This paper is a part of the broader research on “Adaptation of Laws in Science” and explores the limitations and challenges involved in adapting mathematical concepts to describe natural reality in physics. Specifically, the analysis focuses on two major examples: Euler's exponential laws and spacetime dilation derived from Lorentz transformations. By examining these concepts, the paper emphasizes that some complex laws are not universally applicable for deeper studies of nature, as they originate from mathematics and are correct only for specific parts of nature to which they have been adapted. These complex laws are particularly unsuitable where there is limited information available for adaptation. Therefore, without appropriate adaptations and a deep understanding of the physical context under investigation, the direct use of complex laws can lead to incorrect results. It is essential to avoid excessive generalization of these laws, once they become part of physics, unless a corresponding adaptation to the research context can be made. Furthermore, this paper supports the correctness of relativity theories by invoking that, like Euler's exponential growth theory, they were initially mathematical concepts. However, the nature of mathematics coincided with that of the phenomena in our universe, although through certain adaptations.

ATP Synthase is an essential molecule in cell and molecular biology. It is responsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase’s rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total linear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.

The Physics Informed Neural Networks framework is applied to the understanding of the dynamics of Coronavirus of 2019. To provide the governing system of equations used by the framework, the Susceptible-Infected-Recovered-Death mathematical model is used. The study focused on finding the patterns of the dynamics of the disease which involves predicting the infection rate, recovery rate and death rate; thus predicting the active infections, total recovered, susceptible and deceased at any required time. The study used data that was collected on the dynamics of COVID-19 from the Kingdom of Eswatini between March 2020 and September 2021. The obtained results showed less errors thus making highly accurate predictions.

The problems of modeling the human bladder and its stress-strain state under external static influence were considered. A method for identification of the anisotropic biomechanical characteristics of bladder tissue was proposed. A FEM model was created, which accepts into regard that the bladder is surrounded by fiber and affected by surrounding organs, and partially protected by pelvic bones. The model considered the presence of constant hydrostatic pressure on the walls of the bladder when it is full. It has been shown that isotropic mechanical characteristics of biological tissue can be used for studying the deformed state of a filled bladder if the filled bladder 300 ml is considered as initial non-deformed stage. This was shown by modeling and verification the effect of the external static force on the bladder. Numerical experiments were conducted based on the constructed model. To validate the results obtained, a series of natural experiments on the effect of external pressure on the bladder under ultrasound control was conducted. In the future, it is planned to use the constructed model to study rupture deformations of the bladder under the influence of static and dynamic loads.

This paper discovers that current variational principle and Noether theorem for different physics systems with (in)finite freedom systems have missed the double extremum processes of the general extremum functional that both is deduced by variational principle and is necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her famous theorem, which result in the crisis deducing relevant mathematical laws and all physics laws. This paper discovers there is the hidden logic cycle that one assumes Euler-Lagrange equations, and then he finally deduces Euler-Lagrange equations via the equivalent relation in the whole processes in all relevant current references. This paper corrects the current key mistakes that when physics systems choose the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current articles, reviews and (text)books. The real physics should be after choosing the variational extreme values of physics systems, the general extremum functional of the physics systems needs to further choose the minimum absolute extremum zero of the general extremum functional, otherwise, the appearing processes of physics systems are still virtual processes. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical pictures and physics for (in)finite freedom systems are discovered. This paper gives both general variational principle and general Noether theorem as well as their classical and quantum new physics, which would rewrite all relevant current different branches of science, as key tools of studying and processing them.

We present detailed models at the hydrodynamics and decoherence phenomena observed in ideal quantum gases. The model is expressed in terms of a quantum field theory, where the action involves both hydrodynamic and decoherence terms. The density-current relation is derived, and the current Green function is introduced. The effective action for two fields is presented, and the physical field is defined in terms of the bare action. Identities such as CTP symmetry, transposition, and the Ward identity are discussed. The Green function and its inverse for different components are also explored. These notes provide a comprehensive understanding of the theoretical framework for studying the hydrodynamics and decoherence of ideal quantum gases.

Oscillons, fundamental to various physical domains, are examined in-depth in this paper. From Josephson junctions in superconducting circuits to classical and quantum field theories, oscillators reveal profound insights into diverse phenomena. The study primarily focuses on oscillons, distinctive field configurations with enduring localization, establishing intriguing connections with well-known models like the Sine-Gordon breather. Surprising parallels in the weak coupling limit illuminate the rich dynamics of oscillators. A semi-classical quantization method, discretizing the field into spatially homogeneous regions, exposes stability angles, providing insights into the quantum nature of oscillons. The application of this quantization framework to specific cases, including the Sine-Gordon breather, showcases its versatility. The results offer a comprehensive perspective on the quantization of oscillons, unraveling the intricate interplay between classical and quantum dynamics. In conclusion, this paper provides a profound exploration of quantum oscillators, unveiling novel connections and presenting a rigorous quantization framework. The gained insights contribute significantly to the broader understanding of oscillatory systems and their pivotal role in diverse physical phenomena.

This paper discovers that current canonical variational principle and canonical Noether theorem of (in)finite freedom systems for different physics systems have neglected doublet extreme value processes of the general extreme value functional that both is derived by variational principle and is necessarily be taken in deriving all ( quantum ) physics laws in phase space, but which have not been done for over one century since Noether's showing her distinguished theorem, which lead to the crisis deriving all (quantum) physics laws (necessary) in phase space. We discover there is the hidden logic cycle that people assume canonical equations, and then they finally deduce canonical equations by the equivalent relation in the whole processes in all current references. We correct the current key mistake concepts that when physics systems take the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current references. The real physics should be what after taking the physics systems' variational extreme values, the physics systems' general extremum functional needs to further take the general extremum functional's minimum absolute extremum zero, otherwise, the appearing processes of physics systems still are virtual processes. Conservation current equations and conservation currents, in phase space, of general canonical variational principle and general canonical Noether theorem are, respectively, deduced for the first time. Using the general extremum functionals' doublet extreme value processes, the hidden logic cycle and the crisis in current canonical variational principle and current canonical Noether theorem are solved. Consequently, the new mathematical pictures, classical and quantum new physics in phase space and the new mathematical and physical doublet extremum processes for (in)finite freedom systems are discovered. General canonical variational principle and general canonical Noether theorem naturally are given, which would rewrite all the different sciences in phase space, as key tools of studying and dealing with them.

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial successes against B-cell malignancies, what has led to a growing scientific and clinical interest on extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immuno-suppressive tumour microenvironment, that is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, accounting for their immunosuppressive capabilities. Using the mathematical model, we show that the use of large numbers of CAR-T cells targeting the solid tumour antigens could overcome the cancer immunosuppressive potential. To achieve such high levels of CAR-T cells we propose and study computationaly, the manufacture and injection of CAR-T cells targeting two antigens: CD19 and a tumour-associated antigen. We study in-silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive generation of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its inmune suppression capabilities. That strategy could benefit from the combination with PD-1 inhibitors and of low tumour loads. Our computational results provide a theoretical support for the treatment of different types of solid tumours using T-cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD1 drugs after completion of classical cytoreductive treatments.

Mathematical optimization offers a valuable approach to tackle Industry scheduling problems. By formulating the scheduling challenge as a mathematical problem, mathematical optimization enables efficient and effective decision-making processes. Mathematical optimization is particularly beneficial in complex scheduling scenarios, such as in networked manufacturing environments, where multiple jobs and resources need to be coordinated. By leveraging optimization models and algorithms, it becomes possible to generate optimal process plans, considering factors like job dependencies, resource availability, and timing constraints. Through mathematical optimization, organizations can achieve improved efficiency, reduced lead times, and enhanced utilization of resources. Rigorous mathematical formulations and optimization techniques enables to surpass traditional manual planning methods and brings forth powerful computational capabilities. By optimizing various scheduling objectives, from minimizing makespan to maximizing resource utilization, mathematical optimization provides organizations with valuable insights and actionable plans. The purpose of this study is to discuss scheduling solutions for multiple jobs in a networked manufacturing setting based on mathematical optimization process. The study analyses a solver-based approach to generate the optimal process plans for multiple jobs and compare it with a more traditional game-theoretic approach. The objectives aim to develop two solver-based model using Z3 and Gurobi to generate optimal process plans; implement a game-theoretic model to solve for the same set of scheduling problems, and compare the computational time, solution quality, and efficiency of both approaches. To achieve this, the methodology will start with the problem definition. Multiple jobs are to be scheduled on a set of parallel machines. Each job has predefined processing times, deadlines, and priorities. The objective is to minimize the total completion time and maximize machine utilization while meeting all deadlines.

This study presents a dynamic modeling approach to investigate the impact of saturation dynamics on HIV/AIDS transmission in the presence of vertical transmission and treatment strategies. The proposed model incorporates disease-free and endemic equilibria, with a focus on analyzing the basic reproduction number and conducting stability analysis. Results indicate that the disease-free equilibrium is locally asymptotically stable under certain conditions. The findings suggest that a combination of treatment interventions and awareness campaigns, along with other control measures, may play a crucial role in curbing the spread of the HIV/AIDS virus. This research contributes to understanding the complex dynamics of HIV/AIDS epidemics and highlights the importance of considering saturation effects in epidemic modeling.

As global warming intensifies, the development of offshore wind farms is swiftly progressing, especially deep-water floating offshore wind turbines (FOWTs) capable of energy capture in deep-sea regions, which have emerged as a focal point of both academic and industrial interest. Although numerous researchers have conducted comprehensive and multifaceted studies on various components of wind turbines, less attention has been paid to the operational stage response of FOWTs to wind, waves, and currents, and the reliability of structural components. This study primarily employs theoretical analysis to establish mathematical models under a series of reasonable assumptions, examining the possibility of collisions between FOWT transport fleets and other vessels in the passage area during the towing process. Using the model, this paper takes the Wanning Offshore Floating Wind Farm (FOWF) project, which is scheduled to be deployed in the South China Sea, as the research object and calculates the probability of collisions between FOWTs and other vessels in three time periods from the total assembly pier in Hainan Wanning to the predetermined position 22 km away. The findings of the analysis suggest that the mathematical model has the capability to efficiently determine the frequency of collisions between vessels within the domain and the transport team during the transportation process. This holds substantial relevance for future risk assessment and disaster prevention and mitigation measures in the context of FOWT transportation.

In sub-Saharan Africa, malaria is a leading cause of mortality and morbidity. As a result of the interplay between many factors, the control of this disease can be challenging. However, few studies have demonstrated malaria's complexity, control, and modeling although this perspective could lead to effective policy recommendations. This paper aims to be a didactic material providing the reader with an overview of malaria. More importantly, using a system approach lens, we intend to highlight the debated topics and the multifaceted thematic aspects of malaria transmission mechanisms, while showing the control approaches used as well as the model supporting the dynamics of malaria. As there is a large amount of information on each subject, we have attempted to provide a basic understanding of malaria that needs to be further developed. Nevertheless, this study illustrates the importance of using a multidisciplinary approach to designing next-generation malaria control policies.

Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, still remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges.

This paper provides a retrospective analysis of published COVID-19 data and focuses on Costa Rica as an example of data analysis and validation in developing countries. The COVID-19 outbreak has highlighted the importance of robust health systems and adequate resources to test and manage diseases. However, due to limited resources and excessive burdens, developing countries face unique challenges in this regard. This makes it difficult to conduct widespread testing. The lack of testing kits, laboratory facilities, trained personnel, and the necessary infrastructure is a significant barrier. Additionally, logistical issues such as transportation and distribution of testing kits in remote areas further complicate the situation. On the other hand, universal healthcare in developing countries, despite the lack of extensive testing, can still provide reliable data on the spread and impact of the disease. Universal healthcare can lead to better records keeping and data collection, as all individuals, regardless of their economic status, have access to medical services. This inclusivity ensures a more comprehensive and representative data set. Therefore, while testing is an important tool in managing the pandemic, universal healthcare systems can still provide valuable insights in its absence. This description can be applied to the Costa Rica COVID-19 scenario: lack of resources for an adequate testing methodology but a universal healthcare system that ensures inclusivity. In this work, we show that the number of active cases of COVID-19 for Costa Rica does not provide reliable information that can be used to adjust the parameters of a mathematical model, so the effectiveness of the contention measures cannot be precisely stated. However, the number of hospitalizations is more reliable in the centralized and universal healthcare system, but quantifying the effectiveness of such measures requires a different set of tools. Traditionally, most pandemic data analysis is based on the estimation of the Rt number based on the number of active cases. We propose a methodology based on digital signal processing principles and elementary differential calculus. To our knowledge, these kinds of methodologies have not been of widespread use in pandemic data analysis, and, as we show, they may provide a valuable descriptive analysis of pandemic tendencies and they are an accessible, fast and reliable decision-making tool.

The agronomic characteristics of Cenchrus purpureus were assessed through a randomized block experimental design with seven accessions (Taiwan grass, King grass, Elephant grass, Merkeron, CT-115, Purpule grass and Maralfalfa) as treatments and four replications research was carried out at the Instituto Tecnológico Superior de Tantoyuca, in 2019 and 2020, under rainfed conditions. Sowing density was established at 36 tillers in 25 m2. Green and dry matter yield, daily rates of dry matter accumulation in leaves, leaf/stem ratio, height, leaf area index and cutting frequency were assessed. Rainfall amount, temperature, relative humidity and global radiation levels were recorded to assess their effect on the evaluated variables. One-way ANOVA and multivariate analysis techniques, such as multiple linear regression (MLR), Clustering, and Principal component analysis (PCA) with the Statistica V7 software, were used. The leaf area index was greatest (p < 0.05) on the dry season. Green and dry matter yield were greatest in Maralfalfa (p < 0.05). Variation in the results is attributed to weather phenomena; nonetheless, Elephant grass and Maralfalfa showed the highest yields. Quality parameters must be evaluated to identify those grasses with the best attributes.

Antiangiogenic therapy (AAT) is an indirect oncological modality which is aimed at disruption of cancer cells nutrient supply. Invasive tumors have been shown to possess inherent resistant to this treatment, while compactly growing benign tumors react to it by shrinkage. It is generally accepted that AAT by itself is not curative. This study presents a mathematical model of non-invasive tumor growth with physiologically justified account of alteration of microvasculature and biomechanical aspects during tumor growth and AAT. In untreated setting the model reproduces tumor growth with saturation, where the maximum tumor volume depends on the level of angiogenesis. The outcomes of simulations of AAT depend on the tumor size at the moment of treatment initiation. If it is close to the stable size of avascular tumor grown in absence of angiogenesis, then the tumor is rapidly stabilized by AAT. Treatment of large tumors is accompanied by displacement of normal tissue due to the tumor shrinkage. During it, microvasculature undergoes distortion which degree depends on the displacement distance. As it affects tumor nutrient supply, the stable size of a tumor that undergoes AAT negatively correlates with its size at the beginning of treatment. For sufficiently large initial tumors, the long-term survival of tumor cells is compromised by competition with normal cells for severely limited inflow of nutrients, which makes AAT effectively curative.

Introduction. Musculoskeletal disorders related to work might follow with a cumulative effect during working life. We aimed to develop a new model to allow to compare the accuracy of duration of work and intensity/frequency associations in application to severe knee pain. Methods. The CONSTANCES cohort is used with data from n=66553 subjects who were working at inclusion and coded. From a biomechanical job exposure matrix “JEM Constances”, intensity/frequency of heavy lifting and kneeling/squatting were used and applied to the work history in comparison to severe knee pain. An innovative model was developed and evaluated, allowing to compare the accuracy of duration of work and intensity/frequency associations. Results. The mean age is 49 years at inception with 46 percent of women. The G model developed was slightly better than regular models. In men, odds ratios of the highest quartile for the duration and low intensity were not significant for both exposures, whereas intensity/duration were for every duration. Results in women were less interpretable. Conclusion. Though increased duration increased strength of association with severe knee pain, intensity/frequency were important predictors among men. Exposure estimation along working history should have emphasis on such parameters, though other outcomes should be studied such as women.

Synthetic Aperture Radar (SAR) is an active type of microwave remote sensing. Using the microwave imaging system, remote sensing monitoring of the land and global ocean can be done in any weather conditions around the clock. Detection of SAR image targets is one of the main needs of radar image interpretation applications. In this paper, an improved two-parameter CFAR algorithm based on Rayleigh distribution and morphological processing is proposed to perform ship detection and recognition in high resolution SAR images. Through simulation experiments, comprehensive study of the two algorithms for high resolution SAR image target detection is achieved. Finally, the results of ship detection experiments are compared and analyzed, and the effects of detection are evaluated according to the Rayleigh distribution model and algorithms.

Mathematical literacy is a very hot issue in the development of mathematics learning, apart from mathematical literacy, another interesting thing is the entrepreneurial spirit that must be given from an early age, especially for vocational students. This research was conducted at SMK Rosma Karawang in the Department of Computer and Network Engineering, West Java Province with the XI grade students. The teaching materials developed by applying the principles of the development model developed with the ADDIE model consist of analysis, design, development, implementation and evaluation. This research and development model is considered suitable for developing teaching tools and materials which is used for the purposes of the learning process. Based on the results of data analysis and processing that have been carried out in this study, the development of teaching materials using the ADDIE model has met the appropriate and valid criteria by media, language and media expert valuators. Another result of developing this teaching material besides meeting the eligibility criteria is that the teaching materials developed are able to increase mathematical literacy and instill entrepreneurial spirit for students.

Synergy of radiation and immune system is currently receiving significant attention in oncology as numerous studies have shown that cancer irradiation can induce strong antitumor immune responses. It remains unclear, however, what are the best radiation fractionation protocols to maximize the therapeutic benefits of this synergy. Here, we present a novel mathematical model that can be used to predict and dissect the complexity of the immune-mediated response at multiple tumor sites after applying focal irradiation and systemic immunotherapy. We successfully calibrate the proposed framework with published experimental data, in which two tumors were grown in mice at two spatially separated sites from which only one was irradiated using various radiation fractionation protocols with and without concurrent systemic immunotherapy. The proposed model is calibrated to fit the temporal dynamics of tumor volume at both sites and can predict changes in immune infiltration in the non-irradiated tumors. The model was then used to investigate additional radiation fractionation protocols. Model simulations suggest that the optimal radiation doses per fraction to maximize antitumor immunity are between 10-13 Gy, at least for the experimental setting used for model calibration. This work provides the framework for evaluating radiation fractionation protocols for radiation-induced immune-mediated systemic antitumor responses.

Arc sensors have been used in seam tracking and widely studied since the 80s; commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and swing or rotate speed.

The current paper explores the potential interlink between names of individuals in a society and its collective social consciousness, particularly with reference to the pervasive occurrence of the ‘mathematical names’ in the current Hindu society in the Indian subcontinent and beyond. Initially, an attempt is made to put things into mathematical perspective by drawing a quick sketch of some of the stellar achievements of the Indian mathematicians. Under the six broad categories of geometry, trigonometry, numeration, arithmetic, algebra, and mathematics in the Vedic tradition, a concise simple description of these subdivisions is presented, underlining the names of the concepts and terms, sometimes by producing the textual references. Then, upon identification of such mathematical terms, an attempt is made to juxtapose these with the names current in the Indian Hindu society. By employing an extensive dataset of university student names in India and the directories of Facebook and LinkedIn, we produce both qualitative and quantitative evidence of the presence of such names in the Indian subcontinent. Evidently, these names reflect the impressions of the tremendously rich mathematical heritage left by the Hindu stalwart mathematicians. This hypothesis has also been examined by taking surveys of people bearing these mathematical names, as well as by documenting the ‘conscious procedures’ that go behind the naming of a Hindu Indian child. In trying to investigate if such a phenomenon is unique to the Indian tradition, a stark contrast with the ‘names in mathematics’ as prevalent in the European mathematical traditions is presented, as cultural roots of mathematics are explored. Further, we ascribe the presence of these names as the extant remains of the colossal impact of multifarious mathematical traditions existing in India. Interestingly, the present research also brings to the fore, certain unseen facets of the Indian Hindu society as regards the education of mathematics to women – through an indirect exploration of their names. We also show that the pervasive occurrence of these names is not merely the result of semantic chance events, but denotes the richness of the Indian mathematical legacy. Next, we also present cross-cultural comparisons to show the uniqueness of Indian mathematical and scientific traditions that led to the pervasiveness of ‘mathematical names’ in India. Finally, an attempt is made to clarify some subtle points on the associations between mathematics and religion in India and other cultures of the world. It is sincerely hoped that the present study may shed light on the cultural roots of mathematics and may furnish a new dimension in the study of mathematics, culture and civilizations across the world.

(1) Background: The rapid evolution of the internet and technological infrastructure has led to a surge in data generation across various contexts, increasing the use of machine learning tools to extract valuable information. Clustering, particularly using the K-means algorithm, is a common technique. However, determining the optimal number of clusters in K-means is challenging, as traditional methods like the elbow method can be imprecise and subjective. This study proposes a more accurate and objective method to identify the optimal number of clusters. (2) Methods: The proposed method utilizes the numerical derivative of cluster inertias and the maximum value of the ratio between contiguous derivatives. Implemented in Python using sklearn, numpy, and matplotlib, the method was validated with synthetic datasets generated by artificial intelligence, where cluster numbers are clearly distinguishable. (3) Results: The method proved to be more precise and less subjective than the traditional elbow method, accurately identifying the optimal number of clusters in all tested synthetic datasets. Additionally, it demonstrated computational efficiency with minimal RAM usage and execution time, making it suitable for practical data analysis applications. (4) Conclusions: This new mathematical and computational method significantly improves the determination of the optimal number of clusters in K-means, offering a more accurate and objective alternative to traditional techniques. Future work will extend this method to hierarchical clustering and develop a cloud service for wider accessibility.

: Controlling the distribution of water and wastewater between industrial processes is very vital in rationalizing water and preserving the environment. In this paper, a mathematical technique is proposed to optimize water-wastewater networks; a nonlinear program is introduced to minimize the consumption of freshwater, and consequently, the flowrate of the wastewater dis-charge will be also minimized. A general mathematical model, able to handle industrial plants containing up to eight sources and eight sinks, is developed using LINGO optimization software to facilitate dealing with complex case studies. The introduced model can handle single contam-inant networks as well as multiple contaminants cases. The optimal water network is synthe-sized through two steps; the first step is to introduce the case study data to the developed mathematical model. The second step considers using the optimal solution produced after run-ning the developed LINGO model as feed data for a pre-designed Excel sheet able to deal with these results and simultaneously draw the optimal water-wastewater network. The proposed mathematical model is applied to two case studies; The first case study includes actual data from four fertilizer plants located in Egypt; the water resources and requirements are simultaneously integrated to obtain a sensible cutting in both freshwater consumption (lowered by 52.2%) and wastewater discharge (zero wastewater discharge). The second case study is for a Brazilian pet-rochemical plant; the obtained results showed noticeable reductions in freshwater consumption for the second case study by 12.3 % while the reduction percentage of wastewater discharge is 4.5%.

This article describes the methodology used to identify the mathematical model that describes the correlations between the input parameters of an experiment and the parameters being followed. As a technological process, the aerodynamic separation was chosen, respectively, the behavior of a solid particle within an ascending vertical airflow. The experimental data obtained were used to identify two parameters, the average linear velocity, and the angular velocity, and through the Table Curve 3D program was developed a mathematical model which describes the dependence between the input parameters (the shape and size of the solid particle and the velocity of the airflow) and the monitored parameters. In order to determine a single mathematical equation that describes as accurately as possible the correlation between the input variables and those obtained, a pyramid-type analysis was designed. The determination of the mathematical equation started from the number of equations generated by the Table Curve 3D program, then the equations with a correlation coefficient greater than 0.85 were chosen, and finally, the common equations were identified. Respecting the working methodology was identified one equation which has for the average linear velocity a correlation coefficient r2 between 0.88-0.99 and 0.86-0.99 for the angular velocity.

The prevalence of differential equations as a mathematical technique has refined the fields of control theory and constrained optimization due to the newfound ability to accurately model chaotic, unbalanced systems. However, in recent research, systems are increasingly more nonlinear and difficult to model using Differential Equations only. Thus, a newer technique is to use policy iteration and Reinforcement Learning, techniques that center around an action and reward sequence for a controller. Reinforcement Learning (RL) can be applied to control theory problems since a system can robustly apply RL in a dynamic environment such as the cartpole system (an inverted pendulum). This solution successfully avoids use of PID or other dynamics optimization systems, in favor of a more robust, reward-based control mechanism. This paper applies RL and Q-Learning to the classic cartpole problem, while also discussing the mathematical background and differential equations which are used to model the aforementioned system.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

Hidden markov models are a very useful tool in the modelling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden markov model to analyze the underlying structure of an ancient and complex manuscript, known as Voynich's manuscript, that remains still undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscript we train the network by means of the $\alpha$ and $\beta$-pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices in order to compare with known languages concerning the frequency of consonant and vowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.

This paper proposes a new approach to investigation into the aesthetics. Specifically, it argues that it is possible to explain the aesthetic and its underlying dynamic relations with axiomatic structure (the octahedral axiom derived category) based on contemporary mathematics – namely, category theory – and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there was a way to describe the structure of aesthetics with the language of mathematical structures and mathematical axioms – a language completely devoid of arbitrariness – then we would make possible a synthetical argument about the essential human activity of “the aesthetics”, and we would also gain a new method and viewpoint on the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one hypothesis as a first step in constructing the science of dynamic generative aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the functional structure of aesthetics.

The gene sets of the two cells produced by each division of the fertilized egg are different, and these differences gradually accumulate. When the similarity between a certain cell and a certain type of cell is below a threshold, the differentiation ability in that direction is lost. When all cells can only have one developmental direction, the expression of zygotic genes is turned on. When a stem cell differentiates, it first divides into two cells. One of two cells, similar to the next level cell, becomes the next level cell, while the other, similar to the mother cell, continues to become the other stem cell. When a cell undergoes dedifferentiation, it expresses a group of genes. When the gene set is similar to the upper level stem cell, the cell undergoes dedifferentiation and becomes the upper level stem cell.

Using assembly theory of strings of any natural radix $b$ we find some of their salient regularities. In particular, we show that the upper bound of the assembly index depends quantitatively on the radix $b$ and the longest length $N$ of a string that has the assembly index of $N-k$ is given by $N_{(N-k)}=b^2+b+3k-2$ for $k=\{1,2\}$ and by $N_{(N-3)}=b^2+b+6$. We also provide particular forms of such strings. Knowing the latter bound we conjecture that the maximum assembly index of a string of length $N>N_{(N-2)}$ is given by $a_{\text{max}}^{(N,b)} = \lfloor N/2 \rfloor + b(b+1)/2$. For $k=1$ such odd length strings are nearly balanced and there are four such different strings if $b=2$ and seventy-two if $b=3$. We also show that a string containing $k$ copies of an $n$-plet has the assembly index of at most $N-1 - (n-1)k - a$, where $a$ is the assembly index of this $n$-plet. Finally, we show that the assembly depth of a minimum assembly index string is equal to the assembly index of this string, while the assembly depth of a maximum assembly index string has a value between $\left\lceil \log_2(N) \right\rceil$ and the assembly index of this string. Since these results are also valid for $b=1$, assembly theory subsumes information theory.

The blood counts of α thalassemia carriers (α-thal) are similar to those of β thalassemia carriers, except for Hgb A2 that is not elevated. The objective of this study was to determine whether mathematical formulas are effective for detecting suspected α-thal. The data were obtained from the database of the prevention program for detecting couples at risk for having a child with hemoglobinopathy. RBC indices were analyzed using mathematical formulas and the sensitivity and negative predictive value (NPV) calculated. Among 1334 blood counts suspected α-thal analyzed, only the Shine&Lal and the Support Vector Machine formulas revealed high sensitivity and NPV. Sensitivity was 85.54 and 99.33% and NPV 98.93 and 99.93%, respectively. Molecular defects were found in 291, 81 had normal α genes. Molecular analysis was not performed in 962. Based on these results, mathematical formulas incorporating one of these reliable formulas for detecting suspected α or β thalassemia carriers in the program of the automatic analyzers can flag these results and increase the awareness of the primary physicians about the carrier risk and send an alert with a recommendation for further testing.

We extend the concept of metallic ratios to the real argument n considered as a dimension by analytic continuation showing that they are defined by an argument of a normalized complex number, and for rational n ≠ {0, ±2}, they are defined by Pythagorean triples. We further extend the concept of metallic ratios to metallic angles.

In this paper, we study the black hole solution of self-similar gravitational collapse in the Einstein-axion-dilaton system for the elliptic class in four dimensions. The solution is invariant under space-time dilation, which is combined with internal SL(2,R) transformations. Due to the complex and highly nonlinear pattern of the equations of motion in the physics of black holes, researchers typically have to use various numerical techniques to make the equations tractable to estimate the parameters and the critical solutions. To this end, they have to ignore the numerical measurement errors in estimating the parameters. To our knowledge, for the first time in the literature on axion-dilation systems, we propose to estimate the critical collapse functions in a Bayesian framework. We develop a novel methodology to translate the modelling of the complexity of the elliptic black hole to a sampling problem using Hamiltonian Monte Carlo with stacked neural networks. Unlike methods in the literature, this probabilistic approach enables us not only to recover the available deterministic solution but also to explore possibly all physically distinguishable self-similar solutions that may occur due to numerical measurement errors.

Globally, zoonotic diseases have been on the rise in recent years. Predictive modelling approaches have been successfully used in the literature to identify the underlying causes of these zoonotic diseases. We examine the latest research in the field of predictive modeling that verifies the growth of zoonotic pathogens and assesses the factors associated with their spread. The results of our survey indicate that popular mathematical models can successfully be used in modeling the growth rate of these pathogens under varying storage temperatures. Additionally, some of them are used for the assessment of the inactivation of these pathogens based on various conditions. Based on the results of our study, machine learning models and deep learning are commonly used to detect pathogens within food items and to predict the factors associated with the presence of the pathogens.

The present paper is concerned with the study of the quality of life index. Such an index has become an important index for measuring the well-being of individuals. However, the quality of life index is always a subjective, intangible, and often hard to quantify with precision due to the lack of quantitative models dealing with. The main goal of the present paper is thus to propose a mathematical, quantitative model for the measurement of a quality of life index. The main novelty is firstly the construction of a wavelet dynamic multiscale model to quantify and investigate the effect of time scale on the quality of life index measuring. The proposed procedure is acted empirically on a sample corresponding to Saudi Arabia as a case of study during the period from 2003 to 2020 as part of the 2030-vision plan. Saudi Arabia has implemented the so-called 2030-vision plan where the quality of life improvement is one of the main goals to be attempted. The findings show that wavelets are capable to localize the time-wise behavior of the index contrarily to classical studies which estimate a global view of the index. Moreover, the study shows the link between the quality of life behavior and many other indices.

It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structures organizing the foldings. Then one look at the musical forms employed in the classical and contemporary periods. Finally, one investigates in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.

In central Senegal malaria incidences have declined from 2000 to 2010 in response to scaling-up of control measures and then remained stable, making elimination improbable. Additional control measures are needed to reduce transmission. We simulated chemoprophylaxis interventions targeting malaria hotspots, using a meta-population mathematical model based on differential equation framework and incorporating human mobility. The model was fitted to weekly malaria incidences from 45 villages. Three approaches for selecting intervention targets were compared: a) villages with malaria cases during the low transmission season of the previous year; b) villages with highest incidences during the high transmission season of the previous year; c) villages with highest connectivity with adjacent populations. Our modeling, considering human mobility, showed that the intervention strategies targeting hotspots would be effective in reducing malaria incidence in both targeted and untargeted areas. But whatever the intervention, pre-elimination stage (1-5 cases per 1,000 per year) would not be reached without simultaneously increasing vector control by more than 10%. Targeted interventions allow increasing overall malaria control and elimination potential.

In the last few decades, the dynamics of tumor cells and their growths are presented via clinical, experimental, and theoretical approaches, which leads to the development of the new idea of multiple cancer therapies to control and reduce the death rate for earlier detection. In this paper, we discussed the dynamics of tumor cell growth and its treatment process. We analyzed some simple mathematical models and generalized the study to understand the growth of tumor cells. The main proposed model is a system of ordinary differential equations which combines interactions among natural killer cells, dendritic cells and cytotoxic CD8+ T cells. The model is solved numerically to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer. It is also studied that how the cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time. Finally, a couple of spatially distributed models are discussed for tumor cell growth.

In the present time, the biggest problem of the world is the outbreak of novel coronavirus. Novel coronavirus (COVID-19), this one name has become a part of our daily lives over the past few months. Beyond the boundaries of medical science, coronavirus is now the main subject of research in all fields like Applied Mathematics, Economy, Philosophy, Sociology, Politics upto living room. The epidemic has brought unimaginable changes in our traditional habits and daily routines. Thousands of people in our country are fighting with the rest of the world to survive in various new situations. There are different kinds of coronavirus appeared in different times. In this time, Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) is responsible for the coronavirus disease of 2019 (COVID-19). This virus was first identified towards the end of 2019 in the city of Wuhan in the province of Hubei in China. Within very short duration of time and very fast, it has spread throughout a large part of the world. In this study, the main aim is to investigate the spreading rate, death rate, recovery rate due to corona virus infection and to study the future of the coronavirus in India by using mathematical modeling based on the previous data. Mathematical models, in this situation, are the important tools in recruiting effective strategies to fight this epidemic. India is at high risk of spreading the disease and is facing many losses in socio-economic aspects. With current infection rates and existing levels of personal alertness, the number of infected people in India will increase at least in the next three months. Proper social awareness, maintain of social distance, large rate of testing and separation may break the chain of the Coronavirus-2.

The outburst of the CoVid-19 pandemic has raised several questions leading to a complex system in terms of modeling. Indeed, the modeling of the epidemic, at the level of a country, needs considering each of the different sources of contamination as well as the public health authorities' strategy, in a specific way. With this in mind, in the present paper, we develop a mathematical model of the CoVid-19 epidemic in Senegal. In the model, the population is subdivided into five compartments: susceptible, infected but asymptomatic, symptomatic, quarantined, and recovered immune people. In addition, due to its important impact on the propagation of the disease, we add one more variable: the number of infected objects. %\vspace{1mm} Therefore, the model corresponds to a system of six non-linear ordinary differential equations we submit to an analytical study to prove the relevancy of the model, simulate the evolution of the epidemic, and retrieve epidemiological parameters, namely the infection rate and the basic reproduction number, ${\cal R}_0$. Based on the senegalese territory CoVid-19 data, we simulate various scenarios as for the evolution of the epidemic in the country, in order to predict the peak and its magnitude with regard to the application of barrier measures. We also explore the option of collective immunity with special protection for vulnerable people. In doing so, non-available parameters are identified using some mathematical identification technics.

In attempting to predict the further course of the novel coronavirus (COVID-19) pandemic caused by SARS-CoV-2, mathematical models of different types are frequently employed and calibrated to reported case numbers. Among the major challenges in interpreting these data is the uncertainty about the amount of undetected infections, or conversely: the detection ratio. As a result, some models include assumptions about the percentage of detected cases among total infections while others completely neglect undetected cases. Here, we illustrate how model projections about case and fatality numbers vary significantly under varying assumptions on the detection ratio. Uncertainties in model predictions can be significantly reduced by representative testing, both for antibodies and active virus RNA, to uncover past and current infections that have gone undetected thus far.

A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.

This article attempts to formulate a mathematical model for a potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. This working paper formulates a more realistic and simplified mathematical model for open circuit laminar flow over a body, based on the historical data of aerodynamics and theoretical mechanics. This is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict mentioned phenomena. Most of all the mechanism of streamline formation and its deformation with due regards to flow, shape and size of the body in an open-circuit laminar are formulated mathematically to enhance better design theory which can reduce experimentation while designing a streamlined body.

The argument of this article is threefold. First, the article argues that, from its rise in the sixteenth century to our own time, the advancement of modern physics, as mathematical-experimental science, has been defined by the invention of new mathematical structures. Secondly, the article argues that quantum theory, specifically with quantum mechanics, gave this thesis a radically new meaning by virtue of the following two features: one the one hand, quantum phenomena themselves are defined by purely physical features, as essentially different from all previous physics; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism,” RWR, interpretations. This argument allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concern only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena, in terms of probabilistic predictions, while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever discussed, apart from previous work by the present author. It will, however, be given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle.

Investigation into a modified deterministic rumour spread model using mathematical epidemiology approach as an extension of Daley and Kendall (D-K) model was carried out. It is proven that the spread of a rumour is fairly comparable to a contagious disease transmission, except that the spread depends solely on the fraction of individuals who are aware of the rumour at the early stage as well as the intrinsic rumour spread rate . Model simulation reveals a rumour diminishing strategy so far as is maintained.

The studied solar pot is a recent invention, which gained a utility model protection in 2021 from the Hungarian Intellectual Property Office under patent number 5489. The device is made for environmentally friendly cooking or heating (by utilizing solar energy) of foods and liquids. Its structure is similar to a double pipe heat exchanger, it has an outer mantle and an inner cooking tank. The goals of the paper are proposing a new physically-based mathematical model describing the solar pot and carrying out computer experiments with it, assembling an experimental system of the pot connected with a solar collector and performing measurements on it. Based on the results, the solar pot can successfully be used for cooking or sterilizing foods or liquids during the studied time period, in Hungary.

The objective of this research is to propose a utility function that calculates the possible level of satisfaction that a music consumer would achieve after listening to a song according to the emotional response obtained from a song. Assuming that the consumer's musical preferences are satisfied if the predominant emotions of his current emotional state increase; the probabilistic emotional-musical model (Lugos Abarca, 2023) is used to construct such a utility function. By posing a hypothetical scenario, realistic results were obtained, which guarantee, in principle, its use in theoretical practice. The originality of this research lies in proposing a mathematical tool to study, quantitatively, the decision making of a musical consumer influenced by his emotions. The main conclusion being its importance in the music industry, since the function could predict, theoretically, whether a song will be accepted or rejected by the consumer in comparison with the competition.

Due to their high specificity, monoclonal antibodies (mAbs) have garnered significant attention in recent decades, with advancements in production processes, such as high seeding density (HSD) strategies, contributing to improved titers. This study provides a thorough investigation of high seeding processes for mAb production in Chinese hamster ovary (CHO) cells. Using a metabolic network and flux balance analysis, we compared standard fed-batch (STD FB) with HSD cultivations, exploring supplementary lactate and cysteine, and a bolus medium enriched in amino acids. We observed high glycolytic fluxes and depletion of asparagine simultaneously with the lactate shift building kinetic models around this and other observations. An ensemble of kinetic models assessed the impact of a feeding medium enriched with additional asparagine, revealing a missing lactate shift without enhancing mAb productivity in the experiments. This research provides valuable model-based insights into cellular metabolism during HSD processes, laying the foundation for refined CHO cell-based mAb production. The proposed hypothesis on the regulations guides future experimental validation and bioprocess optimization for enhanced mAb production efficiency.

In this paper, we propose to explore a nonlinear fractional mathematical model of HFMD- Hand Foot Mouth Disease with vaccinated compartment. Firstly, we prove the non negativity and boundedness for the fractional order dynamical model. The system’s existence and uniqueness are studied using the formulation of the Caputo derivative operator. The fixed-point approach was used to get results indicating the presence of at least one solution. In numerical simulation, we obtained the approximate solution by using fractional Euler method.

This paper shows the development of a numerical analysis model, which enables the calculation of the cargo transport capacity of a vehicle that circulates through a vacuum tube at high speed, whose effectiveness in transport is analyzed. The simulated transportation system is based on vehicles moving in vacuum tubes at high speed, a concept commonly known as Hyperloop, but assuming the vehicles for cargo containers. For the specific vehicle proposed, which does not include a compressor and levitates on magnets, the system formed by the vehicle and the vacuum tube has been conceptually developed, establishing the corresponding mathematical relationships that define its behavior. To properly model the performance of this transport system, it has been necessary to establish the relationships between the design variables and the associated constraints, such as the Kantrowitz limit, aerodynamics, transport, energy consumption, etc. Once the model was built and validated, it was used to analyze the effects of the variation of the number of containers, the operating speed and the tube length, considering the total and specific consumption of energy. Once the most efficient configuration was found regarding energy consumption and transport effectiveness, the complete system was calculated. The results obtained constitute a first approximation for the pre-design of this transport system and the built model allows different alternatives to be compared according to the design variables.

The paper presents the results of modeling the problem of injecting liquid sulfur dioxide into a porous reservoir initially saturated with methane and ice. The model presented in the paper assumes the formation of three different regions, namely, the near one, saturated with liquid SO2 and its hydrate; the far one, containing methane and ice, and the intermediate one, saturated with methane and water. The effects of various parameters of the porous medium and injected SO2 on the nature of the course of the hydrate formation process have been studied. It is shown that with a decrease in reservoir permeability or injection pressure, the length of the intermediate region decreases, which in the limiting case means the formation of SO2 hydrate in the mode without the formation of an extended region saturated with methane and water. It is shown that such a regime is also typical for the case of high initial injection pressures, as well as low values of the initial reservoir temperature and injection temperature.

Rapid in vitro assessment of antimicrobial drug efficacy under clinically relevant pharmacokinetic conditions is an essential element of both drug development and clinical use. Here we present an overview of a novel integrated methodology for rapid assessment of such efficacy, particularly against emergence of resistant bacterial strains, as jointly researched by the authors in recent years. This methodology enables rapid in vitro assessment of antimicrobial efficacy of a single or multiple drugs in combination, following clinically relevant pharmacokinetics. The proposed methodology entails (a) automated collection of longitudinal time-kill data in an optical-density instrument; (b) processing of collected time-kill data with the aid of a mathematical model to de-termine optimal dosing regimens under clinically relevant pharmacokinetics for a single or mul-tiple drugs; and (c) in vitro validation of promising dosing regimens in a hollow fiber system. Proof-of-concept of this methodology through a number of in vitro studies is discussed. Future directions for refinement of optimal data collection and processing are discussed.

A model is proposed that describes the transfer of ions and the process of water dissociation in a system with a bipolar membrane and adjacent diffusion layers. The model considers the transfer of four types of ions: the cation and anion of salt and the products of water dissociation – hydrogen and hydroxyl ions. To describe the process of water dissociation, a model for accelerating the dissociation reaction with the participation of ionogenic groups of the membrane is adopted. The boundary value problem is solved numerically using COMSOL® Multiphysics 5.5 software. An analysis of the results of a numerical experiment shows that, at least in a symmetric electromembrane system, there is a kinetic limitation of the water dissociation process, apparently associated with the occurrence of water recombination reaction at the of the bipolar region. An interpretation of the entropy factor (β) is given as a characteristic length which shows the possibility of an ion that appeared as a result of the water dissociation reaction to be removed from the reaction zone without participating in recombination reactions.

Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave, had subsequent waves of the COVID-19 infections and it remains to be seen whether there will be more waves. In this paper, we formulate a deterministic model for COVID-19 incorporating dynamic non-pharmaceutical interventions, dubbed social dynamics. The model steady states are determined and their stability analysed. Numerical simulations are carried out to determine the pack of various parameters that influence the social dynamics. In South Africa, the first wave was the only wave in which the only interventions rested solely on human behavior. The model is thus fitted to COVID-19 data on the first wave in South Africa. The results presented in this paper have implications on the trajectory of the pandemic in the presence of changing social processes.

Marketing is the manner of how to make our sales the best in the market, our prices the most accessible, our clients satisfactory, and thus our brand is the largest distributed. This needs sophisticated and advanced understanding of the total network related. Indeed, marketing data may be seen in different forms such as qualitative and quantitative. However, in the literature, it is easily noticed that large bibliography may be collected about qualitative studies, against few studies on the quantitative point of view. This is a major drawback that makes the marketing science still focusing on the design, although the market is strongly depending on quantities such as money and time. Indeed, marketing data may be a time series such as brand sales per specified periods, brand related-prices over specified periods, market shares, ..., etc. The purpose of the present work is to investigate some marketing models based on time series due to brands. We will precisely study the effect of the time scale on the persistence of brands sales in the market and on the forecasting of such a persistence according to the characteristics of the brand and the related market competition or competitors. Our study is acted on a sample of Saudi brands during the period November 22, 2017 to December 30, 2021.

In March 2020, the World Health Organization declared coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2, to be a pandemic. Since the declaration, Nigeria economy has been greatly impacted thus resulting in a recession. This paper considers a couple of misconceptions among Nigerian people in the COVID-19 pandemic era thereby causing the spread of the novel virus and hence making the situation difficult for the government to handle. In particular, we discuss the first and second waves of the pandemic as it affects the Nigerian people. The impact of the pandemic on animals and the role of mathematical epidemiologists in combatting the spread is discussed herein. We give some recommendations that could be adopted by the government and the good people of Nigeria to reduce the further spread of the virus.

Medical Trust-Network is one of the most promising fields of study in network science. Establishment of trust within medical entities ensures better treatment and increases better medical facilities. The word ‘Trust’ signifies a very important behavioral aspect between any human entities, especially among doctors and patients. To represent such relationships Trust Network Models are built to express the interactions between human entities within such networks. Though the idea of a Trust-Network has traditionally been one of the major areas of research, yet the concept of a medical trust network model is relatively a new domain. In this paper, we introduce an overall multilayered Trust Network to represent the entire healthcare architecture. More specifically our model is based on an evolutionary graph system with a discrete relationship between the three most important entities of any healthcare system, namely – Doctors, Departments, and Hospitals. Observations indicate that based on our model, the medical healthcare system is a multilayered model unlike a feed-forward model as indicated by previous studies.

The quantified residence time distribution (RTD) provides a numerical characterization of mixing in the continue casting tundish, thus allowing the engineer to better understand the metallurgical performance of the reactor. This paper describes a computational fluid dynamic (CFD) modelling study for analyzing the flow pattern and the residence time distribution in a five-strand tundish. Two passive scalar transport equations are applied to separately calculate the E-curve and F-curve in the tundish. The numerical modelling results are compared to the water modelling results for the validation of the mathematical model. The volume fraction of different flow regions (plug, mixed and dead) and the intermixing time during the ladle changeover are calculated to study the effects of the flow control device (FCD) on the tundish performance. The result shows that a combination of the U-baffle with deflector holes and the turbulence inhibitor has three major effects on the flow characteristics in the tundish: i) reduce the extent of the dead volume; ii) evenly distribute the liquid streams to each strand and iii) shorten the intermixing time during the ladle changeover operation.

Background: The world, now in an emergency of preventing the drastic spread of COVID-19. After the infection was first reported in December 2019, almost every country did not pay attention to this highly contaminated disease and failed to react swiftly. Now the whole universe is in an vulnerable state, loosing a great loss of lives and facing difficulties in all socio-economic aspects. That is why we have the urge to develop an efficient mathematical model (quarantine) based on social consciousness to control the epidemic. Methods: This is a quarantine mathematical model. The outcome of the system is dependent on social consciousness. We have calculated the awareness level by considering various socio-economic factor of each country. In our model, the parameters are Education Index, GDP per capita, population density, high literacy and stable economy. To maximize the efficiency of the model, it has to be implemented in initial stage. However, strict application of the method in vigorous stage of epidemic will also bring a satisfactory outcome. Results: Higher social consciousness will decrease the number of infected population dramatically while minimal or lower awareness will do a outburst. Conclusion: Outbreak will be in control of health care system, lower the death rate and will ensure social and economic stability.

In the present paper, a measure of the influence of irregularities of the underlying surface (for instance, the real terrain profile) on the dynamics of air flow is estimated. It is shown that these irregularities significantly perturbing the pressure, density, velocity and temperature of air flow; for perturbed pressure, density, velocity and temperature of air flow the closed formulas in the Fourier integral form are obtained. In addition, in the present paper, it is proved that due to these perturbations, at a certain altitude of the atmosphere some surface of the "sturdy wall" form appears, on which the vertical and horizontal components of the air flow velocity become infinitesimal and infinitely large, respectively.

Antimicrobial resistance (AMR) is one of the greatest public health challenges we are currently facing. To develop effective interventions against this, it is essential to understand the processes behind the spread of AMR. These are partly dependent on the dynamics of horizontal transfer of resistance genes between bacteria, which can occur by conjugation (direct contact), transformation (uptake from the environment) or transduction (mediated by bacteriophages). Mathematical modelling is a powerful tool to investigate the dynamics of AMR, however its application to study the horizontal transfer of AMR genes is currently unclear. In this systematic review, we searched for mathematical modelling studies which focused on horizontal transfer of AMR genes. We compared their aims and methods using a list of predetermined criteria, and utilized our results to assess the current state of this research field. Of the 43 studies we identified, most focused on the transfer of single genes by conjugation in Escherichia coli in culture, and its impact on the bacterial evolutionary dynamics. Our findings highlight the existence of an important research gap on the dynamics of transformation and transduction, and the overall public health implications of horizontal transfer of AMR genes. To further develop this field and improve our ability to control AMR, it is essential that we clarify the structural complexity required to study the dynamics of horizontal gene transfer, which will require cooperation between microbiologists and modellers.

Global food insecurity and environmental degradation creates the need to develop more sustainable agricultural solutions. Plant synthetic biology emerges as a promising yet risky avenue to develop such solutions. While synthetic biology promises enhanced crop traits, it also harbors risks of extensive environmental damage. Here, we highlight the complexities and risks associated with plant synthetic biology, while presenting the potential of multilevel mathematical modeling to assess and mitigate those risks effectively. Despite its potential, the application of multiscale mathematical models in plants remains underutilized. We advocate for the integration of technological advancements in agricultural data analysis to foster a comprehensive understanding of crops across scales. By reviewing common modeling approaches and methodologies applicable to plants, the paper sets the stage for the creation and utilization of integrated multiscale mathematical models. Leveraging modeling techniques such as parameter estimation, bifurcation analysis, and sensitivity analysis, researchers can identify mutational targets and anticipate pleiotropic effects, enhancing the safety of genetically engineered species. To illustrate the potential of the combination, we outline ongoing efforts to develop an integrated multiscale mathematical model for maize (Zea mays L.), engineered through synthetic biology to enhance resilience against Striga and drought.

The freeze-drying of camel and mare milk presents challenges due to their unique compositions, such as high lactose and protein content. This research aims to optimize vacuum freeze-drying parameters, including temperature, drying time, and layer thickness, for enhanced product quality and reduced energy consumption. Ultrasound and homogenization techniques were applied to enhance moisture transfer during drying. Experimental data suggest optimal conditions of -50°C to +50°C over 22–24 hours, significantly improving reconstitution quality. Mathematical modeling in Python and Maple helped refine process parameters to achieve desirable product consistency.

A model based on the fitting of stress-strain data by tensile tests of biocomposites made of a bioplastic (polybutylene succinate, PBS) and spent brewer's grain filler (BSGF) is developed. The model is suitable to describe the elastic-plastic behavior of these materials in terms of two mechanical parameters (tensile stress and tensile stiffness or Young's modulus) depending on the filler concentration. The mechanical characteristics, derived from the fitting parameters, show a good agreement with the experimental data. The mathematical model used here could be an important aid for the experimentation and the manufacturing process as it allows to predict the mechanical tensile parameters of a mixture with different filler concentrations, avoiding the long and complex preparation cycle of bio-composites, as well as the specific mechanical tests. The physical properties required by the objects created with the PBS-BSGF bio-composite by the partners/stakeholders of the research project co-financing this research, can be quite different. Therefore, a mathematical model that predicts some of the mechanical properties in terms of the mixture composition may be useful to speed up the selection of the required amount of BSGF in the mixture.

Modeling dense nonaqueous phase liquids (DNAPLs) contamination in groundwater is challenging because of its multiphase distribution. To understand the research trends of DNAPL modeling in groundwater, a bibliometric analysis was conducted using CiteSpace based on 614 publications from the WoS Core Collection database (1993-2023). The publications were statistically analyzed, and the research hotspots and trends were summarized. The statistical analysis of the publications indicates that: the United States is leading the international research on DNAPL models, followed by China and Canada; collaboration between countries and disciplines in this field needs to be strengthened. The summary of keyword clustering and burst detection reveals that: the current research hotspots focus on multiphase flow models, mass transfer models, back diffusion, and practical applications of the models; the research trends are centered on back diffusion mechanisms, characterization of contamination source zones and prediction of contaminant distribution in real-world sites, as well as the optimization of remediation strategies.

In this study, Fluent software 2020R2 is used to simulate vertical axis turbine in two dimensions, aiming to analyze the influence of turbulence intensity on wake characteristics. The detailed flow field data are obtained by simulating the operation of turbine under different turbulence intensities. On this basis, the influence factor of turbulence intensity are creatively introduced into the wake mathematical formula of vertical axis turbine established by Lam, and some parameter calculations of the formula are supplemented and perfected. The results show that the theoretical model can well reflect the influence of turbulence intensity on the wake distribution of vertical axis turbines. The formula can provide a theoretical basis for the design and optimization of vertical axis turbines and the array arrangement, and can be used to predict the wake characteristics under different turbulence intensity operating conditions.

The emphasis in the automotive industry towards sustainable mobility has led to a significant interest in hybrid-electric propulsion systems with high energy density batteries. Addressing the needs of this strategy, the battery market is exploring new technologies to improve the safety and lifespan of electric vehicles. To this end, there is a focus on the all-solid-state battery (ASSB) technology for its cycle capabilities. Filling the current void in the literature pertaining to accurate ageing models for ASSBs, in this work, we present an enhanced version of the numerical ageing model, originally developed for liquid electrolyte based batteries, to forecast the development of the solid electrolyte interface layer that is the major cause of battery capacity fading. The model has been tested on prototype batteries and reveals an accuracy of 99%. The capacity fade in ASSBs has been investigated under different conditions, and the enhanced ageing model has been validated using experimental data from these batteries. The findings suggest that there is potential for solid-state batteries to be commercialized, although significant work is needed to match the manufacturing level of lithium-ion batteries with liquid electrolytes.

Lactic acid production from lactose by Lactiplantibacillus plantarum AC 11S was studied. The influence of initial substrate concentration was investigated, and optimal pH and temperature were determined. An unstructured mathematical model was developed comprising equations for bacterial growth, substrate consumption, and product formation. The model was solved with different terms for specific growth rates considering substrate and/or product inhibition. The best bacterial growth and lactic acid production were achieved at pH = 6.5 and 30 oC. Production of lactic acid was mainly growth-associated and at substrate concentration over 15 g/L a considerable product inhibition was observed. The parameters of different models were determined and compared. While the modified Gompertz equation gave the best fit for biomass growth, a variant of the logistic equation including a term for product inhibition described in the best way the entire set of equations comprising bacterial growth, substrate consumption, and product formation at different initial substrate concentrations.

To achieve a micro-destructive and rapid measurement of the wood density of standing trees, this study investigated the feasibility of using the micro-drilling resistance method, formulated a mathematical model, explored the potential for a unified model across multiple tree species, and analyzed the influence of moisture content on measurement accuracy. First, 231 tree cores and drill resistance data were sampled from Pinus massoniana, Cunninghamia lanceolate, and Cryptomeria fortunei. The basic density and moisture content of each core were measured, and the average value of each resistance data record was calculated. Second, the average drill resistance, the natural logarithm of average drill resistance, and absolute moisture content were used as independent variables, while the wood basic density was used as the dependent variable. Third, the total model of the three tree species and sub-model for each tree species were established through a stepwise regression method. Finally, the accuracy of each model was compared and analyzed with that of using the average basic density of each tree species as an estimated density. The results revealed that the estimation accuracy of the sub-model for each tree species was 1.670 percentage points higher than the average value of each tree species used as the density estimation value for these tree species. Additionally, except for Cryptomeria fortunei, the natural logarithm of drill resistance significantly influenced the wood density model at a significance level of 0.05. Moreover, moisture content significantly affected the total model and sub-models of Pinus massoniana at a significance level of 0.05. The estimation accuracy of the total mathematical model was 2.125 percentage points lower than that achieved using the average basic density of each tree species to predict their density. The results indicated the feasibility of using the micro-drilling resistance method to measure the wood density of standing trees. Moreover, the relationship between wood density and drill resistance did not follow a linear pattern, and moisture content slightly influenced the drill needle resistance. Furthermore, the establishment of a mathematical model for each tree species was deemed essential. This study provides valuable guidance for measuring the wood density of standing trees through the micro-drilling resistance method.

Covid-19 pandemic has greatly affected the whole world since the beginning and it continues to affect it. The main aim of this study is to show how Covid-19 affect other mortal diseases; cancer, heart diseases, and diabetes in near future. With this purpose two mathematical models are proposed via Ordinary Differential Equations (ODEs); one for the relationship between Covid-19 and cancer and one for the relationship between Covid-19, diabetes and heart diseases. Afterwards, stability analyses of these models are demonstrated. In order to see the effect of parameters on the disease compartments, sensitivity analysis is applied. Results of sensitivity analysis revealed that huge percentage of people are still scared of visiting doctors and this may lead a massive increase in the diagnosis of other diseases for upcoming years. Moreover, figures displayed that there exists a relationship between diabetes and heart diseases. Especially, diabetes patients should be careful about their health situations and take care of their heart. In order to provide these, awareness of people should be developed.

Concrete cracks have a detrimental effect on the strength properties and durability of the structures. So, repairing of concrete cracks to recover their strength parameters is more important task in civil engineering. To repair concrete cracks, MICP has been widely analysed in recent times; but, zero research is conducted to deeply investigate the repair effects of MICP on concrete cracks with rough surface by using the theoretic model. In current research, MICP with a novel mathematical model was attained by taking the precipitation of calcium carbonate (CaCO3), ureolysis, suspended biomass, geochemistry, transport of solute and biofilm growth. Furthermore, crack repair experiments were performed to check the workability of the new mathematical method. The outcomes revealed that the designed suspended biomass concentrations in cracks diminished step by step. The comparison in between the experimental results and calculated results verified the precision of migration behaviour of the suspended biomass. At the inlet, the solute concentrations and biofilm volume fractions was higher, causing in rise of yield amounts for calcium carbonate. The consumed solutes concentrations were higher for cracks of less rough surface, ultimately causing in smaller sonic time; and the values of sonic time for upper portions of cracks was smaller, showing good repair impacts. The recommended mathematical model provides a better tool that controls repair time and microbial metabolism process to report a new adjustive, bioremediation and biomineralization to concrete, which could provide a firm base for remediation of material in civil engineering field.

To assess the impact of tourism on the incidence of HIV and AIDS using Malaysian epidemiological data over the period of 1986-2011 with additional consideration for newborns infected with HIV. A population-level mathematical model was used to investigate: i) the role of tourism in the spread of HIV and measures used to reduce HIV spread in Malaysia; ii) whether the stability of infectious disease transmission is dependent on the flow of visiting tourists. We first derived an equation for the reproduction number (R0) threshold to quantify the contagiousness of HIV in Malaysia. Sensitivity analyses were used to determine the effect of various parameters on HIV transmission with respect to the increase in tourism. Our findings suggest that a stable disease-free state is sustainable based on the low value of R0 was 0.0017. This result is encouraging from a public health perspective. Approximately 14% of outbound tourists who leave the country return infected with HIV and the difference between the rate at which tourists move to the susceptible category and the rate at which tourists leave the susceptible is category is 12%. Estimated parameters for the influx of tourist rates, δ=1.1540x10-3[1.1477x10-3 - 1.15954x10-3], δ1=7.7901x10-4[7.7867x10-4 - 7.79418x10-4], and δ2=1.4030x10-8[-7.2287x10-7-7.5096x10-7], significantly impacted the spread of HIV in Malaysia. Some significant adjustments were made to the expected parameters. The methods used are helpful to public health analyses and provide a framework for epidemiological modeling of HIV spread among tourists. The trend and magnitude of tourist inflows may be determinants in the incidence of HIV and AIDS in Malaysia.

This study proposes a nonlinear mathematical model of virus transmission based on the SEIR model. In this study, the interaction between viruses and immune cells is investigated using phase-space analysis of a mathematical model. Specifically, it is focused on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune systems cells. The endemic equilibrium points are found and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis either, at disease-free equilibria, or in endemic equilibria is discussed by constructing the Lyapunov function which shows the validity of the concern model exists. Finally, a simulated solution is achieved and the relationship between viruses and immune cells is highlighted.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

The dynamics of the main photosynthetic structures is studied by mathematical modeling methods in this article. Chlorophyll portion variability in phytoplankton and the formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their participation in the growth of specific biomass. Computational experiments are presented that simulate various degrees of environmental friendliness. The corresponding functions are built in accordance with seasonal fluctuations throughout the year in the Far East region of Russia. The stability of model solutions in long-term dynamics is also investigated. The models were tested for biological adequacy and their effectiveness was compared. For the model selected as a result of the comparison, the optimal control problem has been formulated and solved. It is shown that in this way it is possible to reduce the space of the initial components of the model system.

The use of mathematical models of physiological systems in medicine has allowed the development of diagnostic, treatment, and medical educational tools, but their application for predictive, preventive, and personalized purposes is restricted by their complexity. Although there are strategies that reduce the complexity of applying models by fitting techniques, they focus on a single instant of time, neglecting the effect of the system's temporal evolution. The aim of this work is to propose a dynamic fitting strategy of physiological models with large number of parameters and a constrained amount of experimental data, focused on obtaining better predictions based on the system's temporal trend and useful to predict future states. It was applied in a cardiorespiratory model as a case study. Experimental data from a longitudinal study of healthy adult subjects under aerobic exercise were used for fitting and validation. The model predictions obtained at steady-state using the proposed strategy and the nominal values of the parameters were compared. The best results corresponded mostly to the proposed strategy, mainly regarding the overall prediction error. The results evidenced the usefulness of the dynamic fitting strategy, highlighting its use for predictive, preventive, and personalized applications.

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solu-tions. At the same time, depending on parameter values, different dynamic regimes - stationary, oscillatory, established as a result of transient modes of various types - can be implemented in the system. Predicting changes in the solution dynamics type depending on changes of model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computa-tional experiments, i.e. solving a series of direct problems with various sets of parameters fol-lowed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allow-ing to obtain and analyze information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for visualization and classification of various dy-namic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method allows to obtain a qualitative visualisation of the results of the set of solutions of a mathematical model and to carry out the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka-Volterra model and artificial sets of var-ious dynamics

This paper presents some aspects of command and control of the new generation of machines-tools with numerical control. A problem faced by numerical control programmers is related to the length (relatively long) of the programs, with implications in the costs and duration of the manufacturing preparation. A method of reducing the main program and other redundant expenses is the introduction and use of processing cycles and subroutines for automatic calculation of the cutting tool trajectory, a fact that also allows the optimization and simplification of numerical control programming on flexible order manufacturing systems numeric. The method involves the use of predefined cycles and appropriate subroutines in order to improve the efficiency of the programming activity in a balanced way. It is a new and rapid method for optimize the structure of program using the numerical subroutine for command the movement of tool, in our case, with application for turning and milling.

In the present paper, we investigate the impact of the timescale factor on the quality of life index behavior on specific time intervals characterized by the presence of socio-economic, political, and/or health severe movements such as pandemics and crises. We essentially aim to show that effectively the quality of life measuring based on a single index in the existing studies may be described more adequately by a variable index due to the social, political, economic, and also healthy environment. The variability discovered is expressed by the existence and the estimation of a multi-index instead of a single one relatively to many factors. Our focus is mainly on the effect of the COVID-19 pandemic on the quality of life. Our model is applied empirically to a sample corresponding to Saudi Arabia as a case of study during the period from January 1990 to December 2021 as the main period affected by the COVID-19 pandemic. The sample is based on social media conversations and texts discussing and describing the satisfaction with the quality of life. The study confirms effectively that the role of the timescale factor is more described when considering a multi-index rather than measurement on the whole time interval.

In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.

Schistosomiasis is a parasitic disease acquired through contact with contaminated freshwater. The definitive hosts are terrestrial mammals, including humans, with some Schistosoma species crossing the animal-human boundary through zoonotic transmission. An estimated 12 million people live at risk of zoonotic schistosomiasis caused by Schistosoma japonicum and Schistosoma mekongi, largely in the World Health Organization’s Western Pacific Region and in Indonesia. Mathematical models have played a vital role in our understanding of the biology, transmission, and impact of intervention strategies, however, these have mostly focused on non-zoonotic Schistosoma species. Whilst these non-zoonotic-based models capture some aspects of zoonotic schistosomiasis transmission dynamics, the commonly-used frameworks are yet to adequately capture the complex epi-ecology of multi-host zoonotic transmission. However, overcoming these knowledge gaps goes beyond transmission dynamics modelling. To improve model utility and enhance zoonotic schistosomiasis control programmes, we highlight three pillars that we believe are vital to sustainable interventions at the implementation (community) and policy-level, and discuss the pillars in the context of a One-Health approach, recognising the interconnection between humans, animals and their shared environment. These pillars are: (1) human and animal epi-ecological understanding; (2) economic considerations (such as treatment costs and animal losses); and (3) sociological understanding, including inter- and intra-human and animal interactions. These pillars must be built on a strong foundation of trust, support and commitment of stakeholders and involved institutions.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

In this paper, the computational fluid dynamics (CFD) method has been used to simulate the gas flow and the catalytic hydrogenation process of the C-2 hydrogenation adiabatic reactor in a practical ethylene production unit of a chemical plant. The laminar finite-rate model was used for the chemical reaction model. The standard two-equation model was used for the turbulence model. The exponent-function kinetic model was used for the reaction dynamics model. The simulation results were in good agreement with the actual industrial data obtained from the C-2 hydrogenation reactor, and the distributions of reaction parameters such as temperature and component concentrations in the reactor were further analyzed. Based on the validated CFD models, the structure and operating conditions of the reactor, as well as hydrogen load distribution ratios, are simulated for comparing the comprehensive performance metrics of ethylene selectivity and acetylene conversion rate; as a result, we can obtain the optimal temperature of 312 K, the optimal hydrogen/acetylene ratio of 0.10 as well as the optimal hydrogen load distribution ratio of 4:4:2, and the diameter/height ratio exerts a marginal effect on the selectivity, conversion rate and harmonic mean of the reactor.

The corrected mechanism model of battery voltammetric function is helpful to guide the development and application of battery. There are two scientific issues that need to be answered: First, how many mechanisms do batteries have; Second, how to establish the mechanism model separately under the overlapping of these mechanisms. Volt-ampere characteristics of both linear state and nonlinear state exist; the monotonic decreasing of volt-ampere characteristics indicates that the battery have only three kinds of mechanisms. Without changing the basic form of the function and under the principle of the mechanism function’s working region considered, we propose a mechanism function which satisfies the monotonic decreasing characteristic of the voltammetric curve of battery, via the derivative law of each mechanism function in the voltammetric function of battery. By using the voltammetric data, the obtained cell mechanism function can accurately predict the potential (current or voltage) when the independent variable of the cell is zero, and provide the theoretical basis for the internal working mechanism of the cell, which can guide the practice.

Computational simulation using mathematical models is a useful method for understanding the complex behavior of a living system. The majority of studies using mathematical models to reveal biological mechanisms uses one of the two main approaches: the bottom-up or the top-down approach. When we aim to analyze a large-scale network, such as a comprehensive knowledge-integrated model of a target phenomenon, for example a whole-cell model, the variation of analyses is limited to particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we developed a hybrid method that combines both approaches. To construct a mathematical model, we extracted network motifs, subgraph structures that recur more often in a metabolic network or gene regulatory network than in a random network, from a large-scale regulatory network, detected regulatory motifs among them, and combined these motifs. We confirmed that the model reproduced the known dynamics of HES1 and ASCL1 before and after differentiation, including oscillation and equilibrium of their concentrations. The model also reproduced the effects of overexpression and knockdown of the Id2 gene. Our model suggests that the characteristic change in HES1 and ASCL1 expression in the large-scale regulatory network is controlled by a combination of four feedback loops, including a large loop which has not been focused on. The model extracted by our hybrid method has the potential to reveal the critical mechanisms of neural differentiation. The hybrid method is applicable to other biological events.

An autonomous endogenous time-keeping is ubiquitous across many living organisms known as circadian clock when it has a period of about 24 hours. Interestingly, the fundamental design principle with a network of interconnected negative and positive feedback loops is conserved through evolution, although the molecular components differ. Filamentous fungus \textit{Neurospora crassa} is a well established chrono-genetics model organism to investigate the underlying mechanisms. The core negative feedback loop of the clock of \textit{Neurospora} is composed of the transcription activator White Collar Complex (WCC) (heterodimer of WC1 and WC2) and the inhibitory element called FFC complex which is made of FRQ (Frequency protein), FRH (Frequency interacting RNA Helicase) and CK1a (Casein kinase 1a). While exploring their temporal dynamics we investigate how limit cycle oscillations arise and how molecular switches support self-sustained rhythms. We develop a mathematical model of 10 variables with 26 parameters to understand the interactions and feedbacks among WC1 and FFC elements in nuclear and cytoplasmic compartments. We performed control and bifurcation analysis to show that our novel model produces robust oscillations with a wild-type period of 22.5 hrs. Our model reveals a switch between WC1 induced transcription and FFC assisted inactivation of WC1. Using the new model we also study possible mechanisms of glucose compensation. A fairly simple model with just 3 non-linearities helps to elucidate clock dynamics revealing a mechanism of rhythms production. The model can further be utilized to study entrainment and temperature compensation.

Human African Trypanosomiasis (HAT) commonly known as sleeping sickness, is a neglected tropical vector borne disease caused by trypanosome protozoa. It is transmitted by bites of infected tsetse fly. In this paper we first present the vector-host model which describes the general transmission dynamics of HAT. In the tsetse fly population, the HAT is modelled by three compartments while in the human population, the HAT is modelled by four compartments. The next generation matrix approach is used to derive the basic reproduction number, R₀, and also it is proved that if R₀ ≤ 1 the disease free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persist in the population if the value of R₀ > 1. Furthermore, the optimal control model is determined by using the Pontryagin’s maximum principle with control measures such as education, treatment and insecticides used to optimize the objective function. The model simulations confirm that the use of the three control measures are very efficient and effective to eliminate HAT in Africa.

This paper investigates existing mathematical morphology based techniques applied for performing malaria parasites detection and identification in both Giemsa and Leishman stained blood smears images. Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis; this kind of visual inspection is subjective, errorprone and time consuming. In order to cope with such issues, computer-aided methods have been increasingly evolved for abnormal erythrocyte and/or parasites detection, segmentation and semi/fully automated classification. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection.

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex anti-tumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these fields of research for more efficient development and effective treatments.

Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibres. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualisation such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilise finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.

This paper shows the development of a numerical analysis model which enables the calculation of the life of a reduced-diameter wheel used for freight wagons as a function of its operating factors. Reduced-diameter wheels are being increasingly used for combined transport applications and they can be arranged in a wide range of bogies and operated very differently. Due to the uniqueness of this type of wheels, their life has hardly been analyzed so far. To properly construct the numerical analysis model, it has been necessary to study the rolling phenomenon in-depth, tackle the main problems arising in the vehicle – track interaction and set the relations amongst them. Once the rail-wheel interaction model was built, it was used to calculate the life of an ordinary-diameter wheel, a medium-diameter wheel and a reduced-diameter wheels under the same conditions and compare them. In this way, it is possible to know how long the life of a reduced-diameter wheel is compared to that of an ordinary-diameter one and also the evolution of the life depending on the diameter. The root causes responsible for this evolution can be explained thanks to the comprehension of the rolling phenomenon provided by the full analytical work.

The symptoms of multiple sclerosis (MS) are determined by the location of demyelinating lesions in the white matter of the brain and spinal cord. Currently, magnetic resonance imaging (MRI) is the most common tool for diagnosing MS, understanding the course of the disease, and analyzing the effects of treatments. However, undesirable components may appear during the generation of MRI, such as noise or intensity variations. Mathematical morphology (MM) is a powerful image analysis technique that helps to filter the image and extract relevant structures. Granulometry is an image measurement tool of MM that determines the size distribution of objects in an image without explicitly segmenting each object. While, several methods have been proposed for the automatic segmentation of MS lesions in MRI, in some cases only simple data preprocessing, such as image resizing to standardize the input dimensions, has been performed before the algorithm training. Therefore, this paper proposes an MRI preprocessing algorithm performing elementary morphological transformations in brain images of MS patients and healthy individuals to delete undesirable components and extract the relevant structures such as MS lesions. Also, the algorithm computes the granulometry in MRI to describe the size qualities of lesions and trains two artificial neural networks (ANN) to predict MS diagnosis. The computing of differences in granulometry measurements of an image with MS lesions and a reference image (without lesions) can determine the size characterization of the lesions. Then, the ANNs were evaluated with the validation set and the performance results (test accuracy = 0.9753, and cross-entropy loss = 0.0247) show the proposed algorithm can support the decision of specialists for diagnosing MS and estimating the disease progress, based on granulometry values.

The theory of limited numbers says that the number is not infinite, that is, the number is limited in parts or completely. To reach a conclusion about the limited number, one must understand the meaning of mathematics and varied spaces, therefore, one must understand that mathematics and spaces interact. Mathematics has the function of describing the world precisely, where numbers represent elements or facts that rationally belong to space, and spaces have different intensities of specific physical concepts in each space; therefore, there is no infinite element or fact due to differences in the intensities of specific physical concepts in spaces that do not allow for the fact or fact in all spaces.

The planned closure of potash mines, achieved through the injection of highly mineralized brines into the worked-out area, is a complex and not fully studied process. A critical concern arises when brines obstruct the aerodynamic connections between the flooded mine's airspace and the atmosphere, potentially leading to the formation of closed cavities where explosive gases can accumulate. To address this hazard, it is imperative to develop systems capable of extracting the gas-air mixture from the unflooded domed portions of the worked-out area. This is the focus of this study, in which we analyze gas-dynamic processes within the potassium mine worked-out area during planned flooding. Two distinct scenarios are examined: the first involves controlled flooding with saturated brines, while the second contemplates flooding resulting from a hypothetical breakthrough of supra-salt strata, leading to the ingress of groundwater into the worked-out area. A novel mathematical model is introduced to predict the evolution of gas-air mixture parameters in the unflooded dome segment of the worked-out area. Utilizing this model, we assess the effectiveness of proposed measures designed to eliminate explosive gases from the worked-out area. Specifically, a pipeline system is proposed for the removal of gases, followed by their dilution below the maximum permissible concentrations in the effluent jet. The findings from this study contribute valuable insights into ensuring the safe and efficient closure of potash mines, shedding light on potential risks and effective mitigation strategies for gas-related hazards during planned flooding.

Modeling the reaction time required for the removal of chemical oxygen demand (COD) from wastewater is important because can be an indicator of harmful pollutants that may pose risks to human health.. Here, we evaluate the use of an inverse artificial neural network (ANNi) to optimize the removal of COD from aqueous herbicide solutions using sonophotocatalysis as the treatment process.. This algorithm takes the operating conditions as input and estimates the optimal reaction time to reach the required effluent COD. This model was validated by comparison with both experimental measurements and simulated analysis, resulting in low error (0.5%), high Pearson correlation (R2 = 0.9956), and short computing time (less than one minute). The results for the proposed methodology (ANNi-GAs) were efficient and attractive in a reasonable way providing a satisfactory picture of the relationships between the optimal input parameters. Such parameters control the degradation process of herbicides online and can be used to predict the behavior of COD removal, thus taking actions to reduce the impact of aqueous treatment with alazine and gesaprim herbicides on aquatic, soil biota, and human health. Therefore, this technique constitutes a promising framework for predicting the environmental impact of herbicides within a tolerable degree of error.

Abdominal aortic aneurysm (AAA) is a chronic disease in which the abdominal aorta expands until it ruptures. AAA incidence: 10 million/year (India), deaths: 40%-90% (13th leading cause of death in the USA). Current treatment methods make diagnosis difficult due to the lack of noticeable symptoms and inaccurately planned operations. Rupture Scope is a mathematical model to dramatically reduce AAA deaths and improve treatment efficiency. Using a case-specific replica/simulation of real-time abdominal aortic blood flow for monitoring without frequent imaging scans and a novel derived mathematical linear regression model to predict rupture date and expansion rate with an overall accuracy of 95.64%.