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In the present paper, the effects of cake thickness and time on the efficiency of brown stock washer of the paper mill are studied by using mathematical model of pulp washing for the species of sodium and lignin ions. The mechanism of the diffusion- dispersion washing of the bed of the pulp fibers is mathematically modeled by the basic material balance and adsorption isotherm is used to describe the equilibrium between the concentration of the solute in the liquor and concentration of the solute on the fibers. To study the parametric effect, numerical solutions of the axial domain of the system governed by partial differential equations (transport and isotherm equations) for different boundary conditions are obtained by the “pdepe” solver in MATLAB source code. The effects of both the parameters are shown by three dimensional graphical representation as well as concentration profiles. [ABSTRACT FROM AUTHOR]

The use of digital tools in algebra education is expected to not only contribute to master skill, but also to acquire conceptual understanding. The question is how digital tools affect students' thinking and understanding. This paper presents an analysis of data of one group of three grade seventh students (12-13 year-old) on the use of a digital tool for algebra, the Cover-up applet for solving equations in particular. This case study was part of a larger teaching experiment on initial algebra enriched with digital technology which aimed to improve students' conceptual understanding and skills in solving equations in one variable. The qualitative analysis of a video observation, digital and written work showed that the use of the applet affects student thinking in terms of strategies used by students while dealing with the equations. We conclude that the effects of the use of the digital tool can be traced from student problem solving strategies on paper-and-pencil environment which are similar to strategies while working with the digital tool. In future research, we recommend to use specific theoretical lenses, such as the theory of instrumental genesis and the ontosemiotic approach, to reveal more explicit relationships between students' conceptual understanding and the use of a digital tool. [ABSTRACT FROM AUTHOR]

This paper provides healthy lifestyle of diabetic patients by using mathematical modeling. In this paper we construct a mathematical model of diet planning for diabetes. The formulated mathematical model is the application of linear programming and integer programming. All the requirements and restrictions were fulfilled in the mathematical model which was developed in this paper. An optimal and feasible solution was produced by using linear and integer programming. This optimal solution gives the diet problem of diabetic patients. All the constraints and objective functions are defined in the diet problem. To provide daily needs of supplement for the particular age of diabetic patients. [ABSTRACT FROM AUTHOR]

Entropy is one of the important concepts in physics and thermodynamics and it is one of the quantities surrounded by amount of mystery. The ambiguity of this concept is due to several reasons, including the mathematical and physical interpretation of the concept as presented by Clausius. This ambiguity is also due in part to the widening of the use of the term entropy to represent several physical concepts that are not related to the basic concept of entropy as introduced by Clausius himself. In this paper, the mathematical and physical modeling of this term will be reviewed. Furthermore, this paper will show how does this term has been used to describe some physical concepts which are not related to the original use of it. And finally, in order to remove the confusion and ambiguity surrounded this term, the paper will show how should the entropy explained and understanding from the macroscopic thermodynamics point of view. [ABSTRACT FROM AUTHOR]

The problem of developing alternative energy sources with high efficiency was posed back in the middle of the 20th century. One of the possible ways to solve it is the development of systems based on direct absorption solar collectors based on nanofluids. Systems of this kind are the most environmentally friendly and modern, the disadvantages of which include the complexity of maintenance and climatic restrictions of widespread use. The aim of this paper is to determine ways to increase the efficiency of heat transfer in systems for collecting and storing solar energy by means of mathematical modeling of heat and mass transfer processes in direct absorption solar collectors based on nanofluids. When constructing a mathematical model, the contributions of the diffusion and electrostrictive components were taken into account. A mathematical model of heat and mass transfer in a liquid-phase medium with nanoparticles under the action of a light field is investigated, taking into account one-dimensional concentration convection in the form of a boundary-value problem for a system of second-order partial differential equations. The reported study was funded by RFBR, project number 19-31-90070. [ABSTRACT FROM AUTHOR]

Despite the advantages of cloud computing, such as its scalability and accessibility, the security of the data it holds remains a major concern. This paper proposes a hybrid structure that combines the features of two well-known encryption algorithms. The hybrid structure adopts the DES' flexibility and efficiency while also taking advantage of AES' robustness. Our goal is to offer a higher level of protection for sensitive data that is stored in cloud computing. The paper presents an overview of the various aspects of the proposed architecture, including key management, decryption, and encryption. The first step in the encryption process is to implement the AES before adding the DES for security. The paper provides an overview of the various distribution and key generation techniques. They are designed to ensure that the data is protected from unauthorized access. In addition, we discuss the decryption process, which enables users to retrieve the original data. We performed extensive tests to analyze the security and performance of the proposed architecture. These tests included comparisons with the standalone DES and AES algorithms. The results of the tests revealed that the proposed architecture performed better than the standalone DES and AES algorithms in several aspects. In addition, it exhibited better decryption and encryption speeds. The hybrid structure's improved resource utilization also leads to lower system memory and CPU utilization. Its high throughput helps improve system responsiveness and data processing. The proposed architecture ensures the security of sensitive data by minimizing the time it takes to generate and manage key generation. It also helps improve the efficiency of the process by reducing the file size overhead. The findings of the study highlight the advantages of implementing the hybrid structure in protecting sensitive data stored in cloud computing, as well as its viability. The combination of the DES and the AES offers a flexible and robust approach to safeguarding information. This report serves as a valuable contribution to the field of data security by providing a practical solution to the cloud computing security issues. [ABSTRACT FROM AUTHOR]

With the development of science and technology, UAV technology and application have become an increasingly important field. The four-rotor aircraft has a simple structure and diverse functions and has been widely used in many fields. In practical applications, it is necessary to strictly ensure the stability of its flight, so it is very important to ensure stability when designing the control system. Knowing that the PID control algorithm can improve the stability of the system by adjusting various parameters, and the response speed is fast and easy to realize, this paper adopts the PID control method to design a stable quadrotor aircraft system. In this paper, the mathematical model of the four-rotor aircraft is first established according to the dynamics theory, and its system composition and working principle are shown, which lays a structural foundation for the subsequent design. After that, the basic principle and function of PID control are expounded, and the corresponding controller is designed based on the algorithm in the four attitude directions of vertical, pitch, roll, and yaw. Finally, the control system is simulated by establishing a model on Simulink and inputting appropriate parameters. The results show that the speed of the PID controller can meet the corresponding control requirements in the simulation of four channels, which indicates that the design method is feasible and can guarantee the stability of the system. This study verifies the effectiveness of PID control of four-wing rotary-wing UAVs and provides a basis for further exploration of algorithm improvement and innovation and improvement of aircraft stability. [ABSTRACT FROM AUTHOR]

In this paper, we describe the dynamics of the spread of the COVID-19 disease. In this paper, a mathematical model of the problem is rewritten. Mathematical models can be used to find strategies to prevent the Coronavirus disease spread. A Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model in the spread of COVID-19 disease is solved using fourth and fifth-order Runge-Kutta methods. The simulation results of the two methods show the same pattern of solution behavior as the results of the reference solution obtained using the ODE45 algorithm in the MATLAB software. Theoretically, the accuracy of the fourth-order Runge-Kutta method is not better than that of the fifth-order Runge-Kutta method. We show the correctness of this theory through simulations in this paper by solving the SEIR mathematical model for the COVID-19 disease. [ABSTRACT FROM AUTHOR]

In this paper, the spread of the Covid-19 in.Indonesia is described by the SIRD epidemiological mathematical model. The mathematical model used in this paper is Susceptible, Infected, Recovered, Death (SIRD). The modified extended Kalman filter algorithm is applied to predict the spread of Covid-19 in.the future. We modified the algorithm by generating real data based on the previous estimation results. The real data generated from the generation is used at the correction stage to obtain prediction results in a fairly long period. Simulations were carried out with three types of mobility restrictions, namely mobility 100%, mobility 75%, and mobility 50%. Based on the simulation results, it can be concluded that mobility restrictions in Indonesia, which starts on September 4, 2020, can reduce the number of infected and death individuals and can increase the number of individuals who recover from Covid-19. [ABSTRACT FROM AUTHOR]

The new coronavirus that is the source of the pandemic respiratory infection known as COVID-19 poses a major risk to the public's health. In this paper, we present a mathematical model of the spread of an infectious disease according to the characteristics of the COVID-19 pandemic. The proposed improvedmodel is developed on the AnyLogic system, which will be referred to as the SEAIR (Susceptible-Exposed-Asymptomatically Infected-Symptomatically infected-Recovered) model. The paper considers mathematical models that are used to analyze and predict the development of the COVID-19 pandemic, including time series analysis, equations of mathematical physics and simulation models, their various combinations and generalizations. Due to the novelty and complexity of the COVID-19 disease, the parameters of most mathematical models are usually unknown, and this leads to the need to consider and solve inverse problems. [ABSTRACT FROM AUTHOR]

It is difficult to deal with the uncertainty data issue which has incompleteness, impreciseness and incertitude. Normally, uncertain and vague information is confronted in form of data point. Various mathematical models were developed to resolve issues concerning uncertainty point. In this paper, Neutrosophic Bézier Curve model will be introduced. A mathematical model with a redefinition of the control points that is characterized by three important components of neutrosophic set is designed to solve this problem. These control points are blended with the Bézier basic functions to generate multiple models in the form of neutrosophic spline curve and surface. Then, the related data can be translated through the construction of those models with the neutrosophic concept and its relationships. [ABSTRACT FROM AUTHOR]

The regular propagation of electrical signals in the cardiac tissue is essential for the proper functioning of the heart. Disorders of this rhythm are collectively called cardiac arrhythmias. These diseases include, for example, cardiac fibrillation. This condition is characterized by the chaotic propagation of control signals in the tissue, which prevents its proper function. This paper analyzes the transmembrane potential of cardiac cell mathematical models depending on the stimulation current. In these data, chaotic responses of heart cells are detected using modern and classical methods for analyzing dynamic systems such as entropy, the 0-1 test for chaos, or recurrence quantification analysis. This analysis displays stimulation parameters, during which the mathematical models show chaotic responses. [ABSTRACT FROM AUTHOR]

In this paper, the performance of a supercapacitor (SC) under constant power loads is studied. The equivalent electrical circuit of a SC considered in this study takes advantage of its simplicity to obtain analytical solutions. The mathematical model of the SC neglects the transient response but, due to the consideration of a variable capacitance, it accurately reproduces the steady-state response for a wide range of charging/discharging power. The integration of the governing differential equation of the SC leads to a complex relationship between SC voltage and time. From this equation several explicit expressions (i.e., charging and discharging times, ohmic losses, efficiency, etc.) as a function of the SC voltage are derived. These variables are useful to size and define the energy management strategy of a SC or a bank of SCs in many constant power applications. The performance of a commercial supercapacitor that has been previously tested and modelled is analysed. [ABSTRACT FROM AUTHOR]

Two stroke engines is comparatively small, simple in operation with less cost because of absence of valve mechanism. The performance of the engine is such that it has low brake thermal efficiency and higher exhaust emission because of incomplete combustion which results into high emission and fuel consumption. Scavenging is important for improvement of the engine performance by removing the exhaust gases from the engine. The paper details the modification in the engine for enhancing the scavenging process so that performance of engine in terms of brake power and thermal efficiency will increase. The modification in the two stroke engine is done by providing hole in transfer port for air aspiration. The general concept in using external air aided scavenging is to improve scavenging characteristics of base engine by reducing short-circuiting phenomenon. Investigation of the modified engine were done by evaluating the brake power and thermal efficiency of two stroke engine using the mathematical tools such as mathematical modeling, sensitivity and optimization. The paper highlights the modification in the engine to enhanced the performance of engine and the formulation of mathematical model. The formulated mathematical model predicts the performance of engine with the help of indices of each pie term formed with input variables. The positive indices of the pie term indicate the most influencing pie terms responsible for variation in the output variable such as brake power and thermal efficiency. The negative indices of the pie term indicate the inverse effect on the output variables as it is inversely proportional to the output variables brake power and thermal efficiency. Thus the exact mathematical model help to investigate the performance of the engine at lower cost with less time involved in experimentation. [ABSTRACT FROM AUTHOR]

Investment decision is difficult to be determined as the investors need to earn highest possible return in generating profit and protecting capital. Mathematical model which can provide the ranking and proportion of the investment alternatives will benefit investors as selection guideline. This paper aims to investigate in ranking and allocating proportion of asset funds using fuzzy preference relation and weighting algorithm. The evaluation of asset fund is expressed in trapezoidal fuzzy number. The data used for this study is 30 asset funds that listed in the Bursa Malaysia. This study found that 14 asset funds are suggested based on ranking and proportion allocation obtained from this model. As a conclusion, this study can assist investors in making decision in terms of ranking and allocating asset funds. [ABSTRACT FROM AUTHOR]

It takes millions of years for a star to get formed. The evolutionary process of star formation undergoes various stages. Theoretical and astronomical calculations confirm the series of events from nebula to a white dwarf, neutron star, or black due to conversion of mass into energy. This paper deals with the stability analysis of a mathematical model which governs star formation during the ever-changing process of evolution. Variation matrix or Jacobian Matrix is developed out of the differential equation which arises from three components of the galactic region that is atomic, molecular, and stellar components. The mathematical model is the best way to explore and explain the system of three components in the galactic region. In fact, Mathematical Modelling-is the main, if not the only way one, way for theoretical research of astrophysical processes and objects. Various examples have been taken for comparative studies and computational purposes. [ABSTRACT FROM AUTHOR]

Silicon has remarkable mechanical properties, and it is a very promising material for MEMS pressure sensors. The Silicon diaphragm plays an important role in enhancing the sensitivity and linearity of the pressure sensor. In this paper, a silicon diaphragm is modeled by solving the analytical equations for both rigidly clamped and freely supported diaphragms by exploring the solution of differential equation and dependency on the different parameters of the diaphragm. For obtaining maximum deflection of the diaphragm, boundary conditions are applied for different loads. COMSOL Multiphysics is used to simulate the optimum geometry of the diaphragm for enhancing the sensitivity of the pressure sensor. Results reveal that diaphragm thickness of 20 µm shows the high displacement sensitivity of the pressure sensor. [ABSTRACT FROM AUTHOR]

The task of developing effective granular aggregates, as well as the creation of a mathematical model and management of this process, is the most promising and relevant. The paper deals with the construction of mathematical models based on the results of experimental studies of granular aggregates (GA). We present the processing of the results of experimental studies on the production of granular aggregates using the classical method with the use of the high-level general-purpose Python programming language. The processing of research results is fully object-oriented. This approach to the generation of the obtained results allowed us to automate the processing of the array of data for the planning of the experiment. The results of mathematical modeling and nomograms reflecting the variability of the developed compositions, which allowed to obtain samples with the required technological, physical-mechanical and operational characteristics are presented. The paper calculates the values of reproducibility dispersions: for sand fraction ≤0.16 mm - 0.889; for sand fraction ≤0.315 mm - 0.967; for sand fraction ≤0.63 mm - 0.981. The analysis of nomograms has shown that the greatest strength values have the compositions with the sand fraction of 0.16 mm and the minimum content of sand (as an aggregate). For mixtures with sand fractions ≤0.315 mm it is established that the strongest will be the mixture with the minimum content of aggregate. It is revealed that when using sand fraction ≤0.63 mm the strength is reduced. [ABSTRACT FROM AUTHOR]

Verification activity in a streamline manufacturing system is one of the most important activity to make sure that the design requirements and the actual product specifications are met. It helps designer or manufacturing engineer as a feedback by detecting issue at early stage. However, we have to select the most effective verification method that will lead to low cost and relatively fast production. Many industries make machined components that are mounted to welded frame, the locations of the components may float with a larger tolerance to the welded frame than the feature to feature tolerance needed for mounting hole pattern. The composite tolerance is needed for this particular case. The most suitable method for gathering measurement data for small batch production is either automatically using CMM or manually using pin gages and size measurement devices. While, the data processing step can be done by graphic analysis or paper gage method for inspecting composite positional tolerance. The innovation of this journal is changing the way of data processing method by reducing the papers (coordinate grid and polar overlay) required for graphic analysis and converting them into mathematical model that can be processed by computer. Hence, we call this virtual graphic analysis. The benefits of using virtual graphic analysis are reducing cost and time of overall inspection process. [ABSTRACT FROM AUTHOR]

The introduction of new repair technologies requiring production readjustments is inextricably linked with the development of effective digital modeling methods. The paper presents some research results on the creation of a methodology for the automated design of technological processes for the production of car repair enterprises, based on digital modeling of car structures and technological processes of their repair. The article considers the method of constructing a mathematical model of the car (or its unit) structure, created on the basis of the structural-parametric method, which allows the most efficient way to carry out the exploding of the structure and the formation of the composition of sets of technological documentation for the repair of cars. The block diagram of the automatic coupler and the graph, which is a mathematical description of this structure, are given. [ABSTRACT FROM AUTHOR]

In the paper numerical study results of polymer melt flow on the cable head channels have been presented. The distinctive feature of the present investigation is calculation of a free outflow zone at the flow exit from the cable head. In the work a mathematical model of the isothermal three-layer flow with regard to viscoelastic properties of the processed materials has been given. The ANSYS POLYFLOW software package was used to solve the problem. The Maxwell model describing the viscoelastic properties of the examined materials has been applied. The mathematical model of the flow process was based on the laws of conservation. Calculation results have been velocity, pressure and current functions fields, boundaries of the external free surface at the cable head outlet. Diagrams of changes in the insulation thickness for different sections of the sector are given. [ABSTRACT FROM AUTHOR]

The solution to the problem of the movement of an aircraft along the runway in a turbulent atmosphere is a complex and urgent problem. The complexity of the problem lies in the fact that, in the general case, the mathematical model of the problem is reduced to solving nonlinear differential equations, the right side of which is a random function caused by the presence of a turbulent atmosphere. To solve this problem, simplified models of the problem are used, and linear differential equations describe it. If the plane is an inherently deformable solid, then the problem is mathematically described with weakly singular integrodifferential equations with given initial conditions. The present work is devoted to the solution of such problems. In this paper, using the method of eliminating the features of integral and integrodifferential equations, an algorithm for the numerical solution of weight functions has been developed, which allows, in particular, to obtain numerical solutions to the problem when an airplane is considered an ideally elastic solid. Consequently, the algorithm and method of solving the proposed in this paper allow you to test the accuracy of the solution by comparing it with well-known solutions. [ABSTRACT FROM AUTHOR]

Earlier experimental and theoretical studies of slow-speed compressor stages have shown that the design of the valves has a decisive influence on the efficiency of their operating process. In this paper, we consider the design of self-acting valves with elastomeric elements, the deformation of which changes the perimeter of the valve gap in the closed state. As a result of mathematical modeling and comparative parametric analysis, it was determined that the perimeter of the gap in the closed valve can significantly decrease, which leads to the decrease in the amount of leakage through the closed valve and an increase in such integral characteristics as the volumetric efficiency and the indicator efficiency. [ABSTRACT FROM AUTHOR]

Hoax is an information or explanation with unconfirmed truth. Nowadays, social media is the most used media in hoax propagation. If no action is taken, hoax propagation can cause serious problems. In this paper, a mathematical model representing social media hoax propagation with forgetting mechanism is analyzed in order to study the dynamics of social media hoax propagation in real life. Based on the analysis result, we obtain two equilibria, namely, non-endemic equilibrium and endemic equilibrium whose local stabilities depend on the basic reproduction number or R0. Social media hoax propagation occurs when R0 > 1 and does not occur when R0 < 1. Based on the sensitivity analysis result, the probability that a hoax is considered attractive and the forgetting rate of social media users against hoaxes are the most influential parameters on the dynamics of social media hoax propagation. Next, in order to minimize the number of hoax spreaders and hoax contents on social media, three control variables, namely, anti-hoax campaign, punishment for hoax spreaders, and hoax deletion by authorized parties, are imposed to the mathematical model. The optimal control problem in this paper is solved by using Pontryagin Maximum Principle. The numerical simulation result shows that the bundle implementation of three control strategies is the most effective scenario to minimize the number of hoax spreaders and hoax contents on social media. [ABSTRACT FROM AUTHOR]

In this paper an advanced stochastic approach based a lattice rule with improved generating vector has been obtained and studied. The Unified Danish Eulerian Model (UNI-DEM) is a key element in our investigation since it is one of the most advanced large-scale mathematical models that describes adequately all physical and chemical processes. The calculations are done in a large spatial domain, which covers completely the European region and the Mediterranean, for certain time period. What is more, it studies the transportation of a number of pollutants and all these make it a perfect case study. The paper compares the described lattice rule and demonstrates its superiority over the plain Monte Carlo approach and Fibonacci based lattice rule. The proposed approach is robust and computationally efficient in estimating multidimensional integrals and thus sensitivity indices, which is vital in scientific computing. [ABSTRACT FROM AUTHOR]

This paper consist of mathematical modeling of the Wankel engine simulated in GNU Octave software. Main purpose of this study is to make an algorithm that can simulate a wankel engine that can estimate performance of engine. For any starting initial condition of engine and based on thermodynamic conditions algorithm predict output result from an engine. Simulation code consists of the construction of an engine which consists of radius, thickness and eccentricity of the engine. These construction parameters can be altered to various sizes according to the needs of the user. Code is capable of deriving various engine performance variables, combustion parameters, and cycle parameters such as pressure, temperature, heat transfer coefficient, work done, etc at any rotor angle according to construction parameters. Code is capable of handling various fuel data and conditions. This model can be used to determine values theoretically with any engine size, fuel, rpm, and running condition. Similar to engine size, the condition of the flame propagation can be altered to practically any value. In case of an actual scenario, needs of initial pressure and temperatures can also able to change. As codes are based on a thermodynamic equation model, it benefits low computing power and low simulation time. Codes have been tested by keeping similar conditions of previous research papers and showing good agreement result with this code. [ABSTRACT FROM AUTHOR]

The cylindrical Pirani gauge sensitivity under different conditions is studied in our previous paper. We are modeled the Pirani gauge as cylindrical Couette flow – one dimensional axis symmetrical problem by using a statistical method – Direct Simulation Monte Carlo (DSMC) and the Navier-Stokes-Fourier equations numerical solving. The purpose of this article is to study the cylindrical two-dimensional Taylor-Couette flow with finite length of rarefied gas. The suddenly temperature change of the inner cylinder wall (the fiber) is used to modeling the boundary conditions. The finite volume method and statistical modeling is used to study this problem. This paper is a continuation of our previous work which we extend the study using the NSF model and its numerical solution to assess the applicability of the obtained results. The state of the gas is studied over a long time period close to establishing a steady state in the previous work, while in this paper is studied the initial moment of occurrence and reflection of the wave from the other cylinder. The realization of such conditions is difficult technically feasible in some cases, but their set in mathematical model gives more opportunities to study the stability in the gaseous medium between the cylinders. [ABSTRACT FROM AUTHOR]

The fluctuations in oil prices are very complicated and therefore, it is unable to predict its effects on economies. For modelling complex system of oil prices, linear economic models are not sufficient and efficient tools. Thus, in recent years, economists attached great attention to non-linear structure of oil prices. For analyzing this relationship, GARCH types of models were used in some papers. Distinctively from the other papers, in this study, we aimed to analyze chaotic pattern of oil prices. Thus, it was used the Lyapunov Exponents and Hennon Map to determine chaotic behavior of oil prices for the selected time period. [ABSTRACT FROM AUTHOR]

This paper presents the physico-mathematical model of the airflow in the vicinity of the surfaces of the generating sets. Using the developed model, we have carried out the numerical study on the air motion around the generating sets and obtained the distributions of the temperature and air velocity. We have determined the values of the heat fluxes under the natural convective and forced air flow regimes, providing thermostating of the electrical equipment. [ABSTRACT FROM AUTHOR]

Inventory control problem becomes one of the most crucial parts in a company. Basically, the problem is to determine the optimal time and quantity of replenishment. But, there are many factors affected the decision such as demand uncertainty, lifetime of the product, deterioration, unit sales price and discount offered by the supplier. In this paper, we consider a mathematical model for inventory control problem. We consider a multi-item problem with inventory and price-dependent demand and all-units discount offered by the supplier. In dealing with multi-item problem, there are two replenishment policies to consider, individual order and joint order policy. Numerical examples are given with different inventory and price-dependent demand functions for each item and compare the individual and joint order policy. We found that in our numerical example, joint replenishment policy gives lower total inventory cost compared to the individual order policy. [ABSTRACT FROM AUTHOR]

Good and properly organized inventory management is essentially needed for a company in order to ensure that its production process runs smoothly. There are many factors to be considered since they can distract the inventory management such as demand behavior, the life time of goods, uncertain replenishment time, the political and economic situation, and unexpected natural disaster. There are certain risks involved with bulk replenishment such as the higher holding cost and the possibility of damage to the stored goods. On the other hand, if we order too little, the risks lie in the possibility that the production process will stop, resulting in lost sales due to the unavailability of goods. One strategy to overcome this unavailability of goods is backorder, where the customers will wait until the next replenishment to obtain their goods. This paper develops a mathematical model for inventory-dependent demand with the backorder policy applied. The decisions variables in our model are the optimal order quantity and the number of backorders, which minimize the total inventory cost. We also performed a sensitivity analysis of the optimal solution and found that the decreasing rate of the inventory is affected by the autonomous demand (α) and the increasing demand factor (β). Inventory will deplete faster as α and β increase. The number of backorders is affected by the high demand when inventory reaches zero and backorders entail a certain cost. When demand is higher and the backorder cost is relatively cheap, the number of backorders becomes higher. [ABSTRACT FROM AUTHOR]

Elementary cellular automata (ECA) rule 184 can be used as mathematical models of traffic flows. The slow-to-start model is obtained from the ECA rule 184 model by taking time lag for restart into consideration and is represented by 3-state 3-neighbor cellular automata (CA). In the present paper, we propose a traffic model where vehicles following the slow-to-start rule and those not following the slow-to-start rule are mixed. This model, called the mixed slow-to-start model, is represented by 4-state 3-neighbor CA. Further, we introduce the vector representation of CA with the slow-to-start rule and with the mixed slow-to-start rule, and then get their corresponding fuzzy CA. These fuzzy CA provide continuous-valued traffic models with the slow-to-start effect. Comparing the fundamental diagrams of the the slow-to-start model, the mixed slow-to-start model, and their fuzzy counterparts, we investigate the influence of the density and the mixing ratio of vehicles on traffic jams. [ABSTRACT FROM AUTHOR]

This paper examines the methods of similarity and dimensional analysis. The methods in question are the mathematical modeling theoretical basis in the research of the fixed connection contact of car body parts. The paper provides a detailed overview of the basis of the similarity and modeling theories with regard to solving visco-elastic boundary value problems. The mathematical modeling conditions to examine the stress-strain state of car body parts are presented as well. The analytical dependencies obtained make it possible to model the stress-strain state of car body parts under normal operating conditions. [ABSTRACT FROM AUTHOR]

This review paper explores the pivotal role of mathematical modelling within cancer research, with a specific focus on the prominent mathematical models employed for this purpose, including ordinary differential equations (ODEs), partial differential equations (PDEs), cellular automata (CA), agent-based models (ABMs), and hybrid models. These models are crafted to simulate and predict how tumours respond to various treatment strategies, thereby facilitating the evaluation of hypotheses and therapeutic options before clinical application. The emergence of in silico trials, which can predict patient-specific responses to treatment variations, holds promise for optimising personalised patient care. Nevertheless, it is essential to acknowledge that mathematical models come with inherent limitations, often oversimplifying intricate biological systems and potentially overlooking subtleties in tumour dynamics. The accuracy of these models is heavily reliant on the quality and quantity of data used for calibration. Therefore, to achieve a more comprehensive understanding of tumour biology and treatment outcomes, these models together use both experimental and clinical data. [ABSTRACT FROM AUTHOR]