Mathematical Modelling

A model subglacial drainage system, coupled to an ice-dammed reservoir that receives a time-varying meltwater input, is described and analysed. In numerical experiments an ice-marginal lake drains through a subglacial channel, producing periodic floods, and fills with meltwater at a rate
dependent on air temperature, which varies seasonally with a peak value of Tm. The analysis reveals regions of Tm parameter space corresponding to ‘mode locking’, where flood repeat time is independent of Tm; resonance, where decreasing Tm counter-intuitively increases flood size; and chaotic dynamics,
where flood cycles are sensitive to initial conditions, never repeat and exhibit phase-space mixing. Bifurcations associated with abrupt changes in flood size and timing within the year separate these regions. This is the first time these complex dynamics have been displayed by a glaciohydraulic model
and these findings have implications for our understanding of ice-marginal lakes, moulins and subglacial lakes.

Based on the our October paper "A Generalized Viral Infection Mathematical Model Derived from Covid-19 Simulation", at a conceptual level higher than the classic SIR/SEIR model, we have established the 6 laws of infection regarding the final infection ratio within any given population without any artificial intervention and have shown the final infection ratio in a natural, non-interfered pandemic must fall within a specified lower and upper bound as 1 − 1 R 2 0 ≤ F R ≤ 2 (1 − 1 R 0). Whereas R 0 is the intrinsic R 0 value of the disease. In this paper, we show how human intervention strategies alter the previous assumptions based on 2 factors. First, artificial intervention with cycles of restricting measures and relaxations. Based on our May paper "The Predictions on Worldwide Covid-19 Pandemic Cases Based on Historical Data", we have already demonstrated the dynamic falling R 0 (t) curve during lock down measures. With more historical data and observation, we now expand the scope to include a dynamic rising R 0 (t) curve following the relaxation of measures, completing the cycle of restriction and relaxation. Second, the introduction of vaccination at a steady rate introduced a new variable into the existing infection model, we denote it as function V (t). We demonstrate the optimal strategies of vaccination interpreted within our existing established framework.

In the paper there is presented a dynamic model of the articulated shaft. The model is used for the analysis of critical angular velocities. This model can be rewritten into a computer program to handle rotating parts of gear pumps. Using the knowledge of the custom frequencies of the rotating parts one can prevent operational malfunctions of the pumps. The problems described in the contribution will serve as a basis for the formulation of critical speed of the gear pumps within the Program for Support of Applied Research and Experimental Development ALFA TA04010579 of the Technology Agency of the Czech Republic. Key words: articulated shaft, critical angular speed, geer pump

V článku je prezentován dynamický model kloubového hřídele, který je využíván pro analýzu kritických úhlových rychlostí. Tento model může být přepsán do počítačového programu, pro řešení rotujících částí zubových čerpadel. Využití znalosti vlastních frekvencí rotujících částí může zabránit provozním poruchám čerpadel.
Problematika popsaná v příspěvku bude sloužit jako východisko při formulaci modelu kritických otáček zubových čerpadel v rámci Programu na podporu aplikovaného výzkumu a experimentálního vývoje ALFA TA04010579 Technologické agentury České republiky.
Klíčová slova: kloubový hřídel, kritická úhlová rychlost, zubové čerpadlo

DLP is a data security technology that detects and prevents data breach incidents  by monitoring data in-use, in-motion and at-rest.  It has been widely applied for regulatory compliances, data privacy  and intellectual property protection. This talk will introduce basic concepts and security models to describe DLP systems with high level architecture.  DLP is an interesting discipline with content inspection techniques supported by sophisticated algorithms.  Special investigation will be taken for  a few algorithms:  document fingerprinting,  data record fingerprinting, scalable M-pattern string match and etc..

Identification of flow pattern during the simultaneous flow of two immiscible liquids requires knowledge of the flow rate of each fluid as well as knowledge of other physical parameters like conduit inclination, pipe material, pipe diameter, viscosity of the oil, wetting characteristics of the pipe, design of the entry mixer, and fluid-fluid interfacial tension. This article presents an artificial neural

In this paper, a mathematical model for the transmission dynamics of lymphatic filariasis is presented by incorporating the infected without symptom, the infected with symptom and treatment compartments. The model is shown to have two equilibrium states: the disease-free equilibrium (DFE) and the endemic equilibrium states. An explicit formula for the effective reproduction number was obtained in terms of the demographic and epidemiological parameters of the model. Using the method of linearization, the disease-free equilibrium state was found to be locally asymptotically stable if the basic reproduction number is less than unity. By constructing a suitable Lyapunov function, the disease-free equilibrium state was found to be globally asymptotically stable. This means that lymphatic filariasis could be put under control in a population when the effective reproduction number is less than one. The endemic equilibrium state was found to be locally asymptotically stable. By constructing yet another Lyapunov function, the endemic equilibrium state was found to be globally asymptotically stable under certain conditions. Sensitivity analysis was carried out on the effective reproduction number, the most sensitive parameters were the treatment rate of human population and the infected rate of human population. Results from the simulation carried out showed that treatment 2 OGUNTOLU, BOLARIN, PETER, ENAGI, KAYODE OSHINUBI level coverage of human population should target a success rate of 75% for LF to be under control in the population.

Energy consumption model of peeling process is required to optimise main influenced factors as well as to limit peeling waste and consumed energy. Mechanical peeling process using an abrasive-cutter brush which applies both abrasive a nd cutting forces was modeled. Choosing the input and output variables which would be industria lly applicable was attempted. Three variables, namely, angular velocities of abrasive-c utter brush ( ωp), the degree of unevenness of produce surface ( φ), and the shape of the abrasive-cutter brush ( λ), were chosen as independent variables and the peel losses per unit time were ch osen as the output of the model. The developed model was verified using the experimental results o f peeling by abrasive-cutter brush for two varieties of pumpkin named Jarrahdale and Jap. The results showed correlation coefficients between predicted and experimental values of the Ja p (0.98) and Jarrahdale (0.96) were statistically significant. It is concluded that the relation...

The paper reports on the relationship between a group of pre-service mathematics teachers’ working memory and number sense. South Africa’s murky performance in the Trends in International Mathematics and Science Study (TIMSS) since 1995 instigated several interrogative reports. It was found that teachers’ number sense influence their pedagogies and thus also learner achievement. Furthermore, too many teachers cannot teach quantities and how they feature in our lives properly. A number sense is an intuitive understanding of numbers, their magnitude and interrelationships and arithmetic ability is a good indicator of number sense. A variable reported to relate to number sense, is working memory capacity. The 42 third year student-teachers wrote weekly mental arithmetic tests aimed at strengthening their number sense. Their working memory capacity was measured by the Working Memory Index of Wechsler’s Adult Intelligence Scale. A linear regression ascertained that working memory capacit...

The low-weight newborns and especially the premature infants have difficulty in maintaining their temperature in the range considered to be normal. Several studies revealed the importance of thermal environment and moisture to increase the survival rate of newborns. This work models the process of heat exchange and energy balance in premature newborns during the first hours of life in a closed incubator. In addition, a control problem was proposed and solved in order to maintain thermal stability of premature newborns to increase their rate of survival and weight. For this purpose, we propose an algorithm to control the temperature inside the incubator. It takes into account the measurements of the body temperature of a premature newborn which are recorded continuously. We show that using this model the temperature of a premature newborn inside the incubator can be kept in a thermal stability range.

This paper presents the technique of constructing models of behavior algorithms of radio electronic complex system using new scheme of paths method. This technique allows estimation of the efficiency indexes of RECS taking into account behavior algorithm's features, hardware and software reliability and self-diagnostics procedures.

In this paper, we formulate a broad-based mathematical model for drug absorption in the intestine based on the peristaltic motion of the drug-carrying intestinal fluid which is approximately sinusoidal. Using the background of Fick's laws and perturbation methods, an initial – boundary value problem is formulated and solved and the drug concentration, at a distance along the intestinal tract at time determined. In doing this, we use the result of drug absorption in the gastro-intestinal tract for constant velocity of the intestinal fluid [14]. The solution is analyzed for various frequencies (or wave numbers) of the peristaltic wave for the drug indomethacin. The results do not show marked deviations for low frequencies; but for large frequencies, it has been observed that the absorption is more rapid. Thus, the results show that with higher peristaltic wave frequency, the drug particles that had diffused into intestinal fluid are more in contact with the villi surrounding the intestinal lumen and hence absorption is enhanced.

Based upon previous discussions on the structure of compact stars geared towards undergraduate physics students, a real experiment involving two upper-level undergraduate physics students, a beginning physics graduate, and two advanced graduate students was conducted. A recent addition to the physics curriculum at Florida State University, "The Physics of Stars", sparked quite a few students' interests in the subject matter involving stellar structure. This, coupled with "Stars and Statistical Physics" by Balian and Blaizot and "Neutron Stars for Undergraduates" by Silbar and Reddy, is the cornerstone of this small research group who tackled solving the structure equations for compact objects in the Summer of 2004. Through the use of a simple finite-difference algorithm coupled to Microsoft Excel and Maple, solutions to the equations for stellar structure are presented in the Newtonian regime appropriate to the physics of white dwarf stars.

The fundamental holographic principle is first proposed, then demonstrated in its validity and viability through a thought experiment and then finally derived. The Heisenberg uncertainty relations are shown to follow from this fundamental relation. The quantum blackhole entropy is then demonstrated using this holographic uncertainty relation along with the application of the Landauer’s principle for the thermodynamic erasure of a bit yielding a formula with a logarithmic correction. The blackhole entropy is found to be half the value normally delivered by any other method. So, it is proposed that there is a real relevant physical horizon at the twice the Schwarzschild radius dubbed the holographic information geometric horizon.

The focus of this study was to estimate the economic impact of Romblon State University on the economy of the province of Romblon in terms of the university's direct spending activity. The researchers realized that determining the economic impact of the University would be beneficial to the university itself, to the community where the university is located, to the funding institutions, to the students and other researchers. The general objective of the study was to determine the economic impact of Romblon State University in the province of Romblon. To answer the main objective the following specific objectives were established: identify the source of fund of Romblon State University, determine the direct expenses as to operational expenditure and; capital expenditures; define the spending multiplier that will use to calculate in estimating the impact. The research approached used in this study was quantitative and descriptive. The study used secondary data in conducting the re...

In this project, we extend the work already done in [1.] to include a generalised mathematical framework for studying and explaining the dynamics and behavior of crowds of humans. The method is both analytical and numerical. The numerical methods are used to solve the differential equations of crowds that are derived analytically. The analytical and numerical solutions are compared and their relevance is shown. In this project, we study mainly two types of responses of a crowd: Position Response and Density Response. The latter is formulated using stressors using an approach similar to [2.] which also enables us to derive the General Adaptation Syndrome (GAS) Model in a very generalised form. Finally, we extend stressors to define inter-crowd and intra-crowd interactions using a parameterisation linking it directly to a generalisation of the stressdensity equation. The detailed calculations are done in the later part of this paper. (Refer to Page 21 of this doucument).

Paper presents mathematical model of the human ear. The method of model forming is presented, particular model elements are introduced (mainly in the form of Laplace operator transmittances) and discussed, implementation of the model is described and some experiments performed on the base of model simulation are presented. In final parto of the paper applications of the model are discussed.

In this paper we continue the development of our Python-based package for the solution of partial differential equations using spatial discretization techniques such as the finite element method (FEM), but we take it to a higher level using two approaches: First we define a" Model" class object which makes it easy to break down a complex simulation into simpler sub-models, which then can be linked together into a highly efficient whole. Second, we implement an XML schema in which we can save an entire simulation. Thisn allows ...

The rollout of driverless cars (DC) may reshape human mobility drastically. Urban roads may face a surge of car traffic if DC technologies continue to enhance the use of private cars. Shared DC use can remedy this by reducing the number of urban trips that non-shared-use DC could otherwise make. While recent research has proven the importance of socioeconomic factors on shared DC use, the influence of present sharing behaviour, personality traits, and social norms on shared DC use has not been extensively explored to date. To address this gap in this study, we employed a panel of 500 Edinburgh-based respondents through an online survey to examine the likelihood of accepting the non-shared-use and shared-use DC options for regular urban trips. We have collected data on respondents' present carsharing and ridesharing behaviour, personality traits, social norms, and sociodemographic characteristics. To elicit the impact of these factors on the likelihood of accepting non-shared-use and shared-used DC options, ordered probit models were estimated. The model findings imply that frequent household car users and those influenced by social expectations to preserve the environment are willing to use non-shared-use DC. In contrast, city centre dwellers, cooperative and younger adults with sharing attitudes show a higher tendency towards shared DC. High-earning, working-aged and young respondents are more inclined to use a driverless taxi, whereas city-centre dwellers and those influenced by social expectations to share personal resources are more favourable towards ridesharing with a stranger in DC. These results can assist the policymakers and transport planners shape policies for promoting shared DC use and transport service providers to deliver and operate shared DC fleets efficiently.

The purpose of this paper is designing blood supply chain network in disaster situation considering blood groups and expiration dates. In the proposed network, there are blood collection centers, labs for quality assurance and producing blood products, and hospitals. Donors refer to blood collecting centers. These centers receive blood from donors and transfer to labs. After required tests, labs send blood products to hospitals. In the proposed model of this study, a blood product, i.e. plasma is considered. The proposed model is a MIP model which minimizes the total cost of the network, including: the establishment cost of facilities, cost of transportation, and cost of holding inventory. Furthermore, uncertainty in demand has been considered using different scenarios. Moreover, in order to meet the demand, blood groups and plasma expiration date have also been investigated. Finally, the efficiency of the proposed model is investigated using random problems in different dimensions.

This paper presents current knowledge about the structure and function of the lymphatic system. Mathematical models of lymph flow in the single lymphangion, the series of lymphangions, the lymph nodes, and the whole lymphatic system are considered. The main results and further perspectives are discussed.

The article summarizes the arguments and counterarguments within the scientific discussion on the quantification of various spheres of enterprise activity based on their system representation. The main purpose of the study is to improve the basic model of systemic economics as the basis for developing a method for quantitative assessment of the harmonious process of development of innovative project-oriented enterprises. The systematization of literary sources and approaches to solving the problem of choosing a basic model has shown that the most reasonable and developed approach is based on the model of economic tetrad. Various authors used the model when developing indicators of balance and stability of economic systems. However, the known results were not compared, and the model was not used to describe the innovative development of enterprises. The urgency to solve this scientific problem is in the fact that in the era of the knowledge economy, innovation development is becoming one of the main directions of the activity of modern enterprises, which needs the scientific ground. Studying of the point related to creation of a method for quantitative assessment of the innovative project-oriented enterprises development is carried out in the following logical sequence: making the economic tetrad matching requirements of the system integrity and completeness; conducting an analysis of resource interchange in the triad of the economic tetrad; revealing the essence of the mechanism for managing processes of growth and development of enterprises; developing a mathematical apparatus to describe the dynamic structural changes of enterprises; conducting a computer experiment using five different approaches to calculating the indicators of dynamic structural changes during the introduction of innovations; conducting a comparative analysis of the results. The methodical toolkit of the research considers the postulates of systematicity, scale, harmony, and positions of qualitative mathematics and the triple convolution method. The object of the study is the selected phases of the innovation project life cycle since they determine the peculiarities of the dynamic structural changes of enterprises during the introduction of innovations. The article presents the results of the empirical analysis, carried out based on computer modeling of the innovation project implementation within six different approaches. This showed a fundamentally different nature of the change in structural balance indicators for these approaches. The study theoretically proves and empirically confirms that the proposed indicator of the internal coherence of opposite actions (chaotic and organized) corresponds to the logic of the harmonious implementation of innovation activity. The results of the study can be applied when creating monitoring and management systems for the development of innovative project-oriented enterprises.

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, Ré nyi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.

INTISARI Dalam tesis ini dianalisa mengenai model matematika peningkatan enzim hati akibat mono-infeksi HIV. Model ini dibangun atas dasar asumsi infeksi HIV hanya menyebabkan replikasi virus terjadi hanya pada sel CD4+, dan tidak terjadi pada sel hepatosit. Selain itu, tingginya enzim hati (alanine aminotransferase) merupakan indikator kuat dalam menentukan tingkat kerusakan hati. Model HIV dalam hati ini adalah pengembangan dari model infeksi viral HIV ke sel CD4+ yang diteliti oleh Perelson (1994), yang kemudian dimodifikasi oleh Nampala (2013) dengan penambahan model sel CTLs dalam tubuh. Berbeda dengan apa yang dilakukan dengan peneliti sebelumnya, dalam tesis ini dilakukan suatu koreksi syarat eksistensi ekuilibrium endemik dan dilakukan metode baru dalam menentukan kestabilan lokal dan global titik ekuilibrium bebas penyakit (infeksi). Analisis bifurkasi dilakukan disekitar untuk mengetahui kestabilan titik ekuilibrium endemik. Hasil dari penelitian ini adalah titik ekuilibrium bebas infeksi dan titik ekuilibrium endemik keduanya tidak stabil ketika Hal ini mengindikasikan bahwa HIV dengan berjalannya waktu mampu menyebabkan kerusakan hati yang ekstrim tanpa gejala lazim dalam waktu cukup singkat. Hasil simulasi numerik memberikan hubungan menarik antara peningkatan enzim hati, virus, sel CD4+, dan sel hepatosit. Kata kunci : Level alanine aminotransferase (ALT), HIV, endemik, bifurkasi. ABSTRACT In this thesis, we analyse the mathematical model of liver enzyme elevation due to mono-infection with HIV. This model is built on the assumption of HIV infection only causes viral replication only on CD4+ cells, and it doesn't occur in hepatocytes cell. In addition, high liver enzymes (alanine aminotransferase or ALT) is a strong indicator in determining the extent of liver damage. Models of HIV in the heart is the development of models viral infection of HIV to CD4+ cells were examined by Perelson (1994), and then modified by Nampala (2013) models with the addition of model CTLs cells in the body. In contrast to what is done by the previous researcher, in this thesis we do a correction of conditions existence of endemic equilibrium and perform a new method to determine the local and global stability of the disease-free equilibrium point (infection). Bifurcation analyse around for determine the stability of the endemic equilibrium point. The results of this research is the point of the infection-free equilibrium and endemic equilibrium point which is unstable when both. This indicates that HIV as time goes capable of causing extreme damage to the liver in short time. Numerical simulation results provide an interesting relationship between liver enzymes, viruses, CD4+ cells, and hepatocyte cells.

Forest management planning relies heavily on mathematical models that involve time. Concerns about climate change and ecosystem services have highlighted the limitations of traditional growth and yield prediction tools. Modern dynamical system theory provides a framework for a flexible representation of varying environments, as well as of responses to intensive silviculture and natural disturbances. Emphasis changes from trying to directly model functions of time to modelling rates of change. The fundamental concepts are introduced here in a non-technical manner. The theory is illustrated with a recent whole-stand growth model for even-aged stands, but it is noted that it applies to any system that evolves over time. It is shown also how a modular approach can improve balance and efficiency in the development of such models.
Keywords: modelling, stand dynamics, system theory, system dynamics, forest growth and yield, thinning, hybrid models

The drainage of ice-dammed lakes produces floods that can pose hazards, waste water resources and modulate ice flow. In this thesis I investigate several aspects of ice-dammed lake drainage through the development and analysis of mathematical models.
After an introduction in the first chapter and a description of the mathematical background to the thesis in the second, the third chapter investigates the mechanisms behind observed variability in the size and timing of subglacial floods from ice-dammed lakes. In particular, I examine how environmental controls like the weather and the shape of glaciers affect floods.

In the next chapter, I quantify how well simple models can predict the dates of floods from an ice-marginal lake in Kyrgyzstan. I find that incorporating environmental controls into models improves their prediction ability.

Next I investigate the coupling between subglacial drainage and glacier motion during ice-dammed lake drainage by developing and analysing a model which couples a marginal lake, glacier sliding, subglacial drainage through a channel and subglacial drainage through a distributed system of cavities. I show how changes in lake level cause the rate at which a glacier slides to increase during the first half of floods and decrease during the second half.

The next two chapters are concerned with two lake-drainage scenarios that involve water flowing as an open stream: firstly, the subglacial open-channel flow that occurs after a marginal lake drains completely during a flood, and secondly, the drainage of supraglacial lakes across the surface of ice sheets.

I end the thesis with a summary of my findings and some suggestions of theoretical and field-based investigations that are worthwhile pursing in the future.