Strong Mathematical Background Research Articles

Factors Influencing Business Students’ Effort When Studying Mathematics

Each student’s effort is an important factor in achievement. Mathematics is an important subject for business students since there is a strong connection between performance in mathematics and success in business courses. The purpose of this paper is to identify the factors influencing a student’s choice of how much effort to put into studying business mathematics by questioning 273 students from two business schools in Norway. There is a considerable variation in the study time. By using a linear regression model, we identify the variables linked to effort. Females, and those who have higher enjoyment of mathematics, exert higher effort in business mathematics. Those with a strong background in mathematics from high school and students with parents who have higher education exert less effort in business mathematics. The attitudes toward mathematics do not seem to considerably affect effort.

Searching for Continuous n-Clusters with Boolean Reasoning

A bicluster consists of a subset of rows and columns of a given matrix, whose intersection defines the region (bicluster) of values of precisely defined condition. Through the decades, a variety of biclustering techniques have been successfully developed. Recently, it was proved that many possible patterns defined in two-dimensional data could be found with the application of Boolean reasoning. The provided theorems showed that any existing pattern in the data could be unequivocally encoded as an implicant of a proper Boolean function. Moreover, a prime implicant of that function encoded the inclusion-maximal (non-extendable) pattern. On the other hand, the definition of some two-dimensional patterns may be easily extended to three-dimensional patterns (triclusters) as well as to any number of dimensions (n-clusters). This paper presents a new approach for searching for three- and higher-dimensional simple patterns in continuous data with Boolean reasoning. Providing the definition of the Boolean function for this tasks, it is shown that the similar correspondence—implicants encode patterns, and prime implicants encode inclusion-maximal patterns—has a strong mathematical background: the proofs of appropriate theorems are also presented in this paper.

DIGITAL TOOLS FOR MATCHING QUALIFICATIONS TO THE LEVELS OF THE NATIONAL QUALIFICATIONS FRAMEWORK

Mutual compatibility of different national qualifications frameworks (NQFs) based on their compatibility with the European Qualifications Framework (or another international one) is crucially important for the effective recognition of qualifications between states. In turn, it depends on the quality of “filling” NQF levels with qualifications. Right comparing professional (occupational) qualifications with NQF level is a non-trivial problem for standard developers. The quality of any national system of qualifications depends on the comparability of qualifications with the level of the NQF so the comparison process should be strongly argued to secure the comparability. For qualification standard developers (especially for occupational standard developers) there were no strictly justified recommendations on how to compare qualification with the NQF level. Th. Saaty’s Analytic Hierarchy Process (AHP) is developed to resolve the problem of evidence-based comparing educational or professional (occupational) qualifications with the level of the National Qualification Framework (NQF). Research results give standard developers software tools based on a strong mathematical background to determine NQF level for developed standards. It is shown that Th. Saaty’s Analytic Hierarchy Process (AHP) is close to optimal for solving the problem of qualifications comparing and therefore looks like the best option for such methods. However, AHP demands non-trivial qualifications in mathematics and computing. The key problem resolved by this research is simplifying procedures to ensure effective access to the tool for qualification standard developers with minimal qualification in mathematics and computing. It is proven that each problem of qualification comparison with NQF level may be reduced to three options of decision. At the lower level of the decision-making process, there are 3-4 descriptors of qualification. Therefore, a user should be capable of forming at most four matrices of judgments and computing the main eigenvectors with some level of accuracy. The maximal dimension of matrices is four (for example it's true for the Ukrainian case). But for some national qualification frameworks that use only three descriptors maximal dimension of matrices equals three. Therefore, some simple approximation methods for eigenvector computing may be applied using only minimal means of Microsoft Excel or analogous applications. For the most general case of four NQF descriptors, Microsoft Excel macro is developed to secure achieving any level of accuracy. Corresponding API is developed by PHP programming language. Both Excel and API are accessible for users at the website of the Institute of Educational Analytics in Kyiv. The novelty of the article is that for the first time in national and international practice, it proposes an alternative/supplementary algorithmic method for determining the level of certain full and/or partial professional qualifications by the National Qualifications Framework, thus creating prerequisites for further automation of the activities of professional standards developers.

Demystifying dimensionality reduction techniques in the 'omics' era: A practical approach for biological science students.

Dimensionality reduction techniques are essential in analyzing large 'omics' datasets in biochemistry and molecular biology. Principal component analysis, t-distributed stochastic neighbor embedding, and uniform manifold approximation and projection are commonly used for data visualization. However, these methods can be challenging for students without a strong mathematical background. In this study, intuitive examples were created using COVID-19 data to help students understand the core concepts behind these techniques. In a 4-h practical session, we used these examples to demonstrate dimensionality reduction techniques to 15 postgraduate students from biomedical backgrounds. Using Python and Jupyter notebooks, our goal was to demystify these methods, typically treated as "black boxes", and empower students to generate and interpret their own results. To assess the impact of our approach, we conducted an anonymous survey. The majority of the students agreed that using computers enriched their learning experience (67%) and that Jupyter notebooks were a valuable part of the class (66%). Additionally, 60% of the students reported increased interest in Python, and 40% gained both interest and a better understanding of dimensionality reduction methods. Despite the short duration of the course, 40% of the students reported acquiring research skills necessary in the field. While further analysis of the learning impacts of this approach is needed, we believe that sharing the examples we generated can provide valuable resources for others to use in interactive teaching environments. These examples highlight advantages and limitations of the major dimensionality reduction methods used in modern bioinformatics analysis in an easy-to-understand way.

Nonlinear oscillations for beginners. Calculating period using an elementary computational approach

Determining the period of a nonlinear oscillation is a challenging task that requires a strong mathematical background in solving nonlinear differential equations. However, the procedure can be significantly simplified using the area under the 1/|υ|= f(x) graph, where υ is the velocity of the oscillating object and x is its displacement from its equilibrium position. The proposed method requires elementary computational tools and is appropriate for determining the period of any nonlinear undamped oscillation. Characteristic examples are presented, such as the simple pendulum, the oscillation with a power-law restoring force, and the cubic-quintic Duffing oscillator. The proposed approach provides accurate results and is appropriate for introductory physics and mechanics courses.

Statistical Anxiety from Gender Perspective of State Islamic Religious College Students in Indonesia

This study aims to see the condition of statistical anxiety in terms of the gender of PTKIN students. Considering that State Islamic Religious Higher Education (PTKIN) students generally do not have a strong mathematical background, it is deemed necessary to examine how the statistical anxiety of students who do not have a strong mathematical knowledge is considered. Objective. Statistical anxiety is related to students' view of statistical learning, which is regarded as difficult for those who do not havestrong mathematical background knowledgee. Method. This study is a quantitative study with a comparative design that compares the statistical anxiety of PTKIN students based on a gender perspective. The sample number in this study was 479 respondents from PTKIN from 3 regions of Indonesia, namely the western, central, and eastern parts. The sampling technique used was cluster random sampling from three Indonesia regions. Measurement of statistical anxiety using the Statistical Anxiety Scale (SAS) instrument developed by Pretorius & Norman is divided into three aspects with 17 statements. Result. The results showed differences in statistical anxiety based on the gender perspective of PTKIN students. Conclusion. The difference is due to differences in views between men and women responding to something. Women tend to have a more specific idea of things than men. This causes women tto end to be more anxious than men. Moreover, in general, PTKIN students do not have a strong background of exact knowledge.

Academic program recommendations for graduate degrees in medical physics: AAPM Report No. 365 (Revision of Report No. 197).

Academic program recommendations for graduate degrees in medical physics: AAPM Report No. 365 (Revision of Report No. 197).

Chemical engineering at crossroads

AbstractThrough periodic introspection and assessment, the chemical engineering field has developed a mature undergraduate curriculum built on a strong science background in mathematics, physics, and chemistry. This brings a unique set of skills in transport, reaction engineering, and thermodynamics, coupled with suitable process systems engineering and process design courses, to supply well‐trained engineers to a vast array of process manufacturing facilities. These facilities produce basic chemicals, pharmaceuticals, oil and gas, petrochemicals, food and agricultural products, minerals, and materials. While this maturity has served existing industries well, we argue that the chemical engineering field is at crossroads between managing the curriculum of undergraduate and graduate education to supply the needs of established industries while creating innovators for emerging industries. While this is a great opportunity for yet another introspection, we caution that the inadvertent cannibalization of the field must be avoided. We do argue in favour of adding a biology sequence and a computational science sequence to the core at the undergraduate level in a related perspective article.

A Parametric Study of the Free Undamped Torsional Vibration of One-Dimensional Structural Elements using the Differential Quadrature Method (DQM)

Recently, structures prone to torsional vibration have grabbed the interest of the structural engineering field whose aim has become to design structures with increased torsional stiffness. To the author’s limited knowledge, studies researching this topic couldn’t provide a simplified method to obtain the natural torsional frequencies and the corresponding mode shapes of structures providing ease of use by structural engineers having limited mathematical backgrounds. The purpose of this study is to establish a simplified numerical model of the torsional vibration of rods with non-uniform geometry and material with classical boundary conditions using the differential quadrature method (DQM). To account for geometric and material non- uniformity, any space varying functions in the longitudinal direction of a one- dimensional structural element can be used in the model. The numerical results obtained are compared with previously obtained analytical results in cases of rods with uniform cross sections and linearly non-uniform ones. The comparison proved significant agreement with the analytical results. The illustrated use of the DQM showed efficiency and acceptable accuracy that made it legible to create an alternative to the time-consuming analytical solutions that require a unique solution technique for every type of structural variation where a strong mathematical background of the user is needed.

An ethical visualization of the NorthCOVID-19 model.

When modelling epidemics, the outputs and techniques used may be hard for the general public to understand. This can cause fear mongering and confusion on how to interpret the predictions provided by these models. This article proposes a solution for such a model that was created by a Canadian institute for COVID-19 in their region; namely, the NorthCOVID-19 model. In taking these ethical concerns into consideration, first the web interface of this model is analyzed to see how it may be difficult for a user without a strong mathematical background to understand how to use it. Second, a system is developed that takes this model’s outputs as an input and produces a video summarization with an auto-generated audio to address the complexity of the interface, while ensuring that the end user is able to understand the important information produced by this model. A survey conducted on this proposed output asked participants, on a scale of 1 to 5, whether they strongly disagreed (1) or strongly agreed (5) with statements regarding the output of the proposed method. The results showed that the audio in the output was helpful in understanding the results (80% responded with 4 or 5) and that it helped improve overallcomprehension of the model (85% responded with 4 or 5). For the analysis of the NorthCOVID-19 interface, a System Usability Scale (SUS) survey was performed where itreceived a scoring of 70.94 which is slightly above the average of 68.

ORBoost: An Orthogonal AdaBoost

Ensemble learners and deep neural networks are state-of-the-art schemes for classification applications. However, deep networks suffer from complex structure, need large amount of samples and also require plenty of time to be converged. In contrast, ensemble learners (especially AdaBoost) are fast to be trained, can work with small and large datasets and also benefit strong mathematical background. In this paper, we have developed a new orthogonal version of AdaBoost, termed as ORBoost, in order to desensitize its performance against noisy samples as well as exploiting low number of weak learners. In ORBoost, after reweighting the distribution of each learner, the Gram-Schmidt rule updates those weights to make a new samples’ distribution to be orthogonal to the former distributions. In contrast in AdaBoost, there is no orthogonality constraint even between two successive weak learners while there is a similarity between the distributions of samples in different learners. To assess the performance of ORBoost, 16 UCI-Repository datasets along with six big datasets are deployed. The performance of ORBoost is compared to the standard AdaBoost, LogitBoost and AveBoost-II over the selected datasets. The achieved results support the significant superiority of ORBoost to the counterparts in terms of accuracy, robustness, number of exploited weak learners and generalization on most of the datasets.

On the stability of POD basis interpolation on Grassmann manifolds for parametric model order reduction

Proper Orthogonal Decomposition (POD) basis interpolation on Grassmann manifolds has been successfully applied to problems of parametric model order reduction (pMOR). In this work we address the necessary stability conditions for the interpolation, all defined from strong mathematical background. A first condition concerns the domain of definition of the logarithm map. Second, we show how the stability of interpolation can be lost if certain geometrical requirements are not satisfied by making a concrete elucidation of the local character of linearization. To this effect, we draw special attention to the Grassmannian exponential map and the optimal injectivity condition of this map, related to the cut–locus of Grassmann manifolds. From this, an explicit stability condition is established and can be directly used to determine the loss of injectivity in practical pMOR applications. A third stability condition is formulated when increasing the number p of POD modes, deduced from the principal angles of subspaces of different dimensions p. Definition of this condition leads to an understanding of the non-monotonic oscillatory behavior of the Reduced Order Model (ROM) error-norm with respect to the number of POD modes, and on the contrary, the well-behaved monotonic decrease of the error-norm in the two numerical examples presented herein. We have chosen to perform pMOR in hyperelastic structures using a non-intrusive approach for inserting the interpolated spatial POD ROM basis in a commercial FEM code. The accuracy is assessed by a posteriori error norms defined using the ROM FEM solution and its high-fidelity counterpart simulation. Numerical studies successfully ascertained and highlighted the implication of stability conditions which are general and can be applied to a variety of other linear or nonlinear problems involving parametrized ROMs generation based on POD basis interpolation on Grassmann manifolds.

Existence of wormholes in f(𝒢) gravity using symmetries

The current study examines the geometry of static wormholes with anisotropic matter distribution in the context of modified [Formula: see text] gravity. We consider the well-known Noether and conformal symmetries, which help in investigating wormholes in [Formula: see text] gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the [Formula: see text] gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified [Formula: see text] gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns.

Elements of the anthropological theory of didactics in the selection of contents in a course of fluid mechanics in engineering, a case study in Spanish universities

The Anthropological Theory of Didactics has been applied to the field of didactics of mathematics with remarkable success. Fluid Mechanics is a discipline with a strong mathematical background, where mathematics is used for modeling the continuous nature. In addition, the Fluid Mechanics concepts are essential for the future engineer or scientist. For this reason, it is worth thinking whether the content that developed in engineering schools or science faculties are those demanded by the future professionals. The analysis has been done within the context of a case study framed in the Spanish noosphere, more particularly Universities and Companies. In this direction, the objective of this article is to know the institutional distance between the University and society as a demander of technologies based on Fluid Mechanics. To this end, the methodology based on the issuance of a questionnaire to experts focused on aspects such as present and emerging content associated with the Fluid Mechanics of an engineering degree is used. Note that the number of experts selected is reduced so as to consider the study as a sourcing for introducing expert thoughts on the fluid mechanics conception between university and companies. The results highlight the existence of an institutional distance between the University and the Enterprise (as a technology executor) in the conception of contents, thus establishing an area of potential improvement within the noosphere associated with fluid mechanics in Spain.HighlightsQuestionnaire to experts to understand the current institutional relations between University and Company in the Spanish system.Application of the Anthropological Theory of Didactics (ATD) techniques to Fluid Mechanics.Confirmation of an institutional distance between University and Companies in Fluid Mechanics conceptions.

Determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions showed that the proposed method has almost the same number of steps as the existing method. However, the latter requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.
 Keywords: Additive White Gaussian Noise, Cramer-Rao Lower Bound, DC-Value, Laplace transform, and Minimum Variance Unbiased Estimator (MVUE).

Logistic Regression in Analyzing the Determinants of University Students' Mathematics Performance

Mathematics provides an effective way of building mental discipline, encourages logical reasoning, and plays a crucial role in understanding the contents of other subjects. Mathematics performance is affected by several factors including grade, social economic status, background and many more. The aim of this study is to investigate the factors which are related to students’ mathematics performance and to identify the significant factors which affect the students’ mathematics performance of MAT133 course. This study was conducted in UiTM Negeri Sembilan, Kuala Pilah campus. 480 students were selected from various programs who had registered Pre-Calculus course (MAT133). This study employed Logistic regression analysis to test the relationship between predictor variables and the dichotomous outcome variable which is categorized as low or high achiever in MAT 133 course. About 55.7% of the students are high achiever who achieved higher than 70% marks in MAT133. The research findings reveal that students’ intake on July (OR = 2.941), male students (OR = 0.315), students who scored A+, A and A- in Modern Mathematics in SPM exam (OR = 0.340), students who had B+ and B- in Additional Mathematics in SPM (OR = 0.512) and assessment marks for MAT133 were found to have a significantly higher possibility to be high-achiever in MAT133. Acquiring strong mathematical background is a priority as a fundamental preparation for students to learn mathematics in higher institution.

Determination of CRLB and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions show that the proposed method has almost the same number of steps as the existing method. However, the later requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.

Construction Scheme of Proof Based on Assimilation and Accommodation Processes: Theorem of Number Theory

Number theory is a branch of mathematics that deals with the properties of natural numbers, aimed at finding interesting and unexpected relationships of various types of numbers, then proving that the relationship is true. Problem solutions and proof theorems of number theory often require a strong mathematical background. Weak background, such as: giving examples only applies to definitions not to theorems and lemmas, understanding of the definitions and proven theorems, ways of looking at new theorems built on definitions, and previous theorems, and knowledge of when a definitions or lemma-theorems can be used; enough to affect the ability to solve the problem of number theory. So it is necessary to explore the possibility of other problems in the activity of constructing proof, which in this study uses the framework of the process of assimilation and accommodation, followed by interviews based on student responses. The results obtained are 3 groups of construction schemes, namely: 1) schemes using definitions and theorems, 2) schemes using theorems, and 3) schemes using definitions. Within the three groups there are variations of the problem found that the diantranya occurs is dis-equilibrium in the construction scheme group with theorems and definitions; and group construction schemes by definition only. His advice is to reflect on the ability to understand definitions, theorems and lemmas; and the development of lecture designs that can make the activity of constructing proof into routine activities.

Optimizing the Performance of Containerized Cloud Software Systems Using Adaptive PID Controllers

Control theory has proven to be a practical approach for the design and implementation of controllers, which does not inherit the problems of non-control theoretic controllers due to its strong mathematical background. State-of-the-art auto-scaling controllers suffer from one or more of the following limitations: (1) lack of a reliable performance model, (2) using a performance model with low scalability, tractability, or fidelity, (3) being application- or architecture-specific leading to low extendability, and (4) no guarantee on their efficiency. Consequently, in this article, we strive to mitigate these problems by leveraging an adaptive controller, which is composed of a neural network as the performance model and a Proportional-Integral-Derivative (PID) controller as the scaling engine. More specifically, we design, implement, and analyze different flavours of these adaptive and non-adaptive controllers, and we compare and contrast them against each other to find the most suitable one for managing containerized cloud software systems at runtime. The controller’s objective is to maintain the response time of the controlled software system in a pre-defined range, and meeting the Service-level Agreements, while leading to efficient resource provisioning.

Cryptography in undergraduate education: perceptions of postgraduate students

This paper uses a qualitative methodology to share the experience of students who have made the transition from being an undergraduate student to being a postgraduate student with a research focus on cryptography. In particular, it looks at the motivation of the participants to study cryptography, the training that they received as undergraduates, and how it can be improved. Twenty postgraduate students from fifteen different countries agreed to take part in the study. The data collected suggests that most postgraduate students chose to study cryptography during the second half of their undergraduate program, first gaining a broader knowledge of mathematics or computer science. They view the field as both important and exciting, but cite the value of a strong mathematical background, which could be enhanced by stronger undergraduate programing requirements. Most of the participants plan to stay in academia once their postgraduate program ends and offer a range of ideas to help promote the field of cryptography so that younger students are aware of it.