Formulation Of Mathematical Model Research Articles

Data-driven modelling of bioethanol fuel production from rambutan fruit waste

Owing to lack of confidence on potential yield and subsequent net benefit, wide-scale implementations of bioethanol from food/fruit waste are not gaining momentum. With the aim of enhancing stakeholders’ confidence, this paper presents a simple mathematical model formulation, which can estimate potential bioethanol generation capacity from rambutan waste under different input conditions. The mathematical formulation was derived based on three contributing factors: pH, temperature and fermentation period. The factors were derived based on an earlier experimental study on production of bioethanol from rambutan waste. The results from the derived mathematical model were compared with the experimental measurements from earlier studies. It is found that the proposed model is capable of accurately estimating potential bioethanol production from rambutan waste. The model calculated results have a coefficient of correlation of 0.98 with the measured data. Standard errors of the model's estimations are also quite low, having root mean-squared error = 0.17, mean absolute error = 0.14 and relative absolute error = 0.02. For a wider industrial generation, a mathematical framework is proposed to calculate the cost–benefit ratio of production costs against yield value considering the time value of the money. Such a mathematical framework will assist decision makers on deciding optimum input parameters through optimised energy consumption.

Prediction of the shear strength of RC beam-column joints using new ANN formulations

Beam-column joint is a key part for reinforced concrete (RC) frame building structures under the impact of severe lateral actions of seismic or wind loading. Prior works indicate that there is lacking in the direction of formulation of new mathematical models to predict RC joints strength by artificial neural network (ANN) considering influential design parameters. Present endeavor is devoted to establish new empirical ANN models to estimate shear strength and failure mode for RC exterior and interior beam-column joints. These models were relied on training, testing and validation of a database of over 200 experiments, for the performance of RC joints, using ANN. More than 20 parameters, related to the geometry and loading of the joints, were selected as inputs for these models; but four effective inputs were used in the formulation of the final ANN models. The outputs for ANN models were compared to those counterparts of the commonly utilized models given in codes and other recent studies. This calculation confirms the reliability of current ANN mathematical models and their outstanding performance. Moreover, comparison shows that the proposed models were precise in including the effective independent variables in these models and avoiding the shortcoming of previous models.

Mathematical Modeling for the Industrial 2-Mercaptobenzothiazole Batch Production Process.

As an important chemical intermediate, 2-mercaptobenzothiazole (MBT) is widely used in various processes, especially in the rubber industry. However, there is no first-principles model that describes the synthetic process of MBT. This paper focuses on the formulation of a reliable mathematical model represented by a series of differential and algebraic equations for the industrial batch MBT production process. It is difficult to estimate all of the unknown parameters in the model because of the lack of sufficient industrial/experimental data. Thus, a reduced estimable parameter set is derived by performing estimability analysis on the original estimation problem. A multiple-starting-point strategy is then applied to numerically solve the non-convex parameter estimation problem with the weighted least-squares approach. Subsequently, a cross-validation technique is employed to evaluate the generalizability of the proposed model. Finally, it is confirmed that the proposed model produces encouraging prediction performance with regard to independent test data.

Interval valued demand and prepayment-based inventory model for perishable items via parametric approach of interval and meta-heuristic algorithms

This work mainly focuses on the mathematical formulation of an imprecise inventory model with partial prepayment policy in interval environment. In the proposed model, two different cases (without shortage and with partially backlogged shortages) are taken into consideration. Here, the demand and deterioration rates are considered as interval valued. Also, all the inventory costs, viz. ordering cost, purchase cost, holding cost, shortage cost and lost sale cost are considered as interval valued. Then, the continuous change of inventory level with time of the proposed model is defined mathematically by the interval differential equations. For both cases of the proposed model, the interval valued average profits are obtained by using parametric approach of interval. Here, the selling price and business period are taken as decision variables of the corresponding interval maximization problem. Finally, two numerical examples are considered and solved by using different meta-heuristic algorithms for checking the validity of the proposed model.

Steering response to roll control of a two-line disk kite

Kites are utilized in both professional sporting activities and potential new energy generation applications. Most of these use two or four-line steerable kites, but the steering response is not well understood. Previous work on kite behaviour has focused on single-line kites, and the dynamics of two-line kites has been limited to quasi-static analysis. The mathematical formulation of the few models that consider the dynamics have been based only on energy methods. Furthermore, existing work relies on not-validated generalised aerodynamic models unsuitable for design optimisation tasks. Understanding the dynamics of two-line steerable kites allows for innovative improvements for such applications. In this work we introduce a two-disk kite as a simplified generic model for analysis of steering response. We derive the fully non-linear governing dynamic equations of motion for a two-line four-attachment point disk kite using 4DOF with a Newton–Euler formulation. The aerodynamic model of the kite is taken from previous work of our group (CFD/wind-tunnel tested and validated). The analysis considers the stability regions for flight behaviour and the manoeuvrability of the kite. Kite design parameters are investigated to guide future designs.

A computational view of electrophysiological properties under different atrial fibrosis conditions

The excessive proliferation of fibroblasts causes fibrosis, a hallmark of atrial fibrillation (AF), and leads to alterations in the electrical conduction within the heart. However, the underlying electrophysiological mechanisms behind the multifactorial characteristic of AF fibrosis are not fully understood. This work studies the electrophysiological properties of different fibrosis configurations using computational simulations. For this purpose, the intermingling action of the structural and electrical remodeling due to fibroblasts are implemented in an electrophysiological description of the AF fibrosis. The model is built on the base of complex order operators and a fibroblast ionic formulation. Additionally, three fibrosis textures are considered for designing the atrial tissue representations. The resting and depolarization properties are analyzed by means of information theory and multidimensional scaling. The results evinced that the modulation of cardiomyocytes resting potential, exerted by the fibroblasts, is the mechanism giving rise to emergent electrophysiological properties as a result of the synergetic mathematical formulation of the proposed fibrosis model. The metrics assessing such properties unravel distinctive signatures of each fibrosis texture. Additionally, the multidimensional scaling computational tool reveals clusters specifically determined by the resting and depolarization properties, or by their combination. The observed clusters support an electrophysiological interpretation through the underlying fibrosis configuration, in which the diffuse, patchy and compact textures are relevant in determining the emergent patterns.

A reading model of young EFL learners regarding attention, cognitive-load and auditory-assistance

Audio-assisted reading (reading-while-listening) was commonly used as a pedagogical method in English (L2) learning. Numerous studies had reported its efficacy in English (L2) reading. Its efficacy in reading comprehension has been inconclusive due to the lack of studies on the relationship among attention, cognitive load and L2 reading comprehension, with the possibility that the synchronous auditory input lessens attention to the visual input. We present a study of 41 Mandarin-speaking 8-year-old children reading English texts in three modes in a between-participants design. Data of cognitive load, comprehension scores and attention were fitted to a formal mathematical model, which confirmed that influences on L2 reading comprehension could be captured by interactions between attention and cognitive load. Based on the findings, three implications regarding how to appropriately apply auditory-assistant tools to L2 reading were generated.

Методика оценки безопасности криптографических протоколов

This paper proposes a method for evaluating the security of cryptographic protocols used to protect information in telecommunication networks, as well as in networks of the “Internet of Things”. The procedure for evaluation of information system security is described, including the construction of the list of threats, the threat model, and detailing of the model and the abilities of the intruder. The concept of security property is considered, the extended list of the specified properties, their classification and formal mathematical model are given. As part of the model, for given properties of security, we propose a method for obtaining numerical values of performance parameters depending on the probability of success and algorithmic complexity of the solution of a number of known mathematical problems. In conclusion, the results of the application of the proposed method to the analysis of ESP and IKEv2 protocols of IPSec family standardized in the Russian Federation are presented.

Optimal Disturbance Suppression of Disturbed Underwater Vehicle With State Delay

In this paper, the optimal disturbance suppression problem of disturbed underwater vehicle with state delay is studied. Firstly, we establish the mathematical model of the motion of the disturbed underwater vehicle and linearize it. Secondly, the mathematical model with state delay is transformed into a formal mathematical model without time-delay by using the no time-delay transformation method. Then, according to the optimal control theory, the optimal disturbance suppression control law of the disturbed underwater vehicle with state delay is designed based on the quadratic performance index. This control law can be obtained by solving the Riccati matrix equation and Sylvester matrix equation. Finally, the effectiveness of the method is verified by an AUV system simulation example.

Perspectives on the flexibility analysis for continuous pharmaceutical manufacturing processes.

Pharmaceutical continuous manufacturing, especially under the context of COVID-19 pandemic, is regarded as an emerging technology that can guarantee the adequate quality assurance and mitigate process risk while guaranteeing the desirable economic performance. Flexibility analysis is one approach to quantitively assess the capability of chemical process to guarantee feasible operation in face of variations on uncertain parameters. The aim of this paper is to provide the perspectives on the flexibility analysis for continuous pharmaceutical manufacturing processes. State-of-the-art and progress in the flexibility analysis for chemical processes including concept evolution, mathematical model formulations, solution strategies, and applications are systematically overviewed. Recent achievements on the flexibility/feasibility analysis of the downstream dosage form manufacturing process are also touched upon. Further challenges and developments in the field of flexibility analysis for novel continuous manufacturing processes of active pharmaceutical ingredients along with the integrated continuous manufacturing processes are identified.

Angažovanje generatora i potrebe balansnih rezervi u prisustvu intermitentnih OIE: Studija slučaja elektroenergetskog sistema Srbije

Intermittent electricity generation of the various renewable energy sources sets additional burden on generation unit dispatching and reserve planning in day-ahead electricity market. The conventional unit commitment models which include rump-up and rump-down limits are usually presented with stepwise mathematical functions without clear distinction between power and energy. This paper presents a case study of generation unit dispatching planning approach for the case of pricewise-linear functions from one time interval to another, taking into account actual ramping trajectories thus providing more efficient reserve scheduling particularly during generators’ start-up and shut-down processes. For the representation of reserve schedules, the 10-min and 30-min ramp capabilities of the generation units are assumed where they are obliged to provide secondary, tertiary and offline-tertiary reserves depending on their technical capabilities. The Serbian power system case study represents a 24-hour unit commitment planning and up/down secondary and tertiary reserve requirements during a scarcity event when reserve flexibility of neighbouring power systems cannot be utilised. Formulation of the optimisation mathematical model is performed via GAMS, the General Algebraic Modelling System, and CPLEX optimiser is used for problem optimisation purposes.

Investigation of the process of structure formation during ultrasonic homogenization of milk

The article studies the processes of structure formation of milk during homogenization carried out on various equipment. A comparative analysis of the distribution of the sizes of fat globules before and after homogenization is given. The formulation of the probability mathematical model of milk and milk mixture homogenization give the opportunity to identify the real variabilities of the textural composition of milk and milk mixture in optimum performance with the use of statistics facts about dynamics of the fat globules size. The foundation for developing such model was used for experimental results of fat globules within the ultrasound process. The dependences of the density distribution of the sizes of fat globules after ultrasonic treatment are given. Obtained dependences allow conducting statistics analysis of the homogenization of food mass for the evaluation of its total effectiveness and determination of defects.

Remarks on Mathematical Structure of the Staruszkiewicz Theory

The purpose of this note is threefold: (i) to recall (with some points made more explicit) the mathematical Weyl algebra model formulation, given before, of the Staruszkiewicz theory of quantum Coulomb field; (ii) to add some new elements to the discussion of the representation of the Lorentz group within this model; (iii) to comment on some statements on the structure of the theory which appeared recently.

Production of Biogas from Kitchen Wastes Generated from the Mess of NIT Agartala

A review has been done on the formulation of mathematical models for designing anaerobic batch reactor for the producing of biogas from solid wastes. Using material balance analysis, the design parameters, especially biokinetic behavior of solid wastes are studied. Hydrolysis constants and reaction orders at both low total solids concentrations and high total solids concentrations were thoroughly reviewed by initial rate method. Population growth model and first order hydrolysis model are also studied. It has been found that if sufficient reaction time is given, in terms of reaction kinetics, the hydrolysis process in kitchen waste fermentation can be described as a first order reaction. An attempt is done by utilizing the biodegradable kitchen waste collected from Aryabhatta hostel, NIT Agartala for generation of biogas and demonstrating the possibilities of energy recovery. A simple anaerobic digester has been fabricated to capture the generated biogas. To produce methane as a clean fuel the use of cow dung as substrate is studied to ferment the kitchen wastes.

Formulation of Mathematical Model for Stress-Strain Relationship of Normal and High Strength Concrete Under Compression

Formulation of Mathematical Model for Stress-Strain Relationship of Normal and High Strength Concrete Under Compression

Establishment of mathematical model to predict the dehulling efficiency in miniature pulse splitter machine energized by human powered flywheel motor using dimensional analysis

In India, nearly 58% populations directly or indirectly have their livelihood dependent on farming activity and agricultural food processing. Majority of population in India fulfills their nutritional needs from pulses. India is among the major producer and consumer of pulses contributing nearly 28.34% of pulses globally. The percentage of losses in domestic pulses production nearly equal to its import resulting in decline of pulses per capita. The dehusking and splitting of the grain at the pulse mills are the most important post harvest operation which decides the yield & quality of pulses. The losses at post harvest activities are mainly subjected to the power availability at rural area, availability of technology for use of sustainable energy sources, availability of processing units in reach of farmers and continuous research in post harvesting methods &and techniques & it’s practical viability. The human powered flywheel motor (HPFM) based, pulse producing machine fulfilling the requirements at rural areas is presented here. In the present paper dimensional methodical approach is discussed to determine the effect of the parameters affecting dehulling efficiency of a developed miniature pulse splitter machine energized by HPFM. A dimensional analytical technique using Buckingham Pi-theorem is used to establish an operating relationship between the dependent variable i.e. dehulling efficiency and independent variables which includes diameter of pulse, bulk density, coefficient of friction, feed rate, speed, emery grade, gap between wheel, humidity & air velocity. The present performance of the split pulse machine is improved to its highest value of 80.5% with the feed rate of 45 kg/hr & at the gap of 5 mm between the wheels. The reading obtained from the mathematical data and experimental observation is in good agreement which indicates the minimum error and validation of the mathematical model. The paper presents the method of formulation of mathematical model with the output variable dehulling efficiency which depends on many input variables for the pulse splitting machine. The formulated model can further be used for the other processing units in the agricultural production.

MODELS OF DESCRIPTION OF INDICATORS OF DIGITAL PROGRESS ECONOMIC TRANSFORMATIONS

The study of aspects of the digital economy and indicators of the assessment of the state of the economy and society is relevant for the development of transformation policies in accordance with the goals of sustainable development. The progress of technologies and new possibilities of digitalization of the economy give impetus to the improvement of evaluation methods and the system of indicators. In Ukraine, at the state level, considerable attention is paid to the development of the digital economy and society. Digitization is defined as a mechanism of economic growth due to the ability of technologies to positively influence the efficiency, effectiveness, cost and quality of economic, public and personal activities. The concept of the development of the digital economy and society of Ukraine for 2018-2020 was adopted, and in 2021 the law “On stimulating the development of the digital economy in Ukraine” was adopted by the Verkhovna Rada. Further development tasks are defined in the Digitalization Strategy of Ukraine until 2030. The purpose of this work is to develop a complex of formal mathematical models that provide a description of the task of determining the level of digital development of the country (a description of the task of determining the indicators of the progress of digital transformation in achieving the goals of sustainable development) from the standpoint of system analysis. The scientific studies and recommendations presented in the work are sufficiently substantiated and reliable. They are based on the analysis of the methods and systems of influential international institutions, on the review of the works of domestic and foreign specialists. To achieve the goal of the research, general scientific methods were used: content analysis, grouping and systematization, systems theory and system approach, abstract-logical methods – for theoretical generalizations and conclusions. A literature review was conducted and a nomenclature of indicators of the progress of digital transformation in achieving the goals of sustainable development was determined. On its basis, the structure of a complex of models of system analysis of the subject area of digital transformation progress indicators was formed. For the first time, the structures of component models were developed, which describe the necessary elements of the subject area of ​​the task of determining indicators of the progress of digital transformation.

MODEL OF INDICATORS FOR THE ASSESSMENT OF THE NATIONAL LEVEL OF DIGITALIZATION AND CYBER SECURITY OF THE COUNTRIES OF THE WORLD

Digitalization is one of the main trends in the development of modern society and the growth factors of the global economy in the coming years. But the progress of technology and the new opportunities of digitalization lead to a rapid growth of cyber threats and cyber incidents. Achieving an appropriate level of digitization of the success of the economy and society is interdependent on the levels of development of information and communication technologies and their protection against possible cyber attacks. The purpose of this work is to develop, from the standpoint of system analysis, formal mathematical models for describing the determination of the national level of digital development of countries, taking into account the national level of cyber security and cyber protection. In order to realize the purpose of the study, data was collected and systematized according to four groups of indicators: the general level of development, the level of digital development of the country, the level of technical infrastructure, and the level of the ability to counter cyber threats. The conducted information analysis made it possible to determine the nomenclature of indicators of digitalization progress and the level of cyber security and cyber protection. Based on it, a structure of component models was formed that describe the necessary elements of the subject area of the task of determining the indicators of the national level of digitalization with the coordination of the indicators of the level of cyber security and cyber protection. The results of the study allow us to assert that the development of the digital economy is impossible without strengthening cyber security both at the state level and at the level of individual entities. Further research will focus on the development of mathematical models for an integral assessment of the state of the country's digital transformation, taking into account the country's ability to counter modern cyber threats.

A fractional order mathematical model of teenage pregnancy problems and rehabilitation in Nigeria

<abstract><p>Teenage pregnancy is a social problem in Nigeria, whereby girls between the ages of 10-14 become pregnant by sexual intercourse after ovulation or first menstrual period. This article involves the fractional order mathematical model formulation describing the societal problem of teenage pregnancy in the sense of Caputo. The positivity, existence and uniqueness results of the model were established, and the two equilibria, which are the teenage pregnancy-free and teenage pregnancy-present equilibrium solutions of the model are presented. The graphical illustrations showing the behavior of the model variables when the basic reproduction number $ R_{pr} $ is less and greater than unity are displayed, using the numerical technique of Fractional Multi-Stage Differential Transform Method (FMSDTM) in comparison with the Runge-Kutta fourth order method (RK4) via the maple computational software. In addition, simulations involving the effect of rehabilitation is observed not to lessen $ R_{pr} $ below unity, which shows that further mitigation measures are needed to halt teenage pregnancy problems in Nigeria.</p></abstract>

Analysis of entropy generation and Joule heating on curvilinear flow of thermally radiative viscous fluid due to an oscillation of curved Riga surface

This paper investigates the phenomena of heat transfer and entropy generation on time-dependent electro-magnetohydrodynamic boundary layer flow of viscous fluid past a curved oscillatory stretchable Riga surface. Also, the impacts of thermal radiation and Joule heating are accounted for in the energy equation. To develop the flow model in mathematical form, curvilinear coordinates system is followed. The series solution of the governing nonlinear partial differential equations is attained with the help of the homotopy analysis method (HAM). The impacts of various involved parameters like dimensionless radius of curvature, modified magnetic parameter, the proportion of frequency of oscillation of the sheet to its stretchable rate parameter, magnetic parameter, Prandtl number, Eckert number, radiation parameter and Brinkman number on entropy generation, Bejan number, temperature and flow equations are comprehensively examined and results are displayed through graphs. Numerical variation in the magnitude of surface drag force and local Nusselt number under the influence of aforesaid parameters are presented through the tables. Entropy generation is enhanced with an enhancement in a radius of curvature and Brinkman number, while the Bejan number shows opposite behavior for both parameters. The amplitude of velocity distribution shows growing behavior with modified magnetic parameter.