Mathematical Scheme Research Articles

A computation analysis with heat and mass transfer for micropolar nanofluid in ciliated microchannel: With application in the ductus efferentes

Inherited heat enhancement capabilities and their significance in the field of medical sciences and industry make nanofluids the focus of research nowadays. Furthermore, due to the remarkable advancements in bionanotechnology and its significance in biomedical fields such as drug delivery systems, cancer tumor therapy, bioimaging, and many others, it has emerged as a key research area. Contribution of cilia for the flow in ductus efferentes of human male reproductive tract is elaborated. A novel mathematical scheme is presented for the heat and mass transfer of MHD micropolar nanofluid transport in an asymmetric channel lined with cilia. The pertinent equations of nanofluid transport are exposed to lubrication approximation theory and solution for the physical problem is examined with efficient bvp4c technique in MATLAB. Fluid rheology is explored with the variations of different transport parameters like Hartmann number, Grashof number, Brownian motion, buoyancy, thermophoresis and Darcy number. It is reported that nanofluid transport is affected with rise in the Lorentz force and show reverse behavior with rising permeability. The temperature of the nanofluid in ciliated microchannel is raised with enhanced value of Hartmann number, Grashof number, Prandtl number, and Darcy number while diffusion phenomenon of nanofluid is slowed down with these parameters. Spinning motion of the nanofluid is enhanced with Grashof number and slow down with nanoparticle Grashof number and different behavior is recorded for Darcy and viscosity parameters in different flow regime. Reported investigation presents crucial findings for ciliary transport of micropolar nanofluid and tackled with appropriate selection of micropolar parameter, Brownian motion parameter, thermophoresis and Grashof number. Moreover, this investigation will be handful for cilia-based actuators which work as micro-mixers in controlling the flow in minute bio-sensors and may prove their worth in micro-pumps employed in various drug-delivery systems.

Developing (Pedagogical) content knowledge of constant rate of change: The case of Samantha

We present the results of a teaching experiment designed to foster a pre-service secondary teacher’s construction of a quantitative scheme for constant rate of change. Although the research participant developed a productive conception of constant rate of change as an interiorized ratio, images of chunky continuous covariation constrained her ability to reason efficiently across a variety of applied contexts. The participant constructed a scheme for constant rate of change at the reflected level of thought, which enabled her to become cognizant of its essential aspects and to appreciate its general applicability. Our results suggest that engaging in reflected abstraction is critical for supporting pre-service teachers’ construction of coherent and refined mathematical schemes.

Strong Determinism

A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.'' Such an extraordinary feature may appear unattainable in a world like ours. In this paper, I show that it can be achieved in a simple way and discuss its implications for metaphysics and philosophy of science, including natural properties, free will, explanation, and modality. First, I propose a precise definition of strong determinism. Next, I discuss its philosophical ramifications and a toy example. Finally, I provide a realistic example of a strongly deterministic (and simple) physical theory—the Everettian Wentaculus. A surprising consequence is that whether or not our world is strongly deterministic may be empirically underdetermined. 

Mathematics teachers and learners as collective agents of change

In this article, we report on findings from the Primary Maths and Social Justice research project, a recent collaboration between the three authors and six teacher researchers from two culturally diverse primary schools in London, UK. The project aimed to develop strategies for addressing issues of social justice in the mathematics classroom, and operationalising the recently developed theoretical concept of socio-mathematical agency, defined as learners’ capacity to apply mathematics in arguing collectively for social change. The teacher researchers’ experiences, as captured through audio recordings of research team meetings and interviews, form the basis of our data analysis. Our findings highlight the processes that enabled teachers to reflect critically on existing practice, prompting them to adopt more collaborative, discursive and inclusive problem-solving approaches that resulted in significantly higher levels of student engagement in mathematical activities. The teacher researchers found that cross-curricular projects provided more opportunities to apply mathematical knowledge in tackling social justice issues than the prescriptive and content-focused mastery-style mathematics schemes of work in place. They reported how students embraced opportunities to use mathematics in more meaningful contexts and in presenting arguments for change. We argue that a focus on developing socio-mathematical agency has the potential to enhance the role of teachers and learners as agents of change, an important element that is often underdeveloped in culturally responsive teaching.

Mobile Technologies in Teaching Mathematics

Purpose. The article discusses the use of mobile technologies in teaching mathematics to engineering students. The relevance of the paper is due to the need to introduce new methods and means of teaching in connection with the increasing integration of mobile technologies into all areas of life, the interests and characteristics of the new, networked generation of students, the limited possibilities of using innovative methods and means of teaching mathematics due to the conduct of classes outside the computer lab.Materials and methods. The peculiarity of this study is that the integration of mobile technologies into the process of teaching mathematics is considered as a system of three components: technological, informational and social. The analysis of these components made it possible to obtain answers to research questions: where and how mobile devices should be used when studying mathematics; what mobile applications will provide the most effective learning of the discipline; how to organize the educational process using mobile technologies to increase interest and motivation in learning mathematics.Results. The main reasons for the lack of interest in studying mathematics and low motivation include the high level of abstraction of the discipline and the characteristics of the modern, networked generation of students. Analysis of scientific sources and our own observations made it possible to identify such characteristics as problems with understanding complex and long text, the ability to easily read from a small screen and process information in parallel, the choice of sound and images instead of text, the desire for short-term learning and instant results, and attitude towards mobile devices as vital items. Taking into account the interests and wishes of students, and relying on the didactic capabilities of mobile technologies, the paper proposes mobile applications for studying various topics of a mathematical course, assignment options that help increase motivation, develop group work skills and digital literacy. The importance and effectiveness of using social services for visualizing mathematical concepts and calculation schemes, as well as the WhatsApp messenger for instant messaging between students and receiving timely individual and group consultation from a lecturer, is shown. An important characteristic of the messenger is the presence of video communication.Conclusion. The analysis of scientific literature, the study of the requirements of employers and the interests of the modern, networked generation of students, indicated the need to integrate mobile technologies into the process of teaching mathematics. Working with different groups in terms of both the level of mathematical knowledge and the level of proficiency in mobile technologies made it possible to identify and outline ways to solve the main issues of using mobile technologies in teaching mathematics. With limited time to study mathematics, it is difficult for a lecturer to allocate additional time to present the capabilities and effectiveness of mobile applications. A solution to this issue may be to include a section “Mobile Technologies” in a course related to the study of information and communication technologies. It is noted that group work also contributes to a more effective study of the capabilities and techniques of working with mobile applications.

Functional design of organizational structures in project management

The article considers the function tracing method that provides project organizational structure systematic construction. Interconnectedness of methodological approaches between organizational design on a company scale and the role-based project structures construction has been described. Based on the existing level of organizational design development and its most frequently used methods, the tracing functions method from the project requirements to the functional roles of a project organizational structure have proposed and formalized. Initial data volume for organizational design and parallels between organizational structures of a company in general and a project in particular have been given. A mathematical scheme of the projected organizational structure functional distribution has been proposed considering a five-stage approach in tracing functions. The approach describes the stages of modeling the project organizational structure. On the basis of distributing the tasks required to be performed during the project realization, the principles description providing the correlation of the functionality to the project roles on the basis of the project realization goals has been offered. The factors that have a positive impact on project implementation and based on the considered approach of organizational structures functional design have been presented.

Investigation of thermal radiations impacts with double diffusive convection for Prandtl nanofluid with slip in an asymmetric ciliated channel

Thermal radiations are extensively utilized in the medical sciences, and the investigation of thermal radiation combined with double diffusive phenomena is the burning research area because of its enormous applications in treatment of various diseases. Cilia play significant part in many physiological processes of animal and humans. A novel mathematical prodigy for Prandtl nanofluid with thermal radiations and double diffusion convection by implementing slip at boundaries is presented for cilia induce flow in an asymmetric microchannel. Mathematical scheme for the physiological flow is developed and then pertinent equations are designed exploiting low Reynolds number and long wavelength simplifications. Solution for the physiological nanofluid is gathered by emphasizing on the novel BVP4C technique in MATLAB and resulting outcomes are elaborated with aid of graphical illustrations. Pros and cons of various physical flow parameters like thermal slip parameters, Prandtl fluid parameters, Grashof parameter, Prandtl parameter , Brownian motion parameter, thermal radiation parameter, Brinkmann number, Soret parameter are examined on the velocity, magnetic force function, temperature profile, concentration and nanoparticles volume fraction. It is reported that slip parameter really effects the nanofluid transport within the ciliated microchannel, it reduces the fluid flow, diffusion phenomena of the nanoparticles in the ciliated microchannel surges when radiation parameter is strengthened. The reported investigation will be instrumental in heat radiation effect for regulation of blood circulation to cure the cancer tissues in multiple drug delivery systems and will pave the way for the designs of certain diagnostic and pharmacological devices.

NEW STRATEGY THE FOR DESIGNATION OF THE INTEGRITY PARAMETER IN SBAS POSITIONING IN AIR TRANSPORT

The article shows the results of a study on the determination of SBAS satellite positioning integrity parameters as a HPL and VPL protection levels. To this end, a modified algorithm was developed to determine the HPL and VPL protection levels from a common aircraft position navigation solution based on EGNOS and SDCM augmentation systems. The developed mathematical scheme was verified on real GNSS kinematic data recorded by two onboard Septentrio AsterRx2i and Trimble Alloy receivers installed on a Diamond DA 20-C aircraft. Based on the conducted tests, it was found that the HPL parameter does not exceed 12.24 m, while respectively the VPL does not exceed 18.01 m. In addition, in the course of the study it was found that the proposed EGNOS+SDCM solution improves the HPL/VPL integrity determination in relation to the EGNOS solution by 8÷66%. The mathematical scheme used in the study was also applied to designation the HPL/VPL terms for the UAV platform. The obtained results of the HPL/VPL values for the positioning of the aircraft and the UAV platform show a high efficiency of the developed algorithm for improving the integrity parameter.

COMPARATIVE CHARACTERISTICS OF CHANGES WITHIN SOMATOTYPE COMPONENTS OF YOUNG PEOPLE (RURAL AND CITY RESIDENTS) DURING STUDyi NG IN A HIGHER EDUCATIONAL INSTITUTION

Abstract. Relevance of the research topic. The constant trend towards reforms in the spheres of health care, education, and sanitary-epidemic service leads to changes in the control over the conditions of obtaining education from a medical point of view, and also confirms the urgency of finding solutions to improve the conditions of education in aim to preserve the health of those receiving education. In our opinion, control and observation of changes in physical development makes it possible to solve some urgent needs. Determination of the type of constitution, and especially somatotypological signs, is of actual practical and theoretical importance. The somatotypological characteristic of the human body is a biological portrait of a person that integrates and a set of hereditary somatic characteristics, as well as the influence of socio-economic and environmental factors. The aim of the study. Determining the features somatotype components changes of the rural and urban young main in full time education across the span of a year. Research materials and methods. A somatometric and somatotypological study of 200 practically healthy young men was carried out (100 residents of a village, 100 residents of the city) in the 1st, 2nd and 3rd years of study at the University of Life Safety. To determine the somatotype, the mathematical scheme of somatotyping according to J. L. Carter, B. H. Heath was used. The results. On the basis of the obtained data, a decrease in the indicators of the endomorphic component of the somatotype was discovered during education in both groups of young men, whereby the decrease prevailed in the first year of education, while the indicator of the mesomorphic component of the somatotype showed a tendency to increase throughout the entire course of education of residents of rural area and in the second year of education for urban residents, following the falling in the first year. The indicator of the ectomorphic component decreased during the span of education of students residing in rural areas, mainly in the second year, and remained unchanged among urban residents. Conclusion. The change of intergroup indicators across the span of a year for most components of the somatotype in the first year of education of the villagers were greater compared to that of the city residents, and the indicator for change of the endomorphic component across the span of a year had significant differences. In the second year of study, the intergroup change of somatotype components across the span of a year was again greater among rural residents, and the change of the ectomorphic component had significant differences.

Bioconvection analysis for convectively heated radiative flow of Sutterby fluid involving efficacy of ferromagnetic nanoparticles

In this article explained about the study 2-D Sutterby fluid model with suspension of microorganisms in ferrofluid, while radiation aspect is also considered here. Basic purpose of using microorganism is to obtain more stability in suspension. Here the important characteristics of thermophoresis parameter, viscous dissipation, magnetic interaction parameter and Brownian motion parameter are examined. Now, the system of non-linear P.D.Es is changed into set of O.D.Es then we solved these equations by using famous mathematical scheme bvp4c. Graphical results showed that temperature of Sutterby ferrofluid intensifies with increase in the estimations of thermal Biot number as well as radiation effects whereas results in reduction of Prandtl number. The density of microorganism reduces for greater values of Peclet number.

Numerical analysis of quantization‐based optimization

AbstractWe propose a number‐theory‐based quantized mathematical optimization scheme for various NP‐hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization‐based optimization proposal also depends on stochastic features (i.e., the white‐noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization‐based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes.

Investigation of combustion process in a modular charge system with a primer gap

To clarify the combustion process of a modular charge system with a primer gap, the rules governing the cartridge movement and pressure change in the chamber are analyzed. Based on the characteristics of the modular charge system, an axisymmetric two-phase flow model of the interior ballistics is established, with the monotonic upward-centered scheme for conservation laws adopted to calculate the combustion process. Compared with the experimental results, the difference in the peak pressure is less than 5%, which indicates that the mathematical model and scheme are reliable and accurate. The results show that, during the initial stage of ignition, the combustible container remains unbroken, and the gas and solid particles are prevented from spreading to the chamber by the end cap of the cartridge. Thus, only the gas inside the igniter tube influences the flow field in the chamber. After the combustible container has broken, the gas and solid particles move rapidly toward the cavity from the combustible container. The axial movement of solid particles is more intense than that of the gas particles, but the radial movement of solid particles is relatively weak. Furthermore, the existence of the primer gap leads to a delay in the ignition time of the solid particles, which delays the rupture time of the igniter tube and the module cartridge.

Proceedings of the 2022 Computational Techniques and Applications Conference

CTAC 2022 Queensland University of Technology, Brisbane, Australia 29 November – 2 December, 2022 The 21st Biennial Computational Techniques and Appli- cations Conference (CTAC-2022) was hosted by the School of Mathematical Sciences and Centre for Data Science at Queensland University of Technology in Brisbane. The ANZIAM Special Interest Group in Computational Mathematics is responsible for this series of conferences, the first of which was held in 1981. The meeting provides an interactive forum for researchers interested in the de- velopment and use of computational methods applied to engineering, scientific and other problems. Participants of the conference are able to submit a short article based on their presentation for publication in this special section of the ANZIAM Journal (Electronic Supplement). The ed- itors, Tim Moroney, Qianqian Yang, Vivien Challis and Elliot Carr, thank the referees whose efforts have helped improve the quality of these conference proceedings. This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed conference papers. The eight keynote presentations were as follows. Chris Drovandi, Queensland University of TechnologyLikelihood-Free Bayesian Inference and Model Mis- specification Jennifer Flegg, The University of Melbourne Mathematical Modelling of Avascular Tumour Growth Frances Kuo, The University of New South Wales Lattice Meets Lattice—Application of Lattice Cuba- ture to Models in Lattice Gauge Theory Christian Lubich, University of Tuebingen Convergent evolving surface finite element algo- rithms for geometric evolution equations Marco Palombo, Cardiff University Perspectives on AI-powered brain microstructure imaging Emilie Sauret, Queensland University of TechnologyA hybrid Lattice Boltzmann approach for simulating viscoelastic instabilities and elastic turbulence Karen E Willcox, The University of Texas at Austin Predictive Digital Twins: From Aerospace Engineer- ing to Computational Oncology Andy Wilkins, CSIROThe Importance of Mathematics The presentation by Andy Wilkins was a public lecture. The conference attracted 76 registered participants, and featured a total of 54 contributed talks. CTAC2022 Organising Committee (QUT) • Tim Moroney • Qianqian Yang • Ian Turner• Vivien Challis • Elliot Carr• Sarie Gould CTAC2022 Scientific Committee • Kevin Burrage (QUT)• Vivien Challis (QUT)• Frances Kuo (UNSW)• Bishnu Lamichhane (Newcastle) • Quoc Thong Le Gia (UNSW) • Fawang Liu (QUT)• William Mclean (UNSW) • Tim Moroney (QUT)• Linda Stals (ANU)• Ian Turner (QUT)• Qianqian Yang (QUT) Acknowledgements QUT acknowledges the Turrbal and Yugara, as the First Nations owners of the lands where QUT now stands. We pay respect to their Elders, lores, customs and creation spirits. We recognise that these lands have always been places of teaching, research and learning. QUT acknowledges the important role Aborigi- nal and Torres Strait Islander people play within the QUT community. We gratefully acknowledge support from the following sponsors: School of Mathematical Sciences, QUT Centre for Data Science, QUT Modelling and Simulation Society of Australia and New Zealand Inc Mathematics of Computation and Optimization (MoCaO) special interest group of the Australian Mathematical Society The ANZIAM Student Support Scheme

Correlations of the dermatoscopic index with anthropometric and somatotypological parameters of men with benign nevi

Malignant transformation of benign nevi is one of the factors that leads to increased scientific interest in the study of the pathogenesis of their occurrence, the influence of external factors on them, etc. One of the still unsolved issues is the study of the relationship between the features of nevi indicators and the anthropometric parameters of the human body. The purpose of the work is to investigate the peculiarities of correlations of the dermatoscopic index with anthropometric and somatotypological indicators of Ukrainian men with benign nevi. A clinical, laboratory and pathogistological examination of 34 Ukrainian men of first adulthood with melanocytic benign simple nevi, 27 with melanocytic benign dysplastic nevi, 14 with melanocytic benign congenital nevi, and 17 with non-melanocytic benign nevi was carried out. The dermatoscopic index was calculated according to the “ABCD rule of dermatoscopy”. Anthropometric examination was carried out according to Bunak’s scheme. The Heath-Carter mathematical scheme was used to assess the somatotype. Matiegka formulas were used to calculate fat, bone and muscle components of body mass. In addition, the muscle component of body weight was estimated according to the method of the American Institute of Nutrition. The assessment of correlations between the dermatoscopic index and body parameters was carried out in the license package “Statistica 6.0” using the non-parametric method of Spearman. An analysis of multiple reliable and average strength of unreliable correlations between the value of the dermatoscopic index and anthropo-somatotypological indicators in men with benign nevi was performed. In men with simple melanocytic nevi, only moderately strong direct (r = from 0.30 to 0.34), mostly unreliable, correlations with all sizes of the pelvis were established. In men with melanocytic dysplastic nevi, inverse correlations of medium strength, mostly reliable (r = from -0.38 to -0.52) were established with all dimensions of the pelvis and almost all transverse dimensions of the trunk, as well as with almost half of the indicators of the skinfold thickness. In men with melanocytic congenital nevi, direct, mostly unreliable (r = from 0.30 to 0.47) correlations were established with all dimensions of the pelvis, with almost all transverse dimensions of the trunk, with almost half of the girth of the body and indicators of the skinfold thickness and almost all indicators of the component composition of body weight. In men with non-melanocytic nevi, direct, mostly unreliable (r = from 0.30 to 0.47) correlations were established with all transverse dimensions of the trunk and pelvis, most of the total and girth dimensions of the body. Quantitative analysis of reliable and average strength of unreliable correlations between the value of the dermatoscopic index and anthropo-somatotypological indicators was also carried out. The established features of the correlations expand modern ideas about the risk of benign nevi.

Optical soliton and other solutions to the nonlinear dynamical system via two efficient analytical mathematical schemes

Optical soliton and other solutions to the nonlinear dynamical system via two efficient analytical mathematical schemes

Flow time history representation and reconstruction based on machine learning

Based on deep learning technology, a new spatiotemporal flow data representation and reconstruction scheme is proposed by using flow time history (FTH) data instead of flow snapshots. First, the high-dimensional nonlinear flow system is reduced to a low-dimensional representation latent code using the FTH autoencoder model. Second, the mapping from physical space to latent code space is built using mathematical and machine-learning schemes. Finally, FTH at unavailable positions in physical space is generated by the FTH generator. The proposed scheme is validated by three case studies: (i) representing and recovering the FTH data of periodic laminar flow around a circular cylinder at Re = 200 and generating high-resolution laminar flow data; (ii) reconstructing complex FTH of flow past cylinder at Re = 3900 which including laminar and turbulent flow region and generating three-dimensional high-resolution turbulent flow data, respectively; (iii) representing and generating multi-variable turbulent flow data simultaneously using the multi-channel model. The results show that the proposed scheme is an effective low-dimensional representation for complex flow time variant features, which is suitable for both laminar and turbulent FTH data to generate spatiotemporal high-resolution FTH data in three-dimensional space.

Information encoded in gene-frequency trajectories

In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded within gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard diffusion approximation result, for the probability of fixation, systematically emerges when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.

Fractional simulations for slip flow of Casson CMC-CNTs hybrid nanofluid with Mittag-Leffler kernel and Prabhakar fractional simulations

This work aims to investigate the mixed convection heat transfer in hybrid nanofluids across a vertical pours plate under the influence of Newtonian heating. It is also taken into account walls slipping slide and the applied magnetic field is angled. By using an effective mathematical fractional scheme known as the Prabhakar time-fractional derivative, the non-dimensional leading equations are converted into the fractional model. Water and carboxymethyl cellulose (CMC) are the foundation fluids for carbon nanotubes (CNTs), which are considered as base nanoparticles. The Laplace scheme is used to solve the momentum and energy equations, and several numerical techniques are taken into consideration for the Laplace inverse. The effects of various restrictions are visualized and quantitatively examined for both leading equations. It is concluded the consideration of CMC-based hybrid nanofluid has present peak thermal impact as compared to other hybrid nanofluid models. The increasing applications of nanoparticles volume fraction shows increasing trends for thermal phenomenon for both SWCNTs and MWCNTs.

Design of Hardware-in-the-loop Simulation System for Image-guided Missiles

This paper introduces a design method of a hardware-in-the-loop simulation system applied to a certain type of image-guided missile. By studying the characteristics of a certain type of image-guided missile, the working principle of the image-guidance system is analyzed, the mathematical simulation scheme and the hardware-in-the-loop simulation scheme are designed, and the working mechanism of RTX is analyzed. Established a real-time hardware-in-the-loop simulation system based on RTX+Windows, analyzed the delay of the simulation computer, the simulated launch control computer, the flight motion simulator and the image simulator, and finally integrated the flight data and missed target amount of the hardware-in-the-loop simulation test, and obtained the hardware-in-the-loop simulation system meets the requirements.

Deep Learning Model to Predict Ice Crystal Growth.

The demand for highly specific and complex materials has made the development of controllable manufacturing processes crucial. Among the numerous manufacturing methods, casting is important because it is economical and highly flexible regarding the geometry of manufactured parts. Since solidification is an important stage in the casting process that influences the properties of the final product, the development of a controllable solidification process using modeling methods is necessary to create superior structural properties. However, traditional modeling methods are computationally expensive and require sophisticated mathematical schemes. Therefore, a deep learning model is proposed to predict the morphology of the dendritic crystal growth solidification process, along with a reinforcement learning model to control the solidification process. By training the deep learning model with data generated using the phase field method, the solidification process can be successfully predicted. The crystal growth structures are designed to be altered by adjusting the degree of supercooling in the deep learning model while implementing reinforcement learning to control the dendritic arteries. This research opens new avenues for applying artificial intelligence to the optimization of casting processes, with the potential to utilize it in the processing of advanced materials and to improve the target properties of material design.