Mathematical Strategies Research Articles

Chemometrics and Signal Processing-Assisted Design of a Textile-Based Colorimetric Sensing Platform for Real-Time Monitoring of Glucose

Colorimetric analysis of biomarkers in biological fluids, such as sweat and saliva, using textile- and paper-based platforms promises to be a powerful point-of-care analytical tool. Despite exponential advances in material design, device fabrication and image processing over the past years, the majority of paper/fabric-based analytical strips and devices, thus far, are strictly restricted to controlled laboratory settings. In situ and real time monitoring of biological analytes using familiar garments or accessories are centered around electrochemical sensors. In contrast, colorimetric devices that can theoretically enable the quantification of analyte concentration when coupled with image capture devices (such as a smartphone cameras) are comparatively fewer and less advanced. Here, garment design strategies and various embodiments of wireless communication electronics are applied cooperatively to afford a noninvasive platform for quantitative monitoring of a test-bed biomarker, glucose. The electronics-embedded garments contain two functional parts: a functionalized cotton substrate with enzyme/chromogenic reagent and a near-field communication device. The enzyme/chromogenic reagent mixture is directed into a circular reservoir created on the cotton substrate via the capillary force of the cotton and hydrophobic wax barrier created via a cheap and simple wax-drawing technique. This wax barrier limits the irregular flow of the reagent mixture. The second part is a near-field-communication system that causes no irritation and discomfort to the skin. Once a smartphone is put at a close distance, the electronic system can enable the wireless transmission. A built-in application was developed to automatically detect the sensor spot via a signal processing pipeline and extract the R, G and B channel intensities for database construction and analysis.The chemical properties and geometric structures of the glucose sensor were optimized with the aid of a combinatorial method—materials optimization and mathematical optimization. The former aims to overcome the blurring and the loss of the signal due to enzyme washout from the detection zone under capillary forces exerted during wear. This problem was mitigated by immobilizing the enzyme inside a chitosan-carboxymethyl cellulose hybrid via a precisely controlled layer-by-layer deposition protocol. The sensor was further characterized by field-emission scanning electron microscopy (FESEM) to understand long term storage stability and surface morphology-dependent colorimetric response.A mathematical strategy was utilized for the design and selection of an optimal near-field measurement system. This optimization procedure is particularly important for commercialization. It aims to minimize the number of experiments and reduce the quantity of the chromogenic reagent mixture that needs to be deposited on the cotton substrate. Central composite designs were used to estimate the effect of individual variables (i.e. glucose oxidase concentration, horseradish peroxidase concentration and 3,3’,5,5’-Tetramethylbenzidine concentration) and their interactions on the optimization of the color intensity. The significance of the main and interaction effects and the applicability of the model were inferred from the analysis of variance (ANOVA). The optimum value was verified and validated with experimental results.This textile-based colorimetric sensing platform exhibits simple-to-fabricate, and cost-effective nature which might facilitate the broad commercial usage in health monitoring and clinical diagnosis.

A mathematical modeling strategy to predict the spreading behavior on skin of sustainable alternatives to personal care emollients

Spreadability is one of the most important physicochemical properties of cosmetic products, according to the consumer. Thus, it is fundamental to develop strategies with the aim to improve the knowledge and predict the behavior of alternatives to synthetic emollients. The main goal of this research article was to correlate different physicochemical attributes, namely spreading value, apparent viscosity, density, saponification value, iodine value, peroxide value, acid value and melting range, with the spreading behavior of sustainable alternatives for petrolatum and dimethicone. The sensitivity and adequacy of each parameter were statistically analyzed, and the models were built by forward selection. The two adjusted and optimized models include viscosity and density as parameters and, in the petrolatum case, the model further includes the melting range, which was also validated as a significant predictor. Furthermore, it was also possible to compare the data obtained with the consumer's perception of the spreading behavior of the studied raw materials. A strong correlation was observed, suggesting that these tools mirror the consumer opinion. The application of these mathematical models is a valuable tool to assist the entire replacement process, which usually is a time-consuming procedure.

Consumer-focused solar-grid net zero energy buildings: A multi-objective weighted sum optimization and application for India

Abstract Buildings account for nearly 40% of the world's energy consumption. Renewable energy sources can help decarbonization by facilitating the achievement of Net Zero Energy Buildings (NZEB). NZEB can be achieved by efficient coordination of the grid-connected load in the building tuned to a consumer's energy demand, usage pattern, and available energy sources. An effective NZEB system calls for an energy-efficient management technique. This paper proposes a novel mathematical strategy for electrical energy management in a residential building. The suggested method establishes a Net Zero Energy (NZE) in a residential building with maximum electrical energy comfort and minimum drain on electrical energy. We validate the concept using a Multi-Objective Differential Evolution optimization methodology using a consumer-controlled approach to obtain Pareto points to guarantee optimal solutions in an NZEB. The proposed scheme delineates the net cumulative electrical energy cost savings of the consumer, ensuring minimum electrical energy discomfort, and minimization of carbon footprints in an NZE Photovoltaic-Grid tied residential building. We highlight the socioeconomic benefits of adopting the methodology in identifying the true potential of NZEBs in meeting global challenges. This research provides insights to the engineers and policy makers to increase consumer participation in the energy performance in an NZEB.

Science, Technology, Engineering, Arts, and Mathematics Remote Instruction for Students With Disabilities

The need for all students to have science, technology, engineering, arts, and mathematics (STEAM) experiences has translated into research examinations of what strategies and practices work in learning STEAM-related concepts and ideas. Through research, effective frameworks, strategies, and additional considerations have been identified for teaching and learning STEAM for students with learning disabilities and emotional/behavioral disorders. Along with understanding how to apply teaching and learning frameworks and using specific strategies for science, technology, engineering, the arts, and mathematics, the authors provide details on how to differentiate instruction for remote teaching.

Learning mathematical symbolization: conceptual challenges and instructional strategies in secondary schools

Abstract This paper investigates South African 12th Grade students’ conceptual challenges with mathematical symbolization and instructional strategies that teachers use to mitigate mathematical symbolization. The study is motivated by the students’ failure to connect representations between symbolic and mathematical ideas to understand concepts and procedures. The study attempts to gain insight into mathematical symbols as potential barriers to students’ understanding of mathematical concepts and processes. The study consists of 120 randomly selected 12th Grade students and 15 purposefully selected mathematics teachers from Sekhukhune district of Limpopo Province, South Africa. Data was collected through questionnaires and focus group interviews. A mixed-method sequential explanatory design was employed. An SPSS cluster analysis of data produced three (3) clusters consisting of 50 (41.6%), 47 (39.3%) and 23 (19.1%) students with severe, mild, and minor challenges with mathematical symbols. Two themes emerged from the students’ difficulties with mathematical symbols. Firstly, students lack symbol sense for mathematical concepts and algebraic insight for problem-solving. Secondly, students disregard conceptual and contextual uses of symbols. The study therefore suggests that students’ negotiation of discourse between the mathematical symbol and the mathematical concept or procedure is crucial developing symbolic meaning. Therefore, teachers need to use appropriate strategies to engage students in processes that allow them to make meanings of mathematical symbols. The study recommends that concepts should be understood before symbolised.

THE EFFECTIVENESS OF A PROBLEM-SOLVING PROGRAM IN SOLVING THE MATHEMATICAL PROBLEM AMONG 10TH GRADERS IN LIGHT OF THEIR VARIANCE OF THE MATHEMATICAL SELF-CONCEPT

This study aimed at investigating the impact of a problem-solving based program on mathematical problem-solving among 10th-grade students due to the variance of their mathematical self-concept. The purposive sample of this study consisted of (89) male and female students from Wadi Bani Kharous Basic Education School and Om Hakeem Basic Education School at Sultanate of Oman. The sample was divided into an experimental group, which consisted of (48) students, and the control group consisted of (41) students. The instructional materials of Polynomial and Algebraic Functions Unit and Trigonometric Functions Unit for Grade 10th were designed based on the problem-solving program. The problem-solving test and mathematical self-concept scale were developed, and both were valid and reliable. The findings showed that: there were significant statistical differences in the mathematical problem-solving test in favor of the experimental group. The findings indicated that the significant statistical differences in the mathematical problem-solving test are due to the mathematical self-concept and the absence of statistically significant differences in the mathematical problem-solving test is due to the interaction between teaching methods and mathematical self-concept in light of the findings, the study suggested some crucial recommendations including the importance of enriching mathematics curricula with mathematical problem-solving strategies and having professional development workshops to train teachers on how to use mathematical problem-solving strategies and urge them to use these strategies in teaching Mathematics

Modeling and Analysis of Optimal Strategies for Leveraging Ride-Sourcing Services in Hurricane Evacuation

In many large-scale evacuations, public agencies often have limited resources to evacuate all citizens, especially vulnerable populations such as the elderly and disabled people, and the demand for additional transportation means for evacuation can be high. The recent development of ride-sourcing companies can be leveraged in evacuations as an additional and important resource in future evacuation planning. In contrast to public transit, the availability of ride-sourcing drivers is highly dependent on the price, since surge pricing will occur when the demand is high and the supply is low. The key challenge is thus to find the balance between evacuation demand and driver supply. Based on the two-sided market theory, we propose mathematical modeling and analysis strategies that can help balance demand and supply through a pricing mechanism designed for ride-sourcing services in evacuation. A subsidy is considered in the model such that lower-income and vulnerable individuals could benefit from ride-sourcing services. A hypothetical hurricane evacuation scenario in New York City in the case study showed the feasibility of the proposed method and the applicability of subsidies for ride-sourcing services in evacuation. The methodology and results given in this research can provide useful insights for modeling on-demand ride-sourcing for future evacuation planning.

Electromechanical Design of Synchronous Power Controller in Grid Integration of Renewable Power Converters to Support Dynamic Stability

Nowadays, modern power converters installed in renewable power plants can provide flexible electromechanical characteristics that rely on the developed control technologies such as Synchronous Power Controller (SPC). Since high renewable penetrated power grids result in a low-inertia system, this electromechanical characteristic provides support to the dynamic stability of active power and frequency in the power generation area. This goal can be achieved through the proper tuning of virtual electromechanical parameters that are embedded in the control layers of power converters. In this paper, a novel mathematical pattern and strategy have been proposed to adjust dynamic parameters in Renewable Static Synchronous Generators controlled by SPC (RSSG-SPC). A detailed dynamic modeling was obtained for a feasible design of virtual damping coefficient and virtual moment of inertia in the electrometrical control layer of RSSG-SPC’s power converters. Mathematical solutions, modal analysis outcomes, time-domain simulation results, and real-time validations of the test in IEEE-14B benchmark confirm that the proposed method is an effective procedure for the dynamic design of RSSG-SPC to provide these dynamic stability supports in grid connection.

Modeling the Dynamics of T-Cell Development in the Thymus.

The thymus hosts the development of a specific type of adaptive immune cells called T cells. T cells orchestrate the adaptive immune response through recognition of antigen by the highly variable T-cell receptor (TCR). T-cell development is a tightly coordinated process comprising lineage commitment, somatic recombination of Tcr gene loci and selection for functional, but non-self-reactive TCRs, all interspersed with massive proliferation and cell death. Thus, the thymus produces a pool of T cells throughout life capable of responding to virtually any exogenous attack while preserving the body through self-tolerance. The thymus has been of considerable interest to both immunologists and theoretical biologists due to its multi-scale quantitative properties, bridging molecular binding, population dynamics and polyclonal repertoire specificity. Here, we review experimental strategies aimed at revealing quantitative and dynamic properties of T-cell development and how they have been implemented in mathematical modeling strategies that were reported to help understand the flexible dynamics of the highly dividing and dying thymic cell populations. Furthermore, we summarize the current challenges to estimating in vivo cellular dynamics and to reaching a next-generation multi-scale picture of T-cell development.

Students’ problem solving on mathematical proportion

This study analyzed problem solving abilities of the students on mathematical differential. Descriptive qualitative applied in this study with 26 students of secondary school; 16 males and 11 females. Data analysis reveals the ability of students’ problem solving abilities, namely understanding the problem, drawing up a problem solving plan, implementing the solution and re-checking the solution. The instruments used were test and interview. The findings showed that more than 50% mistake happened on drawing up a problem solving plan and re-checking the solution. So that to reduce the mistake we as lecturer should train the students in mathematical problem solving strategies.

On the Boundary Layer Equations with Phase Transition in the Kinetic Theory of Gases

Consider the steady Boltzmann equation with slab symmetry for a monatomic, hard sphere gas in a half space. At the boundary of the half space, it is assumed that the gas is in contact with its condensed phase. The present paper discusses the existence and uniqueness of a uniformly decaying boundary layer type solution of the Boltzmann equation in this situation, in the vicinity of the Maxwellian equilibrium with zero bulk velocity, with the same temperature as that of the condensed phase, and whose pressure is the saturating vapor pressure at the temperature of the interface. This problem has been extensively studied, first by Sone, Aoki and their collaborators, by means of careful numerical simulations. See section 2 of (Bardos et al. in J Stat Phys 124:275–300, 2006) for a very detailed presentation of these works. More recently, Liu and Yu (Arch Ration Mech Anal 209:869–997, 2013) proposed an extensive mathematical strategy to handle the problems studied numerically by Sone, Aoki and their group. The present paper offers an alternative, possibly simpler proof of one of the results discussed in Liu and Yu (2013).

Exploring Grade R teachers’ mathematics curriculum practices and strategies for improvement: Implications for physics teaching

This study sought strategies to improve teachers’ professional curriculum practices in a Grade R mathematics class. A phenomenological research design was employed to generate data for the study using a sample of fifteen participants. A semi-structured interview guide was used to collect the data for the study. In this regard, the interview guide was properly validated, and trial tested. Data collected for this study were analysed using a thematic analysis. The findings of the study showed that the strategies for improving teachers’ professional curriculum practice in a Grade R mathematics class include employing adequately qualified Grade R teachers; aking available teaching and learning resources;ncouraging sufficient parental involvement; encouraging support by authorities; and, using adequate language for teaching and learning. It was therefore concluded that for Grade R teachers to engage learners in Professional Curriculum Practices (PCP), they need to have access to teacher development programmes. This finding implicates physics teaching in the sense that proficiency in mathematics teaching is imperative for physics teaching. Thus, a practical approach to mathematics teaching can as well be deployed in the teaching of physics concepts due to the abstract nature of the subjects (Mathematics and Physics). In order words these identified strategies for mathematics teaching can be used for physics teaching at a higher education level. Thus, it was recommended that the integrated teacher development programme should be implemented to enable teachers to be fully engaged in Grade R mathematics classes.
 
 Keywords: Improvement, Strategies, Teachers’ Professional Curriculum Practice, Grade R Mathematics.

Non-Invasive Measurement, Mathematical Simulation and In Situ Detection of Biofilm Evolution in Porous Media: A Review

The development of biofilms and the related changes in porous media in the subsurface cannot be directly observed and evaluated. The primary reason that the mechanism of biofilm clogging in porous media cannot be clearly demonstrated is due to the opacity and structural complexity of three-dimensional pore space. Interest in exploring methods to overcome this limitation has been increasing. In the first part of this review, we introduce the underlying characteristics of biofilm in porous media. Then, we summarize two approaches, non-invasive measurement methods and mathematical simulation strategies, for studying fluid–biofilm–porous medium interaction with spatiotemporal resolution. We also discuss the advantages and limitations of these approaches. Lastly, we provide a perspective on opportunities for in situ monitoring at the field site.

Design and Development of Mathematical Models for Computational Neuroscience

Through the use of mathematical and computer models, computational neuroscience is an interdisciplinary study that seeks to comprehend the principles and mechanisms underlying the functioning of the brain. These models are essential for understanding intricate neurological processes, giving information about the dynamics of the brain, and directing experimental research. The design and creation of mathematical models for computational neuroscience are presented in-depth in this study.The sections that follow explore several mathematical modelling strategies used in computational neuroscience. These include statistical models that analyse and infer associations from experimental data, biophysical models that explain the electrical properties of individual neurons and their connections, and network models that capture the connectivity and dynamics of brain circuits. Each modelling strategy is examined in terms of its mathematical foundation, underlying presuppositions, and potential limits, as well as instances of how it has been applied to certain areas of neuroscience study.The research also examines the model parameterization, validation, and refinement stages of the model creation process. It emphasises how the integration of experimental evidence, theoretical understanding, and computational simulations leads to iterative model refining. The difficulties and unanswered concerns associated with modelling complex neurological systems are also covered, emphasising the necessity of multi-scale and multi-modal methods to fully capture the complex dynamics of the brain.The paper ends with a prognosis for mathematical modeling's future in computational neuroscience. The development of virtual brain simulations for comprehending brain illnesses and planning therapeutic approaches are some of the rising trends that are highlighted in this article, along with the incorporation of machine learning techniques, anatomical and physiological restrictions, and the assimilation of these trends into models.

Identifying and Serving Gifted and Talented Students: Are Identification and Services Connected?

The importance of alignment between identification processes and program design is widely noted in gifted and talented education literature. We analyzed publicly available district gifted program plans (Grades 3-5) from two states to examine the extent to which district identification practices matched intervention strategies. Our team developed a coding scheme matrix with 133 items for State 1 ( n = 115) and State 2 ( n = 178). The results of this study indicated that, at least in terms of planning, districts in the two states we examined appeared to be aligning identification and programming practices to meet the needs of gifted students identified in mathematics and/or reading/English language arts. In State 1, at least 60% of the districts reported the following intervention strategies in mathematics and reading/English language arts: faster pace of coverage, regular grade-level standards, in-depth coverage, preassessment, above grade-level standards, and expanded grade-level standards. In contrast, State 2 districts reported faster pace of coverage; however, with less commonly utilized interventions, subject-matter identification significantly influenced their usage. Differentiation was the primary learning environment strategy utilized by districts in both states.

A systematic review of stock market prediction using machine learning and statistical techniques

The stock market prediction patterns are seen as an important activity and it is more effective. Hence, stock prices will lead to lucrative profits from sound taking decisions. Because of the stagnant and noisy data, stock market-related forecasts are a major challenge for investors. Therefore, forecasting the stock market is a major challenge for investors to use their money to make more profit. Stock market predictions use mathematical strategies and learning tools. This paper provides a complete overview of 30 research papers recommending methods that include calculation methods, ML algorithms, performance parameters, and outstanding journals. The studies are selected based on research questions. Hence, these selected studies are helping to find the ML techniques along with their dataset for stock market prediction. Most widely ANN and NN techniques are used to achieve precise predictions of the stock market. While much amount of work is done, the latest stock market-related prediction methodology has many limitations. It can be assumed in this study that stock market forecasting is an integrated process and distinctive parameters for forecast the stock market should be considered more accurate.

Embedding opportunities for participation and feedback in large mathematics lectures via audience response systems

<p style="text-indent:20px;">The purpose of this work is to interpret the experiences of students when audience response systems (ARS) were implemented as a strategy for teaching large mathematics lecture groups at university. Our paper makes several contributions to the literature. Firstly, we furnish a basic model of how ARS can form a teaching and learning strategy. Secondly, we examine the impact of this strategy on student attitudes of their experiences, focusing on the ability of ARS to: assess understanding; identify strengths and weaknesses; furnish feedback; support learning; and to encourage participation. Our findings support the position that there is a place for ARS as part of a strategy for teaching and learning mathematics in large groups.

Do mechanisms matter? Comparing cancer treatment strategies across mathematical models and outcome objectives.

When eradication is impossible, cancer treatment aims to delay the emergence of resistance while minimizing cancer burden and treatment. Adaptive therapies may achieve these aims, with success based on three assumptions: resistance is costly, sensitive cells compete with resistant cells, and therapy reduces the population of sensitive cells. We use a range of mathematical models and treatment strategies to investigate the tradeoff between controlling cell populations and delaying the emergence of resistance. These models extend game theoretic and competition models with four additional components: 1) an Allee effect where cell populations grow more slowly at low population sizes, 2) healthy cells that compete with cancer cells, 3) immune cells that suppress cancer cells, and 4) resource competition for a growth factor like androgen. In comparing maximum tolerable dose, intermittent treatment, and adaptive therapy strategies, no therapeutic choice robustly breaks the three-way tradeoff among the three therapeutic aims. Almost all models show a tight tradeoff between time to emergence of resistant cells and cancer cell burden, with intermittent and adaptive therapies following identical curves. For most models, some adaptive therapies delay overall tumor growth more than intermittent therapies, but at the cost of higher cell populations. The Allee effect breaks these relationships, with some adaptive therapies performing poorly due to their failure to treat sufficiently to drive populations below the threshold. When eradication is impossible, no treatment can simultaneously delay emergence of resistance, limit total cancer cell numbers, and minimize treatment. Simple mathematical models can play a role in designing the next generation of therapies that balance these competing objectives.

Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects

Today, coronavirus appears as a serious challenge to the whole world. Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis. New data on COVID-19 are available daily, yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited, and uncertainty remains around nearly all its parameters’ values. This research provides the scientific and public health communities better resources, knowledge, and tools to improve their ability to control the infectious diseases. Using the publicly available data on the ongoing pandemic, the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections. Formulation of the testing hypotheses for different countries with a 95% level of confidence, and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries. The results will be helpful in decision making as well as in further mathematical analysis and control strategy. Statistical tools are used to investigate this pandemic, which will be useful for further research. The testing of the hypothesis is done for the differences in various effects including standard errors. Changes in states’ variables are observed over time. The rapid outbreak of coronavirus can be stopped by reducing its transmission. Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.

EMM of effective management of the integrated transportation and logistics system

The authors chose the topic of an economic and mathematical model of effective management of an integrated transport and logical system, due to the relevance of the topic throughout the world and in all areas of activity. Effective integration is possible if it is based on the methodological principles of the concept of integrated logistics, when the economic interests of subjects and objects of the transport-logical system are coordinated while ensuring the implementation of the strategy and goals of the functioning of the system as a whole. The object of the research is the JSC “Uzbek Railways” of the Republic of Uzbekistan. The research priority is transport and logistics management. During the research, difficulties emerged that have created multivariance. The article presents modern methods of managing the transport and logistics system, the classification of modern methods of management concepts that make up the theoretical and methodological foundations of the integrated management of the transport and logistics system, the efficiency of delivery times for options A, B, C, D and the economic efficiency of managing the transport and logistics system. Transport and logistics models are considered in economics as a business concept, having calculated the best option, you can optimize the economic process. In the conclusion, recommendations are given on the use of a mathematical model, short-term and long-term strategies for effective management of the transport and logistics system are given.