Статті в журналах: "Mathematical modeols"

1

Suzuki, Takashi. "Mathematical models of tumor growth systems." Mathematica Bohemica 137, no. 2 (2012): 201–18. http://dx.doi.org/10.21136/mb.2012.142866.

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2

Pavankumari, V. "Mathematical and Stochastic Growth Models." International Journal for Research in Applied Science and Engineering Technology 9, no. 11 (November 30, 2021): 1576–82. http://dx.doi.org/10.22214/ijraset.2021.39055.

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Abstract: Many statistical and mathematical models of growth are developed in the literature and effectively applied to various conditions in the existent world that involve many research problems in the different fields of applied statistics. Nevertheless, still, there is an equally large number of conditions, which have not yet been mathematically or statistically modeled, due to the complex situations or formed models are mathematically or statistically inflexible. The present study is based on mathematical and stochastic growth models. The specification of both the growth models is depicted. A detailed study of newly modified growth models is mentioned. This research will give substantial information on growth models, such as proposed modified exponential growth models and their specifications clearly motioned which gives scope for future research.

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3

Kumari, V. Pavan, Venkataramana Musala, and M. Bhupathi Naidu. "Mathematical and Stochastic Growth Models." International Journal for Research in Applied Science and Engineering Technology 10, no. 5 (May 31, 2022): 987–89. http://dx.doi.org/10.22214/ijraset.2022.42330.

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Abstract: Many statistical and mathematical models of growth are developed in the literature and effectively applied to various conditions in the existent world involves many research problems in the different fields of applied statistics. Nevertheless, still, there are an equally a large number of conditions, which have not yet been mathematically or statistically modeled, due to the complex situations or formed models are mathematically or statistically inflexible. The present study is based on mathematical and stochastic growth models. The specification of both the growth models is depicted. A details study of newly modified growth models are mentioned. This research will give substantial information on growth models, such as proposed modified exponential growth models and it’s specifications clearly motioned which gives scope for future research.

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4

Staribratov, Ivaylo, and Nikol Manolova. "Application of Mathematical Models in Graphic Design." Mathematics and Informatics LXV, no. 1 (February 28, 2022): 72–81. http://dx.doi.org/10.53656/math2022-1-5-app.

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The article shares the practical experience in creating graphic design in the implementation of projects in the field of applied information technology. The creation of digital art is largely based on mathematical models and concepts that give a good perception of graphics, and it is scientifically justified. The STEAM approach is considered with the idea of the transdisciplinary level of integration between mathematics, graphic design and production practice in student education. For the development of projects like logo design, magazine cover and others, we use software specialized in the field of graphic design and computer graphics. For the realization of the considered projects, among which there are also awarded ones, we use CorelDRAW, Adobe InDesign and Desmos.

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5

LEVKIN, Dmytro. "ARCHITECTONICS OF CALCULATED MATHEMATICAL MODELS UNDER UNCERTAINTY." Herald of Khmelnytskyi National University. Technical sciences 309, no. 3 (May 26, 2022): 135–37. http://dx.doi.org/10.31891/2307-5732-2022-309-3-135-137.

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This article concerns the improvement of calculated mathematical models of technological, biotechnological, and economic systems. It is necessary to increase the number of considered parameters to increase the accuracy of calculating the parameters of complex systems during mathematical modeling. This leads to the need to solve nonlocal boundary value problems with non-stationary differential equations, to prove the correctness of which it is impossible to apply the traditional theory of existence and unity of solution. Note that after the architecture of boundary value problems assumes the existence of their solution, it is only necessary to prove its uniqueness. To prove the correctness of calculated mathematical models requires neither generalizing the parameters of the goal function and using approximate constraints, which, in turn, will reduce the boundary value problem to a standard form and its correctness will not be in doubt, nor propose a method to prove the correctness of boundary value certain differential equations, which will consider the specific features of the modeled processes. A separate technique must substantiate the correctness of boundary value problems depending on the type of differential equation that describes the physical and economic processes in the simulated systems. This article studied the conditions for the correctness of boundary value problems for differential equations with constant coefficients. It is proved that there is a corresponding boundary value problem for arbitrary homogeneous differential equations. It is defined the parabolic boundary value problems in terms that use constraints from above on the fundamental solution function. The conditions were obtained under which the parabolic boundary value problem exists and cannot exist, respectively. The obtained results will increase the accuracy of the main optimization task of improving the quality of simulated processes.

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6

Gardiner, Tony, and Gerd Fischer. "Mathematical Models." Mathematical Gazette 71, no. 455 (March 1987): 94. http://dx.doi.org/10.2307/3616334.

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7

Leangarun, Teema, Poj Tangamchit, and Suttipong Thajchayapong. "Stock Price Manipulation Detection Based on Mathematical Models." International Journal of Trade, Economics and Finance 7, no. 3 (June 2016): 81–88. http://dx.doi.org/10.18178/ijtef.2016.7.3.503.

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8

Ojha, Pratima, and R. K. Dubey R.K.Dubey. "Mathematical Properties of Homogeneous and Isotropic Cosmological Models." International Journal of Scientific Research 2, no. 2 (June 1, 2012): 83–84. http://dx.doi.org/10.15373/22778179/feb2013/30.

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9

ZAVGORODNIY, OLEXIY, DMYTRO LEVKIN, YANA KOTKO, and OLEXANDER MAKAROV. "RESEARCH OF COMPUTATIONAL MATHEMATICAL MODELS FOR TECHNICAL SYSTEMS." Herald of Khmelnytskyi National University. Technical sciences 319, no. 2 (April 27, 2023): 108–12. http://dx.doi.org/10.31891/2307-5732-2023-319-1-108-112.

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In the theory of analysis and synthesis of technical systems, mathematical modelling and optimization of multilayer systems containing sources of physical fields occupy an important place. This is due to the fact that their state is described by means of boundary value problems with multidimensional differential equations. To solve the boundary value problems and implement the process of optimizing the technical parameters of the modelled systems, it is necessary to conduct interdisciplinary studies of computational and applied optimization mathematical models. Fulfilment of the conditions for the existence of a single solution to boundary value problems by default is possible only when the object of study is a single-layer material under the action of load sources. If it is necessary to calculate and optimize the technical parameters of a multilayer material subjected to load sources, then it is impossible to immediately guarantee the correctness of the calculated and applied optimization mathematical models, since it is necessary to obtain the conditions for the existence and uniqueness of solutions to boundary value problems with systems of differential equations. Maximizing the technical parameters of load sources and averaging the characteristics of material layers will lead to approximate values of the objective function and technical parameters of the modelled system, which leads to irrational consumption of energy and heat resources and uncontrolled losses, and useless losses of the test material in the technological process. The article presents the conditions for the correctness of multipoint boundary value problems with multidimensional differential equations describing the state of a multilayer material under thermal action. It is advisable to use these studies to substantiate the correctness of other technical and biotechnological systems, which will increase the accuracy of the implementation of applied optimization problems of economic and mathematical modelling.

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10

Holdych, D. J., D. Rovas, J. G. Georgiadis, and R. O. Buckius. "An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models." International Journal of Modern Physics C 09, no. 08 (December 1998): 1393–404. http://dx.doi.org/10.1142/s0129183198001266.

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Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

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11

Połowniak, Piotr, and Mariusz Sobolak. "Mathematical model of globoid worm for use of generating CAD model." Mechanik, no. 2 (February 2015): 145/31. http://dx.doi.org/10.17814/mechanik.2015.2.53.

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12

Mazhukin, Vladimir Ivanovich, Žarkop Pavićević, Olga Nikolaevna Koroleva, and Alexander Vladimirovich Mazhukin. "To the 80th anniversary from the birth of A.A. Samokhin, doctor of physical and mathematical sciences, chief researcher of the Prokhorov General Physics Institute of the Russian Academy of Sciences." Mathematica Montisnigri 49 (2020): 111–20. http://dx.doi.org/10.20948/mathmontis-2020-49-9.

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The article is dedicated to the 80th anniversary of the birth of the Soviet and Russian theoretical physicist, Doctor of Physical and Mathematical Sciences A.A. Samokhin, Chief Researcher of the Theoretical Department of the Institute of Prokhorov General Physics Institute of the RAS, a regular contributor to Mathematica Montisnigri and a long-term active participant in the international scientific seminar "Mathematical Models and Modeling in Laser-Plasma Processes and Advanced Scientific Technologies" (LPpM3), one of the founders of which is Mathematica Montisnigri.

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13

Denton, Brian, Pam Denton, and Peter Lorimer. "Making Mathematical Models." Mathematical Gazette 78, no. 483 (November 1994): 364. http://dx.doi.org/10.2307/3620232.

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14

Purwanto, Burhan Eko, Icha Jusmalisa, Indah Permata Sari, Agus Jatmiko, and Andika Eko Pasetiyo. "Learning Models to Improved Mathematical Communication Skills." Desimal: Jurnal Matematika 3, no. 1 (January 23, 2020): 7–16. http://dx.doi.org/10.24042/djm.v3i1.5650.

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The problem faced by students in slow learning is in terms of communication. The use of Auditory, Intellectually, Repetition (AIR) and Cooperative Think Pair Share (TPS) types is needed to help students communicate mathematically in expressing mathematical ideas. This study aims to determine whether or not there are differences in mathematical communication skills of students using the Auditory, Intellectually, Repetition (AIR) learning model with students who use Think Pair Share (TPS) Cooperative learning models. This research uses a quantitative approach using the Quasi Experiment method. The research design is in the form of posttest only, non-equivalent group design. Testing data using the T test with Independent Samples T-Test. Based on the results of hypothesis testing obtained p-value> α 0.05. So it was concluded that there were indications of differences between Auditory, Intellectually, Repetition (AIR) learning models with (TPS) Cooperative learning models and superior (AIR) learning models compared to Cooperative learning models of (TPS) Type in influencing students' mathematical communication skills.

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15

Nogal, Maria, Enrique Castillo, Aida Calviño, and Alan J. O’Connor. "Coherent and Compatible Statistical Models in Structural Analysis." International Journal of Computational Methods 13, no. 02 (March 2016): 1640008. http://dx.doi.org/10.1142/s0219876216400089.

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Modeling problems in structural analysis requires of a statistical approach that allows the consideration of the random nature of the variables as well as the uncertainties involved in the problem analyzed. However, neither all statistical models are valid nor all assumptions are mathematically or physically reasonable. The aim of this paper is twofold: (a) to explain how to build statistical models with mathematical and physical coherence, and (b) to describe the most common mistakes made when building or selecting mathematical and statistical models. Some interesting tools are provided to carry out this important task and some examples are presented showing the inconveniences and consequences derived from an incorrectly established model.

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16

ROTARU, Constantin, Oliver CIUICĂ, Eduard MIHAI, Ionică CÎRCIU, and Radu DINCĂ. "SIMPLIFIED MATHEMATICAL MODEL FOR AIRCRAFTSRESPONSE CHARACTERISTICS." SCIENTIFIC RESEARCH AND EDUCATION IN THE AIR FORCE 18, no. 1 (June 24, 2016): 55–60. http://dx.doi.org/10.19062/2247-3173.2016.18.1.7.

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17

Markov, Svetoslav Marinov. "Building reaction kinetic models for amiloid fibril growth." BIOMATH 5, no. 1 (August 8, 2016): 1607311. http://dx.doi.org/10.11145/j.biomath.2016.07.311.

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In this work we discuss some methodological aspects of the creation and formulation of mathematical models describing the growth of species from the point of view of reaction kinetics. Our discussion is based on familiar examples of growth models such as logistic growth and enzyme kinetics. We propose several reaction network models for the amiloid fibrillation processes in the citoplasm. The solutions of the models are sigmoidal functions graphically visualized using the computer algebra system Mathematica.

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18

Kogalovsky, M. R. "Digital Libraries of Economic-Mathematical Models: Economic-Mathematical and Information Models." Market Economy Problems, no. 4 (2018): 89–97. http://dx.doi.org/10.33051/2500-2325-2018-4-89-97.

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19

Rifki Taufik, Muhammad, Dwi Lestari, and Tri Wijayanti Septiarini. "Mathematical Model for Vaccinated Tuberculosis Disease with VEIT Model." International Journal of Modeling and Optimization 5, no. 3 (June 2015): 192–97. http://dx.doi.org/10.7763/ijmo.2015.v5.460.

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20

Laila, Umi, Rifa Nurhayati, Tyas Utami, and Endang Sutriswati Rahayu. "Prediction of Microbial Population in Sorghum Fermentation through Mathematical Models." Reaktor 19, no. 4 (December 31, 2019): 152–61. http://dx.doi.org/10.14710/reaktor.19.4.152-161.

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The mathematical models can be used as a tool in predicting microbial population in sorghum fermentation, either spontaneous fermentation or fermentation with the addition of lactic acid bacteria (LAB) inoculum. Gompertz model modified by Gibson, Gompertz model modified by Zwietering, Baranyi-Robert model, Fujikawa model, Richards model, Schnute model were used in predicting the growth of lactic acid bacteria (LAB) and coliform bacteria during spontaneous fermentation, and also the growth of LAB during fermentation with the addition of inoculum. Meanwhile, there was death (inactivation) of coliform bacteria during sorghum fermentation with the addition of LAB inoculum. The Geeraerd model and the Gompertz model modified by Gil et al. were used to predict the inactivation. The accuracy and precision of models were evaluated based on the Root Mean of Sum Square Error (RMSE), coefficient of determination (R2), and curve fitting. Gompertz model modified by Gibson had the highest accuracy and precision, which was followed by the accuracy of the Fujikawa model and Baranyi-Robert model in predicting the growth of LAB and the growth of coliform bacteria during spontaneous fermentation. Meanwhile, in predicting LAB growth during fermentation with the addition of inoculum, high accuracy and precision was obtained from Richards and Schnute models. In predicting the inactivation of coliform bacteria, Geeraerd model provided higher accuracy and precision compared to Gompertz model modified by Gil et al. Keywords: fermentation; inoculum; mathematical; model; sorghum; spontaneous

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21

KRAVTSOV, Andrii, Dmytro LEVKIN, Natalija BEREZHNA, and Artur LEVKIN. "METHODOLOGICAL APPROACH TO THE MATHEMATICAL MODELS CONSTRUCTION OF BIOOBJECT PROBLEMS." Herald of Khmelnytskyi National University. Technical sciences 317, no. 1 (February 23, 2023): 105–10. http://dx.doi.org/10.31891/2307-5732-2023-317-1-105-110.

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This article reveals a technique for the mathematical modeling of biotechnological systems that contain sources of laser action. Calculation and optimization mathematical models for finding rational values of the technical parameters of the emitters are the basis for this. The authors researched the main aspects of the theory of analysis and synthesis of complex systems that contain concentrated, moving sources of physical fields. To ensure the viability of embryo cells, it is necessary to carefully monitor the level of embryo heating not only at the points closest to the laser dissection site but also at the end of the laser action. It should also be noted that at the end of the short-term effect of laser radiation, the flow of heat from the border of the embryo dissection passes to other parts of it. The non-stationary process of thermal distribution will occur until a stationary mode is established, which is necessary to maintain the viability of the embryo. Due to the peculiarities of the microbiological object, the authors perform mathematical modeling of a non-stationary, nonlinear, multidimensional biotechnological system, which contains a discrete, moving source of laser action. It is quite difficult to implement applied optimization mathematical models that are used to optimize the modeled system. Therefore, it is advisable to obtain approximate solutions to boundary value problems with averaged values of thermophysical parameters of laser emitters without considering the three-layer structure of the embryo. To increase the level of viability of germ cells, the authors propose to implement an applied optimization mathematical model for minimizing the deviation of the temperature of laser action from its acceptable value. This will make it possible to obtain rational technical parameters of the emitters, which are close to reality and satisfy the needs of the technical use of laser emitters.

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22

STETSIUK, Viktor, and Kostyantyn HORIASCHENKO. "ANALYSIS OF MATHEMATICAL MODELS OF MULTI-FREQUENCY PIONEERING AUTOMOTIVE SYSTEMS." Herald of Khmelnytskyi National University. Technical sciences 315, no. 6 (December 29, 2022): 100–103. http://dx.doi.org/10.31891/2307-5732-2022-315-6(2)-100-103.

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In the work the analysis of mathematical models of multi-frequency piezoresonance oscillatory systems is carried out. It is indicated on the essence of the phenomenon of multifrequency excitation, as a normal physical property of quartz resonators. However, for the tasks of constructing highly stable self-oscillating systems as a source of reference oscillation, this property of the CR is undesirable, moreover, it is struggling with all possible methods. As a result of the analysis of mathematical models of multifrequency oscillation systems, it is established that none of them allows to fully study the dynamics of multifrequency oscillation systems under conditions of vibrational destabilizing effects, which requires their further study. Proposed own approach to solving problems of simulation of multi-frequency PCBs.

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23

Banasiak, J. "Kinetic models – mathematical models of everything?" Physics of Life Reviews 16 (March 2016): 140–41. http://dx.doi.org/10.1016/j.plrev.2016.01.005.

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24

Karouni, Ali, Bassam Daya, Samia Bahlak, and Pierre Chauvet. "A Simplified Mathematical Model for Fire Spread Predictions in Wildland Fires Combining between the Models of Anderson and Rothermel." International Journal of Modeling and Optimization 4, no. 3 (June 2014): 197–200. http://dx.doi.org/10.7763/ijmo.2014.v4.372.

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25

Khasaia, Izolda. "SOME FORECASTING MODELS IN TOURISM (CASE OF GEORGIA)." Economic Profile 19, no. 1(27) (June 20, 2024): 50–55. http://dx.doi.org/10.52244/ep.2024.27.06.

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In tourism, as in any other business, a responsible decision requires serious justification, since a mistake made in making a decision is associated with large financial losses. In such cases, it is necessary to turn to modeling the behavior of the economic system. In most cases, mathematical models are used, which save the researcher from the need to conduct expensive experiments. Tourism processes are usually dynamic, characterized by seasonality and trends. By analytically simplifying the dynamic rows, a certain model - a trend equation is built, which mathematically accurately describes the development trend of the event in time. The change in indicator levels can be described using a time function. Analytical smoothing method provides an opportunity to evaluate, mathematically describe and predict the event. This article discusses a forecasting model with a combination of moving average and regression analysis. The result of modeling on a specific numerical example - the dynamics of visits of foreign travelers to Georgia - indicates that this approach to building trend models provides a good degree of data approximation and forecasting. All calculations necessary to build the model are performed using Excel tools.

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26

Bаzhanova, А. Yu, M. G. Suryaninov, and G. B. Shotadze. "Finite elements mathematical model of geometric nonlinearity." Odes’kyi Politechnichnyi Universytet. Pratsi, no. 2 (June 15, 2015): 138–44. http://dx.doi.org/10.15276/opu.2.46.2015.25.

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27

TRIVEDI, PRATIK H. "An Appropriate Mathematical Model for A Product." Global Journal For Research Analysis 3, no. 5 (June 15, 2012): 11–12. http://dx.doi.org/10.15373/22778160/may2014/5.

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28

Shrivastava, Rajesh, Deepika Basedia, and Keerty Shrivastava. "Predictive Mathematical Model on Breast Cancer: A Study." international journal of mathematics and computer research 12, no. 03 (March 31, 2024): 4107–13. http://dx.doi.org/10.47191/ijmcr/v12i3.05.

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In the present study, we have designed a mathematical model to analyze whether the cases of breast cancer are maximized or minimized in Madhya Pradesh. Especially to check the age range in which it’s more susceptible to the disease and its means of therapy. The important data collected from Jawaharlal Nehru Cancer Hospital, Bhopal (JLNCH) and Gandhi Medical College, Bhopal (GMC) is from over ten years of reviews of the cases. Actual documentary and analytical methods were used to collect and analyze the data. It is concluded from the results that the number of cancer cases is increasing in both hospitals; its projection may reach up to 97.8% by the year 2023; the age range of 40–50 is more vulnerable to the disease. The line of treatment for breast cancer patients is surgery, chemotherapy, and radiotherapy in both hospitals.

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Kleiner, Johannes. "Mathematical Models of Consciousness." Entropy 22, no. 6 (May 30, 2020): 609. http://dx.doi.org/10.3390/e22060609.

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In recent years, promising mathematical models have been proposed that aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully motivated, their mathematical formalism has not. In this article, we aim to remedy this situation. We give an account of what warrants mathematical representation of phenomenal experience, derive a general mathematical framework that takes into account consciousness’ epistemic context, and study which mathematical structures some of the key characteristics of conscious experience imply, showing precisely where mathematical approaches allow to go beyond what the standard methodology can do. The result is a general mathematical framework for models of consciousness that can be employed in the theory-building process.

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30

Byrne, Patrick, S. D. Howison, F. P. Kelly, and P. Wilmott. "Mathematical Models in Finance." Statistician 45, no. 3 (1996): 389. http://dx.doi.org/10.2307/2988481.

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31

Kozhanov, V. S., S. O. Ustalkov, and A. O. Khudoshina. "TOW CABLES MATHEMATICAL MODELS." Mathematical Methods in Technologies and Technics, no. 5 (2022): 62–68. http://dx.doi.org/10.52348/2712-8873_mmtt_2022_5_62.

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32

Logan, J. David, Elizabeth S. Allman, and John A. Rhodes. "Mathematical Models in Biology." American Mathematical Monthly 112, no. 9 (November 1, 2005): 847. http://dx.doi.org/10.2307/30037621.

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33

Zhuk, Tetyana. "Mathematical Models of Reinsurance." Mohyla Mathematical Journal 3 (January 29, 2021): 31–37. http://dx.doi.org/10.18523/2617-70803202031-37.

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Insurance provides financial security and protection of the independence of the insured person. Its principles are quite simple: insurance protects investments, life and property. You regularly pay a certain amount of money in exchange for a guarantee that in case of unforeseen circumstances (accident, illness, death, property damage) the insurance company will protect you in the form of financial compensation.Reinsurance, in turn, has a significant impact on ensuring the financial stability of the insurer. Because for each type of insurance there is a possibility of large and very large risks that one insurance company can not fully assume. In the case of a portfolio with very high risks, the company may limit their acceptance, or give part of the reinsurance. The choice of path depends entirely on the company’s policy and type of insurance.This paper considers the main types of reinsurance and their mathematical models. An analysis of the probability of bankruptcy and the optimal use of a particular type of reinsurance are provided.There are also some examples and main results of research on this topic. After all, today the insurance industry is actively gaining popularity both in Ukraine and around the world. Accordingly, with a lot of competition, every insurer wants to get the maximum profit with minimal e↵ort.

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34

Schneider, B., and G. I. Marchuk. "Mathematical Models in Immunology." Biometrics 42, no. 4 (December 1986): 1003. http://dx.doi.org/10.2307/2530721.

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35

Knapp, David, and Richard Bellman. "Mathematical Models in Medicine." Mathematical Gazette 70, no. 451 (March 1986): 79. http://dx.doi.org/10.2307/3615870.

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36

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

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

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37

Soong, S. J. "Mathematical models of prognosis." Melanoma Research 3, no. 1 (March 1993): 24. http://dx.doi.org/10.1097/00008390-199303000-00081.

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38

Dilão, Rui. "Mathematical models of morphogenesis." ITM Web of Conferences 4 (2015): 01001. http://dx.doi.org/10.1051/itmconf/20150401001.

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39

Mayergoyz, I. "Mathematical models of hysteresis." IEEE Transactions on Magnetics 22, no. 5 (September 1986): 603–8. http://dx.doi.org/10.1109/tmag.1986.1064347.

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40

Protter, Philip. "Mathematical models of bubbles." Quantitative Finance Letters 4, no. 1 (January 2016): 10–13. http://dx.doi.org/10.1080/21649502.2015.1165863.

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41

Hamblin, C. L. "Mathematical models of dialogue1." Theoria 37, no. 2 (February 11, 2008): 130–55. http://dx.doi.org/10.1111/j.1755-2567.1971.tb00065.x.

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42

Jacob, C., F. Charras, X. Trosseille, J. Hamon, M. Pajon, and J. Y. Lecoz. "Mathematical models integral rating." International Journal of Crashworthiness 5, no. 4 (January 2000): 417–32. http://dx.doi.org/10.1533/cras.2000.0152.

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43

Naydenov, Nikolay Dmitriyevich, Vasily Igorevich Spiryagin, and Elena Nikolayevna Novokshonova. "ECONOMIC-MATHEMATICAL CLUSTER’S MODELS." Sovremennye issledovaniya sotsialnykh problem, no. 9 (November 15, 2015): 415. http://dx.doi.org/10.12731/2218-7405-2015-9-31.

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44

Pollard, John. "Mathematical Models of Population." Population Studies 47, no. 2 (July 1, 1993): 369. http://dx.doi.org/10.1080/0032472031000147136.

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45

Gavaghan, David, Alan Garny, Philip K. Maini, and Peter Kohl. "Mathematical models in physiology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1842 (March 22, 2006): 1099–106. http://dx.doi.org/10.1098/rsta.2006.1757.

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Анотація:

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term ( modelling OR modeling ) yields over 58 000 entries in PubMed, with more than 34 000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5–6 years, compared to only about one-third in the preceding 5–6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function—the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations.

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46

Mayergoyz, I. D. "Mathematical Models of Hysteresis." Physical Review Letters 56, no. 15 (April 14, 1986): 1518–21. http://dx.doi.org/10.1103/physrevlett.56.1518.

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47

Traykov, M., and Iv Trenchev. "Mathematical models in genetics." Russian Journal of Genetics 52, no. 9 (September 2016): 985–92. http://dx.doi.org/10.1134/s1022795416080135.

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48

Scherer, Almut, and Angela McLean. "Mathematical models of vaccination." British Medical Bulletin 62, no. 1 (July 1, 2002): 187–99. http://dx.doi.org/10.1093/bmb/62.1.187.

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49

Huheey, James E. "Mathematical Models of Mimicry." American Naturalist 131 (June 1988): S22—S41. http://dx.doi.org/10.1086/284765.

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50

Raup, David M. "Mathematical models of cladogenesis." Paleobiology 11, no. 1 (1985): 42–52. http://dx.doi.org/10.1017/s0094837300011386.

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The evolutionary pattern of speciation and extinction in any biologic group may be described by a variety of mathematical models. These models provide a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns. The simplest model assumes time homogeneity: that is, speciation and extinction probabilities are constant through time and within taxonomic groups. In some cases the homogeneous model provides a good fit to real world paleontological data, but in other cases the model serves only as a null hypothesis that must be rejected before more complex models can be applied. In cases where the homogeneous model does not fit the data, time-inhomogeneous models can be formulated that specify change, regular or episodic, in speciation and extinction probabilities. An appendix provides a list of the most useful equations based on the homogeneous model.

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