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This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.

The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.

Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.

The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.

There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.

This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.

To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.

This study was done to compare the modes of teaching mathematics in higher education in the United Arab Emirates (UAE). The three teaching methods were used as follow: before, during and after the COVID-19 pandemic. The three teaching methods are: (1). Normal on-campus face-to-face teaching and learning activity before the COVID-19 pandemic. (2). Full online teaching and learning activity during the COVID-19 pandemic. (3). Blended teaching and learning activity after the COVID-19 pandemic.

Over the last few years, there has been a considerable amount of literature investigating the efficacy of the various delivery modes: on-campus delivery (face-to-face), online delivery and blended learning (hybrid), in helping college students improve their mathematical skills. However, the extent to which one learner learns best has been hotly debated among the researchers. Therefore, this study aims to compare the efficacy of implementing three teaching and learning delivery modes before, while, and after the COVID-19 pandemic: on-campus delivery (face-to-face), online delivery and blended learning (hybrid) on academic achievement in mathematics at a higher education institution in the UAE. The main research question explores whether there is a statistically significant difference (p = 0.05) in students’ academic based on the delivery methods: on-campus face-to-face, online and blended learning. The participants in the study were students from one of the largest higher education institutions in the UAE, and all of them studied the same mathematics course before, during and after the COVID-19 pandemic. Student scores in the three academic semesters were thoroughly compared and analyzed using the ANOVA test to check if there is a significant difference between the three groups followed by a Tukey test to identify the significant difference in favor of which group. The results showed that there were significant differences in the mean scores in the students’ achievement in the mathematics courses favoring the blended learning delivery mode. The findings also show that the students’ achievement in mathematics using the on-campus face-to-face teaching and learning was better than the students’ achievement in mathematics using online teaching and learning delivery modes.

The main study question was: is there a statistical significant difference at the significance level (a = 0.05) in students’ achievements in mathematics courses at higher education in the UAE, which can be attributed to the method of teaching? The descriptive statistics reveal that the average student’s score in the final exam after the COVID-19 pandemic is 65.7 with a standard deviation of 16.65, which are higher than the average student’s score in the final exam before the COVID-19 pandemic of 58.7 with a standard deviation 20.53, and both are higher than the average students’ score in the final exam during the COVID-19 pandemic 51.8 with standard deviation 21.48. Then, the ANOVA test reveals that there is a statistically significant difference between the three groups in the final exam marks. The researchers used the multiple comparison tests (Tukey test) to determine the difference. The Tukey test reveals that there is a statically significant difference between the average students’ score in the final exam after the COVID-19 pandemic and the average students’ score in the final exam during the COVID-19 pandemic, where p = 0.015 < 0.05 as well as there is a statically significant difference between the average students’ score in the final exam after the COVID-19 pandemic and the average students’ score in the final exam before the COVID-19 pandemic, where p = 0.000 < 0.05 in favor of the average students’ score in the final exam after the COVID-19 pandemic. On the other hand, there is a statically significant difference between the average students’ score in the final exam before the COVID-19 pandemic and the average students’ score in the final exam during the COVID-19 pandemic, where p = 0.016 < 0.05 in favor of the average students’ score in the final exam before the COVID-19 pandemic.

There are several limitations that may reduce the possibility of generalizing the expected results of the current study to students outside the study population: (1) The study is limited to students of a federally funded postsecondary education institution in the UAE, in which most students are studying in their non-native language. (2) The study is limited to the mathematics courses. (3) The achievement test used in the study is a standardized test developed by the college as a cross-campus summative assessment.

The hybrid education model, also known as blended learning, combines traditional face-to-face instruction with online learning components. When applied to teaching mathematics in higher education, this approach can have several implications and benefits. Here are some key points supported by references: (1) Enhanced Accessibility and Flexibility: hybrid models offer flexibility in learning, allowing students to access course materials, lectures and resources online. This flexibility can accommodate diverse learning styles and preferences. A study by Means et al. (2013) in “Evaluation of Evidence-Based Practices in Online Learning” highlights how blended learning can improve accessibility and engagement for students in higher education. (2) Personalized Learning Experience: by incorporating online resources, instructors can create a more personalized learning experience. Adaptive learning platforms and online quizzes can provide tailored feedback and adaptive content based on individual student needs (Freeman et al., 2017). This individualization can improve student performance and understanding of mathematical concepts. (3) Increased Student Engagement: the integration of online components, such as interactive simulations, videos and discussion forums, can enhance student engagement and participation (Bonk and Graham, 2012). Engaged students tend to have better learning outcomes in mathematics. (4) Improved Assessment and Feedback Mechanisms: hybrid models allow for the implementation of various assessment tools, including online quizzes, instant feedback mechanisms and data analytics, which can aid instructors in monitoring students’ progress more effectively (Means et al., 2013). This timely feedback loop can help students identify areas needing improvement and reinforce their understanding of mathematical concepts. (5) Cost-Effectiveness and Resource Optimization: integrating online materials can potentially reduce overall instructional costs by optimizing resources and enabling efficient use of classroom time (Graham, 2013). (6) Challenges and Considerations: despite the benefits, challenges such as technological barriers, designing effective online materials and ensuring equitable access for all students need to be addressed (Garrison and Vaughan, 2014). It requires thoughtful course design and continuous support for both students and instructors. When implementing a hybrid education model in teaching mathematics, instructors should consider pedagogical strategies, technological infrastructure and ongoing support mechanisms for students and faculty.

The research is the first research in the UAE to discuss the difference in teaching mathematics in higher education before, during and after the COVID-19 pandemic.

Studying the shear stress and pressure resulting on the walls of blood vessels, especially during high-pressure cases, which may lead to the explosion or rupture of these vessels, can also lead to the death of many patients. Therefore, it was necessary to try to control the shear and normal stresses on these veins through nanoparticles in the presence of some external forces, such as exposure to some electromagnetic shocks, to reduce the risk of high pressure and stress on those blood vessels. This study aims to examines the shear and normal stresses of electroosmotic-magnetized Sutterby Buongiorno’s nanofluid in a symmetric peristaltic channel with a moderate Reynolds number and curvature. The production of thermal radiation is also considered. Sutterby nanofluids equations of motion, energy equation, nanoparticles concentration, induced magnetic field and electric potential are calculated without approximation using small and long wavelengths with moderate Reynolds numbers.

The Adomian decomposition method solves the nonlinear partial differential equations with related boundary conditions. Graphs and tables show flow features and biophysical factors like shear and normal stresses.

This study found that when curvature and a moderate Reynolds number are present, the non-Newtonian Sutterby fluid raises shear stress across all domains due to velocity decay, resulting in high shear stress. Additionally, modest mobility increases shear stress across all channel domains. The Sutterby parameter causes fluid motion resistance, which results in low energy generation and a decrease in the temperature distribution.

Equations of motion, energy equation, nanoparticle concentration, induced magnetic field and electric potential for Sutterby nano-fluids are obtained without any approximation i.e. the authors take small and long wavelengths and also moderate Reynolds numbers.

A progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS.

In this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using Metropolis–Hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques.

The Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study.

The ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature.

The purpose of the paper is set to minimize the total cost of a manufacturing system when an acceptance sampling plan (ASP) is carried out in a fuzzy environment.

A fuzzy acceptance sampling plan (FASP) is employed for the inspection of the batch of products and a fuzzy cost optimization problem is formulated.

The extent of uncertainty determines an interval for the total cost function with upper and lower bounds. The effect of variation in the ambiguity of the proportion of defectives in the probability of acceptance is determined.

The proposed model is specifically designed for production and supply units with ASP for attributes. Still, the proportion of defectives in the inspection process is fuzzy.

Fuzzy probability distribution is used to model an optimal inspection plan for a general supply chain. Economic design of supply chain under fuzzy proportion of defectives is discussed for the first time.

Aim to the limitations of grey relational analysis of interval grey number, based on the generalized greyness of interval grey number, this paper tries to construct a grey angle cosine relational degree model from the perspective of proximity and similarity.

Firstly, the algorithms of the generalized greyness of interval grey number and interval grey number vector are given, and its properties are analyzed. Then, based on the grey relational theory, the grey angle cosine relational model is proposed based on the generalized greyness of interval grey number, and the relationship between the classical cosine similarity model and the grey angle cosine relational model is analyzed. Finally, the validity of the model in this paper is illustrated by the calculation examples and an application example of related factor analysis of maize yield.

The results show that the grey angle cosine relational degree model has strict theoretical basis, convenient calculation and is easy to program, which can not only fully utilize the information of interval grey numbers but also overcome the shortcomings of greyness relational degree model. The grey angle cosine relational degree is an extended form of cosine similarity degree of real numbers. The calculation examples and the related factor analysis of maize yield show that the model proposed in this paper is feasible and valid.

The research results not only further enrich the grey system theory and method but also provide a basis for the grey relational analysis of the sequences in which the interval grey numbers coexist with the real numbers.

The paper succeeds in realizing the algorithms of the generalized greyness of interval grey number and interval grey number vector, and the grey angle cosine relational degree, which provide a new method for grey relational analysis.

In Brazil, over 4.7 million women enrolled in university in the year 2017. However, Brazilian women have been consistently overrepresented in humanities and care majors and underrepresented in science, technology, engineering and mathematics (STEM). Given that observed gender differences in math-intensive fields have lasting effects on gender inequality in the labor market, and that observed gender variations do not necessarily associate with differences in innate ability, in this paper we explore the paths of societal gender bias and gender differences in a Brazilian university.

We conduct a social experiment at a University in Southeastern Brazil, applying the gender-STEM Implicit Association Test.

We found that women in STEM are less likely to show gender-STEM implicit stereotypes, compared to women in humanities. The results indicate a negative correlation between implicit gender stereotyping and the choice of math-intensive majors by women.

The stereotype-congruent results are indicative of the gender bias in Brazilian society, and suggest that stereotypes created at early stages in life are directly related to future outcomes that reinforce gender disparities in Brazil, which can be observed in career choices.

This study aims to determine the barriers hindering the incorporation of blockchain technology (BCT) in two key service industries – hotel and health care – as well as to assess their readiness for implementing BCT after overcoming the barriers.

The barriers of this study are determined through two phases: a review of prior literature and obtaining expert opinions, which are then analyzed to identify specific barriers that are impeding the incorporation of BCT. Moreover, to generate a blockchain implementation reluctance index (BIRI), this study presents an interval-valued intuitionistic fuzzy set (IVIFS) that uses graph theory and matrix approach (GTMA). The permanent function in the GTMA approach is computed using the PERMAN algorithm. Finally, to compare the readiness of the hotel and health-care industries to adopt BCT, the BIRI values are plotted and evaluated.

The barriers identified by this study are listed under five major headings, namely, financial, operational, behavioral, technical and legal. This study revealed that the operational and technical barriers of BCT are critically hindering its widespread integration in hotel and health-care industries. Furthermore, on comparing the BIRI values of both industries, the result suggested that the hotel industry needs to work more on these barriers to effectively incorporate BCT. Besides the comparison, the BIRI values clearly indicate that both industries have to put a lot of effort into the mitigation of the barriers found by this study to successfully integrate BCT.

The experts’ opinions are used to evaluate the identified barriers, which raises the chance that the opinions are prejudiced based on the experts’ perspectives and ideologies. The sensitivity of decision-maker loads toward preference outcomes is not analyzed in this manuscript. Therefore, any recent sensitivity analysis may be considered a prospective field for future research. This study applies a multicriteria decision-making (MCDM) approach, IVIFS–GTMA, which limits the evaluation of the influence caused by individual barriers on the integration of BCT in the hotel and health-care industries. Henceforth, in future investigations, alternative MCDM methods may be used to analyze individual barriers.

According to the findings, if the hotel or health-care industry aims to incorporate BCT in its supply chain operations, it is recommended to emphasize more on the operational barriers along with the technical and behavioral barriers. The barriers mentioned in this manuscript can be used as guidance for developers in their development activities, such as scalability concerns, establishment costs, the 51% attack and the inefficient nature of BCT. Furthermore, they may address the potential users’ negative perceptions about security, privacy, trust and risk avoidance through creatively developed blockchain solutions to promote BCT implementation.

To the best of the author’s knowledge, this is the first study that identifies barriers toward BCT incorporation in the major service industries, i.e. hotel and health care. Moreover, this is the first study that compares the preparedness of the hotel and health-care industries to determine the industry that requires more work to implement BCT.

This paper aims to reveal the interdisciplinarity of information science (IS) from the perspective of the evolution of theory application.

Select eight representative IS journals as data sources, extract the theories mentioned in the full texts of the research papers and then measure annual interdisciplinarity of IS by conducting theory co-occurrence network analysis, diversity measure and evolution analysis.

As a young and vibrant discipline, IS has been continuously absorbing and internalizing external theoretical knowledge and thus formed a high degree of interdisciplinarity. With the continuous application of some kernel theories, the interdisciplinarity of IS appears to be decreasing and gradually converging into a few neighboring disciplines. Influenced by big data and artificial intelligence, the research paradigm of IS is shifting from a theory centered one to a technology centered one.

This study helps to understand the evolution of the interdisciplinarity of IS in the past 21 years. The main limitation is that the data were collected from eight journals indexed by the Social Sciences Citation Index and a small amount of theories might have been omitted.

This study identifies the kernel theories in IS research, measures the interdisciplinarity of IS based on the evolution of the co-occurrence network of theory source disciplines and reveals the paradigm shift being happening in IS.

This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.

The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example.

We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S²ⁿ⁺¹ and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to Eⁿ⁺¹ × Sⁿ(4) in higher dimension.

All results are novel and generalizations of previously obtained results.