling microscopy and other nanoscale devices. This paper uses calculus of variati

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Azmi, Fatima M., and Heba Bakr Khoshaim. "The COVID-19 Pandemic and the Challenges of E-Assessment of Calculus Courses in Higher Education: A Case Study in Saudi Arabia." International Journal of Learning, Teaching and Educational Research 20, no. 3 (2021): 265–81. http://dx.doi.org/10.26803/ijlter.20.3.16.

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The COVID-19 pandemic has affected many aspects of our lives, including education. Due to this unexpected catastrophe, education has shifted to virtual-learning and auto-grading models in most parts of the world. This study explores the validity and appropriateness of auto-grading-assessment for online exams by comparing students’ online exam scores where they are first auto-graded and then manually graded. Furthermore, it investigates whether the mean differences in their scores are statistically significant. The study included two calculus courses taught by the authors, during the spring sem

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Brdulak, Jacek, and Piotr Pawlak. "Enterprise in the economic calculus of the impact of road investments." Kwartalnik Nauk o Przedsiębiorstwie 42, no. 1 (2017): 47–61. http://dx.doi.org/10.5604/01.3001.0010.0152.

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Development of infrastructure results in reduction of costs of transportation. It is a significant factor that influences both supply and demand side of production. By lowering the costs of transportation, production companies benefit, together with transport companies, who lower their own costs and thus they can be more competitive on the market of services. The article contains an analysis of mathematical and statistical methods used to measure and evaluate the effects of road investments. Gravity and potential, index and generated traffic models have been discussed. Assessment of the profit

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Strang, Kenneth David. "Logistic Planning with Nonlinear Goal Programming Models in Spreadsheets." International Journal of Applied Logistics 3, no. 4 (2012): 1–14. http://dx.doi.org/10.4018/jal.2012100101.

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This is a case study of a coal mining company to demonstrate how algebra principles and nonlinear goal programming can be applied for logistics planning using spreadsheet software. The paper asserts that mathematical programming techniques are not well-accepted by managers because the models are difficult to understand due to abstract notational conventions yet alternative commercial software is inflexible (and sometimes inaccurate). The relevant operations research literature was reviewed, highlighting techniques applicable for analyzing quantitative and qualitative logistics data. A practica

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Wang, Jianlin, Dan Xu, Jiahui Zhou, and Jinlu Mao. "Fractional-Order Modeling and Analysis of a Variable Structure Hybrid Energy Storage System for EVs." Complexity 2020 (December 9, 2020): 1–10. http://dx.doi.org/10.1155/2020/7643812.

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Hybrid energy storage system has been widely studied as an important technology for electric vehicles. Since the hybrid energy storage system is a nonlinear and complex system, the modeling of the system and the high-precision nonlinear control strategy are technical difficulties for research. The establishment of a high-precision mathematical model of the hybrid energy storage system is the basis for the study of high-quality nonlinear control algorithms. Fortunately, the theory of fractional calculus can help build accurate mathematical models of hybrid energy storage systems. In order to ob

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Venetis, J., and E. Sideridis. "A lower bound of longitudinal elastic modulus for three-phase fibrous composites." Mathematics and Mechanics of Solids 24, no. 1 (2017): 72–84. http://dx.doi.org/10.1177/1081286517730667.

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A lower bound of the longitudinal elastic modulus of polymer composite materials reinforced with unidirectional continuous fibres is obtained by means of a Differential Calculus approach. In the mathematical derivations, the concept of interphase between the fibre and matrix was also taken into consideration. The three phases are considered as isotropic. The results obtained from the proposed formula were compared with those arising from some reliable and accurate theoretical models as well as with experimental data found in the literature, and a reasonable agreement was observed.

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